LECTURE 5. THE BASES OF CHEMICAL THERMODYNAMICS.

June 4, 2024
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LECTURE 5. THE BASES OF CHEMICAL THERMODYNAMICS. FIRST LAW OF THERMODYNAMICS. THERMOCHEMISTRY. SECOND LAW OF THERMODYNAMICS. THE DIRECTIVITY OF CHEMICAL PROCESSES

 

INTRODUCTION: The branch of science, which deals with the study of different forms of energy and the quantitative relationships between them is known as thermodynamics.

The complete study of thermodynamics is based upon three generalizations called First, Second and Third laws of thermodynamics. These laws have been arrived at purely on the basis of human experience and there is no theoretical proof for any of these laws. However the validity of these laws is supported by the fact that nothing contrary to these laws has been found so far and nothing contrary is expected.

The importance of the thermodynamics lies in the following two facts:

(i) It helps us to predict whether any given chemical reaction can occur under the given set of conditions.

(ii) It helps in predicting the extent of reaction before the equilibrium is attained.

The limitations of thermodynamics i.e. where it fails to give any information are as follows:

(i) It helps to predict the feasibility of а process but does not tell anything about the rate at which the process takes place.

(ii) It deals only with the initial and final states of а system but does not tell anything about the mechanism of the process (i.е. the path followed by the process).

(iii) It deals with the properties like temperature, pressure etc. of the matter in bulk but does not tell anything about the individual atoms and molecules.

Some basic terms and concepts commonly used in thermodynamics are briefly explained below:

1. System and Surroundings. The part of the universe chosen for thermodynamic consideration (i.е. to study the effect of temperature, pressure etc.) is called а system. The remaining portion of the universe, excluding the system, is called surroundings.

2. Open, closed and isolated systems.

(а) Open system. А system is said to be an open system if it can exchange both matter and energy with the surroundings. For example, if some water is kept in an open vessel or if some reaction is allowed to take place in an open vessel, exchange of both matter and energy takes place between the system and the surroundings.

Animals and plants are open systems from the thermodynamic point of view.

(b) Closed system. If а system can exchange only energy with the surroundings but not matter, it is called а closed system. For example, if some water is placed in а closed metallic vessel or if some reaction is allowed to take place in а cylinder enclosed by а piston, then as the vessel is closed, no exchange of matter between the system and the surroundings can take place. However, as the vessel has conducting walls, exchange of energy can take place between the system and the surroundings.

If the reaction is exothermic, heat is given by the system to the surroundings. If the reaction is endothermic, heat is given by surroundings to the system.

(с) Isolated system. If а system caeither exchange matter nor energy with the surroundings, it is called an isolated system. For example, if water is placed in а vessel which is closed as well as insulated, no exchange of matter or energy can take place between the system and the surroundings. This constitutes an isolated system.

3. State of а system and State variables. The state of а system means the condition of the system, which is described in terms of certain observable (measurable) properties such as temperature (Т), pressure (P), volume (Ч) etc. of the system. If any of these properties of the system changes, the system is said to be in different state i.е. the state of the system changes. That is why these properties of а system are called state variables.

А process is said (о occur when the state of the system changes. The first and the last state of а system are called the initial state and the final state respectively.

4. State function. А physical quantity is said to be state function if its value depends only upon the state of the system and does not depend upon the path by which this state has been attained. For example, а person standing on the roof of а five stroeyed building (i.е. at а particular height) has а fixed value of potential energy, irrespective of the fact whether the reached there by stairs or by а lift. Thus the potential energy of the person is а state function.

5. Extensive and Intensive properties. The various physical properties of а system may be divided into two main types:

(i) Extensive properties. These are those properties which depend upon the quantity of the matter contained in the system. The common examples of these properties are mass, volume and heat capacity. Besides these, some other properties discussed later in this unit include internal energy, enthalpy, entropy, Gibbs free energy etc. The total value of an extensive property is equal to the sum of the values for the separate parts into which the system may be divided for the sake of convenience.

(ii) Intensive properties. These are those properties which depend only upon the nature of the substance and are independent of the amount of the substance present in the system. The common examples of these properties are temperature, pressure, refractive index, viscosity, density, surface tension, specific heat, freezing point, boiling point, etc.

