Question

For the reaction A + B $\to$ Products, the following initial rates were obtained at various initial concentrations of reactants:

Reaction Rate Data

Sl. No.	[A] (mol L−1)	[B] (mol L−1)	Initial rate (mol L−1 s−1)
1	0.1	0.1	0.05
2	0.2	0.1	0.10
3	0.1	0.2	0.05

Hint:

When comparing experiments to determine the order of a reaction, keep the concentration of one reactant constant while varying the other.

Answer 1

The rate law for the reaction can be expressed as: \[ \text{Rate} = k[A]^m[B]^n \] Where: - \( m \) is the order of the reaction with respect to A, - \( n \) is the order of the reaction with respect to B, - \( k \) is the rate constant. To determine the order of the reaction with respect to A and B, we will compare experiments where the concentration of one reactant is changed while the other is kept constant. ### Step 1: Determine the order with respect to A: Comparing the first and second experiments: \[ \frac{\text{Rate}_2}{\text{Rate}_1} = \frac{k[A_2]^m[B_2]^n}{k[A_1]^m[B_1]^n} = \frac{0.10}{0.05} = 2 \] Substitute the known values: \[ \frac{[A_2]^m}{[A_1]^m} = \frac{2}{1} \quad \text{and} \quad [B_2] = [B_1] = 0.1 \] Thus, \[ \left(\frac{0.2}{0.1}\right)^m = 2 \quad \Rightarrow \quad 2^m = 2 \] So, \( m = 1 \). ### Step 2: Determine the order with respect to B: Comparing the first and third experiments: \[ \frac{\text{Rate}_3}{\text{Rate}_1} = \frac{k[A_3]^m[B_3]^n}{k[A_1]^m[B_1]^n} = \frac{0.05}{0.05} = 1 \] Substitute the known values: \[ \frac{[A_3]^m}{[A_1]^m} = \frac{1}{1} \quad \text{and} \quad \frac{[B_3]^n}{[B_1]^n} = 1 \] Thus, \[ \left(\frac{0.2}{0.1}\right)^n = 1 \quad \Rightarrow \quad 2^n = 1 \] So, \( n = 0 \). ### Step 3: Overall order of the reaction: The overall order of the reaction is the sum of the individual orders with respect to A and B: \[ \text{Overall order} = m + n = 1 + 0 = 1 \] Thus, the order of the reaction with respect to A is 1, with respect to B is 0, and the overall order of the reaction is 1.