Question

A mixture of $4\text{g}$ of hydrogen and $8\text{g}$ of helium at pressure $P=1.01\times {10}^5\text{Pa}$ and temperature $T=273\text{K}$ has a density of about

• A. $0.22{\text{kg/m}}^3$
• B. $0.62{\text{kg/m}}^3$
• C. $1.12{\text{kg/m}}^3$
• D. $0.13{\text{kg/m}}^3$

Answer 1

The correct option is D $0.13{\text{kg/m}}^3$

Given,
Mass of hydrogen gas in mixture $=4\text{g}$
Mass of helium gas in mixture $=8\text{g}$
$\therefore$ No. of moles of hydrogen gas $\left(n_1\right)=2$
No. of moles of helium gas $\left(n_2\right)=2$
Molecular weight of mixture $\left(M\right)=\frac{n_1{M}_1+n_2{M}_2}{n_1+n_2}$
$=\frac{2\left(2\right)+2\left(4\right)}{4}=3\text{g/mol}$
Density of mixture, $\left(\rho \right)=\frac{PM}{RT}=\frac{(1.01\times {10}^5)\times (3\times {10}^{-3})}{8.31\times 273}$
$=0.13{\text{kg/m}}^3$