LECTURE 7. MOLECULAR KINETIC. CHARACTERIZATION OF CATALYSTS. CATALYTIC REACTIONS

Catalyst

A catalyst is a species that speeds up a chemical reaction without being chemically changed upon completion of the reaction. In other words, the mass of a catalyst is the same before and after a reaction occurs.

Common examples of catalysts include:

MnO2 in the decomposition of H2O2

Fe in the manufacture of NH3

Pt in the conversion of NO and CO to N2 and CO2

Recall that collisions only result in reactions if the particles collide with enough energy to get the reactions started (i.e. to overcome the activation energy barrier).

Also recall that activation energy corresponds to threshold energy.

Only collisions involving particles with sufficient kinetic energy result in the formation of an activated complex. Particles possessing less than the threshold energy simply bounce apart upon collision.

The number of successful collisions per unit of time be increased by lowering the threshold energy (or in terms of potential energy, lowering the activation energy).

Adding the appropriate catalyst to a chemical system has exactly this effect on threshold/activation energy.

A catalyst provides an alternative pathway for the reaction - a pathway that has a lower activation energy.

The catalyzed pathway (shown as a dotted green line above) has lower activation energy.

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.

Reaction coordinate

(Each potential-energy maximum corresponds to the formation of an activated complex.) Note that 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)

The reaction is believed to proceed through the following preequilibrium:

(In the equilibrium constant, the activity of H2O has been set equal to 1.) Because the second step is rate-determining, the rate law of the overall reaction is predicted to be:

in agreement with the observed dependence of the rate on the Br- concentration and the pH of the solution. The observed activation energy is that of the effective rate coefficient kK. In the absence of Br- ions the reaction cannot proceed through the path set out above, and а different and much higher activation energy is observed.

Two important types of homogeneous catalysis are acid catalysis and base catalysis, and many organic reactions involve one or the other (and sometimes both). Brensted acid catalysis is the transfer of а proton to the substrate:

X + НА — + HX+ + А-; HX+ then reacts

It is the primary process in the solvolysis of esters, keto-enol tautomerism, and the inversion of sucrose, Brensted base catalysis is the transfer of а hydrogen con from the substrate to а base:

ХН+ В-®Х + ВН+; Х- then reacts

It is the primary step in the isomerization and halogenation of organic compounds, and of the Claisen and aldol reactions.

Autocatalysis. The phenomenon of autocatalysis is the acceleration of а reaction by the products. For example, in а reaction А® Р it may be found that the rate law is: u = k[A] [P]

so the reaction rate increases as products are formed. (The reaction gets started because there are usually other reaction routes for the formation of some Р initially, which then takes part in the autocatalytic reaction proper.) An example of autocatalysis is provided by two steps in the Belousov — Zhabotinskii reaction (BZ reaction) that will figure in discussions later in the section:

BrO3- + НВrО2 + Н3О+ ®2ВrО2 + 2Н2О

2ВrО2+ 2Ce(III) + 2Н3О+ ®2HBrO2 + Ce(IV) + 2Н2О

The product HbrO2 is а reactant in the first step.

The industrial importance of autocatalysis (which occurs in а number of reactions, such as oxidations) is that the rate of the reaction can be maximized by ensuring that the optimum concentrations of reactant and product are always present.

Oscillating reactions. One consequence of autocatalysis is the possibility that the concentrations of reactants, intermediates, and products will vary periodically either in space or in time. Chemical oscillation is the analogue of electrical oscillation, with autocatalysis playing the role of positive feedback. Oscillating reactions are much more than а laboratory curiosity. While they are known to occur in only а few cases in industrial processes, there are many examples in biochemical systems where а cell plays the role of а chemical reactor. Oscillating reactions, for example, maintain the rhythm of the heartbeat. They are also known to occur in the glycolytic cycle, in which one molecule of glucose is used to produce (through enzyme-catalysed reactions involving ATP) two molecules of ATP. All the metabolites in the chain oscillate under some conditions, and do so with the same period but with different phases.

The Lotka — Volterra mechanism. We shall use an autocatalytic reaction of а particularly simple form that illustrates how these oscillations may occur. The actual chemical examples that have been discovered so far have а different mechanism. The Lotka — Volterra equations can be solved numerically, and the results can be depicted in two ways. One way is to plot [Х] and [Y] against time. The same information can be displayed more succinctly by plotting one concentration against the other.

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.

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 often necessary. 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 can now 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 О2- 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.

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 materials.

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

Properties of enzymes. By definition а catalyst is а substance that enhances the rate of а chemical reaction but is not permanently altered by the reaction. Catalysts perform this feat because they provide an alternative reaction path-way that requires less energy than the uncatalyzed reaction. During any chemical reaction the energy of the system increases until the transition state is reached. At this point, а high proportion of substrate molecules have become sufficiently energized to enter into an intermediate state that has а high probability of being converted into product. For example, the transition state of the reaction in which ethanol is oxidized to form acetaldehyde

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. For example, enzymes containing free sulfhydryl groups can react with alkylating agents such as iodoacetate:

Competitive inhibition. The structure of а competitive inhibitor closely resembles that of the enzyme's normal substrate. Because of its structure, а competitive inhibitor binds reversibly to the enzyme's active site. In so doing, the inhibitor forms an enzyme-inhibitor complex (El) that is equivalent to the ES complex.

The concentration of El complex depends on the concentration of free inhibitor and on the dissociation constant KI.

The inhibition is said to be competitive because the El complex readily dissociates. The empty active site is then available for substrate binding. Because по productive reaction occurs during the finite amount of time that the ЕI complex exists, the enzyme's activity is observed to decline . The effect of а competitive inhibitor on activity is reversed by increasing the concentration of substrate. At high [S], all the active sites are filled with substrate, and reaction velocity reaches the value observed in the absence of inhibitor. Succinate dehydrogenase, an enzyme in the Krebs citric acid cycle, atalyzes the following redox reaction:

This reaction is inhibited by malonate. Malonate binds to the enzyme's active site but cannot be converted to product. Succinate = Fumarate

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.

Types of catalytic reactions

Catalysts can be divided into two main types - heterogeneous and homogeneous. In a heterogeneous reaction, the catalyst is in a different phase from the reactants. In a homogeneous reaction, the catalyst is in the same phase as the reactants.

What is a phase?

If you look at a mixture and can see a boundary between two of the components, those substances are in different phases. A mixture containing a solid and a liquid consists of two phases. A mixture of various chemicals in a single solution consists of only one phase, because you can't see any boundary between them.

You might wonder why phase differs from the term physical state (solid, liquid or gas). It includes solids, liquids and gases, but is actually a bit more general. It can also apply to two liquids (oil and water, for example) which don't dissolve in each other. You could see the boundary between the two liquids.

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 in neutral 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.

References:

 1.The abstract of the lecture.

2. intranet.tdmu.edu.ua/auth.php

3. Atkins P.W. Physical chemistry. – New York. – 1994. – P.299-307.

4. en.wikipedia.org/wiki

5.Girolami, G. S.; Rauchfuss, T. B. and Angelici, R. J., Synthesis and Technique in Inorganic Chemistry, University Science Books: Mill Valley, CA, 1999

6.John B.Russell. General chemistry. New York.1992. – P. 550-599

7. Lawrence D. Didona. Analytical chemistry. – 1992: New York. – P. 218 – 224.

8. www.youtube.com/watch?v=iEJSOhFaHos

9. www.youtube.com/watch?v=BsClg6z_PSw

10. www.youtube.com/watch?v=O3_hpvYlavA

11. www.youtube.com/watch?v=E9rHSLUr3PU

Prepared by PhD Falfushynska H.