Surface ChemistryHard

Question

Desorption of a gas from metal surface follows first order kinetics. The rate constant of desorption can be given by Arrhenius equation. If the desorption of hydrogen on manganese is found to increases 10 times on increasing the temperature from 600 to1000 K, the activation energy of desorption is (ln10 = 2.3)

Options

A.6.0 kcal/mol
B.6.9 kcal/mol
C.3.0 kcal/mol
D.57.4 kcal/mol

Solution

$K = A.e^{- E_{a}/RT}$

$\therefore\ln\frac{K_{2}}{K_{1}} = \frac{E_{a}}{R}\left( \frac{1}{T_{1}} - \frac{1}{T_{2}} \right) $$$\text{or, }\ln 10 = \frac{E_{a}}{R}\left( \frac{1}{600} - \frac{1}{1000} \right) \Rightarrow E_{a} = 6900\text{cal/mol}$$

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