Question

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

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

Answer 1

Answer: (D)

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

$k_{2}=2.60 \times 10^{-3} s ^{-1}$

$T_{1}=400 \,K$

$T_{2}=500 \,K$

According to Arrhenius equation,

$\log \frac{k_{2}}{k_{1}}=\frac{E_{a}}{2.303 R}\left[\frac{T_{2}-T_{1}}{T_{1} T_{2}}\right]$

$\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} =76.6\, kJ / mol$