The Langmuir adsorption isotherm is represented as . Based on experimental data at constant temperat — Surface Chemistry Chemistry Question
Question
The Langmuir adsorption isotherm is represented as $\frac{x}{m} = \frac{ap}{1+bp}$. Based on experimental data at constant temperature, the constant $a$ evaluates to $0.8\text{ atm}^{-1}$ and $b$ evaluates to $0.04\text{ atm}^{-1}$. Calculate the maximum possible amount of gas that can be adsorbed per gram of the solid (the limit of $x/m$ as pressure approaches infinity).
Answer: 20
💡 Solution & Explanation
At very high pressures, the term $bp \gg 1$, so the Langmuir equation simplifies to $\frac{x}{m} = \frac{ap}{bp} = \frac{a}{b}$. This represents the saturation point where the surface is completely covered with a unimolecular layer. Substituting the given values: $\text{Maximum } \frac{x}{m} = \frac{0.8}{0.04} = 20$.
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