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1. The chemical thermodynamics.

 2. Kinetics of biological reaction. Influence of different factors on the chemic reaction rate.

3. Catalysis and catalysts. Influence of inorganic catalysts and enzymes on chemical reaction rate.

Thermodynamics is a science that describes processes that involve changes in temperature, transformation of energy, and the relationships between heat and work.

In thermodynamics, interaction between objects are studied and categorized.

In important concept in thermodynamics is the thermodynamic system. Certain quantity of matter or the space which is under thermodynamic study or analysis is called as system.

A system is separated from the environment by a boundary which may be fixed or it can be movable.

A thermodynamic view of the world

In thermodynamics, we must be very precise in our use of certain words. The two most important of these are system and surroundings.

A thermodynamic system is that part of the world to which we are directing our attention. Everything that is not a part of the system constitutes the surroundings. The system and surroundings are separated by a boundary. If our system is one mole of a gas in a container, then the boundary is simply the inner wall of the container itself. The boundary need not be a physical barrier; for example, if our system is a factory or a forest, then the boundary can be wherever we wish to define it. We can even focus our attention on the dissolved ions in an aqueous solution of a salt, leaving the water molecules as part of the surroundings. The single property that the boundary must have is that it be clearly defined, so we can unambiguously say whether a given part of the world is in our system or in the surroundings.

Thermodynamic System Types

There are three kinds of systems depending on the kinds of exchanges taking place between a thermodynamic system and its environment:

isolated, closed and open system

Isolated systems are completely isolated from their environment. They do not exchange heat, work or matter with their environment.

An example of an isolated system would be an insulated container, such as an insulated gas cylinder.

Closed systems are able to exchange energy (heat and work) but not matter with their environment. The closed system is fixed mass system. An example is water being heated in the closed vessel, where water will get heated but its mass will remain same.

Open systems may exchange any form of energy as well as matter with their environment. A boundary allowing matter exchange is called permeable.

An example of open system is boiling water in an open vessel, where transfer of heat as well as mass in the form of steam takes place between the vessel and environment.

All living organisms are open thermodynamic systems.

If matter is not able to pass across the boundary, then the system is said to be closed; otherwise, it is open. A closed system may still exchange energy with the surroundings unless the system is an isolated one, in which case neither matter nor energy can pass across the boundary. The tea in a closed Thermos bottle approximates a closed system over a short time interval.

Properties and the state of a system

The properties of a system are those quantities such as the pressure, volume, temperature, and its composition, which are in principle measurable and capable of assuming definite values. There are of course many properties other than those mentioned above; the density and thermal conductivity are two examples. However, the pressure, volume, and temperature have special significance because they determine the values of all the other properties; they are therefore known as state properties because if their values are known then the system is in a definite state.

Change of state: the meaning of Δ

In dealing with thermodynamics, we must be able to unambiguously define the change in the state of a system when it undergoes some process. This is done by specifying changes in the values of the different state properties using the symbol Δ (delta) as illustrated here for a change in the volume:

ΔV = V_final – V_initial(1-1)

We can compute similar delta-values for changes in P, V, n_i (the number of moles of component i), and the other state properties we will meet later.

 

Processes

A thermodynamic process may be defined as the energetic evolution of a thermodynamic system proceeding from an initial state to a final state.

Typically, each thermodynamic process is distinguished from other processes in energetic character according to what parameters, such as temperature, pressure, or volume are held fixed. Several common thermodynamic processes are:

Isobaric process: occurs at constant pressure.

Isochoric process: occurs at constant volume (also called isometric/isovolumetric).

Isothermal process: occurs at a constant temperature

Adiabatic process: occurs without loss or gain of energy by heat

 

Internal Energy

In thermodynamics, the internal energy is the total energy contained by a thermodynamic system.

Internal energy has two major components, kinetic energy and potential energy.

The kinetic energy is due to the motion of the system’s particles (translations, rotation, vibration), and the potential energy is associated with the static constituents of matter, static electric energy of atoms within molecules or crystals, the static energy of chemical bonds.

The internal energy of a system can be changed by heating the system or by doing work on it.

U – is the most common symbol used for internal energy

Internal energy is simply the totality of all forms of kinetic and potential energy of the system. Thermodynamics makes no distinction between these two forms of energy and it does not assume the existence of atoms and molecules. But since we are studying thermodynamics in the context of chemistry, we can allow ourselves to depart from “pure” thermodynamics enough to point out that the internal energy is the sum of the kinetic energy of motion of the molecules, and the potential energy represented by the chemical bonds between the atoms and any other intermolecular forces that may be operative.

How can we know how much internal energy a system possesses? The answer is that we cannot, at least not on an absolute basis; all scales of energy are arbitrary. The best we can do is measure changes in energy. However, we are perfectly free to define zero energy as the energy of the system in some arbitrary reference state, and then say that the internal energy of the system in any other state is the difference between the energies of the system in these two different states.

Pressure-volume work

The kind of work most frequently associated with chemical change occurs when the volume of the system changes owing to the disappearance or formation of gaseous substances. This is sometimes called expansion work or PV-work, and it can most easily be understood by reference to the simplest form of matter we can deal with, the hypothetical ideal gas.

The figure shows a quantity of gas confined in a cylinder by means of a moveable piston. Weights placed on top of the piston exert a force f over the cross-section area A, producing a pressure P = f / A which is exactly countered by the pressure of the gas, so that the piston remains stationary. Now suppose that we heat the gas slightly; according to Charles’ law, this will cause the gas to expand, so the piston will be forced upward by a distance Δx. Since this motion is opposed by the force x, a quantity of work f Δx will be done by the gas on the piston. By convention, work done by the system (in this case, the gas) on the surroundings is negative, so the work is given by

w = – f Δx(3-1)

When dealing with a gas, it is convenient to think in terms of the more relevant quantities pressure and volume rather than force and distance. We can accomplish this by multiplying the second term by A/A which of course leaves it unchanged:

(3-2)

By grouping the terms differently, but still not changing anything, we obtain

(3-3)

Since pressure is force per unit area and the product of the length A and the area has the dimensions of volume, this expression becomes

w = –P ΔV (3-4)

It is important to note that although P and V are state functions, the work is not (that’s why we denote it by a lower-case w.) As is shown farther below, the quantity of work done will depend on whether the same net volume change is realized in a single step (by setting the external pressure to the final pressure P), or in multiple stages by adjusting the restraining pressure on the gas to successively smaller values approaching the final value of P.

Problem Example 1

Find the amount of work done on the surroundings when 1 liter of an ideal gas, initially at a pressure of 10 atm, is allowed to expand at constant temperature to 10 liters by a) reducing the external pressure to 1 atm in a single step, b) reducing P first to 5 atm, and then to 1 atm, c) allowing the gas to expand into an evacuated space so its total volume is 10 liters.

Solution: First, note that ΔV, which is a state function, is the same for each path:

V₂ = (10/1) × (1 L) = 10 L, so ΔV = 9 L.

For path (a), w = –(1 atm)× (9 L) = –9 L-atm.

For path (b), the work is calculated for each stage separately:
w = –(5 atm) × (2–1 L) – (1 atm) × (10–2 L) = –13 L-atm

For path (c) the process would be carried out by removing all weights from the piston in Fig. 1 so that the gas expands to 10 L against zero external pressure. In this case w = (0 atm) × 9 L = 0; that is, no work is done because there is no force to oppose the expansion.

 

Adiabatic and isothermal processes

When a gas expands, it does work on the surroundings; compression of a gas to a smaller volume similarly requires that the surroundings perform work on the gas. If the gas is thermally isolated from the surroundings, then the process is said to occur adiabatically. In an adiabatic change, q = 0, so the First Law becomes ΔU = 0 + w. Since the temperature of the gas changes with its internal energy, it follows that adiabatic compression of a gas will cause it to warm up, while adiabatic expansion will result in cooling.

In contrast to this, consider a gas that is allowed to slowly excape from a container immersed in a constant-temperature bath. As the gas expands, it does work on the surroundings and therefore tends to cool, but the thermal gradient that results causes heat to pass into the gas from the surroundings to exactly compensate for this change. This is called an isothermal expansion. In an isothermal process the internal energy remains constant and we can write the First Law as 0 = q + w, or q = –w, illustrating that the heat flow and work done exactly balance each other.

Because no thermal insulation is perfect, truly adiabatic processes do not occur. However, heat flow does take time, so a compression or expansion that occurs more rapidly than thermal equilibration can be considred adiabatic for practical purposes.

If you have ever used a hand pump to inflate a bicycle tire, you may have noticed that the bottom of the pump barrel can get quite warm. Although a small part of this warming may be due to friction, it is mostly a result of the work you (the surroundings) are doing on the system (the gas.)

Adiabatic expansion and contractions are especially important in understanding the behavior of the atmosphere. Although we commonly think of the atmosphere as homogeneous, it is really not, due largely to uneven heating and cooling over localized areas. Because mixing and heat transfer between adjoining parcels of air does not occur rapidly, many common atmospheric phenomena can be considered at least quasi-adiabatic. A more detailed exposition of this topic is given in Part 5 of this unit.

Reversible processes

From Problem Example 1 we see that when a gas expands into a vacuum (P_external = 0) the work done is zero. This is the minimum work the gas can do; what is the maximum work the gas can perform on the surroundings? To answer this, notice that more work is done when the process is carried out in two stages than in one stage; a simple calculation will show that even more work can be obtained by increasing the number of stages— that is, by allowing the gas to expand against a series of successively lower external pressures. In order to extract the maximum possible work from the process, the expansion would have to be carried out in an infinite sequence of infinitessimal steps. Each step yields an increment of work P ΔV which can be expressed as (RT/V) dV and integrated:

(3-5)

Although such a path (which corresponds to what is called a reversible process) cannot be realized in practice, it can be approximated as closely as desired.

Even though no real process can take place reversibly (it would take an infinitely long time!), reversible processes play an essential role in thermodynamics. The main reason for this is that q_rev and w_rev are state functions which are important and are easily calculated. Moreover, many real processes take place sufficiently gradually that they can be treated as approximately reversible processes for easier calculation.

These plots illustrate the effects of various degrees of reversibility on the amount of work done when a gas expands, and the work that must be done in order to restore it to its initial state by recompressing it. The work, in each case, is proportional to the shaded area on the plot.

Each expansion-compression cycle leaves the gas unchanged, but in all but the one in the bottom row, the surroundings are forever altered, having expended more work in compressing the gas than was performed on it when the gas expanted.

Only when the processes are carried out in an infinite number of steps will the system and the surroundings be restored to their initial states— this is the meaning of thermodynamic reversibility.

 

Enthalpy

In every chemical reaction, some bonds are broken and some are formed. The difference between the energy absorbed in breaking bonds and that released in forming bonds is called the heat of reaction and is a quantity that can be measured.

Heats of reaction measured when a reaction is held at constant pressure are represented by the abbreviation ∆H, where ∆ (the Greek capital letter delta) is a general symbol used to indicate “a change in”, and H is a quantity called Enthalpy. Thus, the value of ∆H represents the enthalpy change that occurs during a reaction.

Enthalpy change (∆H). An alternative name for heat of reaction

Enthalpy is a measure of the total energy of a thermodynamic system. The SI unit of enthalpy is the joule (J), but other units are still in use, such as the calorie (kal).

Heat changes at constant pressure: the Enthalpy

For a chemical reaction that performs no work on the surroundings, the heat absorbed is the same as the change in internal energy: q = ΔU. But many chemical processes do involve work in one form or another:

·                     If the total volume of the reaction products exceeds that of the reactants, then the process performs work on the surroundings in the amount PΔV, in which P is the pressure exerted by the surroundings (usually the atmosphere) on the system.

·                     A reaction that drives an electrical current through an external circuit performs electrical work on the surroundings.

For an isothermal process, pressure-volume work affects the heat q

We will consider only pressure-volume work in this lesson. If the process takes place at a constant pressure, then the work is given by PΔV and the change in internal energy will be

ΔU = q – PΔV    (4-1)

Bear in mind why q is so important: the heat flow into or out of the system is directly measurable. ΔU, being “internal” to the system, is not directly observable.

Thus the amount of heat that passes between the system and the surroundings is given by

q = ΔU + PΔV    (4-2)

This means that if an exothermic reaction is accompanied by a net increase in volume under conditons of constant pressure, some additional heat additional to ΔU must be absorbed in order to supply the energy expended as work done on the surroundings if the temperature is to remain unchanged (isothermal process.)

For most practical purposes, changes in the volume of the system are only significant if the reaction is accompanied by a difference in the moles of gaseous reactants and products.

For example, in the reaction H₂(g) + ½ O₂(g) → H₂O(g), the total volume of the system decreases from that correponding to 1.5 moles of reactants to 1 mole of products. If we define this quantity as Δn_g , then for this reaction,

Δn_g  = (1 – 1.5) mol = –0.5 mol

This corresponds to a net contraction (negative expansion) of the system, meaning that the surroundings perform work on the system. The molar volume of an ideal gas at 25° C and 1 atm is

(298/273) × (22.4 L mol^–1) = 24.5 L mol^–1

Remember the sign convention: a flow of heat or performance of work that supplies energy is positive; if it consumes energy, it is negative. Thus work performed by the surroundings diminishes the energy of the surroundings (w_surr < 0) and increases the energy of the system (w_sys > 0).

and the work done (by the surroundings on the system) is

(1 atm) (–0.5 mol)(24.5 L mol^–1) = –12.2 L-atm.

Thus the energy of the system itself is +12.2 L-atm.

Using the conversion factor 1 J = 101.3 J, and bearing in mind that work performed on the system supplies energy to the system, this work increased the energy of the system by

(101.3 J/L-atm)(12.2 L-atm) = 1136 J = 1.24 kJ

Problem Example 2

The above reaction H₂(g) + ½ O₂(g) → H₂O(g) is carried out at a constant pressure of 1 atm and a constant temperature of 25° C. What quantity of heat q will cross the system boundary (and in which direction?) For this reaction, the change in internal energy is ΔU = –240.59 kJ/mol.

Solution: The reaction itself (that is, the re-arrangement of the atoms from reactants to products releases q = –240.59 kJ of heat. The work performed by the surroundings supplies an additional energy of w = 1.24 kJ to the system. In order to maintain the constant 25° temperature, an equivalent quantity of heat must be released: q = (–240.59 + 1.24) k J = –241.83 kJ

 

About “constant” pressure and temperature processes

This terminology can be somewhat misleading unless you bear in mind that the conditions ΔP and ΔT refer to the differences between the inital and final states of the system — that is, before and after the reaction.

During the time the reaction is in progress, the temperature of the mixture will rise or fall, depending on whether the process is exothermic or endothermic.  But because ΔT is a state function, its value is independent of what happens “in between” the initial state (reactants) and final state (products).   The same is true of ΔV.

Enthalpy hides work and saves it too!

Because most chemical changes we deal with take place at constant pressure, it would be tedious to have to explicitly deal with the pressure-volume work details that were described above. Fortunately, chemists have found a way around this; they have simply defined a new state function that incorporates and thus hides within itself any terms relating to incidental kinds of work
(P-V, electrical, etc.)

