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Q.
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
Kinetic Theory
Solution:
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}} $