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  4. The rate of diffusion of a gas is proportional to

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Q. The rate of diffusion of a gas is proportional to

AMUAMU 2001

Solution:

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