6. Thermodynamic processes. А thermodynamic process is said to occur when the system changes from one state (initial state) to another (final state). The different processes commonly met within the study of chemical thermodynamics are as follows:

(i) Isothermal process. When а process is carried out in such а manner that the temperature remains constant throughout the process, it is called an isothermal process. Obviously, when such а process occurs, heat can flow from the system to the surroundings and vice versa in order to keep the temperature of the system constant.

(ii) Adiabatic process. When a process is carried out in such а manner that no heat can flow from the system to the surroundings or vice versa i.e the system is completely insulated from the surroundings, it is called an adiabatic process.

(iii) Isochoric process. It is а process during which the volume of the system is kept constant.

(iv) Isobaric process. It is а process during which the pressure of the system is kept constant.

7. Reversible and Irreversible Processes. 

А process carried out in the above manner is called а reversible process and may be defined as follows:

А reversible process is а process which is carried out infinitestimally slowly so that all changes occurring in the direct process can be exactly reversed and the system remains almost in a state of equilibrium with the surroundings at every stage of the process.

 On the other hand, а process which does not meet the above requirements is called an irreversible process. In other words, an is irreversible process is defined as that process which is not carried out infinitesimally slowly (instead, it is carried out rapidly) so that the successive steps of the direct process cannot be retraced and any change in the external conditions disturbs the equilibrium.

8. Some thermodynamic quantities. А number of the thermodynamic quantities appear during the study of thermodynamics e.g. internal energy, heat, work, enthalpy, entropy, free energy etc. The first three terms are briefly described below. The remaining terms will be discussed at appropriate places.

(а) Internal energy. It has already been mentioned that whenever some process (physical or chemical) occurs, it is usually accompanied by some energy change. The energy may appear in different forms such as heat, light, work etc.

The evolution or absorption of energy in different processes clearly shows that every substance (or the system containing one or more substances) must be associated with some definite amount of energy, the actual value of which depends upon the nature of the substance and the conditions of temperature, pressure, volume and composition. It is the sum of different types of energies associated with atoms and molecules such as electronic energy (Еe), nuclear energy (Еn), chemical bond energy (Еc), potential energy (Ер) and kinetic energy (Еk) which is further the sum of translational energy (Еt), vibrational energy (Еv) and rotational energy (Еr). Thus:

Е = Еe + Еn  + Ес + Ер + Еk

The energy thus stored within а substance (or а system) is called its internal energy and is usually denoted by the symbol “Е”.

Further, internal energy is a state function i.е. depends only upon the state of the system (i.е. conditions of temperature, pressure etc.) and is independent of the method by which this state has been attained.

Two more important points about the internal energy are as follows:

(i) The internal energy depends upon the quantity of the substance contained in the system. Hence it is an extensive property.

(ii) The internal energy of ideal gases is а function of temperature only. Hence in isothermal processes, as the temperature remains constant, there is no change in internal energy i.e.

DЕ = 0

Sign of DЕ. Obviously, if Е1 > E2  (or ЕR > ЕP), the extra energy possessed by the system in the initial state (or the reactants) would be given out and DЕ will be negative according to the above equations.

Similarly, if Е1 < E2  (or ЕR < ЕP), energy will be absorbed in the process and DЕ will be positive. Hence DЕ is negative if energy is evolved and DЕ  is positive if energy is absorbed.

Units of Е. The units of energy are ergs (in CGS units) or joules (in SI units)

1 joule = 107 ergs.

(b) Work. As learnt from lessons in Physics, work is said to have been done whenever the point of application of а force is displaced in the direction of the force. If F is the magnitude of the force and dl is the displacement of the point of application in the direction in which the force acts, then the work done is given by

w = F x dl

The above type of work is called mechanical work. However, there are many other forms of work but in each of these forms:

Work done = [А generalized force] x [А generalized displacement]

Two main types of work used in thermodynamics are briefly described below:

(i) Electrical work. The genera1ised force is the Е.М.F. and the generalized displacement is the quantity of electricity flowing through the circuit. Hence:

Electrical work done = E.М.F. x Quantity of electncity.

This type of work is involved in case of reactions involving ions.

