Discussion
Adsorption of a gas with pressure P on a solid obeys the Langmuir adsorption isotherm. For a fixed fractional coverage, the correct relation between K and P at a fixed temperature is
[\(K = k_{a}/k_{b}\), \(k_{a}\) and \(k_{b}\) are the rate constants for adsorption and desorption, respectively. Assume non-dissociative adsorption.]
Answer: C
At fixed coverage, \(K \propto P^{-1}\).
For non-dissociative adsorption the Langmuir isotherm gives the fractional coverage as
\[ \theta = \frac{KP}{1 + KP} \]
If \(\theta\) is held fixed, the product \(KP\) must be fixed, \(KP = \theta/(1-\theta)\), so K is inversely proportional to P.
\(K \propto P\) inverts the relation. The square-root forms belong to dissociative adsorption, where \(\theta\) depends on \((KP)^{1/2}\), which the question rules out.
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