Question

The rate constants for a reaction at $400K$ and $500K$ are $2.60\times 10^{-5}{s}^{-1}$ and $2.60\times 10^{-3}{s}^{-1}$ respectively. The activation energy of the reaction in $kJmo{l}^{-1}$ is

• A. 38.3
• B. 57.4
• C. 114.9
• D. 76.6

Answer 1

Answer: (D)

Given, $k_1=2.60\times 10^{-5}{s}^{-1}$

$k_2=2.60\times 10^{-3}{s}^{-1}$

$T_1=400K$

$T_2=500K$

According to Arrhenius equation,

$\log \frac{k_2}{k_1}=\frac{E_a}{2.303R}\left[\frac{T_2-T_1}{T_1{T}_2}\right]$

$\Rightarrow \log \frac{2.60\times 10^{-3}}{2.60\times 10^{-5}}$

$=\frac{E_a}{2.303\times 8.314}\left[\frac{500-400}{500\times 400}\right]$

$E_a=\frac{2\times 2.303\times 8.314\times 2\times 10^5}{100}$

$E_a=76.6\times 10^{3}J/mol$

$\therefore E_a=76.6kJ/mol$