$\mathrm{PV}=\mathrm{nRT}$       $...(i)$

For oxygen : $\mathrm{p}=1$ atm; $\mathrm{V}=1 \mathrm{L} ; \mathrm{n}=n_{O_{2}}$

Therefore, eqn. $(i)$ becomes,

$\therefore 1 \times 1=n_{O_{2}} R T$ or $n_{O_{2}}=\frac{1}{R T}$

For nitrogen : $\mathrm{p}=0.5$ atm; $\mathrm{V}=2 \mathrm{L} ; \mathrm{n}=2_{N_{2}}$

$\therefore 0.5 \times 2=n_{N_{2}} R T \quad$ or $n_{N_{2}}=\frac{1}{R T}$

For mixture of gas:

$P_{\operatorname{mix}} \cdot V_{\operatorname{mix}}=n_{\operatorname{mix}} R T$

Here, $\mathrm{n}_{\operatorname{mix}}=n_{O_{2}}+n_{N_{2}}$

$\therefore \frac{P_{m i x} J_{m i x}}{R T}=\frac{1}{R T}+\frac{1}{R T}$

$\therefore V_{\operatorname{mix}}=1 L ; P_{\operatorname{mix}}=2 a t m$