For the decomposition of azomethane. $\mathrm{CH}_{3} \mathrm{~N}_{2} \mathrm{CH}_{3}(\mathrm{~g}) \rightarrow \mathrm{CH}_{3} \mathrm{CH}_{3}(\mathrm{~g})+\mathrm{N}_{2}(\mathrm{~g})$ a first order reaction, the variation in partial pressure with time at 600 K is given as The half life of the reaction is \_\_\_\_ $\times 10^{-5} \mathrm{~s}$. [Nearest integer]

JEE Main · 2022 · 25 Jul 2022 · Shift 2 · Chemical Kinetics

For the decomposition of azomethane.

CH_{3} N_{2} CH_{3} (g) \to CH_{3} CH_{3} (g) + N_{2} (g)

a first order reaction, the variation in partial pressure with time at 600 K is given as

The half life of the reaction is ____

\times 1 0^{- 5} s

.
[Nearest integer]

Answer: 2

For a first-order reaction, the rate constant

k

is related to the half-life by

t_{1/2} = \frac{l n 2}{k} = \frac{0.693}{k}

. From the given data (pressure vs time plot), the rate constant

k = 3.465 \times 1 0^{4} s^{- 1}

. Therefore,

t_{1/2} = \frac{0.693}{3.465 \times 1 0 ^{4}} = 2 \times 1 0^{- 5} s

. The answer is 2.

JEE Main · 2022 · 25 Jul 2022 · Shift 2 · Integer answer