   Chapter 10, Problem 40PS

Chapter
Section
Textbook Problem

A collapsed balloon is filled with He to a volume of 12.5 L at a pressure of 1.00 atm. Oxygen, O2, is then added so that the final volume of the balloon is 26 L with a total pressure of 1.00 atm. The temperature, which remains constant throughout, is 21.5 °C. (a) What mass of He does the balloon contain? (b) What is the final partial pressure of He in the balloon? (c) What is the partial pressure of O2 in the balloon? (d) What is the mole fraction of each gas?

(a)

Interpretation Introduction

Interpretation:

The mass, partial pressure of He, partial pressure of O2 and mole fraction of both gas has to be given.

Concept Introduction:

• Partial pressure: The pressure of each gas in a mixture of gases is the partial pressure.
• Dalton’s law of partial pressure: The total pressure of gases in a mixture of gases is the sum of the pressure of each gas in the mixture
• Mole fraction: Quantity which defines the number of moles of a substance in a mixture divided by the total number of moles of all substances present.

xa=nantotal

pa=xa×Ptotal

Partial pressure of a gas in the mixture of gases is the product of mole fraction of the gas and the total pressure.

• Ideal gas equation:

PV=nRTP-PressureV-VolumeR-UniversalgasconstantT-Temperaturen-numberofmoles

Explanation

The mass of helium in the balloon can be calculated as

Given:

VolumeofHe=12.5LPressure=1atmTemperature=21.5°C

According to ideal gas equation

PV=nRT

n=PVRT=1atm×12.5L0.082L.atm/K.mol×294.5K=0.517mol

Numberofmoles=massmolarmassmassofhelium

(b)

Interpretation Introduction

Interpretation:

The mass, partial pressure of He, partial pressure of O2 and mole fraction of both gas has to be given.

Concept Introduction:

• Partial pressure: The pressure of each gas in a mixture of gases is the partial pressure.
• Dalton’s law of partial pressure: The total pressure of gases in a mixture of gases is the sum of the pressure of each gas in the mixture
• Mole fraction: Quantity which defines the number of moles of a substance in a mixture divided by the total number of moles of all substances present.

xa=nantotal

pa=xa×Ptotal

Partial pressure of a gas in the mixture of gases is the product of mole fraction of the gas and the total pressure.

• Ideal gas equation:

PV=nRTP-PressureV-VolumeR-UniversalgasconstantT-Temperaturen-numberofmoles

(c)

Interpretation Introduction

Interpretation:

The mass, partial pressure of He, partial pressure of O2 and mole fraction of both gas has to be given.

Concept Introduction:

• Partial pressure: The pressure of each gas in a mixture of gases is the partial pressure.
• Dalton’s law of partial pressure: The total pressure of gases in a mixture of gases is the sum of the pressure of each gas in the mixture
• Mole fraction: Quantity which defines the number of moles of a substance in a mixture divided by the total number of moles of all substances present.

xa=nantotal

pa=xa×Ptotal

Partial pressure of a gas in the mixture of gases is the product of mole fraction of the gas and the total pressure.

• Ideal gas equation:

PV=nRTP-PressureV-VolumeR-UniversalgasconstantT-Temperaturen-numberofmoles

(d)

Interpretation Introduction

Interpretation:

The mass, partial pressure of He, partial pressure of O2 and mole fraction of both gas has to be given.

Concept Introduction:

• Partial pressure: The pressure of each gas in a mixture of gases is the partial pressure.
• Dalton’s law of partial pressure: The total pressure of gases in a mixture of gases is the sum of the pressure of each gas in the mixture
• Mole fraction: Quantity which defines the number of moles of a substance in a mixture divided by the total number of moles of all substances present.

xa=nantotal

pa=xa×Ptotal

Partial pressure of a gas in the mixture of gases is the product of mole fraction of the gas and the total pressure.

• Ideal gas equation:

PV=nRTP-PressureV-VolumeR-UniversalgasconstantT-Temperaturen-numberofmoles

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