Since both ΔP and ΔV in Eq 4-2 are state functions, then q_P  , the heat that is absorbed or released when a process takes place at constant pressure, must also be a state function and is known as the enthalpy change ΔH.

important ⇒ ΔH ≡ q_P = ΔU + PΔV(4-3)

Since most processes that occur in the laboratory, on the surface of the earth, and in organisms do so under a constant pressure of one atmosphere, Eq 4-3 is the form of the First Law that is of greatest interest to most of us most of the time.

Problem Example 3

Hydrogen chloride gas readily dissolves in water, releasing 75.3 kJ/mol of heat in the process. If one mole of HCl at 298 K and 1 atm pressure occupies 24.5 liters, find ΔU for the system when one mole of HCl dissolves in water under these conditions.

Solution: In this process the volume of liquid remains practically unchanged, so ΔV = –24.5 L. The work done is

w = –PΔV = –(1 atm)(–24.5 L) = 24.6 L-atm

(The work is positive because it is being done on the system as its volume decreases due to the dissolution of the gas into the much smaller volume of the solution.) Using the conversion factor 1 L-atm = 101.33 J mol^–1 and substituting in Eq. 3 (above) we obtain

ΔU= q +PΔV = –(75300 J) + [101.33 J/L-atm) × (24.5 L-atm)] = –72.82 kJ

In other words, if the gaseous HCl could dissolve without volume change, the heat released by the process (75.3 kJ) would cause the system’s internal energy to diminish by 75.3 kJ. But the disappearance of the gaseous phase reduces the volume of the system. This is equivalent to compression of the system by the pressure of the atmosphere performing work on it and consuming part of the energy that would otherwise be liberated, reducing the net value of ΔU to –72.82 kJ.

The Heat Capacity

For systems in which no change in composition (chemical reaction) occurs, things are even simpler: to a very good approximation, the enthalpy depends only on the temperature. This means that the temperature of such a system can serve as a direct measure of its enthalpy. The functional relation between the internal energy and the temperature is given by the heat capacity measured at constant pressure:

(5-1)

(or ΔH/ΔT if you don’t care for calculus!) An analogous quantity relates the heat capacity at constant volume to the internal energy:

(5-2)

The difference between C_P and C_V is of importance only when the volume of the system changes significantly— that is, when different numbers of moles of gases appear on either side of the chemical equation. For reactions involving only liquids and solids, C_p and C_v are for all practical purposes identical.

Heat capacity can be expressed in joules or calories per mole per degree (molar heat capacity), or in joules or calories per gram per degree; the latter is called the specific heat capacity or just the specific heat.

The greater the heat capacity of a substance, the smaller will be the effect of a given absorption or loss of heat on its temperature.

What is Energy?

Energy is one of the most fundamental and universal concepts of physical science, but one that is remarkably difficult to define in way that is meaningful to most people. This perhaps reflects the fact that energy is not a “thing” that exists by itself, but is rather an attribute of matter (and also of electromagnetic radiation) that can manifest itself in different ways. It can be observed and measured only indirectly through its effects on matter that acquires, loses, or possesses it.

The concept that we call energy was very slow to develop; it took more than a hundred years just to get people to agree on the definitions of many of the terms we use to describe energy and the interconversion between its various forms. But eveow, most people have some difficulty in explaining what it is; somehow, the definition we all learned in elementary science (“the capacity to do work”) seems less than adequate to convey its meaning.

Kinetic energy and potential energy

Whatever energy may be, there are basically two kinds.

Kinetic energy is associated with the motion of an object, and its direct consequences are part of everyone’s daily experience; the faster the ball you catch in your hand, and the heavier it is, the more you feel it.  Quantitatively, a body with a mass m and moving at a velocity v  possesses the kinetic energy mv²/2.

Problem Example 1

A rifle shoots a 4.25 g bullet at a velocity of 965 m s^–1.  What is its kinetic energy?

Solution:  The only additional information you need here is that

1 J = 1 kg m² s^–1:

KE = ½ × (.00425 kg) (965 m s^–1)² = 1980 J

 

Potential energy is energy a body has by virtue of its location. But there is more: the body must be subject to a “restoring force” of some kind that tends to move it to a location of lower potential energy. Think of an arrow that is subjected to the force from a stretched bowstring; the more tightly the arrow is pulled back against the string, the more  potential energy it has.

More generally, the restoring force comes from what we call a force field— a gravitational, electrostaticl, or magnetic field. We observe the consequences of gravitational potential energy all the time, such as when we walk, but seldom give it any thought.

If an object of mass m is raised off the floor to a height h, its potential energy increases by mgh, where g is a proportionality constant known as the acceleration of gravity; its value at the earth’s surface is 9.8 m s^–2.

Problem Example 2

Find the change in potential energy of a 2.6 kg textbook that falls from the 66-cm height of a table top onto the floor.

Solution: PE =  m g h = (2.6 kg)(9.8 m s^–2)(0.66 m) = 16.8 kg m² s^–2 = 16.8 J

 

Similarly, the potential energy of a particle having an electric charge q depends on its location in an electrostatic field.

 

“Chemical energy”

Electrostatic potential energy plays a major role in chemistry; the potential energies of electrons in the force field created by atomic nuclei lie at the heart of the chemical behavior of atoms and molecules.

“Chemical energy” usually refers to the energy that is stored in the chemical bonds of molecules. These bonds form when electrons are able to respond to the force fields created by two or more atomic nuclei, so they can be regarded as manifestations of electrostatic potential energy.

In an exothermic chemical reaction, the electrons and nuclei within the reactants undergo rearrangment into products possessing lower energies, and the difference is released to the environment in the form of heat. 

Interconversion of potential and kinetic energy

Transitions between potential and kinetic energy are such an intimate part of our daily lives that we hardly give them a thought. It happens in walking as the body moves up and down.

 

Our bodies utilize the chemical energy in glucose to keep us warm and to move our muscles. In fact, life itself depends on the conversion of chemical energy to other forms.

Energy is conserved: it caeither be created nor destroyed. So when you go uphill, your kinetic energy is transformed into potential energy, which gets changed back into kinetic energy as you coast down the other side. And where did the kinetic energy you expended in peddling uphill come from? By conversion of some of the chemical potential energy in your breakfast cereal.

When drop a book, its potential energy is transformed into kinetic energy. When it strikes the floor, this transformation is complete. What happens to the energy then? The kinetic energy that at the moment of impact was formerly situated exclusively in the moving book, now becomes shared between the book and the floor, and in the form of randomized thermal motions of the molecular units of which they are made; we can observe this effect as a rise in temperature.

Much of the potential energy of falling water can be captured by a water wheel or other device that transforms the kinetic energy of the exit water into kinetic energy. The output of a hydroelectric power is directly proportional to its height above the level of the generator turbines in the valley below. At this point, the kinetic energy of the exit water is transferred to that of the turbine, most of which (up to 90 percent in the largest installations) is then converted into electrical energy.

Will the temperature of the water at the bottom of a water fall be greater than that at the top? James Joule himself predicted that it would be. It has been calculated that at Niagra falls, that complete conversion of the potential energy of 1 kg of water at the top into kinetic energy when it hits the plunge pool 58 meters below will result in a temperature increase of about 0.14 C°. (But there are lots of complications. For example, some of the water breaks up into tiny droplets as it falls, and water evaporates from droplets quite rapidly, producing a cooling effect.)

Chemical energy can also be converted, at least partially, into electrical energy: this is what happens in a battery.  If a highly exothermic reaction also produces gaseous products, the latter may expand so rapidly that the result is an explosion — a net conversion of chemical energy into kinetic energy (including sound).

Thermal energy

Kinetic energy is associated with motion, but in two different ways.  For a macroscopic object such as a book or a ball, or a parcel of flowing water, it is simply given by ½ mv².

But as we mentioned above, when an object is dropped onto the floor, or when an exothermic chemical reaction heats surrounding matter, the kinetic energy gets dispersed into the molecular units in the environment.  This “microscopic” form of kinetic energy, unlike that of a speeding bullet, is completely random in the kinds of motions it exhibits and in its direction. We refer to this as “thermalized” kinetic energy, or more commonly simply as thermal energy. We observe the effects of this as a rise in the temperature of the surroundings. The temperature of a body is direct measure of the quantity of thermal energy is contains.

Thermal energy is never completely recoverable

Once kinetic energy is thermalized, only a portion of it can be converted back into potential energy.  The remainder simply gets dispersed and diluted into the environment, and is effectively lost.

To summarize, then:

·                     Potential energy can be converted entirely into kinetic energy..

·                     Potential energy can also be converted, with varying degrees of efficiency,into electrical energy.

·                     The kinetic energy of macroscopic objects can be transferred between objects (barring the effects of friction).

·                     Once kinetic energy becomes thermalized, only a portion of it can be converted back into either potential energy or be concentrated back into the kinetic energy of a macroscopic. This limitation, which has nothing to do with technology but is a fundamental property of nature, is the subject of the second law of thermodynamics.

·                     A device that is intended to accomplish the partial transformation of thermal energy into organized kinetic energy is known as a heat engine.

Some examples of potential-kinetic energy interconversion processes

Schematic diagram of alarge hydroelectric plant

Turbine being installed at Grand Coulee dam, 1974

Hydroelectric power constitutes one of the major engineering accomplishments that exploits conversion of potential energy into kinetic– and thence into electrical energy.

 

The heat that flows across the boundaries of a system undergoing a change is a fundamental property that characterizes the process. It is easily measured, and if the process is a chemical reaction carried out at constant pressure, it can also be predicted from the difference between the enthalpies of the products and reactants. The quantitative study and measurement of heat and enthalpy changes is known as thermochemistry.

Thermochemical equations and standard states

In order to define the thermochemical properties of a process, it is first necessary to write a thermochemical equation that defines the actual change taking place, both in terms of the formulas of the substances involved and their physical states.

To take a very simple example, here is the complete thermochemical equation for the vaporization of water at its normal boiling point:

H₂O(l, 373 K, 1 atm) → H₂O(g, 373 K, 1 atm)    ΔH = 40.7 kJ mol^–1

The quantity 40.7 is known as the enthalpy of vaporization (often referred to as “heat of vaporization”) of liquid water.

The following points should be kept in mind when writing thermochemical equations:

Any thermodynamic quantity such as ΔH that is associated with a thermochemical equation always refers to the number of moles of substances explicitly shown in the equation.

Thus for the synthesis of water we can write

2 H₂(g) + O₂(g)→ 2 H₂O(l)    ΔH = –572 kJ

or

H₂(g) + ½ O₂(g)→ H₂O(l)    ΔH = –286 kJ

 

Thermochemical equations for reactions taking place in solution must also specify the concentrations of the dissolved species.

For example, the enthalpy of neutralization of a strong acid by a strong base is given by

H⁺(aq, 1M, 298 K, 1 atm) + OH^–(aq, 1M, 298 K, 1 atm) →
H₂O(l, 373 K, 1 atm)    ΔH =56.9 kJ mol^–1

in which the abbreviation aq refers to the hydrated ions as they exist in aqueous solution. Since most thermochemical equations are written for the standard conditions of 298 K and 1 atm pressure, we can leave these quantities out if these conditions apply both before and after the reaction. If, under these same conditions, the substance is in its preferred (most stable) physical state, then the substance is said to be in its standard state.

Thus the standard state of water at 1 atm is the solid below 0°C, and the gas above 100°C. A thermochemical quantity such as ΔH that refers to reactants and products in their standard states is denoted by ΔH°.

In the case of dissolved substances, the standard state of a solute is that in which the “effective concentration”, known as the activity, is unity.

For non-ionic solutes the activity and molarity are usually about the same for concentrations up to about 1M, but for an ionic solute this approximation is generally valid only for solutions more dilute than 0.001-0.01M, depending on electric charge and size of the particular ion.

 

Standard enthalpy of formation

The enthalpy change for a chemical reaction is the difference

ΔH = H_products – H_reactants

If the reaction in question represents the formation of one mole of the compound from its elements in their standard states, as in

H₂(g) + ½ O₂(g)→ H₂O(l)    ΔH = –286 kJ

then we can arbitrarily set the enthalpy of the elements to zero and write

H_f ° = ΣH_f °_products – ΣH_f °_reactants= –286 kJ – 0 = –268 kJ mol^–1

which defines the standard enthalpy of formation of water at 298K.

The value H_f ° = –268 kJ tells us that when hydrogen and oxygen, each at a pressure of 1 atm and at 298 K (25° C) react to form 1 mole of liquid water also at 25°C and 1 atm pressure, 268 kJ will have passed from the sytstem (the reaction mixture) into the surroundings. The negative sign indicates that the reaction is exothermic: the enthalpy of the product is smaller than that of the reactants.

The standard enthalpy of formation of a compound is defined as the heat associated with the formation of one mole of the compound from its elements in their standard states.

In general, the standard enthalpy change for a reaction is given by the expression

important ⇒ Δ ΣH_f °_products – ΣH_f °_reactants (2-1)

in which the ΣH_f ° terms indicate the sums of the standard enthalpies of formations of all products and reactants. The above definition is one of the most important in chemistry because it allows us to predict the enthalpy change of any reaction without knowing any more than the standard enthalpies of formation of the products and reactants, which are widely available in tables.

The following examples illustrate some important aspects of the standard enthalpy of formation of substances.

The thermochemical equation defining H_f ° is always written in terms of one mole of the substance in question:

½ N₂(g) + 3/2 H₂(g)→ NH₃(g)    ΔH° = –46.1 kJ (per mole of NH₃)

The standard heat of formation of a compound is always taken in reference to the forms of the elements that are most stable at 25°C and 1 atm pressure.

A number of elements, of which sulfur and carbon are common examples, can exist in more then one solid crystalline form.

In the case of carbon, the graphite modification is the more stable form.

C(graphite) + O₂(g) → CO₂(g)    ΔH° = –393.5 kJ mol^–1

C(diamond) + O₂(g) → CO₂(g)    ΔH° = –395.8 kJ mol^–1

The physical state of the product of the formation reaction must be indicated explicitly if it is not the most stable one at 25°C and 1 atm pressure:

H₂(g) + ½ O₂(g) → H₂O(g)       ΔH° = –285.8 kJ mol^–1

H₂(g) + ½ O₂(g) → H₂O(g)     ΔH° = –241.8 kJ mol^–1

Notice that the difference between these two ΔH° values is just the heat of vaporization of water.

Although the formation of most molecules from their elements is an exothermic process, the formation of some compounds is mildly endothermic:

½ N₂(g) + O₂(g)→ NO₂(g)      ΔH° = +33.2 kJ mol^–1

A positive heat of formation is frequently associated with instability— the tendency of a molecule to decompose into its elements, although it is not in itself a sufficient cause. In many cases, however, the rate of this decomposition is essentially zero, so it is still possible for the substance to exist. In this connection, it is worth noting that all molecules will become unstable at higher temperatures.

The thermochemical reactions that define the heats of formation of most compounds cannot actually take place.

For example, the direct synthesis of methane from its elements

C(graphite) + 2 H₂(g) → CH₄(g)

cannot be observed directly owing to the large number of other possible reactions between these two elements. However, the standard enthalpy change for such a reaction be found indirectly from other data, as explained in the next section.

The standard enthalpy of formation of gaseous atoms from the element is known as the heat of atomization.

Heats of atomization are always positive, and are important in the calculation of bond energies.

Fe(s) → Fe(g)     ΔH° = 417 kJ mol^–1

The standard enthalpy of formation of an ion dissolved in water is expressed on a separate scale in which that of H⁺(aq) is defined as zero.

