Chemical Kinetics

After studying this Unit, you will be able to

Chemical Kinetics helps us to understand how chemical reactions occur.

Chemistry, by its very nature, is concerned with change. Substances with well defined properties are converted by chemical reactions into other substances with different properties. For any chemical reaction, chemists try to find out (a) the feasibility of a chemical reaction which can be predicted by thermodynamics ( as you know that a reaction with $\Delta G<0$, at constant temperature and pressure is feasible); (b) extent to which a reaction will proceed can be determined from chemical equilibrium; (c) speed of a reaction i.e. time taken by a reaction to reach equilibrium. Along with feasibility and extent, it is equally important to know the rate and the factors controlling the rate of a chemical reaction for its complete understanding. For example, which parameters determine as to how rapidly food gets spoiled? How to design a rapidly setting material for dental filling? Or what controls the rate at which fuel burns in an auto engine? All these questions can be answered by the branch of chemistry, which deals with the study of reaction rates and their mechanisms, called chemical kinetics. The word kinetics is derived from the Greek word ‘kinesis’ meaning movement. Thermodynamics tells only about the feasibility of a reaction whereas chemical kinetics tells about the rate of a reaction. For example, thermodynamic data indicate that diamond shall convert to graphite but in reality the conversion rate is so slow that the change is not perceptible at all. Therefore, most people think

that diamond is forever. Kinetic studies not only help us to determine the speed or rate of a chemical reaction but also describe the conditions by which the reaction rates can be altered. The factors such as concentration, temperature, pressure and catalyst affect the rate of a reaction. At the macroscopic level, we are interested in amounts reacted or formed and the rates of their consumption or formation. At the molecular level, the reaction mechanisms involving orientation and energy of molecules undergoing collisions, are discussed. In this Unit, we shall be dealing with average and instantaneous rate of reaction and the factors affecting these. Some elementary ideas about the collision theory of reaction rates are also given. However, in order to understand all these, let us first learn about the reaction rate.

Some reactions such as ionic reactions occur very fast, for example, precipitation of silver chloride occurs instantaneously by mixing of aqueous solutions of silver nitrate and sodium chloride. On the other hand, some reactions are very slow, for example, rusting of iron in the presence of air and moisture. Also there are reactions like inversion of cane sugar and hydrolysis of starch, which proceed with a moderate speed. Can you think of more examples from each category? You must be knowing that speed of an automobile is expressed in terms of change in the position or distance covered by it in a certain period of time. Similarly, the speed of a reaction or the rate of a reaction can be defined as the change in concentration of a reactant or product in unit time. To be more specific, it can be expressed in terms of: (i) the rate of decrease in concentration of any one of the reactants, or (ii) the rate of increase in concentration of any one of the products. Consider a hypothetical reaction, assuming that the volume of the system remains constant. $\text{ce}R->P$ One mole of the reactant R produces one mole of the product P. If $[\text{ce}R{]}_1$ and $[\text{ce}P{]}_1$ are the concentrations of R and P respectively at time $t_1$ and $[\text{ce}R{]}_2$ and $[\text{ce}P{]}_2$ are their concentrations at time $t_2$ then,

$\Delta t=t_2-t_1$ $\Delta [\text{ce}R]=[\text{ce}R{]}_2-[\text{ce}R{]}_1$ $\Delta [\text{ce}P]=[\text{ce}P{]}_2-[\text{ce}P{]}_1$ The square brackets in the above expressions are used to express molar concentration.

Rate of disappearance of R

$=-\frac{\text{Decrease in concentration of R}}{\text{Time taken}}=-\frac{\Delta [\text{ce}R]}{\Delta t}(3.1)$

Rate of appearance of P

$=+\frac{\text{Increase in concentration of P}}{\text{Time taken}}=+\frac{\Delta [\text{ce}P]}{\Delta t}(3.2)$

Since, $\Delta [\text{ce}R]$ is a negative quantity (as concentration of reactants is decreasing), it is multiplied with –1 to make the rate of the reaction a positive quantity. Equations (3.1) and (3.2) given above represent the average rate of a reaction, $r_{av}$. Average rate depends upon the change in concentration of reactants or products and the time taken for that change to occur (Fig. 3.1).

Units of rate of a reaction From equations (3.1) and (3.2), it is clear that units of rate are concentration time${}^{-1}$. For example, if concentration is in mol L${}^{-1}$ and time is in seconds then the units will be mol L${}^{-1}$s${}^{-1}$. However, in gaseous reactions, when the concentration of gases is expressed in terms of their partial pressures, then the units of the rate equation will be atm s${}^{-1}$.

From the concentrations of $\text{ce}C4H9Cl$ (butyl chloride) at different times given below, calculate the average rate of the reaction:

during different intervals of time.

We can determine the difference in concentration over different intervals of time and thus determine the average rate by dividing $\Delta [\text{ce}R]$ by $\Delta t$ (Table 3.1).

