Question

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 $750mm$ pressure contain '$N$' molecule, the number of molecules in two litres of $S{O}_2$ under the same conditions of temperature and pressure will be:

• A. $\frac{N}{2}$
• B. $N$
• C. $2N$
• D. $4N$

Answer 1

Answer: (C)

$2N$

We have $PV=nRT$

Moles of $O_2=\frac{PV}{RT}=\frac{1\times 1}{RT}$

Number of molecules

$N=\frac{Na}{RT}⟶\left(1\right)$

for $S{O}_2=\frac{PV}{RT}=\frac{1\times 2}{RT}$

Number of molecules,

$M=\frac{2Na}{RT}⟶\left(2\right)$

$\left(1\right)/\left(2\right)$

$\Rightarrow \frac{N}{M}=\frac{1}{2}\Rightarrow M=2N$ .