$CH_4$ is adsorbed on 1 g charcoal at $0^\circ C$ following the Freundlich adsorption isotherm. 10.0

Question

$CH_4$ is adsorbed on 1 g charcoal at $0^\circ C$ following the Freundlich adsorption isotherm. 10.0 mL of $CH_4$ is adsorbed at 100 mm of Hg, whereas 15.0 mL is adsorbed at 200 mm of Hg. The volume of $CH_4$ adsorbed at 300 mm of Hg is $10^x$ mL. The value of $x 	imes 10^2$ is.

Professor PC Thomas Classes · Answer

Using $V = kP^{1/n}$: $10 = k(100)^{1/n}$, $15 = k(200)^{1/n} \implies 1.5 = 2^{1/n} \implies 1/n = 0.585$. At 300 mm, $V = 10(3)^{0.585} = 19.01 = 10^{1.279}$. $x = 1.28$, so $x 	imes 10^2 = 128$.