Chapter 13: Gases – Properties, Laws, and Applications

Kinetic Molecular Theory of Gases

Fundamental Assumptions

The kinetic molecular theory explains the behavior of gases based on the motion and interactions of their particles.

• Gases are composed of small atoms or molecules that move in straight lines in all directions.

• Gas molecules are not attracted to one another and their collisions are elastic (no energy is lost).

• There is a large amount of space between gas molecules compared to their size.

• Gas particles move faster at higher temperatures, increasing their kinetic energy.

Properties of Gases

Key Properties

Gases exhibit several important physical properties that distinguish them from solids and liquids:

• Indefinite shape: Gases take the shape of their container, filling it completely.

• Low density: Gases are much less dense than liquids or solids (e.g., air ≈ 0.001 g/mL, water ≈ 1.0 g/mL).

• Compressibility: Gases can be compressed; their volume decreases under pressure and may liquefy if compressed enough.

• Expandability: Gases expand to fill any container; increasing the container's volume increases the gas's volume.

• Mixing: Gases mix completely with other gases in the same container, forming homogeneous mixtures (e.g., air).

Properties of Common Gases

Definitions and Examples

• Gas: A substance that is normally a gas under ordinary temperature and pressure (e.g., O2).

• Vapour: A substance that is normally a liquid under ordinary conditions but exists as a gas (e.g., water vapour).

• Most elemental gases (except noble gases) exist as diatomic molecules (e.g., H2, N2, O2), while noble gases are monatomic (e.g., Ne, Ar).

• Many gases are colorless and odorless, but some (e.g., Cl2, NO2) are colored or have distinct odors.

Gas Pressure

Definition and Units

Gas pressure (P) is the result of gas molecules striking the inside surface of their container.

• Pressure is defined as force per unit area: $\text{Pressure} = \frac{\text{Force}}{\text{Area}}$

Atmospheric Pressure

• Atmospheric pressure (atm): The average pressure from air molecules at sea level.

• Measured using a barometer (invented by Evangelista Torricelli in 1643).

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

Units of Pressure

Unit	Standard Pressure
atmosphere (atm)	1 atm (exactly)
millimeters of mercury (mm Hg)	760 mm Hg (exactly)
torr	760 torr (exactly)
pounds per square inch (psi)	14.7 psi
kilopascal (kPa)	101 kPa

Additional info: 1 kPa = 1000 Pa (SI unit of pressure).

Gas Pressure Conversions

• To convert between units, use the relationships above (e.g., $1\ \text{atm} = 760\ \text{mm Hg}$).

• Example: If a barometer reads 699 mm Hg, the pressure in atm is $\frac{699}{760} = 0.92$ atm.

Variables Affecting Gas Pressure

Key Variables

• Volume (V): Measured in liters (L) or milliliters (mL).

• Temperature (T): Must be in Kelvin ($K = ^\circ C + 273$).

• Number of molecules (n): Usually expressed in moles.

Relationships

• Volume and Pressure: Decreasing volume increases pressure (more collisions); increasing volume decreases pressure.

• Temperature and Pressure: Increasing temperature increases pressure (faster molecules); decreasing temperature decreases pressure.

• Molecules and Pressure: More molecules increase pressure; fewer molecules decrease pressure.

Gas Laws

Boyle's Law (Pressure-Volume Relationship)

• At constant temperature, the volume of a gas is inversely proportional to its pressure.

$V \propto \frac{1}{P}$ (at constant T)

Equation: $P_1 V_1 = P_2 V_2$

Charles' Law (Volume-Temperature Relationship)

• At constant pressure, the volume of a gas is directly proportional to its temperature (in Kelvin).

$V \propto T$ (at constant P)

Equation: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$

Gay-Lussac's Law (Pressure-Temperature Relationship)

• At constant volume, the pressure of a gas is directly proportional to its temperature (in Kelvin).

$P \propto T$ (at constant V)

Equation: $\frac{P_1}{T_1} = \frac{P_2}{T_2}$

Temperature Scales and Absolute Zero

Temperature Scales

• Celsius (°C): Water freezes at 0°C, boils at 100°C.

• Fahrenheit (°F): Water freezes at 32°F, boils at 212°F.

• Kelvin (K): Water freezes at 273 K, boils at 373 K. Kelvin is the absolute temperature scale.

Absolute Zero

• Theoretically, the temperature where the pressure and volume of a gas reach zero.

• Absolute zero: 0 K or -273°C. At this temperature, an ideal gas has no molecular motion.

Celsius-Kelvin Conversions

• To convert °C to K: $K = ^\circ C + 273$

• To convert K to °C: $^\circ C = K - 273$

Applications and Examples

• Scuba diving: Rapid ascent can cause lung overexpansion due to pressure changes (Boyle's Law in action).

• Atmospheric pressure: Lower at higher altitudes due to fewer air molecules above.

• Barometers: Used to measure atmospheric pressure; mercury column height changes with pressure.

Summary Table: Gas Laws

Law	Relationship	Equation	Constant
Boyle's Law	P ∝ 1/V	$P_1 V_1 = P_2 V_2$	T, n
Charles' Law	V ∝ T	$\frac{V_1}{T_1} = \frac{V_2}{T_2}$	P, n
Gay-Lussac's Law	P ∝ T	$\frac{P_1}{T_1} = \frac{P_2}{T_2}$	V, n

Additional info: These laws are foundational for understanding respiratory physiology, gas exchange, and the behavior of gases in biological systems.