Chapter 1, Problem 1.4DQ

Interpretation Introduction

Interpretation:

Molecular interpretations have to be provided for the variation of rates of diffusion and effusion with temperature.

Concept Introduction:

Diffusion:

Diffusion is the process by which the molecules of the different substances mingle with each other in the absence of mechanical mixing such as stirring.

Effusion:

Effusion is process of escape of gas through a small hole such as in a puncture in the inflated balloon or tyre.

Fick’s law:

According to this law flow of particles in unit time per unit area perpendicular to the direction of flow is directly proportional to the negative gradient of the number density i.e. the no. of moles of particle per ${\text{m}}^{\text{3}}$.

${\text{J}}_{\text{z}}\text{=}\text{-}\text{D}\frac{\partial \text{ρ}}{\partial \text{z}}$

$\begin{array}{l}\text{D=}\text{diffusion}\text{constant}\\ \\ \text{ρ}\text{=}\text{no}\text{.}\text{density}\end{array}$

Mean free path:

The average distance that the molecule travels between two successive collisions is called the mean free path which is denoted by $\text{λ}$.

  $\begin{array}{l}\text{λ=}\frac{\text{RT}}{\sqrt{\text{2}}{\text{πd}}^{\text{2}}{\text{N}}_{\text{A}}\text{P}}\\ \\ \text{T}\text{=temperature}\\ \\ {\text{N}}_{\text{A}}\text{=}\text{Avogadro's}\text{number}\\ \\ \text{d}\text{=}\text{collision}\text{diameter}\\ \\ \text{P}\text{=}\text{pressure}\\ \\ \text{R=}\text{universalgasconstant}\end{array}$

Graham’s law:

At a given temperature and pressure the rate of effusion of a gas in inversely proportional to the square root of the molar mass of the gas.

  $\text{rate}\text{of}\text{effusion}\text{α}\frac{\text{1}}{\sqrt{\text{molar}\text{mass}\text{of}\text{the}\text{gas}\text{(M)}}}$