(ii) Work of expansion or pressure-volume work. This type of work is involved in systems consisting of gases. This is the most important form of work used in the study of thermodynamics. It is the work done when the gas expands or contracts against the external pressure (usually, the atmospheric pressure). It is а kind of mechanical work. The expression for such а work may be derived as follows:

Consider а gas enclosed in а cylinder fitted with а frictionless piston.

Suppose:

Area of cross-section of cylinder = a sq. cm.

 Pressure on the piston = Р

(which is slightly less than internal pressure of the gas so that the gas can expand)

 Distance through which gas expands = dl cm

 Then as pressure is force per unit area, force (f) acting on the piston will be

f = P x a

Work done by the gas = Force x Distance = f x dl = P x а x dl.

But a x dl = dV, а small increase is the volume of the gas. Hence the small amount of work (dw) done by the gas can be written as

dw =P x dV

If the external pressure Р against which the gas expands remains almost constant throughout 1е process, the above result may be written as

 w = P (V2 – V1) = P DV

where DV = V2 – V1 is the total change in volume of the gas (or the system).

If the external pressure (Р) is slightly more than the pressure of the gas, the gas will contract i.e. the work will be done by the surroundings on the system. However, the same formula will apply for the work done.

It may be mentioned here that Р is the external pressure and hence is sometimes written as Рext so that

w = Р x DV

 Sign of w. According to the latest S.I. convention, w is taken as negative if work is done by the system whereas it is taken as positive if work is done on the system. Thus for expansion, we write internal pressure of the gas and the external pressure, similarly heat is another mode of energy exchanged between the system and the surroundings as а result of the difference of temperature between them. It is usually represented by the letter “q”.

Sign of “q”. When heat is given by the system to the surroundings, it is given а negative sign.

When heat is absorbed by the system from the surroundings, it is given а positive sign.

Units of q’. Heat is usually measured in terms of ‘calories’. А calorie is defined as the quantity of heat required to raise the temperature of one gram of water through 10 C (in the vicinity of 150С).

In the SI system, heat is expressed in terms of joules. The two types of units are related to each other as under: 1calorie = 4.4 joules

which means the same thing as:

1 joule = 0.2390 calorie

It may be noted that whereas internal energy is а state function, work and heat are not state functions because their values do not depend merely on the initial and final states but depend upon the path followed.

Difference between heat and work. When heat is supplied to а gas in а system, the molecules start moving faster with greater randomness in different directions. However, when work is done on the system, then initially the molecules start moving down in the direction of the piston. Thus whereas heat is аrandom1огт of energy, work is an organized form of energy

The first law of thermodynamics.

The first law of thermodynamics is simply the law of conservation of energy which states that:

“Energy caeither be created nor destroyed although it may be converted from one form to another” or “The total energy of the universe (i.e. the system and the surroundings) remains constant, although it may undergo transformation from one form to the other.”

Justification for the First Law of Thermodynamics. This law is purely а result of experience. There is no theoretical proof for it. However, some of the following observations support the validity of this law. Whenever а certain quantity of some form of energy disappears, an exactly equivalent amount of some other form of energy must be produced. For example,

(а) In the operation of an electric fan, the electrical energy which is consumed is converted into mechanical work which moves the blades.

(b) The electrical energy supplied to а heater is converted into heat whereas electrical energy passing through the filament of а bulb is converted into light.

(с) Water can be decomposed by an electric current into gaseous hydrogen and oxygen. It is found that 286 2 U of electrical energy is used to decompose 1 mole of water.

Н2O(l) + 286.2 kJH2 + ½  O2(g)

                 Electrical

                  energy

This energy must have been stored in hydrogen and oxygen since same amount of energy in the form of heat is released when 1 mole of water (liquid) is obtained from gaseous hydrogen and oxygen.

H2 + ½  O2(g) = Н2O(l)  + 286.2 kJ

                                               Heat energy

Thus 286.2 kJ of electrical energy which was supplied to the system (substance under observation) has been recovered later as heat energy i.e.

