Question

Adsorption of a gas follows Freundlich adsorption isotherm.
The plot of $\log \left(\frac{x}{m}\right)$ vs $\log P$ is shown, $x$ is the mass of the gas adsorbed on mass $m$ of the adsorbent

From the graph above, $\left(\frac{x}{m}\right)$ is proportional to:

• A. $P^3$
• B. $P^{3/2}$
• C. $P^2$
• D. $P^{2/3}$

Answer 1

The correct option is D $P^{2/3}$

Freundlich adsorption isotherm:
$\frac{x}{m}=k{P}^{\frac{1}{n}}..\left(i\right)$
Taking log both sides
$\log \left(\frac{x}{m}\right)=\log \left(k{P}^{\frac{1}{n}}\right)$
$\log \left(\frac{x}{m}\right)=\log \left(k\right)+\frac{1}{n}\log P$
The slope is : $\frac{1}{n}$
From graph:
$\text{Slope}=\frac{2}{3}=\frac{1}{n}$
Putting in (i)
$\frac{x}{m}=k{P}^{\frac{2}{3}}$

$\frac{x}{m}\propto P^{\frac{2}{3}}$