Question

For the reaction A + B → C; starting with different initial concentration of A and B, initial rate of reaction were determined graphically in four experiments.

Rate law for reaction from above data is

• A. r=k[A]²[B]²
• B. r=k[A][B]²
• C. r=k[A]²[B]
• D. r=k[A][B]

Answer 1

Answer: (C)

r=k[A]²[B]

Answer 2

To determine the rate law, we analyze how the initial concentrations of A and B affect the initial reaction rate.

1. Determining the order with respect to A:
   Compare Experiment 1 and Experiment 2 (only [A] changes):

   \frac{[A]_2}{[A]_1} = \frac{3.2\times10^{-3}}{1.6\times10^{-3}} = 2 \quad \text{and} \quad \frac{\text{Rate}_2}{\text{Rate}_1} = \frac{4\times10^{-3}}{1\times10^{-3}} = 4.
   

   Since $2^x = 4$, $x = 2$. Hence, the reaction is second order in A.

2. Determining the order with respect to B:
   Compare Experiment 1 and Experiment 3 (only [B] changes):

   \frac{[B]_3}{[B]_1} = \frac{1.0\times10^{-1}}{5\times10^{-2}} = 2 \quad \text{and} \quad \frac{\text{Rate}_3}{\text{Rate}_1} = \frac{2\times10^{-3}}{1\times10^{-3}} = 2.
   

   Since $2^y = 2$, $y = 1$. Hence, the reaction is first order in B.

3. Rate Law:
   Combining the orders, the rate law is:

   \text{rate} = k[A]^2[B].
   

   Therefore, the rate law is $r = k[A]^2[B]$.