Question

A plot of log (x/m) and log ‘p’ is a straight line at an angle of 45° and the intercept on the y-axis is equal to 0.3010. Calculate the amount of gas adsorbed in gram per gram of adsorbent when pressure is 0.2 atm.

Answer 1

According to Freundlich adsorption isotherm,
$\frac{x}{m}=k{P}^{\frac{1}{n}}$
Where,
$x$ is the mass of gas adsorbed on a mass ${}^{\prime }{m}^{\prime }$, of the adsorbent at a pressure $P$.
Now taking log,
$\log \frac{x}{m}=\log k+\frac{1}{n}\log P$
Given, $\frac{1}{n}=\tan 45°$ or $n=1$ and $\log k=0.3010,P=0.2$ atm

$\log \frac{x}{m}=0.3010+1\times \log 0.2$

$\log \frac{x}{m}=\log 2+\log 0.2$

$\Rightarrow \log \frac{x}{m}=\log 0.4$

$\Rightarrow \frac{x}{m}=0.4\text{g}$