Chapter 1, Problem 1.10P

Interpretation Introduction

Interpretation:

The number of collision frequency in a single methane molecule make in 0.10 mol held at ${25}^{o}C$ in a vessel of volume $1.0d{m}^3$ has to be determined.

Concept introduction:

The number of moles of any substance can be determined using the equation

$\text{Number}\text{of}\text{mole}\text{=}\frac{\text{Given}\text{mass}\text{of}\text{the}\text{substance}}{\text{Molar}\text{mass}}$

The molar mass of an element or compound is the mass in grams of 1 mole of that substance, and it is expressed in the unit of grams per mole (g/mol).

$Mass=Volume\times density$

Ideal gas equation,

$\text{PV}\text{=}\text{nRT}\boxed{\begin{array}{l}\text{Where,}\\ \text{P}\text{:}\text{Pressure}\\ \text{V:}\text{Volume}\\ \text{n:}\text{Number}\text{of}\text{moles}\\ \text{R:}\text{Gas}\text{constant}\\ \text{T}\text{:}\text{Temperature}\end{array}}$

Collision frequency is the number of collisions takes place in one second among the molecules present in one centimetre cube of the gas is called collision frequency.

$\text{Collision}\text{frequency,}\text{Z}\text{=}\frac{{\text{V}}_{\text{rms}}}{\text{λ}}\boxed{\begin{array}{l}\text{where,}\\ {\text{V}}_{\text{rms}}\text{=}\text{Root}\text{mean}\text{square}\text{velocity}\\ \text{λ}\text{=}\text{Mean}\text{free}\text{path}\end{array}}$

$\begin{array}{l}\text{Root}\text{Mean}\text{Square}\text{velocity}\left({\text{μ}}_{\text{rms}}\right)\text{=}\sqrt{\left(\text{3RT/M}\right)}\\ \boxed{\begin{array}{l}\text{where,}\\ \text{R}\text{:}\text{Gas}\text{constant}\\ \text{T}\text{:}\text{Temperature}\\ \text{M}\text{:}\text{Mass}\text{of}\text{one}\text{mole}\text{in}\text{kg}\end{array}}\end{array}$

$\text{Mean}\text{free}\text{path,}\text{λ}\text{=}\frac{\text{RT}}{\sqrt{\text{2}}{\text{πd}}^{\text{2}}{\text{N}}_{\text{A}}\text{P}}\boxed{\begin{array}{l}\text{where,}\\ \text{λ}\text{=}\text{mean}\text{free}\text{path}\\ \text{P}\text{=}\text{Pressure}\\ {\text{N}}_{\text{A}}\text{=}\text{Number}\text{of}\text{atoms/molecules}\\ \text{d}\text{=}\text{Diameter}\\ \text{T}\text{=}\text{Temperature}\end{array}}$