Question

One litre of oxygen at a pressure of $1atm$ and two litres of nitrogen at a pressure of $0.5atm$, are introduced into a vessel of volume $1L$. If there is no change in temperature, the final pressure of the mixture of gas (in atm) is

• A. $1.5$
• B. $2.5$
• C. $2$
• D. $4$

Answer 1

The correct option is C $2$

Ideal gas equation is given by
$pV=nRT$ ...(i)
For oxygen, $p=1atm,V=1L,n=n_0$
Therefore equation (i) becomes
$\therefore 1\times 1=n_{o_2}RT$
$\Rightarrow n_{o_2}=\frac{1}{RT}$
For nitrogen $p=0.5atm,V=2L,n=nN$
$\therefore 0.5\times 2=n_{N_2}RT$
$\Rightarrow n_{N_2}=\frac{1}{RT}$
For mixture of gas
$p_{mix}{V}_{mix}=n_{mix}RT$
Here, $n_{mix}=nO+n_{N_2}$
$\therefore \frac{p_{mix}{V}_{mix}}{RT}=\frac{1}{RT}+\frac{1}{RT}$
$\Rightarrow p_{mix}{V}_{mix}=2$