The desorption of gas molecules from the adsorbent surface obeys Arrhenius equation. The average tim — Surface Chemistry Chemistry Question

💡 Solution & Explanation

The rate constant for desorption is given by the Arrhenius equation: k = A·e^(-Eₐ/RT). Here, Eₐ = 16 kcal/mol = 16000 cal/mol, R = 2 cal/(mol·K), and T = 400 K. So, Eₐ/RT = 16000 / (2 × 400) = 20. Thus, k = 1.25 × 10⁸ × e⁻²⁰. Given e²⁰ = 5 × 10⁸, e⁻²⁰ = 1 / (5 × 10⁸). Substituting this, k = (1.25 × 10⁸) / (5 × 10⁸) = 1.25 / 5 = 0.25 s⁻¹. The average time of residence τ is the reciprocal of the rate constant: τ = 1/k = 1/0.25 = 4 s. Therefore, correct answer is 4.