Question

A vessel contains two non-reactive gases neon (monatomic) and oxygen (diatomic). The ratio of their partial pressures is $3:2$. The ratio of number of molecules is

• A. $\frac{3}{2}$
• B. $\frac{2}{3}$
• C. $\frac{1}{3}$
• D. $\frac{1}{2}$

Answer 1

Answer: (A)

As partial pressure of a gas in a mixture is the pressure it would exert for the same volume and temperature, if it alone occupied the vessel, therefore, for common $V$ and $T$, $P_1$ and $P_2$ are partial pressures.
$P_{1}V={\mu }_{1}RT$ and $P_{2}V={\mu }_{2}RT$.
Here, $1$ and $2$ refer to neon gas and oxygen gas respectively.
Now, $\frac{P_1}{P_2}=\frac{{\mu }_1}{{\mu }_2}\Rightarrow \frac{{\mu }_1}{{\mu }_2}=\frac{3}{2}$ (Given $\frac{P_1}{P_2}=\frac{3}{2}$)
If $N_1$ and $N_2$ are number of molecules of two gases, then
$\therefore \frac{N_1}{N_2}=\frac{{\mu }_1}{{\mu }_2}=\frac{3}{2}$, where ${\mu }_1=\frac{N_1}{N_A}$ and ${\mu }_2=\frac{N_2}{N_A}$