Step 1: 

The plot between the extent of adsorption $\left(\frac{\mathrm{x}}{\mathrm{m}}\right)$ against the pressure of gas (P) at constant temperature (T) is called the adsorption isotherm.

The graph is as follows:



Step 2:

Freundlich adsorption isotherm:

Freundlich adsorption isotherm gives an empirical relationship between the quantity of gas adsorbed by the unit mass of solid adsorbent and pressure at a specific temperature.

Case I- At low pressure:

The plot is straight and sloping, indicating that the pressure directly proportional to

${\frac{\mathrm{x}}{\mathrm{m}}}_{\mathrm{i}.\mathrm{e}.,}\frac{\mathrm{x}}{\mathrm{m}}\mathrm{\alpha } \mathrm{P}.$
$\frac{\mathrm{x}}{\mathrm{m}}=\mathrm{kP} (\mathrm{k} \mathrm{is} \mathrm{a} \mathrm{constant})$

Case II - At high pressure:

When pressure exceeds the saturated pressure, $\frac{\mathrm{x}}{\mathrm{m}}$becomes independent of P values.

$\frac{\mathrm{x}}{\mathrm{m}}\mathrm{\alpha } \mathrm{P}°$
$\frac{\mathrm{x}}{\mathrm{m}}= \mathrm{k} \mathrm{P}°$

Case III - At intermediate pressure:

At intermediate pressure,$\frac{\mathrm{x}}{\mathrm{m}}$ depends on P raised to the powers between 0 and 1. This relationship is known as the Freundlich adsorption isotherm. 

$\frac{\mathrm{x}}{\mathrm{m}}\alpha P^{\frac{1}{n}}$
$\frac{x}{m}=k{P}^{\frac{1}{n}} n >\hspace{0.17em}1$
$\mathrm{Now}, \mathrm{taking} \log :$
$\log \frac{\mathrm{x}}{\mathrm{m}}=\log \mathrm{k}+\frac{1}{\mathrm{n}} \log \mathrm{P}$

On plotting the graph between log $\left(\frac{\mathrm{x}}{\mathrm{m}}\right)$and log P, a straight line is obtained with the slope equal to ${}^{\frac{1}{\mathrm{n}}}$