The standard heat of formation of a dissolved ion such as Cl^– (that is, formation of the ion from the element) cannot be measured because it is impossible to have a solution containing a single kind of ion. For this reason, ionic enthalpies are expressed on a separate scale on which H_f° of the hydrogen ion at unit activity (1 M effective concentration) is defined as zero. Thus for Ca²⁺(aq), H_f° = –248 kJ mol^–1; this means that the reaction

Ca(s) → Ca²⁺(g) + 2e^–

½ H₂(g) → H⁺(aq) + e^–

(Of course, neither of these reactions can take place by itself, so ionic enthalpies must be measured indirectly.)

 

Hess’ law and thermochemical calculations

You probably know that two or more chemical equations can be combined algebraically to give a new equation. Even before the science of thermodynamics developed in the late nineteenth century, it was observed that the heats associated with chemical reactions can be combined in the same way to yield the heat of another reaction. For example, the standard enthalpy changes for the oxidation of graphite and diamond can be combined to obtain ΔH° for the transformation between these two forms of solid carbon, a reaction that cannot be studied experimentally.

C(graphite) + O₂(g)→ CO₂(g)    ΔH° = –393.51 kJ mol^–1

C(diamond) + O₂(g)→ CO₂(g)    ΔH° = –395.40 kJ mol^–1

 

Subtraction of the second reaction from the first (i.e., writing the second equation in reverse and adding it to the first one) yields

C(graphite) → C(diamond)     ΔH° = 1.89 kJ mol^–1

This principle, known as Hess’ law of independent heat summation is a direct consequence of the enthalpy being a state function. Hess’ law is one of the most powerful tools of chemistry, for it allows the change in the enthalpy (and in other thermodynamic functions) of huge numbers of chemical reactions to be predicted from a relatively small base of experimental data.

Germain Henri Hess (1802-1850) was a Swiss-born professor of chemistry at St. Petersburg, Russia. He formulated his famous law, which he discovered empirically, in 1840. Very little appears to be known about his other work in chemistry.

 

Standard enthalpies of combustion

Because most substances cannot be prepared directly from their elements, heats of formation of compounds are seldom determined by direct measurement. Instead, Hess’ law is employed to calculate enthalpies of formation from more accessible data. The most important of these are the standard enthalpies of combustion. Most elements and compounds combine with oxygen, and many of these oxidations are highly exothermic, making the measurement of their heats relatively easy.

For example, by combining the heats of combustion of carbon, hydrogen, and methane, we can obtain the standard enthalpy of formation of methane, which as we noted above, cannot be determined directly.

Problem Example 1

Use the following heat of formation/combustion information to estimate the standard heat of formation of methane CH₄.

C(graphite) + O₂(g) → CO₂(g)    ΔH° = –393 kJ mol^–1(P1-1)
H₂(g) + ½O₂(g) → H₂O(g)    ΔH° = –242 kJ mol^–1(P1-2)
CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(g)    ΔH° = –882 kJ mol^–1(P1-3)

Solution: The standard heat of formation of methane is defined by the reaction

C(graphite) + 2H₂(g) → CH₄(g)    ΔH° = ???(P1-4)

Our task is thus to combine the top three equations in such a way that they add up to (4).

1) Begin by noting that (3), the combustion of methane, is the only equation that contains the CH₄ term, so we need to write it in reverse (not forgetting to reverse the sign of ΔH°!) so that CH₄ appears as the product.

CO₂(g) + 2H₂O(g) → CH₄(g) + 2O₂(g)   ΔH° = +393 kJ mol^–1(P1-3Rev)

2) Since H₂O should not appear in (4), add two times (2) to cancel both out. Notice that this also cancels one of the oxygens in (3Rev):

CO₂(g) + 2H₂O(g) → CH₄(g) + 2O₂(g)   ΔH° = +393 kJ mol^–1(P1-3Rev)
2 H₂(g) + O₂(g) → 2H₂O(g)    ΔH° = –484 kJ mol^–1(P1-2)

3) Finally, get rid of the remaining O₂ and CO₂ by adding (1); this also adds a needed C:

CO₂(g) + 2H₂O(g) → CH₄(g) + 2O₂(g)   ΔH° = +393 kJ mol^–1(P1-3Rev)
2 H₂(g) + O₂(g) → 2H₂O(g)    ΔH° = –484 kJ mol^–1(P1-2)
C(graphite) + O₂(g) → CO₂(g)    ΔH° = –76.4 kJ mol^–1(P1-1)

4) So our creative cancelling has eliminated all except the substances that appear in (4). Just add up the enthalpy changes and we are done:

C(graphite) + 2H₂(g) → CH₄(g)    ΔH° = ???(P1-4)

 

Calorimetry: measuring ΔH in the laboratory

How are enthalpy changes determined experimentally? First, you must understand that the only thermal quantity that can be observed directly is the heat q that flows into or out of a reaction vessel, and that q is numerically equal to ΔH° only under the special condition of constant pressure. Moreover, q is equal to the standard enthalpy change only when the reactants and products are both at the same temperature, normally 25°C.

The measurement of q is generally known as calorimetry.

The most common types of calorimeters contain a known quantity of water which absorbs the heat released by the reaction. Because the specific heat capacity of water (4.184 J g^–1 K^–1) is known to high precision, a measurement of its temperature rise due to the reaction enables one to calculate the quantity of heat released.

The calorimeter constant

In all but the very simplest calorimeters, some of the heat released by the reaction is absorbed by the components of the calorimeter itself. It is therefore necessary to “calibrate” the calorimeter by measuring the temperature change that results from the introduction of a known quantity of heat. The resulting calorimeter constant, expressed in J K^–1, can be regarded as the “heat capacity of the calorimeter”. The known source of heat is usually produced by passing a known quantity of electric current through a resistor within the calorimeter, but it can be measured by other means as described in the following problem example.

Problem Example 2

In determining the heat capacity of a calorimeter, a student mixes
100.0 g of water at 57.0 °C with 100.0 g of water, already in the calorimeter, at 24.2°C. (The specific heat of water is 4.184 J g^–1 K^–1)

After mixing and thermal equilibration with the calorimeter, the temperature of the water stabilizes at 38.7°C. Calculate the heat capacity of the calorimeter in J/K.

Solution:

The hot water loses heat, the cold water gains heat, and the calorimter itself gains heat, so this is essentially a thermal balance problem. Conservation of energy requires that

q_hot + q_cold + q_cal = 0

We can evaluate the first two terms from the observed temperature changes:

q_hot = (100 g) (38.7 – 57.0) K (4.184 J g^–1 K^–1) = –7657 J

q_cold = (100 g) (38.7 – 24.2) K (4.184 J g^–1 K^–1) = 6067 J

So q_cal = (7657 – 6067) J = 1590 J

The calorimeter constant is (1590 J) / (38.7 – 24.2) K = 110 J K^–1

Note: Strictly speaking, there is a fourth thermal balance term that must be considered in a highly accurate calculation: the water in the calorimeter expands as it is heated, performing work on the atmosphere. 

 

For reactions that can be initiated by combining two solutions, the temperature rise of the solution itself can provide an approximate value of the reaction enthalpy if we assume that the heat capacity of the solution is close to that of the pure water — which will be nearly true if the solutions are dilute. 

For example, a very simple calorimetric determination of the standard enthalpy of the reaction H⁺(aq) + OH^–(aq) → H₂O(l) could be carried out by combining equal volumes of 0.1M solutions of HCl and of NaOH initially at 25°C. Since this reaction is exothermic, a quantity of heat q will be released into the solution. From the tmperature rise and the specific heat of water, we obtain the number of joules of heat released into each gram of the solution, and q can then be calculated from the mass of the solution. Since the entire process is carried out at constant pressure, we have ΔH° = q.

For reactions that cannot be carried out in dilute aqueous solution, the reaction vessel is commonly placed within a larger insulated container of water. During the reaction, heat passes between the inner and outer containers until their temperatures become identical. Again, the temperature change of the water is observed, but in this case we need to know the value of the calorimeter constant described above.

The bomb calorimeter

Most serious calorimetry carried out in research laboratories involves the determination of heats of combustion, since these are essential to the determination of standard enthalpies of formation of the thousands of new compounds that are prepared and characterized each month.

In order to ensure complete combustion, the experiment is carried out in the presence of oxygen above atmospheric pressure. This requires that the combustion be confined to a fixed volume.

Since the process takes place at constant volume, the reaction vessel must be constructed to withstand the high pressure resulting from the combustion process, which amounts to a confined explosion. The vessel is usually called a “bomb”, and the technique is known as bomb calorimetry. The reaction is initiated by discharging a capacitor through a thin wire which ignites the mixture.

Another consequence of the constant-volume condition is that the heat released corresponds to q_v , and thus to the internal energy change ΔU rather than to ΔH. The enthalpy change is calculated  according to the formjula

ΔH = q_v + Δn_gRT

in which Δn_g  is the change in the number of moles of gases in the reaction.

Problem Example 3

A sample of biphenyl (C₆H₅)₂ weighing 0.526 g was ignited in a bomb calorimeter initially at 25°C, producing a temperature rise of 1.91 K. In a separate calibration experiment, a sample of benzoic acid C₆H₅COOH weighing 0.825 g was ignited under identical conditions and produced a temperature rise of 1.94 K. For benzoic acid, the heat of combustion at constant pressure is known to be 3226 kJ mol^–1 (that is, ΔU° = –3226 kJ mol^–1.) Use this information to determine the standard enthalpy of combustion of biphenyl.

Solution.The calorimeter constant is given by

The heat released by the combustion of the biphenyl at constant pressure is then ΔU:

(The negative sign indicates that heat is released in this process.) From the reaction equation

(C₆H₅)₂(s) + 19/2 O₂(g)→ 12 CO₂(g) + 5 H₂O(l)

we have Δn_g = 12 – (19/2) = –5/2. Converting to ΔH, we substitute into

ΔH = q_V + Δn_gRT

ΔH° = ΔU° – (5/2)(8.314 J mol^–1 K^–1) = –6440 J mol^–1

This is the amount of heat that is lost by the system if reaction takes place at constant pressure and the temperature is restored to its initial value.

 

Calorimeters

Although calorimetry is simple in principle, its practice is a highly exacting art, especially when applied to processes that take place slowly or involve very small heat changes, such as the germination of seeds.

Calorimeters can be as simple as a foam plastic coffee cup, which is often used in student laboratories.

 Research-grade calorimeters, able to detect minute temperature changes, are more likely to occupy table tops, or even entire rooms:

The ice calorimeter is an important tool for measuring the heat capacities of liquids and solids, as well as the heats of certain reactions. This simple yet ingenious apparatus is essentially a device for measuring the change in volume due to melting of ice. To measure a heat capacity, a warm sample is placed in the inner compartment, which is surrounded by a mixture of ice and water.

The heat withdrawn from the sample as it cools causes some of the ice to melt. Since ice is less dense than water, the volume of water in the insulated chamber decreases. This causes an equivalent volume of mercury to be sucked into the inner reservoir from the outside container. The loss in weight of this container gives the decrease in volume of the water, and thus the mass of ice melted. This, combined with the heat of fusion of ice, gives the quantity of heat lost by the sample as it cools to 0°C.

 

 

Exothermic and Endothermic Reactions

When the total energy of the bonds formed in the products is greater than the total energy of the bond broken in the reactants, energy is released and a reaction is exothermic.

The heat released in an exothermic reaction can be thought of a reaction product, and ∆H is assigned a negative value because heat leaves:

An exothermic reaction – negative ∆H:

When the total energy of the bonds formed in the product is less than the total energy of the bonds broken in the reactants, energy is absorbed and a reaction is endothermic.

The heat added in an endothermic reaction is like a reactant, and ∆H is assigned a positive value because heat is added.

An endothermic reaction – positive ∆H:

The essential points about heat and chemical reactions are summarized as follows:

An exothermic reaction heat releases to the surroundings; ∆H is negative

An endothermic reaction heat absorbs from the surroundings; ∆H is positive

Heat and work

Heat and work are both measured in energy units, so they must both represent energy. How do they differ from each other, and from just plain “energy” itself?

Heat and work are processes and cannot be stored

In our daily language, we often say that “this object contains a lot of heat”, but this kind of talk is a no-no in thermodynamics! It’s ok to say that the object is “hot”, meaning that its temperature is high.

The term “heat” has a special meaning in thermodynamics: it is a process in which a body (the contents of a tea kettle, for example) acquires or loses energy as a direct consequence of its having a different temperqture than its surroundings (the rest of the world).

Thermal energy can only flow from a higher temperature to a lower temperature. It is this flow that constitutes “heat”.

Use of the term “flow” of heat recalls the 18th-century notion that heat is an actual substance called “caloric” that could flow like a liquid.

 

Heat is transferred by conduction or radiation

Transfer of thermal energy can be accomplished by bringing two bodies into physical contact (the kettle on top of the stove, or through an electric heating element inside the kettle). Another mechanism of thermal energy transfer is by radiation; a hot object will convey energy to any body in sight of it via electromagnetic radiation in the infrared part of the spectrum. In many cases, a combination of modes will be active:

Thus when you place a can of beer in the refrigerator, both processes are operative: the can radiates heat to the cold surfaces around it, and absorbs it by direct conduction from the ambient air.

So what is work?

Work refers to the transfer of energy some means that does not depend on temperature difference.

    

Work, like energy, can take various forms, the most familiar being mechanical and electrical. Mechanical work arises when an object moves a distance Δx against an opposing force f: w = f Δx N-m; 1 N-m = 1 J.

Electrical work is done when a body having a charge q moves through a potential difference ΔV.

Work, like heat, exists only when energy is being transferred.

When two bodies are placed in thermal contact and energy flows from the warmer body to the cooler one,we call the process “heat”. A transfer of energy to or from a system by any means other than heat is called “work”.

Interconvertability of heat and work

Work can be completely converted into heat (by friction, for example), but heat can only be partially converted to work. Conversion of heat into work is accomplished by means of a heat engine, the most common example of which is an ordinary gasoline engine.

The science of thermodynamics developed out of the need to understand the limitations of steam-driven heat engines at the beginning of the Industrial Age. A fundamental law of Nature, the Second Law of Thermodynamics, states that the complete conversion of heat into work is impossible. Something to think about when you purchase fuel for your car!

 

Enthalpy diagrams and their uses

Comparison and interpretation of enthalpy changes is materially aided by a graphical construction in which the relative enthalpies of various substances are represented by horizontal lines on a vertical energy scale. The zero of the scale can be placed anywhere, since energies are always arbitrary; it is generally most useful to locate the elements at zero energy, which reflects the convention that their standard enthlapies of formation are zero.

This very simple enthalpy diagram for carbon and oxygen and its two stable oxides shows the changes in enthalpy associated with the various reactions this system can undergo. Notice how Hess’ law is implicit in this diagram; we can calculate the enthalpy change for the combustion of carbon monoxide to carbon dioxide, for example, by subtraction of the appropriate arrow lengths without writing out the thermochemical equations in a formal way.

The zero-enthalpy reference states refer to graphite, the most stable form of carbon, and gaseous oxygen. All temperatures are 298 K.

 This enthalpy diagram for the hydrogen-oxygen system shows the known stable configurations of these two elements. Reaction of gaseous H₂ and O₂ to yield one mole of liquid water releases 285 kJ of heat .