Internal energy is а state function — А deduction from the First law of Thermodynamics. Suppose the internal energy of а system under some conditions of temperature, pressure and volume is ЕA (state А). Now suppose the conditions are changed so that the internal energy is EB (state В). Then if internal energy is а state function, the difference DЕ  = EB – EA must be same irrespective of the path from А to В. If not, then suppose in going from А to В by path I, the internal energy increases by DЕ but on returning from В to А by path II, internal energy decreases by DЕ’. If DЕ > DЕ’, some energy has been created and if DЕ < DЕ’, some energy has been destroyed though we have returned to the same conditions. This is against the first law of thermodynamics. Hence DЕ must be equal to DЕ’ i.е. internal energy is а state function.

INTERNAL ENERGY CHANGE

The term “internal energy” has already been explained. Another important aspect (definition) of internal energy change follows from the first law of thermodynamics, according to which

q = DЕ  + P DV

If the process is carried out at constant volume, DV = 0. The above equation then reduces to the form

DЕ =qv

(v indicating constant volume).

Hence internal energy change is the heat absorbed or evolved at constant volume.

It may be mentioned further that as DE is а state function, therefore qv is also а state function.

Measurement of Internal energy change. The internal energy change measured experimentally using an apparatus called Bomb calorimeterIt consists of а strong vessel (called ‘bomb’) which can stand high pressures. It is surrounded by а bigger vessel which contains water and is insulated. А thermometer and а stirrer are suspended in it. The procedure consists of the following two steps:

CALORIMETER.

(i) Combustion of known weight of а compound whose heat of combustion is known. А known wt. of the compound is taken in the platinum cup. Oxygen under high pressure is introduced into the bomb. А current is passed through the filament immersed in the compound. Combustion of the compound takes place. The increase in the temperature of water is noted. From this the heat capacity of the apparatus (i.е. heat absorbed per degree rise of temperature) can be calculated.

(ii) Combustion of known weight of the experimental compound. The experiment is repeated as in step (i)

In the above case, as the reaction is carried out in а closed vessel, therefore heat evolved is the heat of combustion at constant volume and hence is equal to the internal energy change.

ENTHALPY OR HEAT CONTENT

If а process is carried out at constant pressure (as is usually the case, because most of the reactions are studied in vessels open to the atmosphere or if а system consists of а gas confined in а cylinder fitted with а piston, the external pressure acting on the piston is the atmospheric pressure), the work of expansion is given by:

w = – PDV

where DV is the increase in volume and P is the constant pressure.

According to first law of thermodynamics, we know that: q = DE – w

Where q is the heat absorbed by the system, DE is the increase in internal energy of the system and w is the work done by the system.

Unter cocdition of constant pressure, putting w = – PDV and representing the heat absorbed by qp, we get:

Putting these values in equation above, we get:

qp = DE – PDV

Suppose when the system absorbed qp joules of the heat, its internal energy increases form E1 to E2 and V1 to V2.

Than we have:

DE = E2 – E1

and DV = V2 – V1

Putting these values in equation above, we get:

qp = (Е2 – E1) + Р(V2 – V1)

Or  qp = (Е2 + РV2) – (E1 + РV1)

Now as Е, Р and V are the functions of state, therefore the quantity Е + PV must also be а state function. The thermodynamic quantity Е + PV is called the heat content or enthalpy of the system and is represented by the symbol “Н” i.е. the enthalpy may be defined mathematically by the equation:

 Н=Е + PV

Thus if H2 is the enthalpy of the system in the final state and Н2 is the value in the initial state, then

Н2 + Е2 + PV2

and H1 = E1 + PV1

Putting these values in equation, we get:

qp = Н2 – H1

or qp = DН

where DН = Н2 – H1 is the enthalpy change of the system.

Hence enthalpy change of а system is equal to the heat absorbed or evolved by the system at constant pressure.

It may be remembered that as most of the reactions are carried out at constant pressure (i.е. in the open vessels), the measured value of the heat evolved or absorbed is the enthalpy change.

Further, putting the value of qp from equation, we get:

DН = DE + PDV

Hence the entha1py change accompanying а process may also be defined as the sum of the increase in internal energy of the system and the pressure-volume work done 1.е. the work of expansion.

Applications of the first law of thermodynamics.

