Adsorption of a gas follows Freundlich adsorption isotherm. x is the mass of the gas adsorbed on mass m of the adsorbent. The plot of versus log p is shown in the given graph. log(x/m) is proportional to

The Freundlich adsorption isotherm law states that the change in the amount of gas absorbed by unit mass of a solid is directly proportional to the change in the pressure at a given temperature.

Freundlich equation

$\frac{\mathrm{x}}{\mathrm{m}}={\mathrm{KP}}^{\frac{1}{\mathrm{n}}}-----\left(\mathrm{I}\right)$

Where,

x = mass of the adsorbent at pressure P

k = constant

Taking log both side in equation (I)

$\log (\mathrm{x}/\mathrm{m})=\mathrm{logK}+1/\text{ nlog }\mathrm{P}$

According to the given plot

$\mathrm{y}=\mathrm{mx}$     where m is slop of line

$\mathrm{m}=\mathrm{y}/\mathrm{x}=2/3$ 

$1/\mathrm{n}=2/3$

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

Therefore, option D is correct.