For the adsorption of a gas on a solid surface, the Langmuir adsorption isotherm is given by $\frac{x}{m}=\frac{abP}{1+aP}$. At very high pressure, the fraction of surface coverage $\theta$ approaches:

Solution

1. The Langmuir isotherm for fractional coverage is $\theta =\frac{aP}{1+aP}$.
2. As pressure $P$ approaches infinity, the term $aP$ becomes much larger than $1$.
3. The expression simplifies to $$\begin{array}{rl}\theta & =\underset{P\to \infty }{\lim }\frac{aP}{aP}\\ & =1\end{array}$$.
4. Hence the answer is (C).