Question

A sample of $16\text{g}$ charcoal was brought into contact with $C{H}_4$ gas contained in a vessel of $1$ litre at $27{}^{\circ }\text{C}$. The pressure of gas was found to fall form $760$ to $608\text{torr}$. The density of charcoal sample is $1.6{\text{g/cm}}^3$. What is the volume of the $C{H}_4$ gas adsorbed per gram of the adsorbent at $608\text{torr}$ and $27{}^{\circ }\text{C}$.

• A. $12.5\text{mL/g}$
• B. $16.25\text{mL/g}$
• C. $26.0\text{mL/g}$
• D. $18.05\text{mL/g}$

Answer 1

The correct option is B $16.25\text{mL/g}$

Since we are keeping the temperature constant, final volume of the gas $\left(V_2\right)$, at $608$ torr pressure
$=\frac{P_1{V}_2}{P_2}=\frac{760\times 1}{608}=1.25=1250\text{mL}$
Again,
$\text{Volume occupied by gas = volume of vessel - volume occupied by charcoal}$
$\text{So, volume occupied by the gas}=(1000-\frac{16}{1.6})\text{mL}=990\text{mL}$
Difference of volume is due to adsorption of gas by charcoal.
$\therefore$ volume of gas adsorbed by charcoal
$=1250-990=260\text{mL}$
So, volume of the gas adsorbed per gram of charcoal at $608$ torr and $27{}^{\circ }C$
$=\frac{260}{16}\text{mL}=16.25\text{mL}$