Q. When $r,\ p\ and\ M$ represent rate of diffusion, pressure and molecular mass, respectively, then the ratio of the rates of diffusion $(r_{A}/r_{B})\$of two gases $A\ and\ B,$ is given as
A) $\left( p_{A}/p_{B} \right)^{1/2}\ (M_{A}/M_{B})$
B) $\left( p_{A}/p_{B} \right)\ \left( M_{B}/M_{A} \right)^{1/2}$
C) $\left( p_{A}/p_{B} \right)^{1/2}\ (M_{B}/M_{A})$
D) $\left( p_{A}/p_{B} \right)\ \left( M_{A}/M_{B} \right)^{1/2}$
Explanation
(b)
Rate of diffusion, $r \propto p$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ r \propto \frac{1}{\sqrt{M}}\ \ \therefore r \propto \frac{p}{\sqrt{M}}$
For gas $A,\ \ \ \ \ \ r_{A} \propto \frac{p_{A}}{\sqrt{M_{A}}}\ \ \ \ \ \ \ \ \ \ \ \ \ldots(i)$
For gas $B,\ \ \ \ \ r_{B}\ \propto \frac{p_{B}}{\sqrt{M_{B}}}\ \ \ \ \ \ \ \ \ \ \ \ldots(ii)$
Eqs. (i)/(ii), we get
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{r_{A}}{r_{B}} = \frac{p_{A}}{p_{B}}\sqrt{\frac{M_{B}}{M_{A}}}\$
or $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{p_{A}}{p_{B}}\left( \frac{M_{B}}{M_{A}} \right)^{1/2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.