Question

The rate of diffusion of a gas is proportional to

• A. $\frac{p}{d}$
• B. $\sqrt{\frac{p}{d}}$
• C. $\frac{pV}{M}$
• D. $\sqrt{\frac{pV}{d}}$

Answer 1

Answer: (B)

According to kinetic theory of gases
$pV=\frac{1}{3}mN{v}^2$
where, $m=$ mass of a single molecule
$N=$ number of molecules
$v=$ root mean square velocity
We know that $m\times N=M$
$\therefore pV=\frac{1}{3}M{v}^2$
$v=\sqrt{\frac{3pV}{M}}$
$\frac{M}{V}=d$
where, $d$ is density.
$\therefore v=\sqrt{\frac{3p}{d}}$
or $v\propto \sqrt{\frac{p}{d}}$
Rate of diffusion $(r)\propto v$
$\therefore r\propto \sqrt{\frac{p}{d}}$