JEE Main · 2022 · 26 Jul 2022 · Shift 1 · Chemical Kinetics

For a reaction

A \to 2 B + C

the half lives are 100 s and 50 s when the concentration of reactant A is 0.5 and

1.0 mol L^{- 1}

respectively. The order of the reaction is ______.
(Nearest Integer)

Answer: 2

Solution

For a reaction of order

n

, the half-life is related to initial concentration by:

t_{1/2} \propto \frac{1}{[ A _{0} ] ^{n - 1}}

.

Given:

t_{1/2} = 100

s at

[A_{0}] = 0.5

M, and

t_{1/2} = 50

s at

[A_{0}] = 1.0

M.

Taking the ratio:

\frac{100}{50} = (\frac{1.0}{0.5})^{n - 1}

2 = 2^{n - 1}

n - 1 = 1

n = 2

.

The reaction is second order.

JEE Main · 2022 · 26 Jul 2022 · Shift 1 · Integer answer