Question

One litre vessel having $20$ g charcoal (density $2.0$ g/cm${}^3$), was filled with a gas at $300$ K. The pressure of a gas was $760$ torr. Due to adsorption, the pressure of gas falls to $608$ torr. What is the number of gas molecules adsorbed per g of charcoal?

• A. $2.4\times {10}^{21}$
• B. $2.4\times {10}^{20}$
• C. $2.4\times {10}^{22}$
• D. $2.4\times {10}^{23}$

Answer 1

Answer: (B)

$2.4\times {10}^{20}$

The change in pressure $\left(\Delta P\right)=(760-608)torr=152torr$.

or $\frac{152torr}{760torr/atm}=0.2atm$

The number of moles of gas adsorbed $=\Delta n=\frac{PV}{RT}=\frac{0.2atm\times 1L}{0.08206Latm/molK\times 300K}=8.12\times {10}^{-3}mol$.

The number of gas molecules adsorbed $=8.12\times {10}^{-3}mol\times 6.023\times {10}^{23}molecules/mol=4.89\times {10}^{21}$ molecules.

This corresponds to $20$ g charcoal.

The number of gas molecules adsorbed per g of charcoal $=\frac{4.89\times {10}^{21}molecules}{20gcharcoal}=2.4\times {10}^{20}$ molecules.