If the H₂O is formed in the gaseous state, the energy release will be smaller.

Notice also that…

·                     The heat of vaporization of water (an endothermic process) is clearly found from the diagram.

·                     Hydrogen peroxide H₂O₂, which spontaneously decomposes into O₂ and H₂O, releases some heat in this process.

Ordinarily this reaction is so slow that the heat is not noticed. But the use of an appropriate catalyst can make the reaction so fast that it has been used to fuel a racing car.

Why you can’t run your car on water

You may have heard the venerable urban legend, probably by now over 80 years old, that some obscure inventor discovered a process to do this, but the invention was secretly bought up by the oil companies in order to preserve their monopoly. The enthalpy diagram for the hydrogen-oxygen system shows why this cannot be true — there is simply no known compound of H and O that resides at a lower enthalpy level.

Enthalpy diagrams are especially useful for comparing groups of substances having some common feature. This one shows the molar enthalpies of species relating to two hydrogen halides, with respect to those of the elements. From this diagram we can see at a glance that the formation of HF from the elements is considerably more exothermic than the corresponding formation of HCl. The upper part of this diagram shows the gaseous atoms at positive enthalpies with respect to the elements. The endothermic processes in which the H₂ and the dihalogen are dissociated into atoms can be imagined as taking place in two stages, also shown. From the enthalpy change associated with the dissociation of H₂ (218 kJ mol^–1), the dissociation enthalpies of F₂ and Cl₂ can be calculated and placed on the diagram.

Bond enthalpies and bond energies

The enthalpy change associated with the reaction

HI(g) → H(g)+ I(g)

is the enthalpy of dissociation of the HI molecule; it is also the bond energy of the hydrogen-iodine bond in this molecule. Under the usual standard conditions, it would be expressed either as the bond enthalpy H°(HI,298K) or internal energy U°(HI,298); in this case the two quantities differ from each other by ΔPV = RT. Since this reaction cannot be studied directly, the H–I bond enthalpy is calculated from the appropriate standard enthalpies of formation:

 

Bond energies and enthalpies are important properties of chemical bonds, and it is very important to be able to estimate their values from other thermochemical data. The total bond enthalpy of a more complex molecule such as ethane can be found from the following combination of reactions:

When a molecule in its ordinary state is broken up into gaseous atoms, the process is known as atomization.

The standard enthalpy of atomization refers to the transformation of an element into gaseous atoms:

C(graphite) → C(g)     ΔH° = 716.7 kJ

… which is always, of course, an endothermic process. Heats of atomization are most commonly used for calculating bond energies. They are usually measured spectroscopically.

Pauling’s rule and average bond energy

The total bond energy of a molecule can be thought of as the sum of the energies of the individual bonds. This principle, known as Pauling’s Rule, is only an approximation, because the energy of a given type of bond is not really a constant, but depends somewhat on the particular chemical environment of the two atoms. In other words, all we can really talk about is the average energy of a particular kind of bond, such as C–O, for example, the average being taken over a representative sample of compounds containing this type of bond, such as CO, CO₂, COCl₂, (CH₃)₂CO, CH₃COOH, etc.

Despite the lack of strict additivity of bond energies, Pauling’s Rule is extremely useful because it allows one to estimate the heats of formation of compounds that have not been studied, or have not even been prepared. Thus in the foregoing example, if we know the enthalpies of the C–C and C–H bonds from other data, we could estimate the total bond enthalpy of ethane, and then work back to get some other quantity of interest, such as ethane’s enthalpy of formation.

By assembling a large amount of experimental information of this kind, a consistent set of average bond energies can be obtained. The energies of double bonds are greater than those of single bonds, and those of triple bonds are higher still.

 

Energy content of fuels

A fuel is any substance capable of providing useful amounts of energy through a process that can be carried out in a controlled manner at economical cost. For most practical fuels, the process is combustion in air (in which the oxidizing agent O₂ is available at zero cost.) The enthalpy of combustion is obviously an important criterion for a substance’s suitability as a fuel, but it is not the only one; a useful fuel must also be easily ignited, and in the case of a fuel intended for self-powered vehicles, its energy density in terms of both mass (kJ kg^–1) and volume (kJ m^–3) must be reasonably large. Thus substances such as methane and propane which are gases at 1 atm must be stored as pressurized liquids for transportation and portable applications.

Notes on the above table

^a Ethanol is being strongly promoted as a motor fuel by the U.S. agricultural industry. Note, however, that according to some estimates, it takes 46 MJ of energy to produce 1 kg of ethanol from corn. Some other analyses, which take into account optimal farming practices and the use of by-products arrive at different conclusions; see, for example, this summary with links to several reports.

^b Owing to its low molar mass and high heat of combustion, hydrogen possesses an extraordinarily high energy density, and would be an ideal fuel if its critical temperature (33 K, the temperature above which it cannot exist as a liquid) were not so low. The potential benefits of using hydrogen as a fuel have motivated a great deal of research into other methods of getting a large amount of H₂ into a small volume of space. Simply compressing the gas to a very high pressure is not practical because the weight of the heavy-walled steel vessel required to withstand the pressure would increase the effective weight of the fuel to an unacceptably large value. One scheme that has shown some promise exploits the ability of H₂ to “dissolve” in certain transition metals. The hydrogen can be recovered from the resulting solid solution (actually a loosely-bound compound) by heating.

 

Energy content of foods

What, exactly, is meant by the statement that a particular food “contains 1200 calories” per serving? This simply refers to the standard enthalpy of combustion of the foodstuff, as measured in a bomb calorimeter. Note, however, that iutritional usage, the calorie is really a kilocalorie (sometimes called “large calorie”), that is, 4184 J. Although this unit is still employed in the popular literature, the SI unit is now commonly used in the scientific and clinical literature, in which energy contents of foods are usually quoted in kJ per unit of weight.

Although the mechanisms of oxidation of a carbohydrate such as glucose to carbon dioxide and water in a bomb calorimeter and in the body are complex and entirely different, the net reaction involves the same initial and final states, and must be the same for any possible pathway:

C₆H₁₂O₆ + 6 O₂ → 6 CO₂ + 6 H₂O   ΔH° – 20.8 kJ mol^–1

Glucose is a sugar, a breakdown product of starch, and is the most important energy source at the cellular level; fats, proteins, and other sugars are readily converted to glucose. By writing balanced equations for the combustion of sugars, fats, and proteins, a comparison of their relative energy contents can be made. The stoichiometry of each reaction gives the amounts of oxygen taken up and released when a given amount of each kind of food is oxidized; these gas volumes are often taken as indirect measures of energy consumption and metabolic activity; a commonly-accepted value that seems to apply to a variety of food sources is 20.1 J (4.8 kcal) per liter of O₂ consumed.

For some components of food, particularly proteins, oxidation may not always be complete in the body, so the energy that is actually available will be smaller than that given by the heat of combustion. Mammals, for example, are unable to break down cellulose (a polymer of sugar) at all; animals that derive a major part of their nutrition from grass and leaves must rely on the action of symbiotic bacteria which colonize their digestive tracts.

The amount of energy available from a food can be found by measuring the heat of combustion of the waste products excreted by an organism that has been restricted to a controlled diet, and subtracting this from the heat of combustion of the food.

 

The amount of energy an animal requires depends on the age, sex, surface area of the body, and of course on the amount of physical activity. The rate at which energy is expended is expressed in watts: 1 W = 1 J sec^–1. For humans, this value varies from about 200-800 W. This translates into daily food intakes having energy equivalents of about 10-15 MJ for most working adults. In order to just maintain weight in the absence of any physical activity, about 6 MJ per day is required.

 

The above table is instructive in that although larger animals consume more energy, the energy consumption per unit of body weight decreases with size. This reflects the fact the rate of heat loss to the environment depends largely on the surface area of an animal, which increases with mass at a greater rate than does an animal’s volume (“size”).

Thermodynamics and the weather

Hydrogen bonds at work

It is common knowledge that large bodies of water have a “moderating” effect on the local weather, reducing the extremes of temperature that occur in other areas. Water temperatures change much more slowly than do those of soil, rock, and vegetation, and this effect tends to affect nearby land masses. This is largely due to the high heat capacity of water in relation to that of land surfaces— and thus ultimately to the effects of hydrogen bonding. The lower efficiency of water as an absorber and radiator of infrared energy also plays a role.

Adiabatic heating and cooling of the atmosphere

What is an adiabatic process?

The specific heat capacity of water is about four times greater than that of soil. This has a direct consequence to anyone who lives near the ocean and is familiar with the daily variations in the direction of the winds between the land and the water. Even large lakes can exert a moderating influence on the local weather due to water’s relative insensitivity to temperature change.

During the daytime the land and sea receive approximately equal amounts of heat from the Sun, but the much smaller heat capacity of the land causes its temperature to rise more rapidly. This causes the air above the land to heat, reducing its density and causing it to rise. Cooler oceanic air is drawn in to vill the void, thus giving rise to the daytime sea breeze.

In the evening, both land and ocean lose heat by radiation to the sky, but the temperature of the water drops less than that of the land, continuing to supply heat to the oceanic air and causing it to rise, thus reversing the direction of air flow and producing the evening land breeze.

The above images are from the NDBC site. For a more detailed explanation of land/sea breezes and links to some interesting meteorological images, see this U. Wisconsin page. An animated movie that correlates time and temperature data with wind directions can be seen at the Earth Science textbook site.

Why it gets colder as you go higher: the adiabatic lapse rate

The First Law at work

The air receives its heat by absorbing far-infrared radiation from the earth, which of course receives its heat from the sun. The amount of heat radiated to the air immediately above the surface varies with what’s on it (forest, fields, water, buildings) and of course on the time and season. When a parcel of air above a particular location happens to be warmed more than the air immediately surrounding it, this air expands and becomes less dense. It therefore rises up through the surrounding air and undergoes further expansion as it encounters lower pressures at greater altitudes.

Whenever a gas expands against an opposing pressure, it does work on the surroundings. According to the First Law ΔU = q + w, if this work is not accompanied by a compensating flow of heat into the system, its internal energy will fall, and so, therefore, will its temperature. It turns out that heat flow and mixing are rather slow processes in the atmosphere in comparison to the convective motion we are describing, so the First Law can be written as ΔU = w (recall that w is negative when a gas expands.) Thus as air rises above the surface of the earth it undergoes adiabatic expansion and cools. The actual rate of temperature decrease with altitude depends on the composition of the air (the main variable being its moisture content) and on its heat capacity. For dry air, this results in an adiabatic lapse rate of 9.8 C° per km of altitude.

Santa Anas and chinooks: those warm, wild winds

Just the opposite happens when winds develop in high-altitude areas and head downhill. As the air descends, it undergoes compression from the pressure of the air above it. The surroundings are now doing work on the system, and because the process occurs too rapidly for the increased internal energy to be removed as heat, the compression is approximately adiabatic.

The resulting winds are warm (and therefore dry) and are often very irritating to mucous membranes. These are known generically as Föhn winds (which is the name given to those that originate in the Alps.) In North America they are often called chinooks (or, in winter, “snow melters”) when they originate along the Rocky Mountains.

Among the most notorious are the Santa Ana winds of Southern California which pick up extra heat (and dust) as they pass over the Mohave Desert before plunging down into the Los Angeles basin. Their dryness and high velocities feed many of the disasterous wildfires that afflict the region.

Chemical kinetics

Chemical kinetics, also known as reaction kinetics, is the study of rates of chemical processes. Chemical kinetics includes investigations of how different experimental conditions can influence the speed of a chemical reaction and yield information about the reaction’s mechanism and transition states, as well as the construction of mathematical models that can describe the characteristics of a chemical reaction. In 1864, Peter Waage and Cato Guldberg pioneered the development of chemical kinetics by formulating the law of mass action, which states that the speed of a chemical reaction is proportional to the quantity of the reacting substances.

Chemical kinetics deals with the experimental determination of reaction rates from which rate laws and rate constants are derived. Relatively simple rate laws exist for zero-order reactions (for which reaction rates are independent of concentration), first-order reactions, and second-order reactions, and can be derived for others. In consecutive reactions, the rate-determining step often determines the kinetics. In consecutive first-order reactions, a steady state approximation can simplify the rate law. The activation energy for a reaction is experimentally determined through the Arrhenius equation and the Eyring equation. The main factors that influence the reaction rate include: the physical state of the reactants, the concentrations of the reactants, the temperature at which the reaction occurs, and whether or not any catalysts are present in the reaction.

Factors affecting reaction rate

Nature of the reactants

 

Depending upon what substances are reacting, the reaction rate varies. Acid/base reactions, the formation of salts, and ion exchange are fast reactions. When covalent bond formation takes place between the molecules and when large molecules are formed, the reactions tend to be very slow. Nature and strength of bonds in reactant molecules greatly influence the rate of its transformation into products.

Physical state

The physical state (solid, liquid, or gas) of a reactant is also an important factor of the rate of change. When reactants are in the same phase, as in aqueous solution, thermal motion brings them into contact. However, when they are in different phases, the reaction is limited to the interface between the reactants. Reaction can occur only at their area of contact; in the case of a liquid and a gas, at the surface of the liquid. Vigorous shaking and stirring may be needed to bring the reaction to completion. This means that the more finely divided a solid or liquid reactant the greater its surface area per unit volume and the more contact it makes with the other reactant, thus the faster the reaction. To make an analogy, for example, when one starts a fire, one uses wood chips and small branches — one does not start with large logs right away. In organic chemistry, on water reactions are the exception to the rule that homogeneous reactions take place faster than heterogeneous reactions.

Concentration

 

The reactions are due to collisions of reactant species. The frequency with which the molecules or ions collide depends upon their concentrations. The more crowded the molecules are, the more likely they are to collide and react with one another. Thus, an increase in the concentrations of the reactants will result in the corresponding increase in the reaction rate, while a decrease in the concentrations will have a reverse effect. For example, combustion that occurs in air (21% oxygen) will occur more rapidly in pure oxygen.

Temperature

 

Temperature usually has a major effect on the rate of a chemical reaction. Molecules at a higher temperature have more thermal energy. Although collision frequency is greater at higher temperatures, this alone contributes only a very small proportion to the increase in rate of reaction. Much more important is the fact that the proportion of reactant molecules with sufficient energy to react (energy greater than activation energy: E > Ea) is significantly higher and is explained in detail by the Maxwell–Boltzmann distribution of molecular energies.

The ‘rule of thumb’ that the rate of chemical reactions doubles for every 10 °C temperature rise is a common misconception. This may have been generalized from the special case of biological systems, where the α (temperature coefficient) is often between 1.5 and 2.5.

A reaction’s kinetics can also be studied with a temperature jump approach. This involves using a sharp rise in temperature and observing the relaxation time of the return to equilibrium. A particularly useful form of temperature jump apparatus is a shock tube, which can rapidly jump a gases temperature by more than 1000 degrees.

Catalysts

A catalyst is a substance that accelerates the rate of a chemical reaction but remains chemically unchanged afterwards. The catalyst increases rate reaction by providing a different reaction mechanism to occur with a lower activation energy. In autocatalysis a reaction product is itself a catalyst for that reaction leading to positive feedback. Proteins that act as catalysts in biochemical reactions are called enzymes. Michaelis–Menten kinetics describe the rate of enzyme mediated reactions. A catalyst does not affect the position of the equilibria, as the catalyst speeds up the backward and forward reactions equally.

