Adsorption of a gas follows Freundlich adsorption isotherm. x is the mass of the gas adsorbed on mass m of the adsorbent. The plot of \(\log \frac{{\rm{x}}}{{\rm{m}}}\) versus log p is shown in the given graph. \(\frac{{\rm{x}}}{{\rm{m}}}\) is proportional to:

Concept:

Freundlich adsorption isotherm:

Freundlich gave an empirical relationship between the quantity of gas adsorbed by a unit mass of solid adsorbent and pressure at a particular temperature.

\(\frac{{\rm{x}}}{{\rm{m}}} = {\rm{K}}.{{\rm{p}}^{1/{\rm{n}}}}\)

Taking log on both sides, we get,

\(\log \frac{{\rm{x}}}{{\rm{m}}} = \log {\rm{K}} + \frac{1}{{\rm{n}}}\log {\rm{p}}\)

We know that, the formula of slope is:

\({\rm{m}} = \frac{{\rm{y}}}{{\rm{x}}}\)

In the formula, the slope is \(\frac{1}{{\rm{n}}}\)

Therefore,

\(\Rightarrow \frac{{\rm{y}}}{{\rm{x}}} = \frac{1}{{\rm{n}}}\)

From graph, the value of slope is:

\(\Rightarrow \frac{2}{3} = \frac{1}{{\rm{n}}}\)

\(\therefore {\rm{n}} = \frac{3}{2}\)

The Freundlich equation is:

\(\frac{{\rm{x}}}{{\rm{m}}} = {\rm{K}}.{{\rm{p}}^{1/{\rm{n}}}}\)

\(\Rightarrow \frac{{\rm{x}}}{{\rm{m}}} \propto {{\rm{p}}^{1/\left( {3/2} \right)}}\)

\(\Rightarrow \frac{{\rm{x}}}{{\rm{m}}} \propto {{\rm{p}}^{2/3}}\)