Adsorption Isotherm

An adsorption isotherm is the relationship, at a fixed (constant) temperature, between the amount of a substance adsorbed per unit mass of adsorbent and either the equilibrium pressure of the gas (for gas-solid adsorption) or the equilibrium concentration (for adsorption from solution). Several isotherms are known; the one developed in this chapter is the Freundlich adsorption isotherm, an empirical equation Freundlich proposed for the adsorption of a gas on a solid: $\frac{x}{m} = k P^{1/n}$ (with $n > 1$), where $x$ is the mass of gas adsorbed, $m$ is the mass of the adsorbent, $\frac{x}{m}$ is therefore the mass of gas adsorbed per unit mass of adsorbent, $P$ is the equilibrium pressure, and $k$ and $n$ are constants that depend on the nature of the adsorbate, the adsorbent, and the temperature. For adsorption from solution, $P$ in this equation is simply replaced by the equilibrium concentration $C$, giving $\frac{x}{m} = k C^{1/n}$. Taking logarithms of this form gives $\log \frac{x}{m} = \log k + \frac{1}{n} \log C$ (and equivalently with $\log P$ in place of $\log C$ for the gas case) -- plotting $\log \frac{x}{m}$ against $\log C$ or $\log P$ gives a straight line (Fig 11.4, attached to this section), whose slope is $\frac{1}{n}$ and whose intercept on the y-axis is $\log k$. The factor $\frac{1}{n}$ always lies between 0 and 1: when $\frac{1}{n} \to 0$, $\frac{x}{m}$ tends to a constant, meaning adsorption becomes independent of pressure; when $\frac{1}{n} = 1$, $\frac{x}{m} = kP$, meaning adsorption is directly proportional to pressure. This logarithmic (straight- …