Initial Rate Method

This method is used for reactions where more than one reactant species are involved. Initial rates of the reaction are determined by varying the concentration of only one reactant while keeping the concentrations of other reactants constant. Initial rate of reaction corresponds to the rate at the start of the reaction. The rate is calculated over the first smallest possible time interval. This calculation is done either graphically or numerically.

The same procedure is repeated for other reactants and the corresponding initial rates are determined. After all the relevant data are collected, order of the reaction is calculated using the relation,

where m is the order with respect to the reactant A. This relation is derived as follows:

Suppose, the initial rate of a reaction is given by,

Now, if the concentration of [B]_o and [C]_o are kept constant, then the initial rate (new) is

Now, this new initial rate is measured for two different initial concentrations of A, that is, [A_o]₁, [A_o]₂ such that

Now the value of m can be obtained by dividing equation ( ) by equation

The same calculation is used for the other reactants and their corresponding orders are determined. The overall order of the reaction is then given by (m + n + p ……)

Example 9:

Nitric oxide NO reacts with chlorine Cl₂ to form NOCl initial rates were measured at two different initial concentrations of nitric oxide and chlorine data obtained is given below.

Suggested answer:

The order of the reaction with respect to Cl₂ is determined by using the rates obtained in experiment 1 and 3.

Let the rate law be rate = k [NO]^m [Cl₂]ⁿ

or n = 1

The value of m is now determined by taking the ratio of the rates from experiments 2 and 3.

or m = 2

Therefore the probable rate law for the reaction is

Rate = k [NO₂]² [Cl₂]¹

Hence, overall order of the reaction is 3.