Gases: Properties, Laws, and Applications (Chapter 8 Study Notes)

Gases (Chapter 8)

Introduction and Medical Relevance

Gases play a crucial role in both biological and physical systems. Pulmonologists and respiratory therapists use gas properties to diagnose and monitor breathing capacity, oxygen and carbon dioxide blood concentrations, and blood pH (acidity, alkalinity). Understanding gas behavior is essential for interpreting physiological processes and for applications such as scuba diving and respiratory therapy.

• Breathing capacity: Measurement of lung volume and efficiency.

• Oxygen and carbon dioxide concentrations: Key indicators of respiratory function.

• Blood pH: Reflects the balance between acidic and basic components in blood, influenced by gas exchange.

Gaseous Elements and Compounds

Gaseous Elements at Room Temperature

At room temperature (T) and 1 atmosphere (P), certain elements exist as gases. These include:

• Noble gases: He, Ne, Ar, Kr, Xe, Rn (exist as single atoms)

• Diatomic gases: H2, N2, O2, F2, Cl2

• Halogens: I2 (solid with vapor pressure)

• Oxides of nonmetals: CO, CO2, NO, NO2, SO2, SO3

These gases are found in the upper-right corner of the Periodic Table and are important in atmospheric and chemical processes.

Properties of Gases (Section 8.1)

General Characteristics

Gases represent one of the states of matter and have distinct properties:

• Indefinite shape and volume: Gases take the shape and volume of their container.

• Particles far apart: Minimal interactions between particles.

• Low densities: Much less dense than solids or liquids.

• Mix easily: Gases can form homogeneous mixtures with other non-reactive gases.

• Particles move rapidly: In random directions at high speeds.

Kinetic-Molecular Theory of Gases

Postulates of the Theory

The kinetic-molecular theory explains the behavior of gases at the molecular level:

• Gases consist of atoms or molecules moving randomly at high velocities.

• The volume of gas molecules is negligible compared to the total volume of the container.

• Gas particles act independently; there are essentially no attractive or repulsive forces.

• Particles move in straight paths and collisions result in complete or nearly complete transfer of kinetic energy.

• Average kinetic energy of gas particles is proportional to their absolute temperature (T).

Equation: $KE_{avg} \propto T$

Gas Pressure, P

Definition and Units

Gas pressure arises from collisions of gas particles with the walls of their container. It is measured in several units:

• Pascal (Pa): SI unit for pressure

• Atmosphere (atm): Commonly used in chemistry

• Other units: mmHg, Torr, psi, kPa

Unit	Abbreviation	Equivalent to 1 atm
Atmosphere	atm	1 atm (exact)
Millimeters of Hg	mmHg	760 mmHg (exact)
Torr	Torr	760 Torr (exact)
Pounds per square inch	psi	14.7 psi
Pascal	Pa	101,325 Pa
Kilopascal	kPa	101.325 kPa

Example: To convert 2.00 atm to Pa: $2.00 \text{ atm} \times 101325 \text{ Pa/atm} = 202650 \text{ Pa}$

Atmospheric Pressure

Definition and Measurement

Atmospheric pressure is the force exerted by the column of air (gas mixture) above Earth's surface. It is measured using a barometer as the height of a mercury column.

• At sea level, atmospheric pressure is 1 atm or 760 mmHg.

• Atmospheric pressure decreases as altitude increases.

Location	Altitude (km)	Atmospheric Pressure (mmHg)
Dead Sea	-0.40	800
Sea Level	0.00	760
Los Angeles	0.30	752
Denver	1.60	632
Mount Whitney	4.40	435
Mount Everest	8.80	253

Variables that Define Gas Properties

Four Key Variables

Gas properties are defined by four variables:

• P: Pressure

• T: Temperature (in Kelvin, K)

• V: Volume of container

• n: Number of moles of gas

Property	Description	Units of Measurement
Pressure (P)	Force exerted by gas against container walls	atm, mmHg, Torr, Pa
Volume (V)	Space occupied by gas	L, mL
Temperature (T)	Determines kinetic energy	°C, K
Amount (n)	Quantity of gas present	grams, moles

Containers for Gases: Rigid vs. Flexible

Types of Containers

• Rigid cylinder: Fixed volume, can be pressurized above 1 atm.

• Flexible balloon: Volume can change; expands until internal pressure equals atmospheric pressure.

Volume calculations may differ based on container type (cylinder, sphere, cube).

Ideal Gas Law (Section 8.7)

Fundamental Equation

The ideal gas law relates pressure, volume, temperature, and amount of gas:

Equation: $P V = n R T$

• R: Universal gas constant

• $R = 0.0821 \text{ L} \cdot \text{atm} \cdot \text{mol}^{-1} \cdot \text{K}^{-1}$

• $R = 8.314 \text{ J} \cdot \text{mol}^{-1} \cdot \text{K}^{-1}$

Choose the appropriate value of R based on units in the problem.

Example Calculation

Find the volume (V) of 2.0 moles of gas at T = 600 K and P = 2.00 atm:

$V = \frac{nRT}{P} = \frac{(2.0 \text{ mol})(0.0821 \text{ L} \cdot \text{atm} \cdot \text{mol}^{-1} \cdot \text{K}^{-1})(600 \text{ K})}{2.00 \text{ atm}} = 49 \text{ L}$

Combined Gas Law (Section 8.5)

When Multiple Properties Change

If more than two properties of a gas change simultaneously (with n constant), the combined gas law is used:

Equation: $\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$

This law allows calculation of a new property when initial and final conditions are known.

Example Calculation

Given: $P_1 = 1.0$ atm, $V_1 = 1.0$ L, $T_1 = 300$ K, $P_2 = 4.0$ atm, $T_2 = 600$ K, $n$ constant. Find $V_2$:

$V_2 = \frac{P_1 V_1 T_2}{T_1 P_2} = \frac{(1.0 \text{ atm})(1.0 \text{ L})(600 \text{ K})}{(300 \text{ K})(4.0 \text{ atm})} = 0.50 \text{ L}$

Named Gas Laws Derived from Ideal Gas Law

Boyle's Law (P and V)

At constant n and T:

$P_1 V_1 = P_2 V_2$

Volume is inversely proportional to pressure.

Charles's Law (V and T)

At constant n and P:

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

Volume is directly proportional to absolute temperature.

Gay-Lussac's Law (P and T)

At constant n and V:

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

Pressure is directly proportional to absolute temperature.

Avogadro's Law (V and n)

At constant P and T:

$\frac{V_1}{n_1} = \frac{V_2}{n_2}$

Volume is directly proportional to the number of moles.

Practice Problems and Applications

Sample Calculations

• Convert pressure units: $2.00 \text{ atm} = 202650 \text{ Pa}$

• Calculate moles using ideal gas law: $n = \frac{PV}{RT}$

• Use combined gas law for changing conditions.

Summary Table: Gas Laws

Law	Equation	Constant Variables	Relationship
Boyle's Law	$P_1 V_1 = P_2 V_2$	n, T	V ∝ 1/P
Charles's Law	$\frac{V_1}{T_1} = \frac{V_2}{T_2}$	n, P	V ∝ T
Gay-Lussac's Law	$\frac{P_1}{T_1} = \frac{P_2}{T_2}$	n, V	P ∝ T
Avogadro's Law	$\frac{V_1}{n_1} = \frac{V_2}{n_2}$	P, T	V ∝ n

Additional info:

• All equations are provided in LaTeX format for clarity and academic rigor.

• Tables have been recreated to summarize units, properties, and gas laws.

• Examples and applications are expanded for self-contained study.