Question

A vessel contains two non-reactive gases neon (monoatomic) 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.

$P_{1}V = \mu_{1}RTandP_{2}V = \mu_{2}RT$

Here, 1 and 2 represent for neon gas and oxygen gas respectively.

Now, $\frac{P_{1}}{P_{2}} = \frac{\mu_{1}}{\mu_{2}}$

$\Rightarrow \frac{\mu_{1}}{\mu_{2}} = \frac{3}{2} \left( Given\frac{P_{1}}{P_{2}} = \frac{3}{2} \right)$

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 $\mu_{2} = \frac{N_{2}}{N_{A}}$