Question

A gas diffuse $\frac{1}{5}$ times as fast as hydrogen. Its molecular weight is:

• A. $50$
• B. $25$
• C. $25\sqrt{2}$
• D. $50\sqrt{2}$

Answer 1

The correct option is A $50$

Let,

$R_{H_2}$ be $x$

$R_G$ be $\frac{1}{5}x$

applying Graham's law of diffusion

$\frac{R_{H_2}}{R_G}=\sqrt{\frac{M_G}{M_{H_2}}}$

Where $R_G$ &$M_G$ represents the rate of diffusion and molecular mass of the gas.

Putting the values in the above equation

$\frac{x}{\frac{x}{5}}=\sqrt{\frac{M_G}{2}}$

$5=\sqrt{\frac{M_G}{2}}$

Squaring both sides

$5^2=\frac{M_G}{2}$

$M_G=25\times 2=50$