Question

A cylinder contains hydrogen gas at pressure of \(249 \mathrm{kPa}\) and temperature \(27^{\circ} C .\) Its density is : \(\left(R=8.3 J m o l^{-1} K^{-1}\right)\)
A \(0.5 \mathrm{~kg} / \mathrm{m}^{3}\)
(B) \(0.2 \mathrm{~kg} / \mathrm{m}^{3}\)
c \(0.1 \mathrm{~kg} / \mathrm{m}^{3}\)
D \(0.02 \mathrm{~kg} / \mathrm{m}^{3}\)

Answer 1

Solution:
We can express, an ideal gas equation as
$$
\begin{aligned}
&\frac{p}{\rho}=\frac{R \cdot T}{M w} \\
&\Rightarrow \rho=\frac{p M w}{R T} \\
&=\frac{249 \times 10^{2} \times 2 \times 10^{-3}}{8.314 \times 300} \\
&=0.199 \\
&\Rightarrow \rho=0.2 \mathrm{~kg} / \mathrm{m}^{3}
\end{aligned}
$$