Based on their rate laws, arrange the following reactions in the decreasing sequence of the reaction order.

(A) Rate = $k [A]^{3/2} [B]^{-1}$
(B) Rate = $k [CHCl_3] [Cl_2]^{1/2}$
(C) Rate = $k [CH_3COOC_2H_5] [H_2O]^0$
(D) Rate = $k [A]^{1/2} [B]^{3/2}$

Choose the correct answer from the options given below:

(D), (B), (C), (A)

The correct answer is Option (3) → (D), (B), (C), (A)

First, find the order of each reaction by adding the powers of concentrations in the rate law.

Calculate reaction orders

(A)

$\text{Rate} = k[A]^{3/2}[B]^{-1}$

Order = $\frac{3}{2} - 1 = \frac{1}{2}$​

(B)

$\text{Rate} = k[\text{CHCl}_3][\text{Cl}_2]^{1/2}$

Order = $1 + \frac{1}{2} = \frac{3}{2}$​

(C)

$\text{Rate} = k[\text{CH}_3\text{COOC}_2\text{H}_5][\text{H}_2\text{O}]^{0}$

Order = 1 + 0 = 1

(D)

$\text{Rate} = k[A]^{1/2}[B]^{3/2}$

Order = $\frac{1}{2} + \frac{3}{2} = 2$

Decreasing order of reaction order

$(D)\; (2) > (B)\; (1.5) > (C)\; (1) > (A)\; (0.5)$

Correct answer: (D), (B), (C), (A)