The desorption of gas molecules from an adsorbent surface follows the Arrhenius equation. Given that the pre-exponential factor A = 1.25 * 10⁸ s⁻¹, the activation energy of desorption is 16 kcal/mol, and e²⁰ = 5 * 10⁸, calculate the average time (in seconds) for which a nitrogen molecule r

Question

The desorption of gas molecules from an adsorbent surface follows the Arrhenius equation. Given that the pre-exponential factor A = 1.25 * 10⁸ s⁻¹, the activation energy of desorption is 16 kcal/mol, and e²⁰ = 5 * 10⁸, calculate the average time (in seconds) for which a nitrogen molecule remains adsorbed on a platinum surface at 400 K. (Use R = 2 cal/mol/K.)

Accepted Answer

4 * 10⁻⁹ s. The desorption rate constant k = A*exp(-Ea/RT). With Ea/RT = 16000/(2*400) = 20, k = 1.25*10⁸ * e^(-20) = 1.25*10⁸ / (5*10⁸) = 0.25 s⁻¹. Average residence time = 1/k = 4 s. However, using e²⁰ = 5*10⁸ directly: k = 1.25*10⁸/(5*10⁸) = 1/4. Time = 4 s.

Solution

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