Rate Law and Rate Constant

Rate law expressions

The rate of a chemical reaction at a given temperature may depend on the concentration of one or more reactants and products.

For the chemical reaction,

where a, b, c and d are the stoichiometric coefficients of reactants and products.

The rate expression for this reaction is

Here exponents x and y may or may not be equal to the stoichiometric coefficients (a and b) of the reactants.

We can write,

where ‘k’ is called the rate constant.

Therefore,

The equation which relates the rate of a reaction to concentration of reactants is called rate law or rate expression.

“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.”

Rate law for any reaction cannot be predicted by merely looking at the balanced chemical equation, i.e., theoretically but must be determined experimentally.

Rate constant 

Rate constant may be defined as the specific rate of reaction when the molar concentrations of the reactants is taken to be unity, i.e.,

Units of rate constant or specific reaction rate for a nth order reaction is given as

If concentration is measured in units of mol·L⁻¹ (abbreviated as M), then

· For order (m + n), the rate constant has units of mol^1−(m+n)·L^(m+n)−1·s⁻¹

· For order zero, the rate constant has units of mol·L⁻¹·s⁻¹ (or M·s⁻¹)

· For order one, the rate constant has units of s⁻¹

· For order two, the rate constant has units of mol⁻¹·L·s⁻¹ (or M⁻¹·s⁻¹)

· For order three, the rate constant has units of mol⁻²·L²·s⁻¹ (or M⁻²·s⁻¹)

Characteristics of rate constant

i. Greater the value of rate constant, faster is the reaction.

ii. Each reaction has a particular value of rate constant at a particular temperature.

iii. The value of rate constant for the same reaction changes with temperature.

iv. The value of rate constant for a reaction doesn’t depend upon the concentration of the reactants.

v. Difference between Rate of Reaction and Rate Constant :

S.No.	Rate of reaction	Reaction rate constant
1	It is speed with which reactants are converted into products.	It is proportionally constant.
2	It is measured as the rate of decrease of concentration of reactants or the rate of increase of concentration of products with time.	It is equal to the rate of reaction when the concentration of each of the reactants in unity.
3	It depends upon the initial concentration of reactants	It is independent of the initial concentration of the reactants. It has a constant value at fixed temperature.