Question

Give a mathematical expression showing the relation between the amount of a gas adsorbed on a solid surface and the pressure of the gas.

Answer 1

A mathematical expression showing the relation between the amount of a gas adsorbed on a solid surface and the pressure of the gas is given by Freundlich adsorption isotherm, which is:

\[\frac{x}{m} = k P^{1/n}\] (n > 1)

where, x is the mass of the gas adsorbed on the mass m of the adsorbent at equilibrium pressure P. k and n are constants whose values depend upon the nature of adsorbate, nature of adsorbent and the temperature.

This expression is valid at a constant temperature and represents an empirical relation between the extent of adsorption `(x/m)` and pressure P.

Taking logarithms on both sides.

\[\log_{10}\left(\frac{x}{m}\right) = \log_{10} k + \frac{1}{n} \log_{10} P\]

This linear form helps in determining the constants k and n graphically from a plot of `log_10 ⁡(x/m)` vs log₁₀ ⁡P.

Plot of `(x/m)` against P.

Plot of `log_10 ⁡(x/m)` against P (both at constant temperature).