Question

Describe the integrated rate law method for determining the order of a reaction.

Answer 1

This is the most common method employed for the study of the kinetics of a chemical reaction.

For a reaction

\[\ce{A -> products}\]

The rate law is

\[\ce{Rate = -\frac{d[A]}{dt} = k[A]^n}\]

For first order reactions:

[A] = [A]₀ − kt

If the plot is a straight line, the reaction is zero order.

For first order reactions:

The integrated rate equation for a first order reaction can be represented in the following forms.

[A] = [A]₀​ e^−kt

\[\ce{k = \frac{2.303}{t} log_10 \frac{[A]_0}{[A]}}\]

\[\ce{k = \frac{2.303}{t} log_10 \frac{a}{a - x}}\]

For second order reactions:

For a second order reaction of the type \[\ce{2A -> Products}\], the integrated rate equation is as follows.

\[\ce{k = \frac{1}{t} \times \frac{x}{a(a - x)}}\]

where,

k = Rate constant of the second order reaction

a = Initial concentration of A in mol L⁻¹

a − x = Concentration in mol L⁻¹ of A after time t.