Question

Consider the reaction A + B ---> products

From the following data obtained at a certain temperature, determine the rate law, the order of the reaction, and calculate the rate constant k.

Experiment 1: [A] = 1.50 M; [B] = 1.50 M; Initial Rate = 3.20 x 10-1 M/s

Experiment 2: [A] = 1.50 M; [B] = 2.50 M; Initial Rate = 3.20 x 10-1 M/s

Experiment 3: [A] = 3.00 M; [B] = 1.50 M; Initial Rate = 6.40 x 10-1 M/s

Answer 1

$Rate = k[A]^a[B]^b$

$\frac{Rate_1}{Rate_2} = (\frac{[A_2]}{[A_1]})^a \times (\frac{[B_2]}{[B_1]})^b$

$\frac{3.2 \times 10^{-1}}{3.2 \times 10^{-1}} = (\frac{[1.5]}{[1.5]})^a \times (\frac{[2.5]}{[1.5]})^b$

$1 = 1^a \times 1.67^b$

b =0

$\frac{Rate_3}{Rate_1} = (\frac{[A_3]}{[A_1]})^a \times (\frac{[B_3]}{[B_1]})^b$

$\frac{6.4 \times 10^{-1}}{3.2 \times 10^{-1}} = (\frac{[3.0]}{[1.5]})^a \times (\frac{[1.5]}{[1.5]})^b$

$2 = 2^a \times 1^b$

a = 1

Rate = k[A]

Overall order of reaction = a + b = 1 + 0 = 1

Reaction is the first order.

Substituting values from Exp. 1 into the rate low:

$3.2 \times 10^{-1} = k \times 1.5$

$k = 0.213 \;s^{-1} = 2.13 \times 10^{-1} \;s^{-1}$