Question

If rate of diffusion of an unknown gas is half of that of $He$-gas under identical conditions, then the molar mass of unknown gas is:

• A. $4$
• B. $2$
• C. $8$
• D. $16$

Answer 1

Answer: (D)

$16$

Rate of diffussion $\propto \frac{1}{\sqrt{MolarMass}}$

$R_{He}=\frac{1}{\sqrt{M_{He}}},R_{Un}=\frac{1}{\sqrt{M_{Un}}}$

$\Rightarrow \frac{R_{He}}{R_{Unk.}}=\sqrt{\frac{M_{Unk}}{M_{He}}}$

Given, $R_{Unk.}=\frac{R_{He}}{2}$

$\Rightarrow \frac{R_{He}}{R_{He/2}}=\sqrt{\frac{M_{Unk.}}{4}}\Rightarrow 2=\frac{1}{2}\sqrt{M_{Unk.}}$

$M_{Unk.}=16$

Thus, molar mass of unknown gas is $16$ .