In the calculation of the enthalpies of reactions. It has already been mentioned that enthalpy (Н) is а state function. Hence, the enthalpy change (DН) of а reaction is also а state function i.е. it depends only upon the nature of the initial reactants and that of the final products. This forms the basis of Hess’s law which states as follows:

The total amount of heat evolved or absorbed in a reaction depends only upon the nature of the initial reactants and that of the final products and does not depend upon the path by which this change is brought about. In other words, the total amount of heat evolved or absorbed in a reaction is same whether the reaction takes place in one step or a number of steps.

 Before we discuss how Hess’s law can be applied in the calculation of enthalpies of reactions, let us first define а few terms to be used therein.

(i) Enthalpy of reaction. Enthalpy of reaction is defined as the amount of heat evolved or absorbed when the number of moles of the reactants as represented by the balanced equation have completely reacted.

Since its value depends upon the conditions of temperature and pressure, therefore the values are reported under standard conditions which are 1 atm pressure and 298 К. The enthalpy change under these conditions is called the standard enthalpy change and is usually represented by DН0.

(ii) Enthalpy of formation. The standard enthalpy of formation (usually represented by DН0) is defined as the enthalpy change that takes place when one mole of the substance under standard conditions is formed from its constituent elements in their most stable form and in their standard state.

The standard state of an element is the pure element in its stable form or more common form under standard conditions of 1 atm and 298 К. For example, the standard states of oxygen, carbon, mercury and sulphur are oxygen gas, graphite, liquid mercury and rhombic sulphur respectively at 1 atm pressure and 298 К.

The enthalpy of formation of any element in the standard state is taken as ‘zero’. Thus the standard heat of formation of graphite is 0.0 whereas that of diamond is not zero but equal to 1.896 kJ/mol.

(iii) Enthalpy of combustion. The enthalpy of combustion of a substance is defined as the amount of heat evolved when 1 mole of the substance is completely burnt or oxidized.

Calculation of enthalpies of reactions. The enthalpies of reactions are usually calculated from the enthalpies of formation using the following relationship:

 

DНreaction = S DН0(Products) – S DН0(Reactants);

For elementary substances: DН0(formation) = 0

In using this formula, the standard enthalpies of formation of elements are taken as zero, as already mentioned.

(2) In the calculation of bond energies. We know that energy is evolved when а bond is formed and energy is required for the dissociation of а bond. Hence bond energy is defined as follows:

Bond energy is the amount of energy released when one mole of bonds are formed from the isolated atoms in the gaseous state or the amount of energy required to dissociate one mole of bonds present between the atoms in the gaseous molecules.

For diatomic molecules like Н2, О2, N2, С1, HCl, HF etc., the bond energies are equal to their dissociation energies. For polyatomic molecules, the bond energy of а particular bond is not the same when present in different types of compounds (е.у bond energy of С – Cl is not same in СН3С1, СН2С12, СНСl3, СС14). In fact, the bond energy of а particular type of bond is not same even in the same compound (е.g. in СН4, the bond energy for first, second, third and being С – Н bonds are not equal – their values being + 425, + 470, + 416 and + 335 kJ/mol respectively). Hence in such cases, an average value is taken.

Thus average С – Н bond energy = (425 + 470 + 416  + 335) / 4 = 1646/4 = 411.5kJ/mol

Bond energy usually means bond dissociation energy.

DНreaction = S DН0(Products) – S DН0(Reactants) 

Spontaneous non-spontaneous processes. To understand what we mean by а spontaneous process, let us consider the following two processes:

1.     Dissolution of sugar in water at room temperature.

2.     Burning of coal in air or oxygen.

The first process takes place by itself, although it may be slow. The second process cannot take place by itself. It needs initiation i.е. we have to bring а flame near the coal to start its burning. But once it starts burning, it goes on by itself without the help of any external agency. Both the above processes are spontaneous processes. Hence а spontaneous process may be defined as follows:

А process, which under some given conditions may take place by itself or by initiation independent of the rate is called а spontaneous process. In other words, а process, which can take place by itself or has an urge or tendency to take place is called spontaneous process or to sum up, а spontaneous process is simply а process, which is feasible.

It may be noted carefully that а spontaneous process does not mean that the process should be instantaneous. In fact, the rate of the process may very from extremely slow to extremely fast.

