The Langmuir adsorption isotherm equation is given by . When rearranged, a graph of versus yields a — Surface Chemistry Chemistry Question
Question
The Langmuir adsorption isotherm equation is given by $\frac{x}{m} = \frac{ap}{1+bp}$. When rearranged, a graph of $\frac{p}{x/m}$ versus $p$ yields a straight line. In a particular experiment, this plot gives a slope of $0.05\text{ g L}^{-1}$ and an intercept of $2\text{ atm g L}^{-1}$. Calculate the maximum saturation adsorption capacity ($x/m$) of the solid at very high pressure (in $\text{L g}^{-1}$).
💡 Solution & Explanation
Rearranging the Langmuir equation gives $\frac{p}{x/m} = \frac{1}{a} + \frac{b}{a}p$. Plotting $\frac{p}{x/m}$ vs $p$ yields a straight line with slope $= \frac{b}{a}$ and intercept $= \frac{1}{a}$. At very high pressures, the isotherm simplifies to $\frac{x}{m} = \frac{a}{b}$ (the saturation capacity). Since the slope $\frac{b}{a} = 0.05$, the saturation capacity $\frac{a}{b} = \frac{1}{0.05} = 20\text{ L g}^{-1}$.