A first order gaseous reaction is $25 \%$ complete in 30 minutes at 227 oC and in 10 minutes at $237^{\circ} \mathrm{C}$. The activation energy of the reaction is closest to $\left(\mathrm{R}=2 \mathrm{cal} \mathrm{K}^{-1} \mathrm{mol}^{-1}\right)$
(a)$27 \mathrm{kcal} \mathrm{mol}^{-1}$
(b)$110 \mathrm{kcal} \mathrm{mol}^{-1}$
(c)$55 \mathrm{kcal} \mathrm{mol}^{-1}$
(d)$5.5 \mathrm{kcal} \mathrm{mol}^{-1}$
Answer
Answer: C ✓ checked by 4AB · confidence high
The source book printed no answer; this one was worked out and checked — see the explanation.
Explanation
Same fractional conversion in 30 vs 10 min ⇒ k₂/k₁ = 3. ln 3 = (Ea/R)(1/500 − 1/510) = (Ea/2)(3.92×10⁻⁵) ⇒ Ea = 56,000 cal ≈ 55 kcal mol⁻¹.