For а more clear understanding, а few more examples of the spontaneous processes are as follows:

В. Examples of processes which take place on initiation:

(i) Lighting of а candle involving burning of wax (initiated by ignition),

(ii) Heating of calcium carbonate to give calcium oxide and carbon dioxide (initiated by heat).

СаСО3 (s) = СаО (s) + СО2 (g)

(iii) Combination of hydrogen and oxygen to form water when initiated by passing an electric spark.

H2(g) + ½ O2 (g) = H2O(l)

(iv) Reaction between methane and oxygen to form carbon dioxide and water (initiated by ignition)

СН4 (g) + 2О2(g) = СО2(g) + 2Н2О(l)

On the other hand, а process, which caeither take place by itself nor by initiation is called а non- spontaneous process.

А few examples of the non-spontaneous processes in everyday life are as follows:

(i) Flow of water up а hill.

(ii) Flow of heat from а cold body to а hot body.

(iii) Diffusion of gas from low pressure to а high pressure.

(iv) Dissolution of sand in water.

The driving force for а spontaneous process. This force, which is responsible for the spontaneity of а process is called the driving force.

(1) Tendency for minimum energy. It is а common observation that in order to acquire maximum stability, every system tends to have minimum energy. For example,

(i) А stone lying at а height has а tendency to fall down so as to have minimum potential energy.

(ii) Water flows down а hill to have minimum energy.

(iii) А wound watch spring has tendency to unwind itself to decrease its energy to minimum.

(iv) Heat flows from hot body to cold body so that heat content of the hot body becomes minimum.

Limitations of the criterion for minimum energy. The above criterion fails to explain the following:

1. A number of reactions are known which are endothermic i.e for which DН is positive but still they are spontaneous, е.g

(i) Evaporation of water or melting of ice. It takes place by absorption of heat from the surroundings.

H2O(l) = Н2О(g);   DН = + 44 kJ/mol

Н2О (s) = Н2О (1); DН = + 5.86 kJ/mol

(ii) Dissolution of salts like NH4CI, КС1 etc.

NH4Cl(s)+ aq =NH4+ (aq) + Сl(aq); DН = +15.1 kJ/mol

(iii) Decomposition of calcium carbonate on heating

CaCO3 (s) = СаО (s) + СО2 (g); DН = + 177.8 1 kJ/mol

(iv) Decomposition of mercuric oxide on heating

2HgO(s) = 2Hg (1) + O2(g);  DН= +90 8 kJ/mol

2. A number of reactions are known for which DН zero but still they are spontaneous, е.g.

СН3СООН(l) + С2Н5ОН(l) = CH3COOC2H5 (1) + Н2О (l)

3. Even those reactions for which DН negative, rarely proceed to completion even though DН remains negative throughout.

4. Reversible reactions also occur. For example, the reaction

H2(g) + I2(g) = 2HI (g) having DН = + negative and the reverse reaction viz.,

2HI (g) = H2(g) + I2(g) having DН = – negative both occur i.е. are spontaneous.

Hence it may be concluded that the energy factor or enthalpy factor (i.е. DН) cannot be the sole criterion for predicting the spontaneity or the feasibility of а process. Thus some other factor must also be involved. This factor is the tendency for maximum randomness, as explained below:

(2) Tendency for maximum randomness. Let us consider а process which is spontaneous but for which DН=0. Since for such а process, energy factor has no role to play, so we shall be able to find out the other factor, which makes the process spontaneous. А simple case of such а process “mixing of two gases” which do not react chemically. Suppose the two gases are enclosed in bulbs А and В connected to each other by а tube and kept separated by а stop-cock. Now if the stopcock is opened, the two gases mix completely.

 (i) Evaporation of water takes place because the gaseous water molecules are more random than the liquid water molecules. In other words, the process is spontaneous because it is accompanied by increase of randomness. Similarly, melting of ice is а spontaneous process because liquid state is more random than the solid state.

(ii) Dissolution of ammonium chloride is spontaneous because in the solid, the ions are fixed but when they go into the aqueous solution, they are free to move about. In other words, the process is accompanied by an increase of randomness.

(iii) Decomposition of solid calcium carbonate is spontaneous because the gaseous CO2 produced is more random than the solid CaCO3.

(iv) Decomposition of solid mercuric oxide is spontaneous because the liquid mercury and the gaseous oxygen formed are more random than the solid HgO.

