Chapter 8 Gases - Chemistry Notes

Chapter 8 Gases

Introduction

• Respiratory therapists use gas measurements to assess patients, including:
  • Breathing capacity.
  • Concentrations of oxygen and carbon dioxide in blood.
  • Blood pH.

Chapter Objectives

• Describe the kinetic molecular theory of gases.
• Describe and convert units of measurement for pressure.
• Apply gas laws to determine new pressure, volume, temperature, or moles of a gas.
• Describe the relationship between the amount of gas and its volume.
• Calculate total pressure in a gas mixture using partial pressures.
• Use mole fraction to calculate partial pressure of a gas in a mixture.

Readiness Key Math Skills

• Solving Equations (1.4D)

Core Chemistry Skills

• Using Significant Figures in Calculations (2.3)
• Writing Conversion Factors from Equalities (2.5)
• Using Conversion Factors (2.6)
• Using Molar Mass as a Conversion Factor (7.2)
• Using Mole–Mole Factors (7.6)

8.1 Properties of Gases

• Gases at room temperature typically consist of molecules with fewer than five atoms from the first two periods.
• Examples:
  • H2, N2, O2, F2, and Cl_2
  • Oxides of nonmetals: CO, CO2, NO, NO2, SO2, and SO3
  • Noble gases
• Learning Goal: Describe the kinetic molecular theory of gases and the units of measurement used for gases.

Kinetic Molecular Theory

• A gas consists of small particles that:
  • Move rapidly in straight lines.
  • Have essentially no attractive or repulsive forces.
  • Are very far apart.
  • Have very small volumes compared to the volume of the container they occupy.
  • Have kinetic energies that increase with an increase in temperature.

Properties That Describe a Gas

• Gases are described by four properties:
  • Pressure (P)
  • Volume (V)
  • Temperature (T)
  • Amount (n)

Volume

• The volume of a gas:
  • Is the same as the volume of the container it occupies.
  • Is usually measured in liters (L) or milliliters (mL).
  • Increases with an increase in temperature at a constant pressure.

Temperature

• The temperature of a gas relates to the average kinetic energy of the molecules and is measured in Kelvin (K).
• Temperature effects:
  • Decreased temperature: Fewer molecular collisions.
  • Increased temperature: More molecular collisions.

Pressure

• Pressure is a measure of the gas particle collisions with the sides of a container.
• Units of pressure:
  • millimeters of mercury (mmHg) or torr
  • atmospheres (atm)
  • pascals (Pa) or kilopascals (kPa)
  • pounds per square inch (psi)
• Atmospheric pressure: Gas particles in the air exert pressure on us.

Barometers Measure Pressure

• A barometer:
  • Measures the pressure exerted by the gases in the atmosphere.
  • Indicates atmospheric pressure as the height in millimeters of the mercury column.
  • 760 mmHg = 1 atm = 760 torr
• The barometer was invented by Evangelista Torricelli.
• At exactly 1 atm, the barometer tube is exactly 760 mm high.

Atmospheric Pressure

• Atmospheric pressure:
  • Is the pressure exerted by a column of air from the top of the atmosphere to the surface of Earth.
  • Decreases as altitude increases.
  • Is 1 atm at sea level.

Altitude and Atmospheric Pressure

• Atmospheric pressure changes with variations in weather and altitude.
  • Hot, sunny day: Mercury column rises, indicating higher atmospheric pressure.
  • Rainy day: Atmosphere exerts less pressure, causing the mercury column to fall.

8.2 Pressure and Volume: Boyle’s Law

• Boyle’s law: The inverse relationship between the pressure and volume of a gas.
  • Changes occur in opposite directions.
  • When volume increases, the pressure decreases provided the temperature and moles of the gas remain constant.
• Learning Goal: Use the pressure–volume relationship (Boyle’s law) to determine the final pressure or volume when the temperature and amount of gas are constant.

Boyle’s Law

• Boyle’s law states that:
  • The pressure of a gas is inversely related to its volume when T is constant.
  • The product P × V is constant when temperature and amount of a gas are held constant.
  • If volume decreases, the pressure increases.
• Equation: P1V1 = P2V2

Boyle’s Law: PV = Constant

• Pressure × volume is a constant, provided that the temperature and amount of the gas remain the same.
• P1V1 = 8.0 atm Imes 2.0 L = 16 atm Imes L
• P2V2 = 4.0 atm Imes 4.0 L = 16 atm Imes L
• P3V3 = 2.0 atm Imes 8.0 L = 16 atm Imes L
• Boyle’s law can be stated as P1V1 = P2V2 (T is constant.)

Chemistry Link to Health: Boyle’s Law and Breathing

• During an inhalation:
  • The lungs expand.
  • The pressure in the lungs decreases.
  • Air flows toward the lower pressure in the lungs.
• During an exhalation:
  • Lung volume decreases.
  • Pressure within the lungs increases.
  • Air flows from the higher pressure in the lungs to the outside.

