A sample of 16 gm of charcoal was brought into contact with CH₄  gas contained in a vessel of 1litre at 27°C and pressure of gas was found to fall form 760 to 608 torr. The density of charcoal sample is 1.6 gm/cm³ . The volume of the CH₄ gas adsorbed per gram of  adsorbent at 608 torr and 27°C is (x^y+0.25). The value of x+y =

Final volume of gas, at 608 torr pressure 
$\begin{array}{l}{\mathrm{V}}_2=\frac{{\mathrm{P}}_1{\mathrm{V}}_1}{{\mathrm{P}}_2}\\ =\frac{760\times 1}{608}\\ \Rightarrow 1.25\text{ or }{\mathrm{V}}_2=1250\mathrm{mL}\end{array}$

Volume occupied by gas = Volume of vessel - Volume occupied by charcoal
$=1000-\frac{16}{1.6}=990\mathrm{mL}$

Difference of volume is due to adsorption of gas by charcoal.
∴ Volume of gas adsorbed by charcoal 
=1250−990 
⇒260mL 
Volume of the gas adsorbed per gram of charcoal 
$$\begin{gathered} =\frac{260}{16}=16.25\mathrm{mL}/\mathrm{g} \mathrm{at} 608 \mathrm{torrand} {27}^{\circ }\mathrm{C}. =( 4^2+0.25) \mathrm{comparing} \mathrm{with} {\mathrm{x}}^{\mathrm{y}}+0.25 \\ \mathrm{then} \mathrm{x}=4,\mathrm{y}=2: \mathrm{x}+\mathrm{y}=6 \end{gathered}$$