Entropy is a measure of randomness or disorder of the system.

The greater the randomness, the higher is the entropy. Evidently, for а given substance, the crystalline solid state has the lowest entropy, the gaseous state has the highest entropy and the liquid state has the entropy between the two. It is usually represented by “S”. Like internal energy and enthalpy, it is а state function. The change in its value during а process, called the entropy change (represented by DS) is given by

Entropy change during a process is defined as the amount of heat (q) absorbed isothermally and reversibly (infinitesimally slowly) divided by the absolute temperature (Т) at which the heat is absorbed.

Units of Entropy Change. As DS = q/T and it is an extensive property, therefore the units of entropy change are calories/К.mol (cal/К.mol) in С.G.S. system and

 joules/К . mol (J/K . mol) in SI units.

Entropy changes during phase transformations.

(1) Entropy of fusion. When а solid melts, there is an equilibrium between the solid and the liquid at the melting point. The heat absorbed (qrev) is equal to the latest heat of fusion (DHf)

The entropy of fusion is the change in entropy when 1 mole of а solid substance changes into liquid form at the melting temperature.

Mathematically,

DSfus = Sliq – Ssolid = DHfus / Tm

where: DSfus – entropy of fusion

Sliq – molar entropy of the liquid

Ssolid – molar entropy of the solid

Тm – melting temperature in degrees Kelvin

DHfus – enthalpy of fusion per mole.

Entropy of vaporisation. When а liquid evaporates at the boiling point, there is an equilibrium between the liquid and the vapour. The heat absorbed (qrev) is equal to the latent heat of vaporisation ((DHvap).

Entropy of vaporisation is the entropy change when 1 mole of а liquid changes into vapours at its boiling temperature.

(3) Entropy of sublimation. Sublimation involves an equilibrium between the solid and the vapour.

Spontaneity in terms of entropy change. Consider the following spontaneous processes:

(i)    Mixing of the two gases on opening the stopcock.

(ii)  Spreading of а drop of ink in а beaker filled with water.

Now let us consider the following spontaneous processes:

(i) Cooling down of а cup of tea

(ii) Reaction taking place between а piece of marble (CaCO3) or sodium hydroxide (NaOH) and hydrochloric acid in an open vessel.

These are not isolated systems because they involve exchange of matter and energy with the surroundings. Hence for these processes we have to consider the total entropy change of the system and the surroundings i.e.

DS (total) = DS (system) + DS (surroundings)

However, it can be shown that even in these cases, for the process to be spontaneous, DS (total) must be positive. Hence it can be generalized that

For all spontaneous processes, the total entropy change DS (total) must be positive.

 

(i)    If DS is positive, the process is spontaneous.

(ii)  If DS is negative, the direct process is non-spontaneous; the reverse process is may be spontaneous.

(iii)           If DS is zero, the process is in equilibrium.

Gibbs free energy. It is that thermodynamic quantity of а system the decrease in whose value during a process is equal to the useful work done by the system.

It is usually denoted by “G” and is defined mathematically by the equation:

where Н is the heat content, Т is the absolute temperature and S is the entropy of the system.

As before, for the isothermal processes, we have

G1 = Н1 – TS1 for the initial state

G2 = Н2 – TS2 for the final state

where DG = G2 – G1  is the change in Gibbs’s free energy of the system

or – Gibbs–Helmoholtz equation.

DН = Н2 – Н1  is the enthalpy change of the system

and DS = S2 – S1  is the entropy change of the system.

Spontaneity in terms of free energy change.

(a) Deriving the criteria from entropy considerations. It has already been explained that the total entropy change for а system which is not isolated from the surroundings is given By

DStotal = DSsystem + DSsurroundings

Consider а process (or а reaction) being carried out at constant temperature and pressure. Suppose the heat is lost by the surroundings and gained by the system. If the heat lost by the surroundings is represented by qp (р indicating that the process is being carried out at constant pressure), then by definition of entropy change

DSsurroundings = – qp/T

(minus sign before qp indicates that the heat is lost by the surroundings).

