Chapter 11: Gases – Properties, Laws, and Applications

Gases: Properties and Behavior

Introduction to Gases

Gases are one of the fundamental states of matter, characterized by their ability to expand and fill any container. Understanding gases is essential for explaining phenomena such as breathing, weather, and chemical reactions involving gases.

Kinetic Molecular Theory

Basic Postulates

The kinetic molecular theory provides a model for understanding the behavior of gases. It is based on several key assumptions:

• Constant, straight-line motion: Gas particles are in continuous, random motion.

• No attractions or repulsions: Gas particles do not interact except during elastic collisions.

• Large spaces between particles: The volume of the particles is negligible compared to the space between them.

• Kinetic energy and temperature: The average kinetic energy of gas particles is directly proportional to the temperature in kelvin.

Properties Explained by Kinetic Molecular Theory

• Compressibility: Gases can be compressed because of the large amount of empty space between particles.

• Shape and volume: Gases assume the shape and volume of their container due to negligible intermolecular forces.

• Low density: Gases have much lower densities than solids or liquids because of the large distances between particles.

Pressure and Its Origin

Definition of Pressure

Pressure is defined as the force exerted per unit area by gas particles colliding with surfaces. The SI unit is the pascal (Pa), but atmospheres (atm) and millimeters of mercury (mm Hg) are also commonly used.

• Atmospheric pressure: The pressure exerted by Earth's atmosphere at sea level is about 1 atm.

• Pressure and number of particles: Increasing the number of gas particles in a fixed volume increases the pressure.

Pressure in Everyday Life

• Pressure differences allow us to drink through straws, inflate objects, and breathe.

• Atmospheric pressure decreases with altitude, affecting the human body (e.g., ear pain during airplane ascent).

Units of Pressure

Common Units

• Atmosphere (atm): Standard atmospheric pressure at sea level.

• Pascals (Pa): SI unit, where 1 Pa = 1 N/m2.

• Millimeters of mercury (mm Hg): Based on the height of a mercury column in a barometer; 1 atm = 760 mm Hg.

• Torr: 1 torr = 1 mm Hg.

Gas Laws

Boyle’s Law: Pressure and Volume

Boyle’s law states that the volume of a gas is inversely proportional to its pressure at constant temperature and amount of gas.

• Mathematical form: $P_1V_1 = P_2V_2$

• As pressure increases, volume decreases, and vice versa.

Charles’s Law: Volume and Temperature

Charles’s law states that the volume of a gas is directly proportional to its temperature (in kelvin) at constant pressure and amount of gas.

• Mathematical form: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$

• As temperature increases, volume increases.

Avogadro’s Law: Volume and Moles

Avogadro’s law states that the volume of a gas is directly proportional to the number of moles of gas at constant temperature and pressure.

• Mathematical form: $\frac{V_1}{n_1} = \frac{V_2}{n_2}$

• As the amount of gas increases, volume increases.

The Combined Gas Law

The combined gas law relates pressure, volume, and temperature for a fixed amount of gas:

• Mathematical form: $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$

The Ideal Gas Law

The ideal gas law combines Boyle’s, Charles’s, and Avogadro’s laws into a single equation:

• Mathematical form: $PV = nRT$

• Where R is the ideal gas constant ($R = 0.0821$ L·atm·mol−1·K−1)

• Applies best under conditions of low pressure and high temperature.

Applications of Gas Laws

Partial Pressures and Dalton’s Law

In a mixture of gases, each gas exerts its own pressure, called partial pressure. Dalton’s law states that the total pressure is the sum of the partial pressures of all components:

• Mathematical form: $P_{\text{total}} = P_1 + P_2 + P_3 + \ldots$

• Partial pressure: $P_{\text{component}} = \text{fractional composition} \times P_{\text{total}}$

Collecting Gases Over Water

When collecting gases over water, the total pressure is the sum of the gas pressure and the vapor pressure of water. The vapor pressure depends on temperature and must be subtracted to find the pressure of the collected gas.

Molar Volume at STP

At standard temperature and pressure (STP: 0°C and 1 atm), one mole of any ideal gas occupies 22.4 L. This is useful for stoichiometric calculations involving gases.

Non-Ideal Gas Behavior

Deviations from Ideal Gas Law

Real gases deviate from ideal behavior at high pressures and low temperatures, where intermolecular forces and the finite size of particles become significant.

Gases in the Environment

Air Pollution

Major gaseous pollutants include sulfur dioxide (SO2), carbon monoxide (CO), ozone (O3), and nitrogen dioxide (NO2). These pollutants can cause respiratory problems and environmental damage. Legislation such as the Clean Air Act has significantly reduced pollutant levels in many cities.

Summary Table: Common Units of Pressure

Unit	Symbol	Equivalent to 1 atm
Atmosphere	atm	1 atm
Millimeter of mercury	mm Hg	760 mm Hg
Torr	torr	760 torr
Pounds per square inch	psi	14.7 psi
Pascals	Pa	101,325 Pa

Key Equations

• Boyle’s Law: $P_1V_1 = P_2V_2$

• Charles’s Law: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$

• Avogadro’s Law: $\frac{V_1}{n_1} = \frac{V_2}{n_2}$

• Combined Gas Law: $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$

• Ideal Gas Law: $PV = nRT$

• Dalton’s Law: $P_{\text{total}} = P_1 + P_2 + P_3 + \ldots$

Learning Objectives

• Describe how kinetic molecular theory predicts the main properties of a gas.

• Identify and explain the relationship between pressure, force, and area.

• Convert among pressure units.

• Restate and apply Boyle’s, Charles’s, Avogadro’s, and the ideal gas law.

• Apply Dalton’s law of partial pressures and stoichiometry to chemical reactions involving gases.