Chemical Kinetics Branch of physical chemistry that deals with the rate of reaction and the factors influencing the rate of reaction.

Types of Chemical Reaction

1.) Very fast ( instantaneous ) reaction Reaction is so fast , that the determination of rate of reaction is difficult Involve ionic species Occurs within 10-14 to 10-16

Ex.) NaCl + HCl NaCl + H2O BaCl2 + H2SO4 BaSO4 + 2HCl

2.) Very Slow Reaction Reaction is extremely slow Determination of rate of reaction is difficult task Take months to show measurable change

Ex.) Rusting of iron

3.) Normal / Moderate Reactions Occurs at moderate and measurable rates at room temperature Study of kinetics is simple

Ex.) 2N2O5 4NO2 + O2

PCl5 PCl3 + Cl2

Rate Of reaction

Rate means speed. Speed involves time (t). Therefore, the study of chemical kinetics involves time. The rate of a reaction is often called the reaction rate.

The reaction rate is a measure of the change in the concentration of a reactant or product with time. The concentration of a reactant or product is expressed as molarity ( expressed in [ ] ) .

i) Average Rate Rate measured over a long time interval.

Here , Δ [ ] means the change in concentration ( Δ[ ] = [ ] Final – [ ] Initial )

- sign represents concentration of reactant decreases with increase in time

+ sign represents concentration of product increases with increase in time

ii) Instantaneous Rate

Rate measured over a very small interval of time ( rate at any particular instant ).

For the reaction : R P

The tangent at any point on the graph gives it`s rate of reaction.

iii) Initial Rate

The slope or tangent of the graph between the concentration and time at t = 0 sec .

iv) For the reaction m1 A + m2 B n1C + n2 D

v) Unit of rate of reaction

Rate Law and Rate constant

The relationship between the rate of reaction and concentration of the reactants is known as rate law or rate expression.

It can be derieved only by performing experiments.

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 the reaction , m1 A + m2 B P

Where k is Rate constant

- Rate law equation is applicable only for slowest step and it is also called rate determining step.- If the concentration of all the reactants is 1 , then the rate of reaction is equal to rate constant.

Elementary Reaction

The reaction that takes place in a single step and no intermediate product is produced is called Elementary Reaction.

m1 A + m2 B P

Complex Reaction

The reaction that takes place in two or more steps and intermediate product is produced is called Complex Reaction.

For the reaction : 2A + B D + E

Mechanism :

A + B C + D ( slow )

A + C E ( fast )

----- rate depends on slowest step only

Order Of a Reaction

The sum of the exponents by which the concentration terms are raised in the rate law is known as order of the reaction.

It is an experimental quantity and can be predicted by balanced chemical equations.

For the reaction , m1 A + m2 B P

- Order of reaction can be 0 , positive , negative or can be fractional values.- Generally , maximum order is 3.

Unit of Rate Constant

For the reaction , m1 A + m2 B P

Molecularity of a Reaction

The number of atoms , ions or molecules taking part in an elementary reaction is called molecularity of a reaction.

It is a theoretical concept and it is defined as the sum of the number of molecules participating in a balanced chemical reaction.

Molecularity of a reaction cannot be zero , negative or fractions values.

It can be determined just by the balanced chemical reaction.

Generally , maximum molecularity of a reaction is 3.

Ex.) PCl5 PCl3 + Cl2 M = 1 Unimolecular

H2 + I2 2 HI M = 2 Bimolecular

2FeCl3 + SnCl2 2 FeCl2 + SnCl4 M = 3 Trimolecular

Integrated Rate Law

The differential rate law describes how the rate of reaction varies with the concentrations of reactants.

Consider the reaction, A   →   B

Rate of the reaction ,

Suppose this reaction obeys a first-order rate law: r = k [A]

Rate law can also be written as ,

This equation is a differential equation that relates the rate of change in a concentration to the concentration itself.

Integration of this equation produces the corresponding integrated rate law, which relates the concentration to time.

At t = 0, the concentration of A is [A]0. The integrated rate law is thus

Zero Order Reaction

R P

First Order Reaction

Pseudo First Order Reactions

A Pseudo Order Reaction is the reaction where the order of reaction is less than the normal order.

There are circumstances where a second order reaction might appear, in an experiment, to be first order. That is when one of the reactants in the rate equation is present in great excess over the other in the reaction mixture.

For example, A + B C [ a second order reaction ]

If [ B ] >>> [ A ] , then [ B ] would be essentially unchanged and could be considered to be essentially a constant  and the reaction could be considered pseudo first order with respect to [A].

Collision Theory

This theory is based on the idea that reactant particles must collide for a reaction to occur, but only a small percentage of the total collisions ( effective collisions ) have the energy and "orientation" to cause the reactants to form into the products.

Collision theory states that the rate of a chemical reaction is proportional to the number of collisions between reactant molecules.

Requirements for an effective collision (for a chemical reaction to occur):  

1. The reactants must collide with each other. 2. The molecules must have sufficient energy to initiate the reaction (called

activation energy). 3. The molecules must have the proper orientation. 

 

This theory is applicable for bimolecular reactions.

The number of collisions per second per unit volume of the reaction mixture is known as collision frequency ( Z ).

For the reaction , A + B Product

Rate of the reaction is expressed as Where , ZAB is the collision frequency of the reactants Ea is the activation energy R is the gas constant T is the temperature

Effective collision have to cross two barriers :i) Energy Barrierii) Orientation barrier

i) Energy Barrier

a) Threshold Energy The molecules of the reactants must necessarily possess certain minimum value of kinetic energy for the collision with other reactant and to from product .

This minimum energy that the reactant molecules should possess is known as threshold energy

b) Activation Energy

All the molecules will not possess this particular minimum kinetic energy required to form products.

Only few molecules possess this minimum kinetic energy. So for other molecules also to participate in the reaction you need to provide certain extra energy to them by some means which is known as activation energy.

Threshold energy = Average energy of the reactant + Activation energy

ii) Orientation Barrier

Only the proper orientation of the reactant molecules leads to bond formation.

Consider the reaction : CH2=CH2 + HCl CH3CH2Cl

As a result of the collision between the two molecules, the double bond between the two carbons is converted into a single bond. A hydrogen atom gets attached to one of the carbons and a chlorine atom to the other.

The reaction can only happen if the hydrogen end of the H-Cl bond approaches the carbon-carbon double bond. Any other collision between the two molecules doesn't work.

Arrhenius equation

Relationship between the rate a reaction and temperature is determined by the Arrhenius Equation.

Arrhenius Equation , K = A e -Ea / RT

Where , k is the rate constant A is a constant (Arrhenius factor / pre-exponential factor / frequency factor ) Ea is the activation energy R is the universal gas constant T is the temperature (in kelvin)