Calculations Using Boyle’s Law

• Freon-12, CCl2F2, was used in refrigeration systems. What is the new volume of an 8.0-L sample of Freon gas initially at 550 mmHg after its pressure is changed to 2200 mmHg at constant temperature and moles?
  • Step 1: Organize the data in a table of initial and final conditions. Temperature and moles remain constant.
  • Step 2: Rearrange the gas law equation to solve for the unknown quantity.
    • P1V1 = P2V2
    • To solve for V2, divide both sides by P2.
  • Step 3: Substitute values into the gas law equation and calculate.

8.3 Temperature and Volume: Charles’s Law

• If we increase the temperature of a gas sample, kinetic molecular theory states that the motion (kinetic energy) of the gas particles will also increase.
• If the amount and pressure of the gas is held constant, the volume of the container will increase.
• Learning Goal: Use the temperature–volume relationship (Charles’s law) to determine the final temperature or volume when the pressure and amount of gas are constant.

Charles’s Law

• In Charles’s law,
  • the Kelvin temperature of a gas is directly related to the volume
  • pressure and moles of gas are constant
  • when the temperature of a sample of gas increases, its volume increases at a constant pressure

Charles’s Law: V and T

• For two conditions, Charles’s law is written (P and n are constant.)
• \frac{V1}{T1} = \frac{V2}{T2}
• Rearranging Charles’s law to solve for V2, we obtain the following:
• V2 = V1 \frac{T2}{T1}

8.4 Temperature and Pressure: Gay-Lussac’s Law

• Gay-Lussac’s law: When the Kelvin temperature of a gas doubles at constant volume and amount of gas, the pressure also doubles.
• Learning Goal: Use the temperature–pressure relationship (Gay-Lussac’s law) to determine the final temperature or pressure when the volume and amount of gas are constant.

Gay-Lussac’s Law

• In Gay-Lussac’s law,
  • the pressure exerted by a gas is directly related to the Kelvin temperature of the gas
  • volume and amount of gas are constant

8.5 The Combined Gas Law

• Under water, the pressure on a diver is greater than the atmospheric pressure.
• The combined gas law comes from the pressure–volume–temperature relationships for gases that we have studied.
• Learning Goal: Use the combined gas law to calculate the final pressure, volume, or temperature of a gas when changes in two of these properties are given and the amount of gas is constant.

The Combined Gas Law

• The combined gas law uses the pressure–volume–temperature relationships from Boyle’s law, Charles’s law, and Gay-Lussac’s law where n is constant.
• Boyle’s law P1V1 = P2V2
• Charles’s law \frac{V1}{T1} = \frac{V2}{T2}
• Gay-Lussac’s law \frac{P1}{T1} = \frac{P2}{T2}
• Combined gas law \frac{P1V1}{T1} = \frac{P2V2}{T2}

8.6 Volume and Moles: Avogadro’s Law

• The molar volume of a gas at STP is about the same as the volume of three basketballs.
• The volume of 1 mole of gas is 22.4 liters.
• Learning Goal: Use Avogadro’s law to calculate the amount or volume of a gas when the pressure and temperature are constant.

Avogadro’s Law: Volume and Moles

• In Avogadro’s law,
  • the volume of a gas is directly related to the number of moles (n) of gas
  • T and P are constant

Standard Temperature and Pressure

• The volumes of gases can be compared at STP, Standard Temperature and Pressure, when they have
  • the same temperature standard temperature (T) 0 °C or 273 K
  • the same pressure standard pressure (P) 1 atm (760 mmHg)

Molar Volume, STP

• At standard temperature and pressure (STP), 1 mole of a gas occupies a volume of 22.4 L, which is called its molar volume.
• Use this equality as a conversion factor for gas at STP: 22.4 L = 1 mole gas

The Ideal Gas Law

• The relationships among the four variables P, V, T, and n, are combined into a single expression: the ideal gas law.
• PV = nRT
• The term “R” in this equation is the ideal gas constant. The value of R can be calculated as follows for one mole of a gas at STP.
• R = \frac{PV}{nT}
• R = \frac{(1.00 atm)(22.4 L)}{(1.00 mole)(273 K)} = 0.0821 \frac{L Imes atm}{mol Imes K}

8.7 Partial Pressure: Dalton’s Law

• Our cells continuously use oxygen and produce carbon dioxide. Both gases move in and out of the lungs through the membranes of the alveoli, the tiny air sacs at the ends of the airways in the lungs.
• Learning Goal: Use Dalton’s law of partial pressures to calculate the total pressure of a mixture of gases.

Partial Pressure

• The partial pressure of a gas is the pressure that each gas in a mixture would exert if it were by itself in the container.

Dalton’s Law of Partial Pressures

• Dalton’s law of partial pressures indicates that
  • pressure depends on the total number of gas particles, not on the types of particles
  • the total pressure exerted by gases in a mixture is the sum of the partial pressures of those gases
• PT = P1 + P2 + P3 + ….