A vessel contains two non-reactive gases neon (monoatomic) 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 neon = 20.2 u, and molecular mass of oxygen = 32.0 u.

Explanation

Let us denote neon gas by 1 and oxygen gas by 2. We are given `(P_1)/(P_2) = 3/2`
As partial pressure of a gas in a mixture is the pressure it would exert for the same volume and temperature, if it along occupied the vessel, therefore, for common V and T
`P_(1)V = mu_(1) RT and P_(2)V = mu_(2) RT`
`:. (mu_1)/(mu_2) = (P_1)/(P_2) = 3/2`
(i) if `N_(1), N_(2)` are number of molecules of two gases, then by definition.
`mu_(1) =(N_1)/(n_2) and mu_(2)=(N_2)/(N_1)`
where, `N_(A)` is the Avogadro's number .
(ii) If `rho_(1), rho_(2)` are mass densities of the two gases, then
` (rho_1)/(rho_2) = (m_(1)//V)/(m_(2)//V) = (m_1)/(m_2) = (mu_(1)xx M_(1))/(mu_(2) xx M_(2)) = 3/2 xx (20.2)/(32.0)`
`= 0.947`