What is Chemical Kinetics?

Chemistry deals with change of a substance with precise properties to another substance with completely different and new properties via a chemical reaction. For a chemical reaction taking place, we should try to analyze the feasibility of the reaction, extent to which it proceeds and the speed of the reaction. For instance, formation of water from hydrogen and oxygen accompanies decrease in Gibbs free energy indicating the feasibility of the reaction. The equilibrium state of the reaction tells us about the extent of the reaction taking place. But, when hydrogen and oxygen are kept in contact, the reaction does not take place as it is very slow reaction. On other hand, reaction between HCl and AgNO₃ occurs instantaneously. Thus, ‘kinesis’ is a Greek word which means movement. Chemical kinetics deals with the study of the speed of the reaction and other factors which affect the rate of reaction. It also extends towards the mechanism involved in the reaction.

Rate of a Reaction

Rate or speed of any event can be measured by the change of the event at regular time intervals. When the reaction begins, reactants are mixed and there is no products formed. As time increases, the reactants concentration decreases, increasing the concentration of products. Thus, the rate of a reaction can be determined by the rate of change in concentration of products or reactants with respect to time.

$\text{ Rate=}\frac{\text{Conc}\text{. of reacants or products}}{\text{Time duration}}$

The units of rate is given as M sec^-1

M = Molarity -mol litre^-1

In general, the concentration of any compounds is represented with the square brackets. The changes in any quantity of the compounds are represented as delta (Δ) or d. Thus, the rate equation is written as

$\text{Rate= }\frac{\left[\text{Reactant}\right]\text{or }\left[\text{products}\right]}{\text{dt}}$

Consider, the following equation,

$\text{A }\stackrel{}{\to }\text{ B}$

$\text{Rate= }\frac{\left[\text{A}\right]}{\text{dt }}\text{ or }\frac{\left[\text{B}\right]}{\text{dt }}$

where,  [A] – concentration of reactant

            [B] – concentration of products   

  dt – change in time

Similarly, when two different reactants with different moles are involved in the reaction to form products, then the rate of reaction also depends on the number of moles of the reactants involved. Considering the reaction

$\text{A + 2B }\stackrel{}{\to }\text{ 2C + D}$

$\text{Rate= }\frac{\left[\text{A}\right]}{\text{dt}}\text{ = }\frac{\left[\text{B}\right]}{\text{2 x dt}}\text{ = }\frac{\left[\text{C}\right]}{\text{2 x dt}}\text{ = }\frac{\left[\text{D}\right]}{\text{dt}}$

When calculating the rate of reaction with respect to time in terms of disappearance of the reactants, a negative symbol indicating the decrease in concentration is to be considered. 

$\text{Rate= -}\frac{\left[\text{A}\right]}{\text{dt}}\text{ = -}\frac{\left[\text{B}\right]}{\text{2 x dt}}$

Collision Theory

Collision theory helps us to understand what happens between the molecules during a reaction. Based on collision theory, it is said that, the reactant molecules should collide with each other in a proper orientation so as to the reaction should occur. If the orientation of the reactant molecules is not proper, then there is chance of no reaction to occur.

To orient and undergo collision, the reactant molecules should also have a minimum amount of energy. This energy termed as activation energy (E_a) helps the reactant molecules to arrange in proper orientation and undergo collision. If the reactant molecules do not have this minimum energy, then no collision occurs. 

Factors Effecting Rate of Reaction

Various factors affect the rate of reaction. The main important factors on which reaction rate is dependent are:

• Temperature: As temperature increases, the reactant molecules move faster with increase in activation energy leading to greater collision between the reactant molecules. This further increases the formation of the product. Thus, temperature is directly proportional to the rate of reaction.
• Catalyst: In presence of catalyst, the reaction occurs faster or slower than in absence of catalyst. Catalyst alters the reaction without getting consumed. In presence of catalyst, the activation energy is decreased increasing the rate of reaction. 
• Surface area of the reactants: This parameters works for only solids. As the surface area of solid reactant is large, more number of reactant molecules will be present to undergo collision leading to increase in formation of product. This leads to increase in the rate of reaction.
•  Pressure: This parameter holds for only gases. When the pressure is high, there is less space for the molecules to move freely. This leads to easy collision between the molecules. If pressure is low, the space is more for the molecules to move freely which decreases the number of collisions leading to decrease in rate of reaction.
• Concentration of reactants: As the concentration of reactant increases, more number of reactant molecules is present which undergo effective collision increasing the formation of products. Thus as concentration of reactant increases, reaction rate is also expected to increase. 

