Adsorption Isotherms

The way the amount of gas adsorbed changes with pressure at a constant temperature is captured by a curve called an adsorption isotherm.

Freundlich adsorption isotherm

In 1909 Freundlich proposed an empirical link between the mass of gas adsorbed per unit mass of adsorbent and the pressure at a fixed temperature:

where $x$ is the mass of gas adsorbed on mass $m$ of adsorbent at pressure $p$, and $k$ and $n$ are constants fixed by the adsorbent, the gas and the temperature.

Plotting $\frac{x}{m}$ against $p$ gives a curve that rises steeply then flattens, approaching saturation at high pressure. As Fig. 5.1 shows, three isotherms drawn at 195 K, 244 K and 273 K stack so that at any fixed pressure the amount adsorbed $\frac{x}{m}$ is greatest at the lowest temperature — confirming that physical adsorption falls as temperature rises.

Testing the isotherm

Taking logarithms of equation (5.1):

A plot of $\log \frac{x}{m}$ (y-axis) against $\log p$ (x-axis) should be a straight line if the Freundlich isotherm holds. As Fig. 5.2 illustrates, the slope of that line equals $\frac{1}{n}$ and the y-intercept equals $\log k$.

Range of validity

The factor $\frac{1}{n}$ lies between 0 and 1 (usually 0.1 to 0.5), so the relation holds only over a limited pressure range:

• When $\frac{1}{n} = 0$, $\frac{x}{m}$ is constant — adsorption is independent of pressure. …