Question

Choose the correct answer:
A gas cylinder of capacity of 20 dm³ is filled with gas X the mass of which is 10 g. When the same cylinder is filled with hydrogen gas at the same temperature and pressure the mass of the hydrogen is 2 g, hence the relative molecular mass of the gas is:
(a) 5
(b) 10
(c) 15
(d) 20

Answer 1

According to Avogadro's law, the number of moles of both the gases will be same at the same temperature and pressure.
Number of moles of gas X = $\frac{\mathrm{Mass}\mathrm{of}\mathrm{gas}X}{\mathrm{Molecular}\mathrm{mass}\mathrm{of}\mathrm{gas}X}=\frac{10}{M}$
Number of moles of hydrogen gas = $\frac{\mathrm{Mass}\mathrm{of}\mathrm{hydrogen}\mathrm{gas}}{\mathrm{Molecular}\mathrm{mass}\mathrm{of}\mathrm{hydrogen}\mathrm{gas}}=\frac{2}{2}=1$
Equating the number of moles of both the gases, we get:
$$\begin{gathered} \frac{10}{M}=1 \\ \mathrm{M}=10 \end{gathered}$$
So, the relative molecular mass of gas is 10.

Hence, the correct answer is option (b).