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 O2 = 32.0 u.

Explanation

Since V and T are common to the two gases,we have `P_(1)V=mu_(1)RT` and `P_(2)V=mu_(2)RT`
`therefore (P_(1))/(P_(2))=(mu_(1))/(mu_(2))`
Where 1 and 2 refer to neon and oxygen respectively
Given `(P_(1))/(P_(2))=(3)/(2)therefore(mu_(1))/(mu_(2))=(3)/(2)`
(i)By definition `mu_(1)=(N_(1))/(N_(A))` and `mu_(2)=(N_(2))/(N_(A))`
`therefore` The ratio of number of molecules `(N_(1))/(N_(2))=(mu_(1))/(mu_(2))=(3)/(2)`
(ii)If `rho_(1)` and `rho_(2)` are mass densities of 1 and 2 repectively.
we have `(rho_(1))/(rho_(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))`
`therefore (m_(1))/(m_(2))=(mu_(1))/(mu_(2))xx(M_(1))/(M_(2))=(3)/(2)xx(20.2)/(32.0)=0.947`