Chapter 8: Gases – Properties, Laws, and States of Matter

Chapter 8: Gases

Overview

This chapter explores the fundamental properties of gases, the physical laws that describe their behavior, and the relationship between kinetic and potential energy in the context of the states of matter. The focus is on understanding how gases differ from solids and liquids, and how variables such as pressure, volume, temperature, and the number of moles interact.

Kinetic and Potential Energy

Definitions and Concepts

• Potential Energy: The stored energy of an object due to its position or composition. In chemistry, this often refers to the energy stored within chemical bonds or due to the arrangement of particles.

• Kinetic Energy: The energy of motion. In the context of gases, it is the energy that causes molecules to move and spread apart.

• Intermolecular Forces: The attractive forces that hold molecules together. These forces are significant in solids and liquids but negligible in gases.

The state of matter of a substance depends on the balance between intermolecular forces (which hold particles together) and kinetic energy (which drives them apart).

States of Matter

Classification and Properties

Matter exists in three primary states: solid, liquid, and gas. Each state is characterized by distinct physical properties, which are determined by the relative strengths of intermolecular forces and kinetic energy.

State	Density	Volume	Relative Strengths
Solid	Dense	Fixed	Intermolecular forces > kinetic energy
Liquid	Dense	Fixed (takes shape of container)	Intermolecular forces > kinetic energy
Gas	Less dense	Expands to fill container	Kinetic energy > intermolecular forces

Compressibility and Squeezability

The ability to compress a substance ("squeezability") varies by state:

State	Fluid?	Compressible?
Solid	No	No
Liquid	Yes	Slightly
Gas	Yes	Yes

Gases are highly compressible due to the large amount of empty space between particles, while solids and liquids are much less compressible.

8.1 Properties of Gases

Kinetic Molecular Theory

• Constant, Random Motion: Gas particles move in straight lines until they collide with each other or the walls of their container.

• Negligible Volume: The actual volume of gas particles is very small compared to the volume of the container.

• Negligible Attractive Forces: Intermolecular attractions are so weak in gases that they can be ignored for most calculations.

• Temperature and Kinetic Energy: The temperature of a gas is directly proportional to the average kinetic energy of its particles.

Gases and Pressure

Definition and Measurement

• Pressure (P): The force exerted per unit area. In gases, this is due to collisions of particles with the walls of the container.

• Mathematically: $P = \frac{\text{Force}}{\text{Area}}$

• Barometer: An instrument used to measure atmospheric pressure.

• Units of Pressure:

  • Atmosphere (atm)

  • Millimeters of mercury (mm Hg) or torr (1 mm Hg = 1 torr)

  • Standard atmospheric pressure: 1 atm = 760 torr = 760 mm Hg

Gas Laws

Pressure and Volume (Boyle’s Law)

Boyle’s Law describes the inverse relationship between the pressure and volume of a gas at constant temperature.

• At constant temperature, as the volume of a gas decreases, its pressure increases, and vice versa.

• Mathematically: $P V = \text{constant}$

• Example: Compressing a syringe decreases its volume and increases the pressure inside.

Volume and Temperature (Charles’s Law)

Charles’s Law states that the volume of a gas is directly proportional to its temperature (in Kelvin) at constant pressure.

• As temperature increases, volume increases.

• Mathematically: $\frac{V}{T} = \text{constant}$

• Temperature must be in Kelvin: $T_{\text{K}} = T_{\text{C}} + 273$

• Example: A balloon expands when heated.

Pressure and Temperature (Gay-Lussac’s Law)

Gay-Lussac’s Law states that the pressure of a gas is directly proportional to its temperature (in Kelvin) at constant volume.

• As temperature increases, pressure increases.

• Mathematically: $\frac{P}{T} = \text{constant}$

• Example: A sealed aerosol can may burst if heated.

Volume and Moles (Avogadro’s Law)

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.

• As the number of moles increases, volume increases.

• Mathematically: $\frac{V}{n} = \text{constant}$

• Example: Inflating a tire increases the number of moles of air, increasing its volume.

Pressure and Moles

At constant volume and temperature, the pressure of a gas is directly proportional to the number of moles.

• As the number of moles increases, pressure increases.

• Mathematically: $\frac{P}{n} = \text{constant}$

The Ideal Gas Law

The relationships between pressure, volume, temperature, and moles are combined in the Ideal Gas Law:

• $P V = n R T$

• Where:

  • $P$ = pressure (atm)

  • $V$ = volume (L)

  • $n$ = number of moles

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

  • $T$ = temperature (K)

Note: The Combined Gas Law and Dalton’s Law of Partial Pressures are skipped in this section.

Negative Pressure Breathing (Application)

Breathing in mammals is an example of Boyle’s Law in action:

• Inhalation: The diaphragm moves down, increasing lung volume and decreasing pressure, causing air to enter the lungs.

• Exhalation: The diaphragm moves up, decreasing lung volume and increasing pressure, causing air to exit the lungs.

Summary Table: Gas Laws

Law	Variables Held Constant	Relationship	Equation
Boyle’s Law	Temperature, moles	$P \propto \frac{1}{V}$	$P V = \text{constant}$
Charles’s Law	Pressure, moles	$V \propto T$	$\frac{V}{T} = \text{constant}$
Gay-Lussac’s Law	Volume, moles	$P \propto T$	$\frac{P}{T} = \text{constant}$
Avogadro’s Law	Pressure, temperature	$V \propto n$	$\frac{V}{n} = \text{constant}$

Additional info: The notes skip the Combined Gas Law and Dalton’s Law of Partial Pressures, but these are important for a complete understanding of gas behavior in more advanced contexts.