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:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (D), (B), (C), (A)
The order of a reaction is the sum of the powers of the concentration terms in the rate law. For Rate \( = k[\mathrm{A}]^{x}[\mathrm{B}]^{y} \) the order is \( x + y \). The powers come from experiment: they can be fractions, zero or even negative.
(A) Rate \( = k[\mathrm{A}]^{3/2}[\mathrm{B}]^{-1} \): order \( = \frac{3}{2} + (-1) = \frac{1}{2} \)
(B) Rate \( = k[\ce{CHCl3}][\ce{Cl2}]^{1/2} \): order \( = 1 + \frac{1}{2} = \frac{3}{2} \)
(C) Rate \( = k[\ce{CH3COOC2H5}][\ce{H2O}]^{0} \): order \( = 1 + 0 = 1 \)
(D) Rate \( = k[\mathrm{A}]^{1/2}[\mathrm{B}]^{3/2} \): order \( = \frac{1}{2} + \frac{3}{2} = 2 \)
Shortcut: (D) has the highest order and (A) the lowest, so the sequence starts with (D) and ends with (A): Options (2) and (3). Since (B), 3/2, is higher than (C), 1, Option (3) remains.