In certain organic molecules, specific substituents can have an influence on reaction rate ieighbouring group participation.

Agitating or mixing a solution will also accelerate the rate of a chemical reaction, as this gives the particles greater kinetic energy, increasing the number of collisions between reactants and, therefore, the possibility of successful collisions.

Pressure

      

Increasing the pressure in a gaseous reaction will increase the number of collisions between reactants, increasing the rate of reaction. This is because the activity of a gas is directly proportional to the partial pressure of the gas. This is similar to the effect of increasing the concentration of a solution.

In addition to this straightforward mass-action effect, the rate coefficients themselves can change due to pressure. The rate coefficients and products of many high-temperature gas-phase reactions change if an inert gas is added to the mixture; variations on this effect are called fall-off and chemical activation. These phenomena are due to exothermic or endothermic reactions occurring faster than heat transfer, causing the reacting molecules to have non-thermal (non-Boltzmann) energy distributions. Increasing the pressure increases the heat transfer rate between the reacting molecules and the rest of the system, reducing this effect.

Condensed-phase rate coefficients can also be affected by (very high) pressure; this is a completely different effect than fall-off or chemical-activation. It is often studied using diamond anvils.

A reaction’s kinetics can also be studied with a pressure jump approach. This involves making fast changes in pressure and observing the relaxation time of the return to equilibrium.

Equilibrium

While chemical kinetics is concerned with the rate of a chemical reaction, thermodynamics determines the extent to which reactions occur. In a reversible reaction, chemical equilibrium is reached when the rates of the forward and reverse reactions are equal and the concentrations of the reactants and products no longer change. This is demonstrated by, for example, the Haber–Bosch process for combining nitrogen and hydrogen to produce ammonia. Chemical clock reactions such as the Belousov–Zhabotinsky reaction demonstrate that component concentrations can oscillate for a long time before finally attaining the equilibrium.

Free energy

 

In general terms, the free energy change (ΔG) of a reaction determines whether a chemical change will take place, but kinetics describes how fast the reaction is. A reaction can be very exothermic and have a very positive entropy change but will not happen in practice if the reaction is too slow. If a reactant can produce two different products, the thermodynamically most stable one will in general form, except in special circumstances when the reaction is said to be under kinetic reaction control. The Curtin–Hammett principle applies when determining the product ratio for two reactants interconverting rapidly, each going to a different product. It is possible to make predictions about reaction rate constants for a reaction from free-energy relationships.

The kinetic isotope effect is the difference in the rate of a chemical reaction when an atom in one of the reactants is replaced by one of its isotopes.

Chemical kinetics provides information on residence time and heat transfer in a chemical reactor in chemical engineering and the molar mass distribution in polymer chemistry.

Applications

The mathematical models that describe chemical reaction kinetics provide chemists and chemical engineers with tools to better understand and describe chemical processes such as food decomposition, microorganism growth, stratospheric ozone decomposition, and the complex chemistry of biological systems. These models can also be used in the design or modification of chemical reactors to optimize product yield, more efficiently separate products, and eliminate environmentally harmful by-products. When performing catalytic cracking of heavy hydrocarbons into gasoline and light gas, for example, kinetic models can be used to find the temperature and pressure at which the highest yield of heavy hydrocarbons into gasoline will occur. Kinetics is also a basic aspect of chemistry.

Concentration Changes

Chemical kinetics is the study of the speed with which a chemical reaction occurs and the factors that affect this speed. This information is especially useful for determining how a reaction occurs.

What is meant by the speed of a reaction? The speed of a reaction is the rate at which the concentrations of reactants and products change.

Consider the following hypothetical example. The letters A, B, and C represent chemical species (in this context, the letters do not represent elements). Suppose the following imaginary reaction occurs:

A + 2 B   →   3 C

The simulation below illustrates how this reaction can be studied. The apparatus at the left is called a stopped-flow apparatus. Each syringe contains a solution filled with a different reactant (A or B). When the two solutions are forced out of the syringes, they are quickly mixed in a mixing block and the reaction starts. The reacting solution passes through the tube at the bottom. An analytical technique such as spectrophotometry is used to measure the concentrations of the species in the reaction mixture (which is in the tube at the bottom) and how those concentrations change with time.

In this example, the syringe at the left contains a solution of species A, which has a yellow color. The syringe at the right contains a solution of species B, which has a light blue color. The product C has a red color.

Chemical Kinetics

Chemical kinetics is the study and discussion of chemical reactions with respect to reaction rates, effect of various variables, re-arrangement of atoms, formation of intermediates etc. There are many topics to be discussed, and each of these topics is a tool for the study of chemical reactions. By the way, the study of motion is called kinetics, from Greek kinesis, meaning movement.

 At the macroscopic level, we are interested in amounts reacted, formed, and the rates of their formation. At the molecular or microscopic level, the following considerations must also be made in the discusion of chemical reaction mechanism.

Molecules or atoms of reactants must collide with each other in chemical reactions.

The molecules must have sufficient energy (discussed in terms of activation energy) to initiate the reaction.

In some cases, the orientation of the molecules during the collision must also be considered.

Reaction Rates

Chemical reaction rates are the rates of change in concentrations or amounts of either reactants or products. For changes in amounts, the units can be one of mol/s, g/s, lb/s, kg/day etc. For changes in concentrations, the units can be one of mol/(L s), g/(L s), %/s etc.

 

With respect to reaction rates, we may deal with average rates, instantaneous rates, or initial rates depending on the experimental conditions.

 

 

Thermodynamics and kinetics are two factors that affect reaction rates. The study of energy gained or released in chemical reactions is called thermodynamics, and such energy data are called thermodynamic data. However, thermodynamic data have no direct correlation with reaction rates, for which the kinetic factor is perhaps more important. For example, at room temperature (a wide range of temperatures), thermodynamic data indicates that diamond shall convert to graphite, but in reality, the conversion rate is so slow that most people think that diamond is forever.

Factors Influence Reaction Rates

 Many factors influence rates of chemical reactions, and these are summarized below. Much more extensive discussion will be given in other pages.

Nature of Reactants

 

 Acid-base reactions, formation of salts, and exchange of ions are fast reactions. Reactions in which large molecules are formed or break apart are usually slow. Reactions breaking strong covalent bonds are also slow.

Temperature

 Usually, the higher the temperature, the faster the reaction. The temperature effect is discussed in terms of activation energy.

Concentration Effect

 The dependences of reaction rates on concentrations are called rate laws. Rate laws are expressions of rates in terms of concentrations of reactants. Keep in mind that rate laws can be in differential forms or integrated forms. They are called differential rate laws and integrated rate laws. The following is a brief summary of topics regarding rate laws.

rate laws: differential and integrated rate laws.

Integrated rate laws: First Order Reactions

 Second Order Reactions

 Rate laws apply to homogeneous reactions in which all reactants and products are in one phase (solution).

Heterogeneous reactions: reactants are present in more than one phase

 For heterogeneous reactions, the rates are affected by surface areas.

Catalysts: substances used to facilitate reactions

 By the nature of the term, catalysts play important roles in chemical reactions.

Reaction Mechanisms

 The detailed explanation at the molecular level how a reaction proceeds is called reaction mechanism. The explanation is given in some elementary steps. Devising reaction mechanisms requires a broad understanding of properties of reactants and products, and this is a skill for matured chemists. However, first year chemistry students are often given a mechanism, and be asked to derive the rate law from the proposed mechanism. The steady-state approximations is a technique for deriving a rate law from the proposed mechanism.

 

 

 

 

 

 

Rate of Reaction

 The rate of a reaction is the speed at which a reaction happens. If a reaction has a low rate, that means the molecules combine at a slower speed than a reaction with a high rate. Some reactions take hundreds, maybe even thousands, of years while others can happen in less than one second. The rate of reaction depends on the type of molecules that are combining. If you want to think of a very slow reaction, think about how long it took dinosaur bones to become fossils through breakdown. You can thank chemical processes in bacteria for most of those dinosaur bones in the museum.

There is another big idea for rates of reaction called collision theory. The collision theory says that as more collisions in a system occur, there will be more combinations of molecules bouncing into each other. If there are a higher number of collisions in a system, more combinations of molecules can occur. The reaction will go faster and the rate of that reaction will be higher. Even though they are both liquids, think about how slowly molecules move in honey when compared to your soda. There are a lower number of collisions in the honey.

 Reactions happen – no matter what. Chemicals are always combining or breaking down. The reactions happen over and over, but not always at the same speed. A few things affect the overall speed of the reaction and the number of collisions that can occur.

Concentration: If there is more of a substance in a system, there is a greater chance that molecules will collide and speed up the rate of the reaction. If there is less of something, there will be fewer collisions and the reaction will probably happen at a slower speed. Sometimes when you are in a chemistry lab, you will add one solution to another. When you want the rate of reaction to be slower, you will add only a few drops at a time instead of the entire beaker.

Temperature: When you raise the temperature of a system, the molecules bounce around a lot more because they have more energy. When they bounce around more, they are more likely to collide. That fact means they are also more likely to combine. When you lower the temperature, the molecules are slower and collide less. That temperature drop lowers the rate of the reaction. Back to the chemistry lab! Sometimes you will mix solutions in ice so that the temperature of the system stays cold and the rate of reaction is slower.

Pressure: Pressure affects the rate of reaction, especially when you look at gases. When you increase the pressure, the molecules have less space in which they can move. That greater density of molecules increases the number of collisions. When you decrease the pressure, molecules don’t hit each other as often. The lower pressure decreases the rate of reaction.

Rates of Reaction

What factors influence the rate of a chemical reaction?

1. Temperature

2. Catalysts

3. Concentrations of reactants

3. Surface area of a solid reactant

4. Pressure of gaseous reactants or products

If you are planning an investigation, I suggest that you investigate the effects of temperature or the effects of the concentration of the reactants because these will allow you to choose a suitable range of values for the controlled or independent variable. The dependent variable will be the rate of the reaction. Keep all the other variables fixed.

 

To make a prediction for your investigation you will have to ask yourself the question: What will happen to the rate of the reaction when I increase the temperature? or What will happen to the rate of the reaction if I increase the concentration of one of the reactants? The answer to that question is your prediction. The next thing to do is to explain your prediction. You will have to answer the question: Why will the reaction go faster if I increase the temperature? or Why will the reaction go faster if I increase the concentration of one of the reactions? The answer to this question is your explanation, and to get the highest possible marks, you will have to provide a full scientific explanation.

Once you have written your hypothesis (prediction with explanation) you will decide how to do the experiments, i.e. write the proposed method.

How does temperature affect the rate of a chemical reaction?

When two chemicals react, their molecules have to collide with each other with sufficient energy for the reaction to take place. This is collision theory. The two molecules will only react if they have enough energy. By heating the mixture, you will raise the energy levels of the molecules involved in the reaction. Increasing temperature means the molecules move faster. This is kinetic theory. If your reaction is between atoms rather than molecules you just substitute “atom” for “molecule” in your explanation.

How do catalysts affect the rate of a reaction?

Catalysts speed up chemical reactions. Only very minute quantities of the catalyst are required to produce a dramatic change in the rate of the reaction. This is really because the reaction proceeds by a different pathway when the catalyst is present. Adding extra catalyst will make absolutely no difference. There is a whole page on this site devoted to catalysts.

How does concentration affect the rate of a reaction?

Increasing the concentration of the reactants will increase the frequency of collisions between the two reactants. So this is collision theory again. You also need to discuss kinetic theory in an experiment where you vary the concentration. Although you keep the temperature constant, kinetic theory is relevant. This is because the molecules in the reaction mixture have a range of energy levels. When collisions occur, they do not always result in a reaction. If the two colliding molecules have sufficient energy they will react.

If reaction is between a substance in solution and a solid, you just vary the concentration of the solution. The experiment is straightforward. If the reaction is between two solutions, you have a slight problem. Do you vary the concentration of one of the reactants or vary the concentration of both? You might find that the rate of reaction is limited by the concentration of the weaker solution, and increasing the concentration of the other makes no difference. What you need to do is fix the concentration of one of the reactants to excess. Now you can increase the concentration of the other solution to produce an increase in the rate of the reaction.

How does surface area affect a chemical reaction?

If one of the reactants is a solid, the surface area of the solid will affect how fast the reaction goes. This is because the two types of molecule can only bump into each other at the liquid solid interface, i.e. on the surface of the solid. So the larger the surface area of the solid, the faster the reaction will be.

Smaller particles have a bigger surface area than larger particle for the same mass of solid. There is a simple way to visualize this. Take a loaf of bread and cut it into slices. Each time you cut a new slice, you get an extra surface onto which you can spread butter and jam. The thinner you cut the slices, the more slices you get and so the more butter and jam you can put on them. This is “Bread and Butter Theory”. You should have come across the idea in your biology lessons. By chewing your food you increase the surface area so that digestion can go faster.

What affect does pressure have on the reaction between two gasses?

You should already know that the atoms or molecules in a gas are very spread out. For the two chemicals to react, there must be collisions between their molecules. By increasing the pressure, you squeeze the molecules together so you will increase the frequency of collisions between them. This is collision theory again.

In a diesel engine, compressing the gaseous mixture of air and diesel also increases the temperature enough to produce combustion. Increasing pressure also results in raising the temperature. It is not enough in a petrol engine to produce combustion, so petrol engines need a spark plug. When the petrol air mixture has been compressed, a spark from the plug ignites the mixture. In both cases the reaction (combustion) is very fast. This is because once the reaction has started, heat is produced and this will make it go even faster.

The Rate Law

The rate law for a chemical reaction links the reaction rate with concentrations or pressures of reactants and constant parameters.

Rate Laws for Various Reactions

A variety of reaction orders are observed, and they cannot be easily correlated with the stoichiometry of the reaction.

 

 

Rate Law

Rate = K[A]x[B]y

 Rate = Reaction Rate Reaction Order

The sum of x and y.

 The reaction of bromine and formic acid is first order in bromine, zeroth order in formic acid, and first order overall.

 K = rate constant

 x/y = determined numbers

 A/B = concentrations

 

How fast is Fast? The Mathematics of Change

Consider a reaction of Red molecules (A) to make Blue molecules (B), i.e. A -> B. If we were able to see the reaction on a molecular scale, the reaction of each individual molecule of occurs very rapidly, but the overall color of the vessel changes more slowly. Snapshots of the reaction in progress might look like this:

 

The number of reactants and products in the reaction vessel changes with time, with the relative number of reactant molecules destroyed and number of products formed per reaction event determined by the reaction stoichiometry. Each reactant molecule is identical to every other one, but they all don’t react at the same instant. At each point in time, the probability of reaction per unit time is the same for each molecule in the sample, and that probability influences the overall reaction rate. But that isn’t the only thing that determines the overall reaction rate. The total number of reactions at any instant is the probability of reaction per unit time multiplied by the number of reactants remaining in the vessel. Thus the reaction proceeds quickly at first, when there are lots of reactants around, and appears to slow as the reactants are consumed. A  simulation of a similar reaction involving reactive collisions between molecules can be run on you browser. A plot of the time dependence of the number of molecules of each type looks ‘smooth’ when there are lots and lots of molecules in the sample, so individual reaction events get ‘averaged’ out. The concentrations of the reactants and products change in time like this:

The Rate Law

The equation that describes the dependence of the reaction rate on the concentrations of the species in the reactor is called a rate law. The rate law for a given reaction is determined from the reaction mechanism. Several important kinds of simple rate laws are worth noting

 

First Order Rate Law

The simplist reaction mechanism is that of unimolecular decomposition (or isomerisation). In such a process, a single reactant undergoes a transformation at a constant probability per unit time. Such a mechanism leasds to a first-order reaction rate law. Examples of reactions such as these are radioactive decay, bacterial growth, and compound interest. Let’s assume the reaction has a simple stoichimetry:

A → B

A First-Order Rate Law is called such because the rate of product formation ( or reactant depletion ) is proportional to the first power of the number of available reactants (or reactant concentration):

rate =k[A]

where [A] represents the concentration (number density) of species A in the sample.