Rate Law

The dependence of the concentration of the reactants on the reaction rate is explained in terms of rate law. In general, as concentration of reactants increases, rate of reaction also increases. As the reaction progresses, after some time it is noticed that as the reactants are consumed, the rate of reaction decreases indicating that the rate of reaction is directly related to the concentration of the reactants. Thus, rate law depicts the mathematical relationship between the rate of the reaction and concentration of reactants. 

Example: $\text{aA + bB }\stackrel{}{\to }\text{ Products}$

For the above reaction, the rate law is given as

$\begin{array}{l}\text{Rate α }{\left[\text{A}\right]}^{\text{a}}{\left[\text{B}\right]}^{\text{b}}\hfill \\ \text{ Rate =k}{\left[\text{A}\right]}^{\text{a}}{\left[\text{B}\right]}^{\text{b}}\hfill \end{array}$

k is proportionality constant termed as rate constant. Its value is unique and each reaction has its own rate constant. The rate constant value depends on temperature and is independent on concentration of reactants. The units of rate constant k, is based on the order of the reaction. 

The powers of the concentration terms in the rate law (a, b) or the coefficients of the reactants give the order of the reaction with respect to the reactant A and B. The sum of the powers (a + b) gives the overall order of the reaction.

Based on the order of the reaction, the reactions are of zero order reaction, first order reaction, second order reaction.

In a Zero order reaction, the rate constant is independent of the concentration of reactants. So the unit of rate constant is same as that of rate of the reaction.

$\begin{array}{l}\text{Rate =k}{\left[\text{M}\right]}^{\text{o}}\hfill \\ \text{Rate =k}\hfill \\ {\text{Units ofk= mol L}}^{\text{-1}}{\text{s}}^{\text{-1 }}\hfill \end{array}$

In case of first order reaction,

$\begin{array}{l}\text{Rate =k}{\left[\text{M}\right]}^{\text{1}}\hfill \\ {\text{ Mol L}}^{\text{-1}}{\text{s}}^{\text{-1}}{\text{ =kmol L}}^{\text{-1}}\hfill \\ {\text{ So, Units ofk= s}}^{\text{-1 }}\hfill \end{array}$

In case of second order reactions,

$\begin{array}{l}\text{Rate =k}{\left[\text{M}\right]}^{\text{2}}\hfill \\ {\text{Mol L}}^{\text{-1}}{\text{s}}^{\text{-1}}\text{ =k}{\left({\text{mol L}}^{\text{-1}}\right)}^{\text{2}}\hfill \\ {\text{ So, Units ofk= mol}}^{\text{-1}}{\text{L s}}^{\text{-1 }}\hfill \end{array}$

The unit for rate constant for an nth order reaction will be $\text{k= }{\left({\text{mol L}}^{\text{-1}}\right)}^{\text{1-n}}{\text{s}}^{\text{-1}}$

Practice Problems

1. In a reaction X  → Y, the concentration of X decreases from 1.2 M to 1.0 M in 10 min. Calculate the rate of reaction?

Solution:  Given

$\begin{array}{l}\left[\text{X}\right]\text{ = 1}\text{.0 – 1}\text{.2 = 0}\text{.2 }\\ \text{Time }\left(\text{dt}\right)\text{ = 10 min = 10 x 60 = 600 sec}\text{. }\\ \text{= - 0}\text{.2 / 600 = 3}{\text{.33 x 10}}^{\text{-4}}\text{M/s}\end{array}$

Thus the rate of the reaction is found to be 3.33 x 10^-4 M/s.  

2. The rate law of a reaction is given as, $\text{Rate = k }{\left[\text{X}\right]}^{\text{1}}{\left[\text{Y}\right]}^{\text{1/2}}$. What is the order of the reaction?

Solution: Given rate law

$\text{Rate = k }{\left[\text{X}\right]}^{\text{1}}{\left[\text{Y}\right]}^{\text{1/2}}$

    The order of reaction is 3/2.

Context and Applications   

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for 

• B.Sc. in Chemistry
• M.Sc. in Chemistry