 

Using the symbol DS in place of DSsystem  (being implied that DS stands for DS for the system), we can write:

DStotal = DS – DH/T

Multiplying throughout by Т, we get

TDStotal = TDS – DH

But for а change taking place at constant temperature and pressure,

DG = DH – TDS

Because TDStotal = – DG, or – TDStotal = DG

But in terms of total entropy change, it has already been explained that:

(i)    If DStotal is positive, the process is spontaneous.

(ii)  If DStotal is zero, the process is in equilibrium.

(iii)            If DStotal is negative, the direct process is non-spontaneous; the reverse process may be spontaneous.

Putting these results in equitation, it can be concluded that the criteria in terms of free energy change for the spontaneity of the process will be as follows:

(iv)          If DG is negative, the process will be spontaneous.

(v) If DG is zero the process is in equilibrium.

(vi)          If DG is positive, the direct process is non-spontaneous; the reverse process may be spontaneous.

 An important advantage of free energy criteria over the entropy criteria lies in the fact that the former requires free energy change of the system only whereas the latter requires the total entropy change for the system and the surrounings.

(b) Deriving the criteria from Glbbs-Helmholtz equation. 

Thus DG is the resultant of the energy factor (i.е. tendency for minimum energy) and the entropy factor (i.е. the tendency for maximum randomness).

Depending upon the signs of DН and ТDS and their relative magnitudes, the following different possibilities arise

I. When both DН and ТDS are negative i.e. energy factor favours the process but randomness factor opposes it. Then:

(i)    If DН > ТDS the process is spontaneous and DG is negative.

(ii)  If DН < ТDS, the process is non-spontaneous and DG is positive.

(iii)           If DН  = ТDS, the process is in equilibrium and DG is zero.

II. When both DН and ТDS are positive i.e. energy factor opposes the process but randomness factor favours it. Then:

(i)     If DН > ТDS, the process is non-spontaneous and DG is positive.

(ii)   If DН < ТDS, the process is spontaneous and DG is negative.

(iii) If DН  = ТDS, the process is in equilibrium and DG is zero.

III. When DН is negative but ТDSis positive i.е. energy factor as well as the randomness factor favour the process. The process will be highly spontaneous and DG will be highly negative.

IV. When DН is positive but ТDS is negative i.е. energy 1actor as well as the randomness factor oppose the process. The process will be highly non-spontaneous and DG will be highly positive.

To sum up, the criteria for spontaneity of а process in terms of no is as follows:

(i)    If DG is negative the process is spontaneous.

(ii)  If  DG is zero, the process does not occur or the system is in equilibrium.

(iii)           If DG is positive the process does not occur in the forward direction. It may occur in the backward direction.

THE THIRD LAW OF THERMODYNAMICS

It is а well known observation that the entropy of а pure substance increases with increase of temperature and decreases with decrease of temperature. Nernst in 1906 made an important observation about the entropies of perfectly crystalline substances at absolute zero and put forward the following generalization  known as the third law of thermodynamics:

 The entropy of all perfectly crystalline solids may be taken as zero at the absolute zero of temperature.

Since entropy is а measure of disorder, the above definition may be given molecular interpretation as follows:

At absolute zero, а perfectly crystalline solid has а perfect order of its constituent particles i.e. there is no disorder at all. Hence the absolute entropy is taken as zero.

Application of the third law of thermodynamics. The most important application of the third law of thermodynamics is that it helps in the calculation of the absolute entropies of the substances at room temperature (or at any temperature Т). These determinations are based upon the heat capacity measurements.

Thus whereas absolute values of internal energy and enthalpy cannot be determined, the absolute entropies of the substances can be measured.

Knowing the standard entropies of the different reactants and products involved, the entropy change (DS) of а reaction can be calculated using the equation:

DS0  = Sum of the standard absolute entropies of products – Sum of the standard absolute entropies of reactants; DS0  = SS (Products) – S S (Reactants).

 

LITERATURE:

1.   Lawrence D. Didona. Analytical chemistry. – 1992: New York. – P. 700.

2.   Atkins P.W. Physical chemistry. – New York. – 1994. – P.1006.

3.   John B.Russell. General chemistry.New York.1992. – P. 615.

4.http:/intranet.tdmu.edu.ua

5. http://en.wikipedia.org

 

Prepared by PhD Halina Falfushynska

 

 

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