Question

According to Graham's law, at a given temperature, the ratio of the rates of diffusion $\frac{r_A}{r_B}$ of gases $A$ and $B$ is given by:

(where $P$ and $M$ are pressures and molecular weights of gases $A$ and $B$ respectively)

• A. $\left(\frac{P_A}{P_B}\right){\left(\frac{M_A}{M_B}\right)}^{\frac{1}{2}}$
• B. $\left(\frac{M_A}{M_B}\right){\left(\frac{P_A}{P_B}\right)}^{\frac{1}{2}}$
• C. $\left(\frac{P_A}{P_B}\right){\left(\frac{M_B}{M_A}\right)}^{\frac{1}{2}}$
• D. $\left(\frac{M_A}{M_B}\right){\left(\frac{P_B}{P_A}\right)}^{\frac{1}{2}}$

Answer 1

The correct option is C $\left(\frac{P_A}{P_B}\right){\left(\frac{M_B}{M_A}\right)}^{\frac{1}{2}}$

According to Graham's law of diffusion,
$\text{Rate of diffusion of a gas}\left(r\right)\propto \frac{P}{\sqrt{M}}$
$\therefore \frac{r_A}{r_B}=\sqrt{\frac{M_B}{M_A}}\times \frac{P_A}{P_B}$