The activation energy for the desorption of hydrogen gas from iron and charcoal surfaces are 8.0 and — Surface Chemistry Chemistry Question
Question
The activation energy for the desorption of hydrogen gas from iron and charcoal surfaces are 8.0 and 20.0 kcal/mol, respectively. Assume that the pre-exponential factor have same value of 10¹² s⁻¹, in both, and the ratio of half-lives of hydrogen molecules at the iron and charcoal surfaces is 1:e^x at 327°C, the value of x is
💡 Solution & Explanation
The half-life of desorption is inversely proportional to the rate constant (t_1/2 ∝ 1/k). Ratio of half-lives t_Fe / t_C = k_C / k_Fe. Using Arrhenius equation k = A·e^(-Eₐ/RT): k_C / k_Fe = e^(-E_C/RT) / e^(-E_Fe/RT) = e^(-(E_C - E_Fe)/RT). Given E_C = 20000 cal/mol, E_Fe = 8000 cal/mol, T = 327°C = 600 K, and R = 2 cal/(mol·K). E_C - E_Fe = 12000 cal/mol, and RT = 2 × 600 = 1200 cal/mol. k_C / k_Fe = e^(-12000 / 1200) = e⁻¹⁰. Thus, t_Fe / t_C = e⁻¹⁰ = 1 / e¹⁰. Given the ratio is 1:e^x, we identify x = 10. Therefore, correct answer is 0010.