A cylinder contains hydrogen gas at pressure of 249 kPa and temperature 27°C. Its density is
(Take, $\mathrm{R} = 8.3 \mathrm{J} {\mathrm{mol}}^{-1} {\mathrm{K}}^{-1}$) [NEET 2020]

Given, pressure, P = 249 kPa = 249 $\times$ 10³ Pa
Temperature, T = 27° C = 273 + 27 = 300 K
Density, $\rho$ = ?
From ideal gas equation, pV = nRT

$\Rightarrow$              $pV=\frac{m}{M}RT \left(\because n=\frac{m}{M}\right)$

$\Rightarrow$             pVM = mRT

$\Rightarrow$             $pM=\frac{m}{V}RT=\rho RT \left(\because \frac{m}{V}=\rho \right)$

$\Rightarrow$            $\rho =\frac{pM}{RT}=\frac{249\times {10}^3\times 2\times {10}^{-3}}{8.3\times 300} kg/m^3$

                               ($\because$For hydrogen gas, M = 2 $\mathrm{g} = 2 \times {10}^{-3}\mathrm{kg}$)

$\Rightarrow$           $\mathrm{\rho } = 0.2 \mathrm{kg}/{\mathrm{m}}^3$