Chapter 5, Problem 5.87PAE

Interpretation Introduction

Interpretation:

A gas mixture contains 10.0% CH₄ and 90.0% $\text{Ar}$ by moles. The density of this gas at 250.0 ⁰C and 2.50 atm needs to be calculated.

Concept introduction:

An ideal gas which is known as the perfect gas is a gas whose volume V, Pressure P and temperature T are related through the ideal gas as: -

$\text{PV = nRT}$

Here,

n = number of moles of the gas

R = ideal gas constant

T = Temperature

P = Pressure

Ideal gases are described as the molecules which have negligible size but have an average molar kinetic energy which is dependent on the temperature. When temperature is low, and pressure is high, most of the gases behave like ideal gases and the ideal gas law might be applied to them.

Also, density of a substance is related to number of moles as follows:

$\begin{array}{c}\rho =\frac{\text{m}}{\text{V}}\\ =\frac{\text{n}\times \text{M}}{\text{V}}\end{array}$

Here, $\rho$ is density, n is number of moles, M is molar mass and V is volume.

Given:

Percentage of ${\text{CH}}_{\text{4}}$ =10%

Percentage of $\text{Ar}$ =90%

Temperature= $250{}^{\circ }\text{C}$

And,

Pressure= 2.50 atm