Question

A mixture of $4\text{g}$ of hydrogen and $8\text{g}$ of helium at NTP has a density about

• A. $0.22{\text{kg/m}}^3$
• B. $0.62{\text{kg/m}}^3$
• C. $0.12{\text{kg/m}}^3$
• D. $0.43{\text{kg/m}}^3$

Answer 1

The correct option is C $0.12{\text{kg/m}}^3$

Given:
mass of hydrogen, $m_1=4\text{g}$

mass of helium, $m_2=8\text{g}$

So, Number of moles of hydrogen, $n_1=\frac{4}{2}=2$

Number of moles of helium, $n_2=\frac{8}{4}=2$

Now, molecular mass of mixture,

$M=\frac{n_1{M}_1+n_2{M}_2}{n_1+n_2}=\frac{2\times 2+2\times 4}{2+2}=3\text{g}$

Further, using ideal gas equation

$PM=\rho RT$

$\Rightarrow \rho =\frac{PM}{RT}........\left(1\right)$

At NTP (Normal temperature and pressure)

$T={20}^{\circ }\text{C}=293\text{K}$ and
$P=1\text{atm}={10}^5{\text{N/m}}^2$

putting in eq. $\left(1\right)$, we get

$\rho =\frac{1\times {10}^5\times 3\times {10}^{-3}}{8.3\times 293}$

$\Rightarrow \rho =0.12{\text{kg/m}}^3$

So, option $\left(c\right)$ is correct choice..