Question

The rates of diffusion of an unknown gas and chlorine are in the ratio of $6:5$. Assuming the density of chlorine is $36$. Calculate the molecular weight of the unknown gas.

Answer 1

The rate of diffusion of a goal is inversely proportional to the square root of Mol.wt of goal.

So, we get

$r\propto \frac{1}{\sqrt{M}}$

From that, we get

$\frac{r_1}{r_2}=\sqrt{\frac{M_2}{M_1}}.....\left(1\right)$

W.K.T, Molecular weight $=2\times vapourdensity$

So, Avg. Mol. wt of $Cl=2\times 36=72$

From (1)

$\frac{6}{5}=\sqrt{\frac{72}{M_{unknown}}}$

$=\frac{36}{25}=\frac{72}{M_{unknown}}$ [Squaring both sides]

$=\frac{25}{36}=\frac{M_{unknown}}{72}$

$=M_{unknown}=\frac{25,72}{36}$

$=M_{unknown}=50$.