JEE Main 2025 · Chemistry · Chemical Kinetics · easy

A substance A decomposes by two parallel first-order paths, Axrightarrowk1B and Axrightarrowk2C. The ratio [B]/[C] is found to be 3 throughout, and…

Single correct option

A substance A decomposes by two parallel first-order paths,

\mathrm{A}\xrightarrow{k_1}\mathrm{B}

and

\mathrm{A}\xrightarrow{k_2}\mathrm{C}

. The ratio

[\mathrm{B}]/[\mathrm{C}]

is found to be

3

throughout, and the half-life for the disappearance of A is

6.93\ \mathrm{min}

. The value of

k_1

\mathrm{min^{-1}}

is (

\ln2=0.693

)

Show answer and solution

Answer: (B) $0.075$

For parallel first-order reactions A disappears with

k=k_1+k_2

, so

k=0.693/6.93=0.100\ \mathrm{min^{-1}}

. The product ratio equals the rate-constant ratio:

k_1/k_2=3

. Hence

k_1=\frac34(0.100)=0.075\ \mathrm{min^{-1}}

and

k_2=0.025

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