It can be seen (Table 3.1) that the average rate falls from $1.90\times 10^{-4}$ mol L${}^{-1}$s${}^{-1}$ to $0.4\times 10^{-4}$ mol L${}^{-1}$s${}^{-1}$. However, average rate cannot be used to predict the rate of a reaction at a particular instant as it would be constant for the time interval for which it is calculated. So, to express the rate at a particular moment of time we determine the instantaneous rate. It is obtained when we consider the average rate at the smallest time interval say $dt$ ( i.e. when $\Delta t$ approaches zero). Hence, mathematically for an infinitesimally small $dt$ instantaneous rate is given by

$r_{av}=-\frac{\Delta [\text{ce}R]}{\Delta t}=+\frac{\Delta [\text{ce}P]}{\Delta t}(3.3)$

As $\Delta t\to 0$ or $r_{inst}=-\frac{d[\text{ce}R]}{dt}=+\frac{d[\text{ce}P]}{dt}$

It can be determined graphically by drawing a tangent at time $t$ on either of the curves for concentration of R and P vs time $t$ and calculating its slope (Fig. 3.1). So in problem 3.1, $r_{inst}$ at 600s for example, can be calculated by plotting concentration of butyl chloride as a function of time. A tangent is drawn that touches the curve at $t=600$ s (Fig. 3.2).

The slope of this tangent gives the instantaneous rate.

$=-\frac{(0.0165-0.037)}{(900-400)\text{s}}{\text{mol L}}^{-1}=5.12\times 10^{-5}{\text{mol L}}^{-1}{\text{s}}^{-1}$

So, $r_{inst}$ at 600 s $=$

At $t=250$ s\quad $r_{inst}=1.22\times 10^{-4}{\text{mol L}}^{-1}{\text{s}}^{-1}$

$t=350$ s\quad $r_{inst}=1.0\times 10^{-4}{\text{mol L}}^{-1}{\text{s}}^{-1}$

$t=450$ s\quad $r_{inst}=6.4\times 10^{-5}{\text{mol L}}^{-1}{\text{s}}^{-1}$

Now consider a reaction

$\text{ce}Hg(l)+Cl2(g)->HgCl2(s)$

Where stoichiometric coefficients of the reactants and products are same, then rate of the reaction is given as

i.e., rate of disappearance of any of the reactants is same as the rate of appearance of the products. But in the following reaction, two moles of HI decompose to produce one mole each of $\text{ce}H2$ and $\text{ce}I2$, $\text{ce}2HI(g)->H2(g)+I2(g)$

Similarly, for the reaction

$\text{ce}5B{r}^{-}(aq)+BrO{3}^{-}(aq)+6H^{+}(aq)->3Br2(aq)+3H2O(l)$

For a gaseous reaction at constant temperature, concentration is directly proportional to the partial pressure of a species and hence, rate can also be expressed as rate of change in partial pressure of the reactant or the product.

The decomposition of $\text{ce}N2O5$ in $\text{ce}CCl4$ at 318K has been studied by monitoring the concentration of $\text{ce}N2O5$ in the solution. Initially the concentration of $\text{ce}N2O5$ is $2.33{\text{mol L}}^{-1}$ and after 184 minutes, it is reduced to $2.08{\text{mol L}}^{-1}$. The reaction takes place according to the equation

Calculate the average rate of this reaction in terms of hours, minutes and seconds. What is the rate of production of $\text{ce}NO2$ during this period?

It may be remembered that

3.1 For the reaction $\text{ce}R->P$, the concentration of a reactant changes from 0.03M to 0.02M in 25 minutes. Calculate the average rate of reaction using units of time both in minutes and seconds.

3.2 In a reaction, $\text{ce}2A->Products$, the concentration of A decreases from $0.5{\text{mol L}}^{-1}$ to $0.4{\text{mol L}}^{-1}$ in 10 minutes. Calculate the rate during this interval?

Rate of reaction depends upon the experimental conditions such as concentration of reactants (pressure in case of gases), temperature and catalyst.

The rate of a chemical reaction at a given temperature may depend on the concentration of one or more reactants and products. The representation of rate of reaction in terms of concentration of the reactants is known as rate law. It is also called as rate equation or rate expression.

The results in Table 3.1 clearly show that rate of a reaction decreases with the passage of time as the concentration of reactants decrease. Conversely, rates generally increase when reactant concentrations increase. So, rate of a reaction depends upon the concentration of reactants.

Consider a general reaction

where $a$, $b$, $c$ and $d$ are the stoichiometric coefficients of reactants and products. The rate expression for this reaction is $\text{Rate}\propto [\text{ce}A{]}^x[\text{ce}B{]}^y(3.4)$ where exponents $x$ and $y$ may or may not be equal to the stoichiometric coefficients ($a$ and $b$) of the reactants. Above equation can also be written as $\text{Rate}=k[\text{ce}A{]}^x[\text{ce}B{]}^y(3.4a)$ $-\frac{d[\text{ce}R]}{dt}=k[\text{ce}A{]}^x[\text{ce}B{]}^y(3.4b)$

This form of equation (3.4 b) is known as differential rate equation, where $k$ is a proportionality constant called rate constant. The equation like (3.4), which relates the rate of a reaction to concentration of reactants is called rate law or rate expression. Thus, rate law is the expression in which reaction rate is given in terms of molar concentration of reactants with each term raised to some power, which may or may not be same as the stoichiometric coefficient of the reacting species in a balanced chemical equation. For example:

We can measure the rate of this reaction as a function of initial concentrations either by keeping the concentration of one of the reactants constant and changing the concentration of the other reactant or by changing the concentration of both the reactants. The following results are obtained (Table 3.2).