Chapter 8.6, Problem 8.9PSP

Interpretation Introduction

Interpretation:

Total pressure of mixture containing $7.0{\text{ g N}}_2$ and $6.0{\text{ g H}}_2$ has to be calculated.  Also partial pressure and mole fraction of each gas has to be determined using the given data.

Concept Introduction:

Total pressure of a flask containing mixture of gases is the sum of individual partial pressures of constituted gases.

A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture.

Equation for mole fraction of a molecule in a mixture of three molecules (A, B and C) is,

  ${\text{χ}}_{\text{A}}\text{=}\frac{{\text{n}}_{\text{A}}}{{\text{n}}_{\text{A}}{\text{+n}}_{\text{B}}{\text{+n}}_{\text{C}}}$

  ${\text{χ}}_{\text{A}}$ is mole fraction of A.

  ${\text{n}}_{\text{A}}$ is numbers of moles of molecule A.

  ${\text{n}}_{\text{A}}{\text{+n}}_{\text{B}}{\text{+n}}_{\text{C}}$ is Total number of moles.

  $\text{n}\text{ =}\frac{\text{m}}{\text{M}}$

  $\text{n}$ = Number of moles.

  M = Molar mass

  m = mass.

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.

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

Here,

  n = moles of gas

    P = Pressure

    T = Temperature

    R = gas constant