Example

Question:

A vessel contains two non-reactive gases: neon (monatomic) and oxygen (diatomic). The ratio of their partial pressures is 3:2. Estimate the ratio of (i) number of molecules and (ii) mass density of neon and oxygen in the vessel. Atomic mass of Ne = 20.2 u, molecular mass of O\(_2\) = 32.0 u.

Solution:

The partial pressure ratio is \( \frac{P_1}{P_2} = \frac{3}{2} \).
(i) By the ideal gas law, \[ \frac{P_1}{P_2} = \frac{\mu_1}{\mu_2} \] where \( \mu_1 = \frac{N_1}{N_A} \) and \( \mu_2 = \frac{N_2}{N_A} \) are mole numbers. Thus, \[ \frac{N_1}{N_2} = \frac{\mu_1}{\mu_2} = \frac{3}{2} \] (ii) For mass density, \[ \frac{\rho_1}{\rho_2} = \frac{m_1/V}{m_2/V} = \frac{m_1}{m_2} = \frac{\mu_1}{\mu_2} \times \frac{M_1}{M_2} \] where \( M_1 = 20.2~\text{u} \), \( M_2 = 32.0~\text{u} \), \[ \frac{\rho_1}{\rho_2} = \frac{3}{2} \times \frac{20.2}{32.0} = 0.947 \]