Chapter 9, Problem 9.126CHP

Interpretation Introduction

Interpretation:

The mole fraction of the two gases in the ${\text{NO}}_{\text{2}}{\text{/N}}_{\text{2}}{\text{O}}_{\text{4}}$ mixture which exerts a pressure of $\text{0}\text{.487}\text{atm}\text{in}\text{a}\text{volume}\text{of}\text{6}\text{.51}\text{L}$ has to be given.

Concept Introduction:

Ideal gas Equation:

Any gas is described by using four terms namely pressure, volume, temperature and the amount of gas. Thus combining three laws namely Boyle’s, Charles’s Law and Avogadro’s Hypothesis the following equation could be obtained. It is referred as ideal gas equation.

$\begin{array}{l}\text{V }\propto \frac{\text{nT}}{\text{P}}\\ \text{V = R}\frac{\text{nT}}{\text{P}}\\ \text{PV = nRT}\end{array}$

Where,

$\begin{array}{l}\text{n = moles}\text{of}\text{gas}\\ \text{P = pressure}\\ \text{T = temperature}\\ \text{R = gas }\text{constant}\end{array}$

Mole fraction of a gas is defined as the ration of number of moles of one component to the ratio of total number of moles.

Average molecular mass of a mixture and mole fraction of each component in the mixture can be related by the equation:

$\overline{\text{M}}\text{=}{\displaystyle \sum _{\text{all}\text{component}}{\text{y}}_{\text{i}}{\text{M}}_{\text{i}}}$

Where ${\text{y}}_{\text{i}}$ is the mole fraction of the ${\text{i}}^{\text{th}}$ component of the mixture and $\overline{\text{M}}$ is the average molecular mass of the mixture.

Average molecular mass of the mixture can be calculated by the equation:

$\text{Number}\text{of}\text{moles}\text{=}\frac{\text{mass}}{\text{molar}\text{mass}}$

$\text{molar}\text{mass}\text{=}\frac{\text{mass}}{\text{Number}\text{of}\text{moles}}$