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)

$\frac{3}{2}$

Answer 2

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, $\frac{P_{1}}{P_{2}} = \frac{\mu_{1}}{\mu_{2}} \Rightarrow \frac{\mu _{1}}{\mu _{2}} = \frac{3}{2}\quad$ (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 $\mu_{2} = \frac{N_{2}}{N_{A}}$