Freundlich adsorption isotherms for the physical adsorption of a gas at temperature T 1 ,   T 2 and T 3…

Freundlich adsorption isotherm: This gives an empirical relationship between the quantity of a gas adsorbed by a unit mass of solid adsorbent and pressure at a particular temperature. It is expressed as:

$$\begin{gathered} \frac{\mathrm{x}}{\mathrm{m}}=\mathrm{k}·{\mathrm{p}}^{1/\mathrm{n}} \left(\mathrm{n}>1\right) \\ \Rightarrow \log \frac{\mathrm{x}}{\mathrm{m}}=\log \mathrm{k}+\frac{1}{\mathrm{n}}\log \mathrm{P} \end{gathered}$$

Since adsorption is an exothermic process, it decreases with increase in temperature and varies inversely proportional to temperature.

$\frac{\mathrm{x}}{\mathrm{m}}\propto \frac{1}{\mathrm{T}}$

So, according to the given graph, $\frac{\mathrm{x}}{\mathrm{m}}$ is more for ${\mathrm{T}}_3$. So, ${\mathrm{T}}_3$ is the least temperature and the correct order is ${\mathrm{T}}_3<{\mathrm{T}}_2<{\mathrm{T}}_1$.