Introduction to Chemical kinetics

 

Introduction

Chemical kinetics is the branch of physical chemistry which deals with a study of the speed of chemical reactions. Such studies also enable us to understand the mechanism by which the reactions occur. In chemical equilibria, only the initial and final states were considered, the energy relations between the reactants and the products being governed by thermodynamics where the time or the intermediate states were of no concern. In chemical kinetics the rate of the reaction process is followed; in other words, the time variable is introduced. This, we shall see, reveals not only the influence of different factors on the progress of the reaction but it also throws light on the mechanism through which reactant molecules are transformed into products.

It is a common knowledge that apart from the chemical nature, the rates of reaction depend on the concentration of reactants and the temperature. It will be seen later that many reaction rates are greatly influenced by the presence of foreign substances i.e., the catalysts. Also some reaction rates are accelerated by absorption of specific light waves, which are called photochemical reactions. The catalysed and photochemical reactions will be dealt with later.

From the kinetic standpoint, the reactions are classified into two groups:

(a) homogeneous reactions which occur entirely within one phase and

(b) heterogeneous reactions where the transformation takes place on the surface of a catalyst or the walls of a container. In the beginning we shall restrict our discussion only to homogeneous reaction kinetics.

Measurement of Reaction Rates

For many reactions, the measurement of the rate of reaction is quite difficult. The ionic reactions and some explosive reactions occur almost instantaneously. The time of mixing the reactants and measuring the change in concentration is greater than the time in which the reaction would be practically complete.

On the other hand, there are reactions which are so slow that months and years are required for any appreciable amount of transformation. In between the very fast and very slow reactions, there are reactions such as, decomposition of HI or H₂O₂, hydrolysis of esters, mutarotation of sugars, etc. for which the speed can be easily measured.

Since the velocity of a reaction is very sensitive to temperature, the rate is invariably studied at a constant temperature by maintaining the reaction mixture in a well-controlled thermostat. The decrease in concentration of one or more of the reactants or the increase in concentration of the products is followed at different time intervals. Both chemical as well as physical methods of analysis are employed according to suitability in measuring the change in concentration.

In chemical methods, definite volumes of samples are separated or pipetted out from the reaction mixture from time to time. The samples are immediately chilled and diluted with inert media so as to 'freeze' the reaction. The freezing of the reaction means abruptly slowing down the reaction or practically stopping the reaction in the separated sample. These samples are then quickly estimated, very often by titration with suitable reagents.

Use of physical methods is often taken recourse to as these are more convenient and accurate. The physical measurement is made with the reaction mixture as such and the change in concentration of the reactant or the product with time is deduced directly therefrom. Any physical property of a constituent of the system which changes with the progress of reaction may be taken advantage of. Very frequently, optical rotation, optical density with a specific wavelength, conductivity, refractive index, dielectric constant, colorimetry, light-scattering, etc. Are measured to pursue the variation in concentration with time.

In gaseous reactions which are associated with change in volume, dilatometric method is employed or the pressure-changes at constant volume may be followed at different time intervals. Special techniques have also been employed in recent times to study the kinetics of very fast reactions, which will be discussed later.

Molecularity of a Reaction

The molecularity of a reaction is defined as the number of molecules or atoms which take part in the process of a chemical change. The reactions are said to be unimolecular, bimolecular or termolecular according as one, two or three molecules are involved in the act leading to a chemical change.

In the early days, no distinction was made between the order and the molecularity of a reaction. The term 'unimolecular' was used for all 1st order reactions, the term 'bimolecular' for 2nd order etc. But the term molecularity, as distinct from the order, of a reaction is now applied in explaining the mechanism of the reaction.

In the decomposition of hydrogen-iodide, it is believed that when two molecules having sufficient energy come together or collide, the bonds between hydrogen and iodine snap and new bonds between H-atoms and between I-atoms are formed, leading to the dissociation. Since two molecules are involved, it is a bimolecular reaction.

H–I + H–I → H–H + I–I

2HI → H₂ + I₂

Incidentally, the dissociation of hydrogen-iodide is also a second order reaction. In fact all bimolecular reactions are of the second order but all second order reactions are not necessarily bimolecular.

