Introduction

This article explains how to determine the overall order of reaction from initial rate data for the IIT JAM kinetics
problem involving the reaction A + B → C at 25 °C.

By comparing experimental rates for different initial concentrations of reactants, you can obtain the individual
reaction orders with respect to A and B and hence the overall order of the reaction.

Question statement

In the reaction A + B → C at 25 °C, the initial rate of formation of C is measured for different initial concentrations
of A and B as shown below.

The task is to find the overall order of the reaction with respect to both A and B.

1. Write general rate law

For the reaction A + B → C, assume the rate law:

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

Here, x and y are the reaction orders with respect to A and B, respectively, and k is the rate constant.

2. Find order with respect to A

Choose experiments where [B] is constant and [A] changes. In Experiments 1 and 2, [B] = 0.3 mol L⁻¹.

• Experiment 1: [A]₁ = 0.4, Rate₁ = 0.078
• Experiment 2: [A]₂ = 0.8, Rate₂ = 0.312

Form the rate ratio:

Rate₂ / Rate₁ = k(0.8)^x(0.3)^y / [k(0.4)^x(0.3)^y] = (0.8 / 0.4)^x = 2^x

Numerically, 0.312 / 0.078 = 4, so 2^x = 4 ⇒ x = 2.

Thus, the reaction is second order in A. The same conclusion follows from Experiments 3 and 4 where [B] = 0.6 and [A] doubles from 0.4 to 0.8 while the rate quadruples from 0.156 to 0.624.

3. Find order with respect to B

Next choose experiments where [A] is constant and [B] changes. In Experiments 1 and 3, [A] = 0.4 mol L⁻¹.

• Experiment 1: [B]₁ = 0.3, Rate₁ = 0.078
• Experiment 3: [B]₂ = 0.6, Rate₂ = 0.156

Rate₃ / Rate₁ = k(0.4)^x(0.6)^y / [k(0.4)^x(0.3)^y] = (0.6 / 0.3)^y = 2^y

Numerically, 0.156 / 0.078 = 2, so 2^y = 2 ⇒ y = 1.

Thus, the reaction is first order in B. In Experiments 2 and 4 where [A] = 0.8, doubling [B] from 0.3 to 0.6 also doubles the rate from 0.312 to 0.624, confirming first order in B.

4. Calculate overall order of reaction

The overall order of the reaction is the sum of the individual orders:

Overall order = x + y = 2 + 1 = 3

Hence, the integer answer for the overall order of the reaction A + B → C is 3.

5. Final rate law

The specific rate law for this IIT JAM kinetics problem is:

Rate = k[A]²[B]¹

The overall order of 3 shows that the reaction rate depends quadratically on the concentration of A and linearly on the concentration of B under the given experimental conditions.