   # The density of air 20 km above Earth’s surface is 92 g/m 3 . The pressure of the atmosphere is 42 mm Hg, and the temperature is −63 °C. (a) What is the average molar mass of the atmosphere at this altitude? (b) If the atmosphere at this altitude consists of only O 2 and N 2 , what is the mole fraction of each gas? ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640

#### Solutions

Chapter
Section ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 10, Problem 75GQ
Textbook Problem
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## The density of air 20 km above Earth’s surface is 92 g/m3. The pressure of the atmosphere is 42 mm Hg, and the temperature is −63 °C. (a) What is the average molar mass of the atmosphere at this altitude? (b) If the atmosphere at this altitude consists of only O2 and N2, what is the mole fraction of each gas?

(a)

Interpretation Introduction

Interpretation:

For the given reaction under given set of conditions the mole fraction of N2 and the mass of N2 produced should be determined.

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.

nTPV = RnTPPV = nRTwhere,n = moles of gasP = pressureT = temperatureR = gas constant

Under some conditions gases don not behave like ideal gas that is they deviate from their ideal gas properties.  At lower temperature and at high pressures the gas tends to deviate and behave like real gases.

Boyle’s Law:

At given constant temperature conditions the mass of given ideal gas in inversely proportional to its volume.

Charles’s Law:

At given constant pressure conditions the volume of ideal gas is directly proportional to the absolute temperature.

Two equal volumes of gases with same temperature and pressure conditions tend to have same number of molecules with it.

### Explanation of Solution

Given:

T = -63 oC = 273.15-63 = 210.15KP = 42 mmHgD= 92g/m3Molarmass=?D=MassVolumeV=Mass92g/m3

PV=nRTn=PVRTMassMolarmass=42mmHg760mmHg×Mass92g/m3×103L0.0821×210.15K

(b)

Interpretation Introduction

Interpretation:

For the given reaction under given set of conditions the mole fraction of N2 and the mass of N2 produced should be determined.

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.

nTPV = RnTPPV = nRTwhere,n = moles of gasP = pressureT = temperatureR = gas constant

Under some conditions gases don not behave like ideal gas that is they deviate from their ideal gas properties. At lower temperature and at high pressures the gas tends to deviate and behave like real gases.

Boyle’s Law:

At given constant temperature conditions the mass of given ideal gas in inversely proportional to its volume.

Charles’s Law:

At given constant pressure conditions the volume of ideal gas is directly proportional to the absolute temperature.

Two equal volumes of gases with same temperature and pressure conditions tend to have same number of molecules with it.

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