Kinetic Theory - Result Question 1
1. A cylinder contains hydrogen gas at pressure of $249 kPa$ and temperature $27^{\circ} C$.
[2020]
Its density is : $(R=8.3 J mol^{-1} K^{-1})$
(a) $0.2 kg / m^{3}$
(b) $0.1 kg / m^{3}$
(c) $0.02 kg / m^{3}$
(d) $0.5 kg / m^{3}$
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Solution:
- (a) Given : Pressure $P=249 kPa$
$ =249 \times 10^{3} N / m^{2} $
Mass of hydrogen, $M=2 g=2 \times 10^{-3} kg$
Temperature, $T=27+273=300 K$
Using, ideal gas equation, $P V=n R T$
$ P M=\rho R T \Rightarrow \rho=\frac{P M}{R T} \quad(\because \rho=\frac{M}{V}) $
$\therefore \rho=\frac{(249 \times 10^{3})(2 \times 10^{-3})}{8.3 \times 300}=0.2 kg / m^{3}$.
