Question

According to Graham's law at a given temperature, the ratio of the rates of diffussion ${\gamma }_A/{\gamma }_B$ of gases $A$ and $B$ is given by

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

Answer 1

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

According to Graham's law at a given temperature $r\propto \frac{P}{\sqrt{M}}$
Here, P is the pressure of gas and M is its molar mass.
The ratio of the rates of diffusion $\frac{{\gamma }_A}{{\gamma }_B}$ of gases A and B is given by the expression
$\frac{{\gamma }_A}{{\gamma }_B}=\frac{P_A}{P_B}\cdot {\left(\frac{M_B}{M_A}\right)}^{1/2}$
Thus, the option (C) is the correct answer.