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laws

Question

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

Moderate

A

0.2 kg/m³
B

0.1 kg/m³
C

0.02 kg/m³
D

0.5 kg/m³

Solution

Given, pressure, P = 249 kPa = 249 $\times$ 10³Pa
Temperature, T = 27° C = 273 + 27 = 300 K
Density, $ρ$ = ?
From ideal gas equation, pV = nRT
$\Rightarrow$ $p V = \frac{m}{M} R T (∵ n = \frac{m}{M})$
$\Rightarrow$ pVM = mRT
$\Rightarrow$ $p M = \frac{m}{V} R T = ρ R T (∵ \frac{m}{V} = ρ)$
$\Rightarrow$ $ρ = \frac{p M}{R T} = \frac{249 \times 10^{3} \times 2 \times 10^{- 3}}{8.3 \times 300} k g / m^{3}$
( $∵$ For hydrogen gas, M = 2 $g = 2 \times 10^{- 3} kg$ )
$\Rightarrow$ $ρ = 0.2 kg / m^{3}$

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