Second Order Rate Law

If two molecules undergo a bimolecular reaction such as a reaction that involves a collisional encounter to produce products, and has a stoichiometry like this:

A + A → B + C

Zeroth Order Rate Law

If a reaction is catalysed by a surface and has enough (excess) reactant, the rate of the reaction depends on the area of the catalyst, not on how much reactant is present. This is an unusual circumstance outside of the realm of catalyzed reactions and is described by a Zeroth Order rate law:

rate =k

THE EFFECT OF CONCENTRATION ON REACTION RATES

This page describes and explains the way that changing the concentration of a solution affects the rate of a reaction. Be aware that this is an introductory page only. If you are interested in orders of reaction, you will find separate pages dealing with these. You can access these via the rates of reaction menu (link at the bottom of the page).

For many reactions involving liquids or gases, increasing the concentration of the reactants increases the rate of reaction. In a few cases, increasing the concentration of one of the reactants may have little noticeable effect of the rate. These cases are discussed and explained further down this page.

Don’t assume that if you double the concentration of one of the reactants that you will double the rate of the reaction. It may happen like that, but the relationship may well be more complicated.

The Temperature Dependence of Reaction Rates

Chemical Activation

Consider the reaction

H₂ + Cl₂ -> 2HCl

On a molecular level, bonds must be broken (H-H and Cl-Cl) before the reaction can proceed too far into products. This means that as the reactant molecules come together, the collision must have enough energy to initiate the bond breakage for the reaction to occur. Not all collisions will have this amount of energy. The collisions that do not have sufficient energy to react end up as elastic scattering events.

 

Only collisions with enough energy react to form products. The energy of the system changes as the reactants approach each other. The critical amount of energy to make the reaction proceed is called the Activation Energy.

The Reaction Coordinate is the ‘distance’ along the path of the reaction, and is plotted along the horizontal axis. The energy of interaction of the reactive system is plotted vertically, and is called the Chemical potential, or just potential energy. You fight gravitational potential energy when you try to roll a boulder over a mountain.

A chemical potential of interaction usually looks like something like the graph above, which is similar to the ‘pushing a boulder over a hill’ graph above. The Graph above is drawn for the isomerization of an isonitrile that we discussed before. The barrier to the isomerization keeps the unstable CH3NC from reacting away quickly at low temperature, even though energy is released upon the net reaction.

 

Catalyst and Catalysis

A catalyst increases the rate of a particular reaction without itself being used up. A catalyst can be added to a reaction and then be recovered and reused after the reaction occurs. The process or action by which a catalyst increases the reaction rate is called catalysis. The study of reaction rates and how they change when manipulated experimentally is called kinetics.

The term catalysis was proposed in 1835 by the Swedish chemist Jöns Berzelius (1779-1848). The term comes from the Greek words kata meaning down and lyein meaning loosen. Berzelius explained that by the term catalysis he meant “the property of exerting on other bodies an action which is very different from chemical affinity. By means of this action, they produce decomposition in bodies, and form new compounds into the composition of which they do not enter.”

Most chemical reactions occur as a series of steps. This series of steps is called a pathway or mechanism. Each individual step is called an elementary step. The slowest elementary step in a pathway determines the reaction rate. The reaction rate is the rate at which reactants disappear and products appear in a chemical reaction, or, more specifically, the change in concentration of reactants and products in a certain amount of time.

While going through a reaction pathway, reactants enter a transitional state where they are no longer reactants, but are not yet products. During this transitional state they form what is called an activated complex. The activated complex is short-lived and has partial bonding characteristics of both reactants and products. The energy required to reach this transitional state and form the activated complex in a reaction is called the activation energy. In order for a reaction to occur, the activation energy must be reached. A catalyst increases the rate of reaction by lowering the activation energy required for the reaction to take place. The catalyst forms an activated complex with a lower energy than the complex formed without catalysis. This provides the reactants a new pathway which requires less energy. Although the catalyst lowers the activation energy required, it does not affect reaction equilibrium or thermodynamics. The catalyst does not appear in the overall chemical equation for a pathway because the mechanism involves an elementary step in which the catalyst is consumed and another in which it is regenerated.

Catalysts exist for all types of chemical reactions. A specific catalyst can be classified into one of two main groups; homogeneous and heterogeneous. A catalyst that is in the same phase as the reactants and products involved in a reaction pathway is called a homogeneous catalyst. When a catalyst exists in a different phase than that of the reactants, it is called a heterogeneous catalyst. For example, nickel is a catalyst in the hydrogenation of vegetable oils. Nickel is a solid, while the oil is a liquid, therefore nickel is a heterogeneous catalyst. An advantage of using heterogeneous catalysts is their ease of separation from the reactants and products involved in a pathway.Metals are often used as heterogeneous catalysts because many reactants adsorb to the metal surface, increasing the concentration of the reactants and therefore the rate of the reaction. Ionic interactions between metals and other molecules can be used to orient the reactants involved so that they react better with each other, or to stabilize charged reaction transition states. Metals also can increase the rate of oxidation-reduction reactions through changes in the metal ion’s oxidation state.

Another group of catalysts are called enzymes. Enzymes are catalysts that are found in biological systems. The role of catalysts in living systems was first recognized in 1833. French chemists Anselme Payen (1795-1871) and Jean François Persoz isolated a material from malt that accelerated the conversion of starch to sugar. Payen called the substance diatase. A half century later German physiologist Willy Kühne suggested the name enzyme for biological catalysts.

Enzymes are proteins and therefore have a highly folded three-dimensional configuration. This configuration makes an enzyme particularly specific for a certain reaction or type of reaction. Synthetic catalysts, on the other hand, are not nearly as specific. They will catalyze similar reactions that involve a wide variety of reactants. Enzymes, in general, will lose activity more easily than synthetic catalysts. Very slight disturbances in the protein structure of enzymes will change the three-dimensional configuration of the molecule and, as a result, its reactivity. Enzymes tend to be more active, i.e., they catalyze reactions faster, than synthetic catalysts at ambient temperatures. Catalytic activity for a reaction is expressed as the turnover number. This is simply the number of reactant molecules changed to product per catalyst site in a given unit of time. When temperature is increased, synthetic catalysts can become just as active as enzymes. With an increase in temperature, many enzymes will become inactive because of changes to the protein structure.

There are endless reactions that can undergo catalysis. One example is the decomposition of hydrogen peroxide (H2O2). Without catalysis, hydrogen peroxide decomposes slowly over time to form water and oxygen gas. A 30% solution of hydrogen peroxide at room temperature will decompose at a rate of 0.5% per year. The activation energy for this reaction is 75 kJ/mol. This activation energy can be lowered to 58 kJ/mol with the addition of iodide ions (I-). These ions form an intermediate, HIO-, which reacts with the hydrogen peroxide to regenerate the iodide ions. When the enzyme catalase is added to the hydrogen peroxide solution, the activation energy is lowered even further to 4 kJ/mol. The catalase is also regenerated in the reaction and can be separated from the solution for reuse. This example shows how a catalyst can lower the activation energy of a reaction without itself being used up in the reaction pathway.

Another example of catalysis is the catalytic converter of an automobile. Exhaust from the automobile can contain carbon monoxide and nitrogen oxides, which are poisonous gases. Before the exhaust can leave the exhaust system these toxins must be removed. The catalytic converter mixes these gases with air and then passes them over a catalyst made of rhodium and platinum metals. This catalyst accelerates the reaction of carbon monoxide with oxygen and converts it to carbon dioxide, which is not toxic. The catalyst also increases the rate of reactions for which the nitrogen oxides are broken down into their elements.

 

A well-known example of catalysis is the destruction of the ozone layer. Ozone (O3) in the upper atmosphere serves as a shield for the harmful ultraviolet rays from the Sun. Ozone is formed when an oxygen molecule (O2) is split into two oxygen atoms (O) by the radiation from the Sun. The free oxygen atoms then attach to oxygen molecules to form ozone. When another free oxygen atom reacts with the ozone molecule, two oxygen molecules are formed. This is the natural destruction of ozone. Under normal circumstances, the rate of destruction of ozone is the same as the rate of ozone formation, so no net ozone depletion occurs. When chlorine (Cl) atoms are present in the atmosphere, they act as catalysts for the destruction of ozone. Chlorine atoms in the atmosphere come from compounds containing chlorofluorocarbons, or CFCs. CFCs are compounds containing chlorine, fluorine, and carbon. CFCs are very stable and can drift into the upper atmosphere without first being broken down. Once in the upper atmosphere, the energy from the Sun causes the chlorine to be released. The chlorine atom reacts with ozone to form chlorine monoxide (ClO) and an oxygen molecule. The chlorine monoxide then reacts with another oxygen atom to form an oxygen molecule and the regenerated chlorine atom. With the help of the chlorine catalyst, the degeneration of ozone occurs at a faster rate than its formation, which has caused a net depletion of ozone in the atmosphere.

The previous examples illustrate some of the many practical applications of catalysis. Almost all of the chemicals produced by the chemical industry are made using catalysis. Catalytic processes used in the chemical industry decrease production costs as well as create products with higher purity and less environmental hazards. A wide variety of products are made using catalytic processes. Catalysis is used in industrial chemistry, pharmaceutical chemistry, and agricultural chemistry, as well as in the specialty chemical industry. Useful chemicals such as sulfuric acid, penicillin, and fructose are made more efficiently using catalytic processes. Research and development efforts in the chemical industry are significantly more productive with the use of catalysis in fields such as fuel refining, petrochemical manufacturing, and environmental management.

 

The majority of manufacturing processes in use today by the chemical industry employ catalytic reactions. These reactions are highly efficient, but research is continuing to increase the efficiency even more. The focus of this research is on separation and regeneration of the catalysts in order to decrease costs of production while increasing the purity of the product. The field of catalysis research is rapidly growing and will continue to do so as new catalysts and catalytic processes are discovered.

Factors affection the reaction rate.

The fate of any particular reaction depends upon the following factors:

1. Nature of the reactants. Consider the following two reactions

These reactions appear to be similar but the first is fast while the second is slow. This is because different amounts of energies are required for breaking of different bonds and different amounts of energies are released in the formation of different bonds.

2. Concentration of the reactants. Greater are the concentrations of the reactants, faster is the reaction, as the concentrations of the reactants decrease, the rate of reaction also decreases.

3. Temperature. The rate of reaction increases with increase of temperature. In most of the cases, the rate of reaction becomes nearly double for 10К rise of temperature. In коте смея, reactions do not take place at room temperature but take place at higher temperature.

4. Presence of Catalyst. А catalyst generally increases the speed of а reaction without itself being consumed in the reaction. In case of reversible reactions, а catalyst helps to attain the equilibrium quickly without disturbing the state of equilibrium.

5. Surface area of the reactants. For а reaction involving а solid reactant or catalyst, the smaller is the particle size i.е., greater is the surface area, the fast r is the reaction.

6. Presence of light. Some reactions do not take place in the dark but take place in the presence of light e.g.,

Н₂ + С1₂ = 2НС1. Such reactions are called “photochemical reactions”

Rate laws and rate constants. It is often found that the rate of reaction is proportional to the concentrations of the reactants raised to а power. For example, 1с may be found that the rate is proportional to the concentrations of two reactants А and В, and that:

where each concentration is raised to the first power. The coefficient k is called the rate constant for the reaction or velocity constant. The rate constant is independent of the concentrations but depends on the temperature. An experimentally determined equation of this kind is called the rate law of the reaction. More formally, а rate law is an equation that expresses the rate of reaction as а function of the concentrations of all the species present in the overall chemical equation for the reaction.

If all concentrations are take as unity, [A] = [B] = 1 mole/liter, then rate = k.

Hence rate constant may be defined as the rate of the reaction when the concentration of each reactants is take as unity. That is why the rate constant is also called specific reaction rate.

Characteristics of rate constant. Some important characteristics of the rate constant are as follows:

1.                 Rate constant is a measure of the rate of reaction. Greater is the value of the rate constant, factors is the reaction.

2.                 Each reaction has a definite value of the rate constant at particular temperature.

3.                 The value of the rate constant for the same reaction changes with temperature.

4.                 The value of the rate constant of a reaction does not depend upon the concentration of the reactants.

5.                 The units of the rate constant depend upon the order of reaction.

А practical application of а rate law is that, once we know it and the value of the rate constant, we can predict the rate of reaction from the composition of the mixture. Moreover, as we shall see later, by knowing the rate law we can go on to predict the composition of the reaction mixture at а later stage of the reaction. The theoretical usefulness of a rate law is that it is а guide to the mechanism of the reaction, for any proposed mechanism must be consistent with the observed rate law.

Order of reaction

The sum of the concentration terms on which the rate of а reaction actually depends as observed experimentally is called the order of the reaction. For example, in the above case, order of reaction = а + p. Thus the orders a reaction may also be defined as the sum of the exponents (powers) to which the concentration terms in the rate law equation are raised to express the observed rate of the reaction.

The power to which the concentration of а species is raised in а rate law is the order of the reaction with respect to that species. А reaction with the rate law is first-order in А and first-order in В. The overall order of а reaction is the sum of the orders of all the components. The rate law is therefore second-order overall.

Some reactions obey а zero-order rate law, and therefore have а rate that is independent of the concentration of the reactant (so long as some is present). Thus, the catalytic decomposition of phosphine (РН₃) on hot tungsten at high pressures has the rate law: u = k

The PH₃ decomposes at а constant rate until it has almost entirely disappeared. Only heterogeneous reactions can have rate laws that are zero-order overall.

These remarks point to three problems. First, we must see how to identify the rate law and obtain the rate constant from the experimental data. We shall concentrate on this aspect in this chapter. Second, we must see how to construct reaction mechanisms that are consistent with the rate law. k₂ + k₃[В]₀

It is most important to distinguish molecularity from order: Reaction order is an empirical quantity, and obtained from thy experimental rate law. The molecularity refers to an elementary reaction proposed as an individual step in а mechanism.

In contrast to reactions in general, the rate law of an elementary reaction can be written down from its chemical equation. Thus, the rate law of а unimolecular elementary reaction is first-order in the reactant;

А ® Products : d[А]/dt = – k [А]

А unimolecular reaction is first-order because the number of А molecules that decay in а short interval is proportional to the number available to decay. (Ten times as many decay in the some interval when there are initially 1000 А molecules than when there are only 100 present). Therefore, the rate of decomposition of А is proportional to its molar concentration.

