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`.

Explanation

Since V and T are common to the two gases, we have `P_1V=mu_(1)RT and P_2V=mu_(2)RT`
`P_1/P_2=mu_1/mu_2`
where 1 and 2 refer to neon and oxygen respt.
Given `P_1/P_2=3/2 " "mu_1/mu_2=3/2`
(i) By definition `mu_(1)=N_1/N_A and mu_(2)=N_2/N_A`
Where `N_1 and N_2` are the number of molecules of 1 and 2.
The ratio of number of molecules `N_1/N_2=mu_(1)/mu_(2)=3/2`
(ii) If `p_1 and p_2` are mass densities of 1 and 2 respt. we have `p_1/p_2=(m_(1)//V)/(m_2//V)=m_1/m_2`
But we can also write `mu_(1)=(m_(1))/M_1 and mu_2=m_2/M_2`
`m_(1)/m_(2)=(mu_(1))/(mu_(2)) xx M_1/M_2=3/2 xx (20.2)/(32.0)=0.947`