   # Given that a sample of air is made up of nitrogen, oxygen, and argon in the mole fractions 0.78 N 2 , 0.21 O 2 , and 0.010 Ar, what is the density of air at standard temperature and pressure? ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 8, Problem 80E
Textbook Problem
804 views

## Given that a sample of air is made up of nitrogen, oxygen, and argon in the mole fractions 0.78 N2, 0.21 O2, and 0.010 Ar, what is the density of air at standard temperature and pressure?

Interpretation Introduction

Interpretation: The density of given sample of air made up of nitrogen, oxygen and argon is to be calculated at STP where the moles fractions are 0.78N2 , 0.21O2 and 0.010Ar .

Concept introduction:

A mole fraction of a molecule in a mixture is the ratio of number of moles of these molecules to sum of number of moles of all molecules in the mixture. Average molar mass of mixture is calculated by adding all mass fractions of constituent molecules. The mass fraction of a molecule is the product of its mole fraction and the molar mass.

Equation for density is,

Density=MassVolume

According to ideal gas equation,

Pressure×Volume=Mass×R×TemperatureMolecularmass

Ideal gas equation in terms of Density,

Density=Pressure×Molecular massR×Temperature

### Explanation of Solution

Explanation

In the given sample of air, for 1 mole of sample air,

Mole fraction of N2 is 0.78N2 ,

Mole fraction of O2 is 0.21O2 ,

Mole fraction of Ar is 0.010Ar ,

Mass fraction of N2 is,

0.78×28g=21.84g

Mass fraction of O2 is,

0.21×32g=6.72g

Mass fraction of Ar is,

0.010×39.95g=0.3995g

The average molar mass of a mixture is sum of all mass fractions of constituted molecules.

Therefore, the average molar mass of given sample is,

21.84+6.72+0.3995=28.95=29g

Hence, the average molar mass of given sample is 29 g

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