IIT JEE Revision - Rate constant

Rate law

The rate for a reaction is a mathematical expression that relates the rate of reaction to the concentrations of the reactants.

For the reaction aA + bB → products

The rate law is expressed as, rate of reaction is proportional to [A]^x[B]^y.
x and y are determined experimentally. These values can be whole or fractional numbers or zero.

Rate = k[A]^x[B]^y

k = the rate constant.

[A] and [B] are molar concentrations of reactants mol/litre

Units of rate: Rate is the change in concentration with time.

If the concentrations are expressed in moles/litre and time in seconds, then the units for rate of reaction are mol litre^-1 s^-1 or mol L^-1s^-1

Units of rate constant

Units of rate constant are different for different orders of reaction.

For zero order reactions units of rate constant are mol L^-1s^-1

For first order reactions units of rate constant are s^-1

For second order reactions units of rate constant are L mol^-1s^-1

Basically units of rate constant are changing to give the rate of reaction in required units mol L^-1s^-1 (change in concentration with time).

In case of gases, the concentrations are expressed in terms of pressure in the units of atmosphere. Therefore the rate of reaction has the units of atm per second.

Integrated Rate Expressions

For zero order reactions

k₀ = {[A]₀ - [A]}/t

Where k₀ = rate constant in the case of zero order reactions

[A]₀ = Initial concentration of reactant A

[A] = concentration of reactant A at time t.

t = time

This can be alternatively expressed.

a = Initial concentration of reactant A (in moles per litre)

x = moles reactants that changed into products in time t

a-x = concentration of reactant A after time t

k₀ = x/t

Where k₀ = rate constant in the case of zero order reactions

x = moles reactants that changed into products in time t

For first order reactions

k₁ = (2.303/t)log{[A]₀/[A]}

Where k₁ = rate constant for first order equations

Alternative expression

a = Initial concentration of reactant A (in moles per litre)

x = moles reactants that changed into products in time t

a-x = concentration of reactant A after time t

k₁ = (2.303/t)log{a/(a-x)}