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A first order reaction is 50% complete in 30 minutes at 300 K and in 10 minutes at 320 K. The activation energy of the reaction ($E_a$) is: [R = 314 J K$^{-1}$ mol$^{-1}$, log 2 = 3010; log 3 = 4771]
A first order reaction is 50% complete in 30 minutes at 300 K and in 10 minutes at 320 K. The activation energy of the reaction ($E_a$) is: [R = 314 J K$^{-1}$ mol$^{-1}$, log 2 = 3010; log 3 = 4771]
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Since rate constant $k$ is inversely proportional to half-life, a decrease in half-life from 30 to 10 minutes means the reaction rate tripled ($k_2/k_1 = 3$). Plugging $\log 3 \approx 0.477$ straight into the simplified Arrhenius multiplier leads directly to $43.8\text{ kJ mol}^{-1}$.
Updated On: May 16, 2026
- $75.2\text{ kJ mol}^{-1}$
- $43.8\text{ kJ mol}^{-1}$
- $23.7\text{ kJ mol}^{-1}$
- $52.5\text{ kJ mol}^{-1}$
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The Correct Option is B
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