The molecular weight of $O_2$ and $S{O}_2$ are $32$ and $64$ respectively. If one litre of $O_2$ at ${15}^0$C and $759$mm pressure contains N molecules, the number of molecules in two litre of $S{O}_2$ under the same conditions of temperature and pressure will be:

The correct option is A $2N$
Solution:- (C) $2N$

From ideal gas equation-

$PV=nRT$

$\Rightarrow n=\frac{PV}{RT}$

For $O_2$-

$V=1L\left(\text{Given}\right)$

No. of moles of $O_2=\frac{P}{RT}$

Therefore,

No. of molecules of $O_2=n\times N_a=N\left(\text{Given}\right)$

$\Rightarrow \frac{P}{RT}\times N_a=N.....\left(1\right)$

For $S{O}_2$-

$V=2L\left(\text{Given}\right)$

No. of moles of $S{O}_2=\frac{2P}{RT}$

Therefore,

No. of molecules of $S{O}_2=n\times N_a$

$\Rightarrow$ No. of moles of $S{O}_2=\frac{2P}{RT}\times N_a$

$\Rightarrow$ No. of molecules of $S{O}_2=2N\left(\text{From}\left(1\right)\right)$

Hence the no. of molecules of $S{O}_2$ is $2N$.