A plot of log ( x / m ) verses log ( P ) for adsorption of a gas on a solid gives a straight line with a…

According to the Freundlich's Adsorption Isotherm,

$\frac{\mathrm{x}}{\mathrm{m}}=\mathrm{k}·{\mathrm{p}}^{1/\mathrm{n}}$

By taking the log both sides,

$\log \frac{\mathrm{x}}{\mathrm{m}}=\mathrm{logk}+\frac{1}{\mathrm{n}}\mathrm{logp}$

Compare this equation with $\mathrm{y}=\mathrm{mx}+\mathrm{c}$

Here, $\mathrm{m}$ is the slope of reaction.

So, from the equation $\log \frac{\mathrm{x}}{\mathrm{m}}=\mathrm{logk}+\frac{1}{\mathrm{n}}\mathrm{logp}$ the slope is $=\frac{1}{\mathrm{n}}$.