An elementary bimolecular reaction has а second-order rate law:

А bimolecular reaction is second-order because its rate is proportional to the rate at which the reactant species meet, which is proportional their concentrations. Therefore, if we believe (or simply postulate) that a reaction is а single-step, bimolecular process, then we can write down the rate law (and then go on to test it). Bimolecular elementary reactions are believed to account for many homogeneous reactions, such as the dimerizations of alkenes and dienes and reactions such as:

CH₃I(alc) + СН₃СН₂О^– (alc) ®СН₃ОСН₃СН₂(аlс) + I^–(а1с);

(where ‘alc’ signifies alcohol solution). The mechanism of the last reaction is believed to be the single elementary step: CH₃I + СН₃СН₂О^– ®СН₃ОСН₃СН₂ + I^–

u = k[CH₃I] [CH₃CH₂O^–]

The interpretation of а rate law is full of pitfalls, partly because а second-order rate law, for instance, can also result from а complex reaction scheme. We shall see below how to string simple steps together into а mechanism and how to arrive at the corresponding rate law. For the present we emphasize that if the reaction is an elementary bimolecular process, then it has second-order kinetics, but if the kinetics are second-order, then the reaction might be complex. The postulated mechanism can be explored only by detailed detective work on the system, and by investigating whether side products or intermediates appear during the course of the reaction. Detailed analysis of this kind was one of the ways, for example, in which the reaction H₂(g) + I₂(g) ® 2HI(g) was shown to proceed by а complex reaction after many years during which it had been accepted on good, but insufficiently meticulous evidence, that it was а fine example of а simple bimolecular reaction in which atoms exchanged partners during а collision.

It is found that the rates of most reactions increase as the temperature is raised. Many reactions fall somewhere in the range spanned by the hydrolysis of methyl ethanoate (where the rate constant at 35⁰С is 1.82 times that at 25⁰С) and hydrolysis of sucrose (where the factor is 4.13).

The Arrhenius parameters. An empirical observation is that many reactions have rate constants that follow the Arrhenius equation:

That is, for many reactions it is found that а plot of ln k against 1/Т gives а straight line. The Arrhenius equation is often written as

The factor А is called the pre-exponential factor or the frequency factor; Е_a is called the activation energy. Collectively, the two quantities are called the Arrhenius parameters of the reaction. This equation is sometimes written in an alternative form that combines the two parameters:

The quantity D⁺G is called the activation Gibbs energy. In this form, the expression for the rate constant strongly resembles the formula for the equilibrium constant in terms of the standard reaction Gibbs energy.

For the present chapter we shall regard the Arrhenius parameters as purely empirical quantities that enable us to discuss the variation of rate constants with temperature. There we shall see that the activation energy is the minimum energy that reactants must have in order to from products. For example, in а gas-phase reaction there are numerous collisions each second, but only а tiny proportion of them are sufficiently energetic to lead to reaction. The fraction of collisions with a kinetic energy in excess of an energy Е_a is given by the Boltzmann distribution as е^-Ea/RT. Hence, the exponential factor can be interpreted as the fraction of collisions that have enough energy to lead to reaction.

The analogous interpretation of the pre-exponential factor is that it is a measure of the rate at which collisions occur irrespective of their energy. Hence the product of А and the exponential factor gives the rate of successful collisions.

The temperature dependence of some reactions is not Arrhenius-like. However, it is still possible to express the strength of the dependence by defining an activation energy as

This definition reduces to the earlier one (as the slope of an Arrhenius plot) for а temperature-independent activation energy. Thus, by using d(l/Т) = – dT/Т² we can rearrange equation:

CATALYSIS.

It is found that the rates of many reactions are increased by the presence of а catalyst, а substance that increases the rate of а reaction without being consumed by it. Although at first thought this may seem impossible, it can indeed occur, because а catalyst is а substance that is used in one step in the mechanism for а reaction and is regenerated in а subsequent step. А catalyst acts by making available а new reaction mechanism with а lower activation energy.

Figure.1.shows the uncatalyzed path of а reaction contrasted with its catalyzed path. (Each potential-energy maximum corresponds to the formation of an activated complex.) Note that ЬН for the reaction is independent of the reaction mechanism, and depends only upon the identity of the reactants and products. However, the activation energy for the catalyzed path is less than that for the uncatalyzed path. Thus, at any given temperature more reactant molecules possess the activation energy for the catalyzed reaction than for the uncatalyzed one. The catalyzed mechanism thus predominates. А catalyst does not eliminate а reaction mechanism; rather, it offers а new, faster one. Mоre molecules, often almost all of them, will follow the new (catalyzed) pathway the products, instead of the old.

If the activation energy of а reaction is high, at normal temperatures only а small proportion of molecular encounters result in reaction. А catalyst lowers the activation energy of the reaction by providing an alternative path that avoids the slow, rate-determining step of the uncatalysed reaction, and results in а higher reaction rate at the same temperature. Catalysts can be very effective; for instance, the activation energy for the decomposition of hydrogen peroxide in solution is 76 kJ/mol, and the reaction is slow at room temperature. When а little iodide is added, the activation energy falls to 57 kJ/mol, and the rate increases by а factor of 2000. Enzymes, which are biological catalysts, are very specific and can have а dramatic effect on the reactions they control. The activation energy for the acid hydrolysis of sucrose is 107kJ/mol, but the enzyme saccharase reduces it to 36 kJ/mol, corresponding to an acceleration of the reaction by а factor of 10⁰ at blood temperature (310 К).

А homogeneous catalyst is а catalyst that is in the same phase as the reaction mixture (е.g. an acid added to an aqueous solution).

 

А heterogeneous catalyst is in а di6erent phase (е.g. а solid catalyst for а gas-phase reaction).

Homogeneous catalysis.

 In homogeneous catalysis, the catalyst and the reactants are present in the same phase. Consider the elementary process

А + В ® products (slow)

Assume that this process has а high activation energy. If we now add catalyst C the reaction mixture, а new, two-step mechanism is possible, in which rate-determining step (step 1, below) has а lower activation energy:

Step 1: А + С ® АС (fast)

Step 2: АС + В ® products + С (faster)

Here, both activation energies are low, and each reaction is faster than original, uncatalyzed reaction. Notice that the overall net equation is changed, and that while catalyst С is used up in step 1, it is regenerated step 2. The rate law for the uncatalyzed reaction is: rate = k[A][B]

and for the catalyzed reaction, rate = k'[А][C]

An example of homogeneous catalysis is found in the oxidation of sulfur dioxide to sulfur trioxide by oxygen, using nitrogen oxide, NO, as а catalyst.

The net equation for the reaction is

2SO₂ (g) + O₂ (g) ®2 SO₃ (g)

The uncatalyzed reaction is very slow, either because it is termolecular (unlikely) or because one step in its reaction mechanism has а very high activation energy. Addition of nitrogen oxide, NO, to the mixture greatly speeds the reaction by making the following mechanism available:

Step 1: O₂ (g) + 2NO(g) ® 2NO₂ (g)

Step 2: [NO ₂ (g) + SO₂ (g) ® NO (g) + SO₃(g)] х 2

The sum of these gives the original net equation, and because the activation energy for each step is fairly low, the reaction proceeds more rapidly than via the uncatalyzed path.

Sоmе idea of the mode of action of homogeneous catalysts can be obtained by examining the kinetics of the bromide-catalysed decomposition of hydrogen peroxide:

2Н₂О₂(aq) ®2Н₂О₂(aq) + О₂(g)

Heterogeneous catalysis.

А heterogeneous catalyst is one which provides а surface on which molecules can readily combine. The process of heterogeneous catalysis begins with the adsorption of а molecule on the surface of the catalyst. There are two general types of adsorption: the relatively weak physical, or van-der-Waals, adsorption and the stronger chemisorption. Evidence that а chemisorbed molecule is relatively strongly bonded at the surface comes from the fact that much more heat is usually evolved during chemisorption than during physical adsorption.

Chemisorption is common in surface catalysis; it apparently takes place preferentially at certain sites on the surface, called active sites or active centers.

These are believed to be related to surface defects or emergences of dislocations.

The chemisorbed molecule is structurally changed at the active site so that it can more readily react with another molecule. There is evidence that some molecules become dissociated into highly reactive fragments. On certain metal surfaces hydrogen, for example, is dissociated into atoms which can react more rapidly than H~ molecules. The reaction of ethylene, С₂Н₂, with hydrogen,

H₂ (g) + C₂H₄ (g) ® C₂H₆ (g)

is thought To be surface-catalyzed by nickel metal in this way.

Catalytic activity at surfaces.

А catalyst acts by providing an alternative reaction path with а lower activation energy. It does not disturb the final equilibrium composition of the system, only the rate at which that equilibrium is approached. In this section we shall consider heterogeneous catalysis, in which the catalyst and the reagents are in different phases. For simplicity, we shall consider only gas/solid systems and the solids we consider will be primarily metals. In practice, industry makes use of а wide range of complex solid catalysts, including oxides and zeolites.

Adsorption and catalysis. Heterogeneous catalysis normally depends on at least one reactant being adsorbed (usually chemisorbed) and modified to а form in which it readily undergoes reaction. Often this modification takes the form of а fragmentation of the reactant molecules.

The Eley-Rideal mechanism. In the Еlеу-Rideal mechanism of а surface-catalysed reaction, а gas-phase molecule collides with another molecule adsorbed on the surface. The rate of formation of product is expected to be proportional to the partial pressure p_b of the non-adsorbed gas В and the extent of surface coverage О„of the adsorbed gas А. It follows that the rate law should be

А + В ® Р; u = kp_Bq

The rate constant k might be much larger than for the uncatalysed gas-phase reaction because the reaction on the surface has а low activation energy and the adsorption itself is ofteot activated.

Molecular beam studies are able to give detailed information about catalysed reactions. It has become possible to investigate How the catalytic activity of а surface depends on its structure as well as its composition. For instance, the cleavage of С–Н and Н –Н bonds appears to depend on the presence of steps and kinks, and а terrace often has only minimal catalytic activity. The reaction

Н₂ +D₂ ®2HD

has been studied in detail, and it is found that terrace sites are inactive but one molecule in ten reacts when it strikes а step. Although the step itself might be the important feature, it may be that the presence of the step merely exposes а more reactive crystal face (the step face itself). Likewise, the dehydrogenation of hexane to hexene depends strongly on the kink density, and it appears that kinks are needed to cleave С – С bonds. These observations suggest а reason why even small amounts of impurities may poison а catalyst: they are likely to attach to step and kink sites, and so impair the activity of the catalyst entirely. А constructive outcome is that the extent of dehydrogenation may be controlled relative to other types of reactions by seeking impurities that adsorb at kinks and act as specific poisons.

Examples of catalysis. Almost the whole of modern chemical industry depends on the development, selection, and application of catalysts. All we can hope to do is this section is to give а brief indication of some of the problems involved. Other than the ones we consider, these include the danger of the catalyst being poisoned by by-products or impurities and economic considerations relating to cost and lifetime.

In order to be active, the catalyst should be extensively covered by adsorbate, which is the case if chemisorption is strong. On the other hand, if the strength of the substrate-adsorbate bond becomes too great, the activity declines either because the other reactant molecules cannot react with the adsorbate or because the adsorbate molecules are immobilized on the surface. This suggests that the activity of а catalyst should initially increase with strength of adsorption (as measured, for instance, by the enthalpy of adsorption) and then decline, and that the most active catalysts should be those lying near the summit of the volcano. The most active metals are those lying close to the middle of the d block..

Manу metals are suitable for adsorbing gases, and the general order of adsorption strengths decreases along the series O₂, С₂Н₂, С₂Н₄, CO, Н₂, CO₂, N₂. Some of these molecules adsorb dissociatively (е.g. Н,). Elements from the d block, such as iron, vanadium, and chromium, show а strong activity towards all these gases, but manganese and copper are unable to adsorb N₂ and CO₂. Metals towards the left of the periodic table (е.g. magnesium and lithium) can adsorb (and, in fact, react with) only the most active gas (О₂).

Hydrogenation. An example of catalytic action is found in the hydrogenation of alkenes. The alkene (5) adsorbs by forming two bonds with the surface (6), and on the вате surface there may be adsorbed Н atoms. When an encounter occurs, one of the alkene – surface bonds is broken (6 ®7 or 8) and later an encounter with а second Н atom releases the fully hydrogenated hydrocarbon, which is the thermodynamically more stable species.

The evidence for а two-stage reaction is the appearance of different isomeric alkenes in the mixture. The formation of isomers comes about because while the hydrocarbon chain is waving about over the surface of the metal, it might chemisorb again (8 ® 9) and desorb to 10, an isomer of the original 5. The new alkene would not be formed if the two hydrogen atoms attached simultaneously.

А major industrial application of catalytic hydrogenation is to the formation of edible fats from vegetable and animal oils. Raw oils obtained from sources such as the soya bean have the structure CH₂(O₂CR)CH-(O₂CR’)CH₂(О₂CR’’), where R, R’, and R’’ are long-chain hydrocarbons with several double bonds. One disadvantage of the presence of many double bonds is that the oils are susceptible to atmospheric oxidation, and therefore are liable to become rancid. The geometrical configuration of the chains is responsible for the liquid nature of the oil, and in many applications а solid fat is at least much better and ofteecessary. Controlled partial hydrogenation of an oil with а catalyst carefully selected so that hydrogenation is incomplete and so that the chains do not isomerize (nickel, in fact), is used on а wide scale to produce edible fats. The process, and the industry, is not made any easier by the seasonal variation of the number of double bonds in the oils.

Oxidation: Catalytic oxidation is also widely used in industry and in pollution control. Although in после cases it is desirable to achieve complete oxidation (as in the production of nitric acid from ammonia); in others partial oxidation is the aim. For example, the complete oxidation of propene to carbon dioxide and water is wasteful, but its partial oxidation to propenal (acrolein, СН₂=СНСНО) is the start of important industrial processes. Likewise, the controlled oxidations of ethene to ethanol, acetaldehyde, and (in the presence of acetic acid or chlorine) to vinyl acetate or vinyl chloride are the initial stages of very important chemical industries.

Some of these reactions are catalysed by d-metal oxides of various kinds. The physical chemistry of oxide surfaces is very complex, as can be appreciated by considering what happens during the oxidation of propene to acrolein on bismuth molybdate. The first stage is the adsorption of the propene molecule with loss of а hydrogen to form the allyl radical, СН₂=СНСН₃. An O atom in the surface caow transfer to this radical, leading to the formation of acrolein and its desorption from the surface. The Н atom also escapes with а surface O atom, and goes on to form Н₂О, which leaves the surface. The surface is left with vacancies and metal ions in lower oxidation states. These vacancies are attacked by О, molecules in the overlying gas, which then chemisorb as О^2- ions, so reforming the catalyst. This sequence of events involves great upheavals of the surface, and some materials break up under the stress.

Cracking and reforming. Many of the small organic molecules used in the preparation of all kinds of chemical products toте from oil. These small building blocks of polymers, perfumes, and petrochemicals in general, are usually cut from the long-chain hydrocarbons drawn from the Earth as petroleum. The catalytically induced fragmentation of the long-chain hydrocarbons is called cracking, and is often brought about on silica – alumina catalysts. These catalysts act by forming unstable carbocations, which dissociate and rearrange to more highly branched isomers. These branched isomers burn more smoothly and ef5ciently in internal combustion engines, and are used to produce higher octane fuels.

