Answer to Question #88459 in Molecular Physics | Thermodynamics for Sridhar

Question

The main constituents of air are 80% of nitrogen molecules of molar mass 28 kg/k mol and
20% oxygen molecules of molar mass 32 kg/k mol. The mass of air in 50 cm3 volume at
9.3 × 104 Pa pressure at room temperature (20°C) is
[use ideal gas law] (R = 8.314 × 103 J/k mol/K)
(1) 5.5 kg (2) 55 × 10–3 kg
(3) 55 kg (4) 5.5 × 10–5 kg

Answer 1

Dalton's law of partial pressure

$$p=p_1+p_2$$

From ideal gas law we have 3 equation

$$p_1V=\frac{m_1}{M_1}RT$$ $$p_2V=\frac{m_2}{M_2}RT$$ $$pV=(\frac{m_1}{M_1}+\frac{m_2}{M_2})RT$$

But,

$$m_1=0.2m; m_2=0.8m$$ $$pV=(\frac{0.2m}{M_1}+\frac{0.8m}{M_2})RT$$ $$m=\frac{pV}{(\frac{0.8}{M_1}+\frac{0.2}{M_2})RT}$$ $$m=\frac{93000\cdot 0.00005}{(\frac{0.8}{28}+\frac{0.2}{32})8314\cdot 293}=5.5\cdot 10^{-5} kg$$

Answer: (4) 5.5*10^-5