# Question 95169

Jul 25, 2016

The relative molecular mass of gas Z is 32

To get feasible result the volume of hydrogen gas diffused is considered $200 c {m}^{3}$.

#### Explanation:

To solve this problem we are to apply Graham's law of diffusion which states that the rate of effusion or of diffusion (R)of a gas is inversely proportional to the square root of its molecular weight or relatve molecular mass (M) at constant temperature and pressure.

$\textcolor{red}{\text{Symbolically, } R \propto \frac{1}{\sqrt{M}}}$

Let

M_Z->"Relative molecular mass of gas Z"=?#

${M}_{H} \to \text{Rel. molecular mass of Hydrogen} = 2$

${R}_{Z} \to {\text{Rate diffusion of gas Z"=100/10=10"cm}}^{3} / s$

${R}_{H} \to {\text{Rate diffusion of Hydrogen"=200/5=40"cm}}^{3} / s$

Now by Graham's law

${R}_{H} / {R}_{Z} = \sqrt{{M}_{Z} / {M}_{H}}$

$\implies \frac{40}{10} = \sqrt{{M}_{Z} / 2}$

${M}_{Z} = {4}^{2} \cdot 2 = 32$

The relative molecular mass of gas Z is 32