Catalytic reforming uses а dual-function catalyst, such as а dispersion of platinum and acidic alumina. The platinum provides the metal function, and brings about dehydrogenation and hydrogenation. The alumina provides the acidic function, being able to form carbocations from alkenes. The sequence of events in catalytic reforming shows up very clearly the complications that must be unravelled if а reaction as important as this is to be understood and improved. The first step is the attachment of the long-chain hydrocarbon by chemisorption to the platinum. In this process first one and then а second Н atom is lost, and an alkene is formed. The alkene migrates to а Brensted acid site, where it accepts а proton and attaches to the surface as а carbocation. This carbocation can undergo several different reactions. It can break into two, isomerize into а more highly branched form, or undergo varieties of ring-closure. Then it loses а proton, escapes &от the surface, and migrates (possibly through the gas) as an alkene to а metal part of the catalyst where it is hydrogenated. We end up with а rich selection of smaller molecules that can be withdrawn, fractionated, and then used as raw materials for other products.

INHIBITORS.

 

Inhibitors, once inappropriately called “negative catalysts,” are substances which, when added to а reaction mixture, slow down the reaction. Inhibitors can act in а number of ways. One kind of inhibition occurs when the added substance combines with а potential catalyst, rendering it inactive and thus slowing the rate. For example, inhibition of а surface-catalyzed reaction can occur when foreign molecules bond at the active sites, blocking them from substrate molecules. Such inhibition is frequently called poisoning and the inhibitor, а poison.

ENZIMS

Incroduction. Life is inconceivable without enzymes. Most of the thousands of biochemical reactions that sustain living processes would occur at imperceptible rates in the absence of enzymes. The remarkable properties of enzymes include enormous catalytic power and а high degree of

One of the most important functions of proteins is their role as catalysts. Recall that living processes consist almost entirely of biochemical reactions. Without catalysts these reactions would not occur fast enough to sustain the living state.

То proceed at an acceptable rate, most chemical reactions require an initial input of energy. In the laboratory the energy required for reactions to proceed is usually supplied in the form of heat. Heating а reaction mixture increases the reaction rate for the following reason. At temperatures above absolute zero – 273.1⁰С), all molecules possess vibrational energy, which increases as the molecules are heated. Consider the following reaction: А + В = С

As the temperature rises, the likelihood of collisions between vibrating molecules (i.е., between А and В) increases. А chemical reaction occurs when the colliding molecules possess а minimum amount of energy called the activation energy. Not all collisions result in chemical reactions, because only а fraction of the molecules have sufficient energy to enter into the reaction (i.е., to break bonds or rearrange atoms into the product moIecuIes). Another way of increasing the likelihood of collisions, thereby increasing the formation of product, is to increase the concentration of the reactants.

In living systems the aforementioned strategies are not feasible. Elevated temperatures are harmful to delicate biological structures, and reactant concentrations are usually quite low. Living organisms circumvent these problems by using enzymes.

Enzymes have several remarkable properties. First, the rates of enzymatically catalyzed reactions are often phenomenally high. (Rate increases by factors of 10⁶ or greater are common.) Second, in marked contrast to inorganic catalysts the enzymes have а high degree of specificity with respect to the react ions they catalyze. The formation of side products is also гаге. Finally, because of their complex structures, enzymes are capable of being regulated. This is an especially important consideration in living organisms that must conserve energy and гаи materials.

Because enzymes are involved in so many aspects of living processes, any understanding of biochemistry depends on an appreciation of these remarkable catalysts.

Even in the presence of an inorganic catalyst, most laboratory reactions require an input of energy. In addition, most of these catalysts are nonspecific, that is, the accelerate а wide variety of reactions. Enzymes perform their work at mild temperatures and are quite specific in the reactions that each one catalyzes. The difference between inorganic catalysts and enzymes is directly related to their structures.in contrast to inorganic catalysts, each type of enzyme molecule contains а unique intricately shaped binding surface called an active site. Reactant molecules, called substrates, bind to the enzyme’s active site, which is typically а small cleft or crevice on an otherwise large protein molecule. The active site is not just а binding site, however. Many of the amino acid side chains that line the active site actively participate in the catalytic process.

The lock-and-key model of enzyme action, originally introduced by Emil Fischer in 1890, accounts for enzyme specificity in the following way. Each enzyme binds to а single type of substrate because the active site and the substrate have complementary structures. The substrate’s overall shape and charge distribution allow it to enter and interact with the enzyme’s active site. In а modern variation by Daniel Koshland of the lock-and-key model, called the induced-fit model, the flexible structure of proteins is taken into account. In this model, substrate does not fit precisely into а rigid active site. Instead, noncovalent interactions between the enzyme and substrate cause а change in the three-dimensional structure of the active site. As а result of these interactions the shape of the active site conforms to the shape of the substrate.

Although the catalytic activity of some enzymes depends only on interactions between active site amino acids and the substrate, other enzymes require nonprotein components for their activities. Enzyme cofactors may be ions, such as Mg²⁺or Zn²⁺, or complex organic molecules, referred to as coenzymes. An enzyme that lacks an essential cofactor is called an apoenzyme. Intact enzymes with their bound cofactors are referred to as ho1oenzymes.

Some enzymes have another remarkable feature. Their activities can be regulated to an extraordinary extent. Regulation is necessary to the maintenance of a stable intracellular environment. For example, adjustments in the rates of enzymecatalyzed reactions allow cells to respond effectively to changes in the concentrations of various nutrients. Organisms use а variety of techniques to control enzyme activities. In some mechanisms, enzymes are regulated directly, principally through the binding of activators or inhibitors. Моте indirect methods involve the regulation of enzyme synthesis.

Classification of enzimes. In the early days of biochemistry, enzymes were named at the whim of their discoverers. Often, enzyme names provided по clue to their function (е.g., trypsin), or several names were used for the same enzyme. Enzymes were often named by adding the suffix “-ase” to the пате of the substrate. For example, urease catalyzes the hydrolysis of urea. To eliminate confusion, the International Union of Biochemistry (КВ) instituted а systematic naming scheme for enzymes. Each enzyme is now classified and named according to the type of chemical reaction it catalyzes. In this scheme an enzyme is assigned а four number classification and а two-part пате called а systematic паше. In addition, a shorter version of the systematic name, called the recommended name, is suggested by the IUB for everyday use. Because many enzymes were discovered before the institution of the systematic nomenclature, тапу of the old well-knowames have been retained.

The following are the six major enzyme categories:

1. Oxidoreductases. Oxidoreductases catalyze various types of oxidation-reduction reactions. Subclasses of this group include the dehydrogenases, oxidases, oxygenases, reductases, peroxidases, and hydroxylases.

2. Transferases. Transferases catalyze reactions that involve the transfer of groups from one molecule to another. Examples of such groups include amino, carboxyl, carbonyl, methyl, phosphoryl, and acyl (RC=0). Common trivial names for the transferases often include the prefix “trans.” Examples include the transcarboxylases, transmethylases, and transaminases.

3. Hydrolases. Hydrolases catalyze reactions in which the cleavage of bonds is accomplished by the addition of water. The hydrolases include the esterases, phosphatases, and peptidases.

4. Lyases. Lyases catalyze reactions in which groups (е.g., Н₂O, CO₂, and NH₃) are removed to form а double bond or added to а double bond. Decarboxylases, hydratases, dehydratases, deaminases, and synthases are examples of lyases.

5. Isomerases. This is а heterogeneous group of enzymes. lsomerases catalyze several types of intramolecular rearrangements. The epimerases catalyze the inversion of asymmetric carbon atoms. Mutases catalyze the intramolecular transfer of functional groups.

6. Ligases. Ligases catalyze bond formation between two substrate molecules. The energy for these reactions is always supplied by ATP hydrolysis. The names of many ligases include the term synthetase. Several other ligasesare called carboxylases.

Enzyme Inhibition.

   

 The activity of enzymes can be inhibited. Study of the methods by which enzymes are inhibited have practical applications. For example, many clinical therapies and biochemical research tools are based on enzyme inhibition.

А variety of substances have the ability to reduce or eliminate the catalytic activity of specific enzymes. Inhibition may be irreversible or reversible. Irreversible inhibitors usually bond covalently to the enzyme, often to а side chain group in the active site.

Noncompetitive Inhibition.

 

In noncompetitive inhibition the inhibitor binds to the enzyme at а site other than the active site. Both ЕI and EIS complexes form. Inhibitor binding causes an alteration in the enzyme’s three-dimensional configuration that prevents the reaction from occurring. For example, АМР is а noncompetitive inhibitor of fructose bisphosphate phosphatase, the enzyme that catalyzes the conversion of fructose-1,6-bisphosphate to fructose-6-phosphate. Noncompetitive inhibition is not reversed by increasing the concentration of substrate.

Catalysis.

 However valuable kinetic studies are, they reveal little about how enzymes catalyze biochemical reactions. Biochemists use а variety of other techniques to investigate the catalytic mechanisms of enzymes. (А mechanism is а description of the specific steps that occur as а chemical reaction takes place.) The goal of enzyme mechanism investigations is to relate enzyme activity to the structure and function of the active site. Methods that are used to provide insight into catalytic mechanisms include Х-ray crystallography, chemical inactivation of active site side chains, and studies using simple model compounds as substrates and as inhibitors.

Catalytic Mechanisms.

Despite extensive research, the mechanisms of only а few enzymes are known in significant detail. However, it has become increasingly clear that enzymes utilize the same catalytic mechanisms as nonenzymatic catalysts. The significantly higher catalytic rates that enzymes achieve are largely Же to the fact that their active sites possess structures that are uniquely suited to promote catalysis.

Several factors contribute to enzyme catalysis. The most important of these are (1) proximity and strain effects, (2) electrostatic effects, (3) acid base catalysis, and (4) covalent catalysis. Each factor will be described briefly.

Proximity and Strain Effects. For а biochemical reaction to occur, the substrate must come into close proximity to catalytic functional groups (side chain groups involved in а catalytic mechanism) within the active site. In addition, the substrate must be precisely oriented in relation to the catalytic groups. Once the substrate is correctly positioned, а change in the enzyme’s conformation may result in а strained enzyme-substrate complex. This strain helps to bring the enzyme-substrate complex into the transition state. In general, the more tightly the active site is able to bind the substrate while it is in its transition state, the greater the rate of the reaction.

Electrostatic Effects.

Recall that the strength of electrostatic interactions is related to the capacity of surrounding solvent molecules to reduce the attractive forces between chemical groups. Because water is largely excluded from the active site as substrate binds, the local dielectric constant is often low. The charge distribution in the relatively anhydrous active site may influence the chemical reactivity of the substrate. In addition, weak electrostatic interactions, such as those between permanent and induced dipoles in both the active site and the substrate, are believed to contribute to catalysis. А more efficient binding of substrate causes а lowering in the free energy of the transition state, which results in an acceleration of the reaction.

Acid-Base Catalysis.

 

 

Chemical groups can often be made more reactive by the addition or removal of а proton. Enzyme active sites contain side chain groups that act as proton donors or acceptors. Transfers of protons are а common feature of chemical reactions. For example, consider the hydrolysis of an ester: Because water is а weak nucleophile, ester hydrolysis is relatively slow ieutral solution. Ester hydrolysis takes place much more rapidly if the pH is raised. As hydroxide ion attacks the polarized carbon atom of the carbonyl group, and а tetrahedral intermediate is formed. As the intermediate breaks down, а proton is transferred from а nearby water molecule. The reaction is complete when the alcohol is released. However, hydroxide ion catalysis is not practical in living systems. Enzymes use several functional groups that behave as general bases to aid in the efficient transfer of protons. Such groups can be precisely positioned in relation to the substrat. Ester hydrolysis can also be catalyzed by а general acid. As theoxygen of the ester’s carbonyl group binds to the proton, the carbon atom becomes more positive. The ester then becomes тоге susceptible to the nucleophilic attack of а water molecule.

Because such groups are only weakly ionizable, they are referred to as general acids or general bases. (The terms general acid and general base refer to substances that are capable of releasing а proton or accepting а proton, respectively. Enzymes almost always use general acids or general bases in preference to protons or hydroxide groups. For the sake of simplicity, however, the symbols Н⁺ and ОН^– are often used in illustrations of reaction mechanisms.) For example, the side chain of histidine (referred to as an imidazole group) often participates in catalytic mechanisms. It does so because its рК, is approximately 6. Therefore the histidine side chain ionizes within the hysiological pH range. The protonated form of histidine is а general acid. Once it loses its proton (and becomes а conjugate base), histidine is а general base.

 

Covalent Catalysis.

In some enzymes а nucleophilic side chain group forms an unstable covalent bond with the substrate. The enzyme-substrate complex then undergoes further reaction to form product. А class of enzymes called the serine proteases use the – СН₂ – ОН group of serine as а nucleophile to hydrolyze peptide bonds. (Examples of the serine proteases include the digestive enzymes trypsin and chymotrypsin and the blood- clotting enzyme thrombin.) During the first step, the nucleophile attacks the carbonyl group. As the ester bond is formed, the peptide bond is broken. The resulting highly reactive intermediate is hydrolyzed in а second reaction by water.

 

 

Several other amino acid side chains may act as nucleophiles. The sulfhydryl group of cysteine, the carboxylate groups of aspartate and glutamate, and the imidazole group of histidine can play this role.

 

 

Irreversible inhibitors usually bind covalently to enzymes. In reversible inhibition the inhibitor can dissociate from the enzyme. The most common types of reversible inhibition are competitive and noncompetitive. The kinetic properties of allosteric enzymes are not explained by the Michaelis-Menten model. Most allosteric enzymes are composed of subunits called protomers. The binding of substrate or effector to one protomer affects the binding properties of other protomers. Enzymes use the same catalytic mechanisms as nonenzy- matic catalysts. Several factors contribute to enzyme catalysts: proximity and strain effects, electrostatic effects, acid-base catalysis, and covalent catalysis. Each enzyme mechanism results from the simultaneous use of various combinations of these factors.

Enzymes are biological catalysts. They enhance reaction rates because they provide an alternative reaction pathway that re quires less energy than an uncatalyzed reaction. In contrast to some inorganic catalysts, most enzymes catalyze reactions at mild temperatures. In addition, enzymes are specific in regard to the types of reactions they catalyze. Each type of enzyme contains а unique, intricately shaped binding surface called an active site. Substrate binds to the enzyme’s active site, which is а small cleft or crevice in an otherwise large protein molecule. In the look-and-key model of enzyme action the structures of the enzyme’s active site and the substrate are complementary. In the induced fit model the protein molecule is assumed to be flexible.

Each enzyme is currently classified and named according to the type of reaction it catalyzes. There are six major enzyme categories: oxidoreductases, transferases, hydrolases, lyases, isomerases, and ligases.

Enzyme inhibition may be reversible or irreversible. Active site amino acid side chains are primarily responsible for catalyzing proton transfers and nucleophilic substitutions. Nonprotein cofactors (metals and coenzymes) are used by enzymes to catalyze other types of reactions.

Enzymes are sensitive to environmental factors such as temperature and pH. Each enzyme has an optimum temperature and an optimum pH.

The chemical reactions in living cells are organized into а series of biochemical pathways. Control of biochemical path-ways is achieved primarily by adjusting the concentrations andactivities of enzymes. This control is accomplished by utilizing various combinations of the following mechanisms: genetic control, covalent modification, allosteric regulation, and compartmentation.