Question

At constant volume and temperature conditions, the rates of diffusion $D_A$ and $D_B$ of gases A and B having densities ${\rho }_A$ and ${\rho }_B$ are related by the expression:

• A. $D_A={\left(D_B\frac{{\rho }_A}{{\rho }_B}\right)}^{1/2}$
• B. $D_A=D_B{\left(\frac{{\rho }_A}{{\rho }_B}\right)}^{1/3}$
• C. $D_A=D_B{\left(\frac{{\rho }_A}{{\rho }_B}\right)}^{1/2}$
• D. $D_A=D_B{\left(\frac{{\rho }_B}{{\rho }_A}\right)}^{1/2}$

Answer 1

The correct option is D $D_A=D_B{\left(\frac{{\rho }_B}{{\rho }_A}\right)}^{1/2}$

According to Graham's law of diffusion, the rate of diffusion of a gas is inversely proportional to the square root of its density, or simply

$D\propto \frac{1}{\sqrt{\rho }}$

$\Rightarrow \frac{D_A}{D_B}=\sqrt{\frac{{\rho }_B}{{\rho }_A}}$

Hence, B is correct