The plot of the amount of adsorption (x/m) against the pressure of the gas (P) at constant temperature is known as the adsorption isotherm (T).
Three cases arise from the graph which are as follow :-
Case I – At low pressure :
The pressure in the straight and sloping plot which directly proportional to
$$
\frac{x}{m} \text { i.e. } \frac{x}{m} \alpha P \quad \frac{x}{m}=\mathrm{kP} \quad(\mathrm{k} \text { is constant })
$$
Case II – High-Pressure Situation:
When pressure exceeds the saturated pressure, (x/m) becomes independent of P values.
$$
\frac{x}{m} \alpha P^{o} \frac{x}{m}=\mathrm{kP}^{\circ}
$$
Case lll – At intermediate pressure:
At intermediate pressure, (x/m) is independent of P values when pressure exceeds the saturated pressure,
$$
\log \frac{x}{m}=\log k+\frac{1}{n} \log P
$$
Now, taking log of the equation gives :
$$
\log \frac{x}{m}=\log k+\frac{1}{n} \log P
$$
On plotting the graph between log(x/m) and log P, a straight line is obtained having slope equal to 1/n.
