Answer
e) is the correct answer.
Work Step by Step
1. $rate = k[A]^x[B]^y$
2. Divide rate1 by rate2:
$$\frac{rate_1}{rate_2} = \frac{k(0.12)^x(0.010)^y}{k(0.36)^x(0.010)^y} =\frac{(0.12)^x}{(0.36)^x} = (1/3)^x$$
$$\frac{rate_1}{rate_2} = \frac{2.2 \times 10^{-3} }{6.6 \times 10^{-3}} = 1/3$$
$$ (1/3)^x = 1/3$$
x must be equal to 1.
3. Do the same thing for 1 and 3:
$$\frac{rate_1}{rate_2} = \frac{k(0.12)^x(0.010)^y}{k(0.12)^x(0.020)^y} =\frac{(0.010)^y}{(0.020)^y} = (1/2)^y$$
$$\frac{rate_1}{rate_2} = \frac{2.2 \times 10^{-3} }{2.2 \times 10^{-3}} = 1$$
$$ (1/2)^y = 1$$
y must be qual to 0.
$$rate = k[A]^1[B]^0 = k[A]$$
