$\mathrm{A} \rightarrow \mathrm{B}$ The rate constants of the above reaction at 200 K and 300 K are $0.03 \mathrm{~min}^{-1}$ and $0.05 \mathrm{~min}^{-1}$ respectively. The activation energy for the reaction is ______ J (Nearest integer) (Given: $\ln 10=2.3$ $\mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ $\log 5=0.70$ $\log 3=0.48$ $\log 2=0.30$)

JEE Main · 2023 · 31 Jan 2023 · Shift 1 · Chemical Kinetics

A \to B

The rate constants of the above reaction at 200 K and 300 K are

0.03 min^{- 1}

and

0.05 min^{- 1}

respectively. The activation energy for the reaction is ______ J (Nearest integer)

(Given:

ln 10 = 2.3

R = 8.3 J K^{- 1} mol^{- 1}

lo g 5 = 0.70

lo g 3 = 0.48

lo g 2 = 0.30

)

Answer: 2520

From the Arrhenius equation,

lo g \frac{k _{2}}{k _{1}} = \frac{E _{a}}{2.303 R} (\frac{1}{T _{1}} - \frac{1}{T _{2}})

. Here

lo g \frac{0.05}{0.03} = lo g \frac{5}{3} = 0.70 - 0.48 = 0.22

and

\frac{1}{200} - \frac{1}{300} = \frac{1}{600}

. Hence

0.22 = \frac{E _{a}}{2.303 \times 8.3} \times \frac{1}{600}

, giving

E_{a} = 0.22 \times 19.1 \times 600 \approx 2520 J mo l^{- 1}

JEE Main · 2023 · 31 Jan 2023 · Shift 1 · Integer answer