Again, the disintegration of thorium atom as

Th → Msthl + α

takes place singly and independently. It is thus a unimolecular reaction. This is also a 1st order reaction.

For relatively simple reactions or isolated reactions in which the reactants are directly transformed into product without any intermediate step, the molecularity can be easily defined. But it it now generally known that most of the reactions do occur in a sequence of steps, each step is called an elementary process. Every step or elementary process has its molecularity. As such it is not desirable to express molecularity for the overall reaction, as one elementary process may involve two molecules and another step only one molecule.

The molecularity must be integral but the order may be fractional also. Whereas the order of a reaction is obtained from the experimental results, the molecularity is given on the basis of some proposed theoretical mechanism so as to satisfy the experimental findings.

There is also no correlation between the order and the molecularity of a reaction or between the stoichiometric representation and the molecularity. Thus the decomposition of nitrogen pentoxide stoichiometrically represented as:

2N₂O₅ = 4NO₂ + O₂

has been found to be of the first order and is believed to have the mechanism as suggested by Ogg (1974):

(i) N2O5 = NO2+NO2

(ii) NO2+NO3 = NO2+O2+NO

(iii) NO+N2O5 = 3NO2

(iv) NO2+NO3 = N2O5

some steps are bimolecular, and one unimolecular. But often the molecularity of the slowest step in a sequence of steps is found to be the order of the overall reaction.

Rate of a Reaction

The rate of a reaction, i.e., the velocity of a reaction is the amount of chemical change occurring per unit time. The rate is generally expressed as the decrease in concentration of reactant or as the increase in concentration of a product per unit time. So, if ‘c’ is the concentration of a chosen reactant at any time t, the rate is

−dc/dt

Or, if the concentration of a product be x at any time t, the rate would be

dx/dt

The reactant or the product chosen should be specified. The time is usually expressed in seconds. The rate will have units of concentration divided by time. The concentrations are taken in gm-moles/litre, hence rate is moles per litre per second.

Order of a Reaction

By stating the order of a reaction, the quantitative dependence of its rate on the concentrations of a reacting substance can be indicated. The order is the number of concentration terms on which reaction rate depends. Thus, if the rate of a reaction depends on the first power of the concentration of reactant, i.e.

Rate = kC₁,

then the reaction is said to be of the first order. When the rate is proportional to the product of two reactant concentrations or the square of the concentration of a reactant, the reaction is of the second order. For example, the decomposition of hydroiodic acid,

2HI → H₂ + I₂,

is given by,

Rate = kC²_HI

and the hydrogen-iodine reaction,

H₂ + I₂ → 2HI,

is found to follow,

Rate = kC[H₂] C[I₂]

Both are second order reactions. Hence, if the reaction rate is experimentally found to be represented by

−dc/dt = kCⁿ 

the order of the reaction is n. Generally speaking, if several reactants A, B, C, etc. are involved and it is observed experimentally that the rate of the process is given by

−dc/dt = kC_A^α C_B^β C_C^γ 

then the order of the reaction would be n = α + β + γ + .... The reaction is said to be of the α-th order with respect to A, the β-th order with respect to B, etc.

The order of a reaction may thus be defined as the sum of the exponents of the concentration terms in the rate equation.

Through theoretically reactions of high order are possible, but it is doubtful if reactions higher than third order exist. But there are reactions in which the order is fractional, i.e., n = 3/2 etc. For instance, the ortho-para hydrogen conversion has its rate expressed by

−d[H₂]/dt = kC_H₂^3/2

In some heterogeneous or surface reactions, the rate has been found to be independent of concentration. These are zero-order reactions. It is important to realise that the order of a reaction and the rate equations are derived from experimental results. Any attempt or theory proposed to explain the mechanism of a chemical process must satisfy the rate equations experimentally observed.

It is also seen that there is no necessary connection between the kinetic order and the form of the stoichiometric equation of a reaction.

For the reaction,

2N₂O₅ → 4NO₂ + O₂,

the order is one. Again, for the reaction

CH₃CHO → CH₄ + CO,

the order is three halves (3/2).