For the elementary reaction $\mathbf{M} \rightarrow \mathbf{N}$, the rate of disappearance of $\mathbf{M}$ increases by a factor of 8 upon doubling the concentration of $\mathbf{M}$. The order of the reaction with respect to M is

JEE Advanced · 2014 · 25 May 2014 · Paper 2 · Chemical Kinetics

For the elementary reaction

M \to N

, the rate of disappearance of

M

increases by a factor of 8 upon doubling the concentration of

M

. The order of the reaction with respect to M is

(A)4
(B)3✓ Correct
(C)2
(D)1

Answer: (B)

Solution

For a reaction with rate law

r = k [M]^{x}

, where

x

is the order:

Initial rate:

r_{1} = k [M]^{x}

After doubling concentration:

r_{2} = k [2 M]^{x} = k \cdot 2^{x} [M]^{x}

Given that

r_{2} = 8 r_{1}

k \cdot 2^{x} [M]^{x} = 8 \cdot k [M]^{x}

2^{x} = 8 = 2^{3}

Therefore,

x = 3

. The order of the reaction with respect to M is 3.

JEE Advanced · 2014 · 25 May 2014 · Paper 2 · Single correct option

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