Chapter 19, Problem 19.71E

Interpretation Introduction

Interpretation:

The ratios of diffusion of $\text{HCl}$ and ${\text{NH}}_{\text{3}}$ through air by first taking only the masses of $\text{HCl}$ and ${\text{NH}}_{\text{3}}$, then, the reduced masses of ($\text{HCl}\text{+}$ air) and (${\text{NH}}_{\text{3}}\text{+}$ air) are to be stated. The ratios are to be compared to the experimentally determined ratio of about $0.7$. The ratio that represents the better model of reality is to be stated.

Concept introduction:

The mutual diffusion constant involves the three mean free paths, that is, between like gas particles and between the different gas particles. The mutual diffusion constant is given by,

$D_{12}=\frac{3}{8}\cdot \sqrt{\frac{RT}{2\pi \mu }}\cdot \frac{1}{{\left(r_1+r_2\right)}^2{\rho }_{\text{tot}}}$

Where,

• $D_{12}$ is the mutual diffusion constant.

• $\mu$ is the reduced molar mass.

• $r_1$ and $r_2$ are the radius of two particles $1$ and $2$

• ${\rho }_{\text{tot}}$ is the total particle density.

• $R$ is the gas constant.

• $T$ is the temperature.

The mutual diffusion constant does not depend on the mole fractions of the involved gases.