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

Gases in Biological and Practical Contexts

Medical and Environmental Relevance

• Pulmonologists and respiratory therapists use gas laws to interpret diagnostic tests such as breathing capacity, oxygen and carbon dioxide blood concentrations, and blood pH (acidity/alkalinity).

• Gas laws are essential for understanding how gases are exchanged in the lungs and transported in the blood.

• Applications include scuba diving, respiratory therapy, and understanding atmospheric pressure effects on the body.

Gaseous Elements and Compounds

Gaseous Elements at Room Temperature and 1 atm

• Noble gases (He, Ne, Ar, Kr, Xe, Rn, Og) exist as monatomic species.

• Hydrogen, nitrogen, oxygen, and some halogens (H2, N2, O2, F2, Cl2, I2) exist as diatomic gases (I2 is a solid with vapor pressure at room temperature).

• Oxides of nonmetals in the upper-right corner of the periodic table often exist as gases (e.g., CO, CO2, NO, NO2, SO2, SO3).

Properties of Gases

General Characteristics

• Gases have indefinite shape and volume, taking the shape and volume of their container.

• Gas particles are far apart with essentially no interactions between them.

• Gases have low densities compared to solids and liquids.

• They are compressible due to the large spaces between particles.

• Gas particles move very fast in random directions.

• Gases form homogeneous mixtures with other non-reactive gases.

Kinetic-Molecular Theory of Gases

Postulates and Implications

• 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 of each other; there are essentially no attractive or repulsive forces.

• Gas particles move in straight paths until they collide with other particles or the container walls, transferring kinetic energy.

• The average kinetic energy of gas particles is proportional to their Kelvin temperature.

Gas Pressure

Definition and Units

• Pressure (P) of a gas inside a container arises from collisions of gas particles with container walls.

• The SI unit for gas pressure is the Pascal (Pa); however, atmosphere (atm) is widely used.

Unit	Abbreviation	Unit Equivalent to 1 atm
atmosphere	atm	1 atm (exact)
millimeters of Hg	mmHg	760 mmHg (exact)
torr	Torr	760 Torr (exact)
inches of Hg	inHg	29.9 inHg
pounds per square inch	psi	14.7 lb/in2
pascal	Pa	101,325 Pa
kilopascal	kPa	101.325 kPa

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

Atmospheric Pressure

Definition and Measurement

• Earth is covered with a gas mixture called the atmosphere.

• Atmospheric pressure is the pressure exerted by the column of this gas mixture towards Earth's surface.

• At sea level, atmospheric pressure is 1 atm (760 mmHg or 101,325 Pa).

Constituent	% Volume
N2	78.08
O2	20.95
Ar	0.93
CO2	0.04
Ne	0.0018
He	0.0005
CH4	0.0002
Kr	0.0001

• A barometer measures atmospheric pressure as the height (in mm) of a mercury column. At 1 atm, the height is exactly 760 mmHg (or 760 Torr).

• Atmospheric pressure decreases as altitude increases.

Variables that Define Gas Properties

Four Key Variables

• P: Pressure

• T: Temperature (must be in Kelvin, K, for calculations)

• V: Volume of container

• n: Number of moles of gas

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

Containers for Gases: Rigid vs. Flexible

• Rigid cylinders have a fixed volume and can be pressurized above 1 atm.

• Flexible balloons can change volume; when inflated, the volume expands until the internal pressure equals atmospheric pressure.

Ideal Gas Law

Equation and Application

• The ideal gas law relates pressure, volume, temperature, and number of moles for an ideal gas:

$P V = n R T$

• R is the ideal gas constant. Common values:

  • $R = 0.0821\ \text{L} \cdot \text{atm} / (\text{mol} \cdot \text{K})$

  • $R = 8.314\ \text{J} / (\text{mol} \cdot \text{K})$

• Always use Kelvin for temperature in calculations: $T(\text{K}) = T(°\text{C}) + 273.15$

Example Calculation

• Given: $n = 2.0$ mol, $T = 600$ K, $P = 2.00$ atm

• Find: $V$

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

Combined Gas Law

When Multiple Properties Change

• When more than two properties of a gas change, the combined gas law is used (keeping n constant):

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

• Initial state: 1, Final state: 2

Example Calculation

• Given: $V_1 = 1.0$ L, $T_1 = 300$ K, $P_1 = 1.0$ atm, $n = 0.10$ mol

• Find: $V_2$ if $T_2 = 600$ K, $P_2 = 4.0$ atm

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

Named Gas Laws Derived from the Ideal Gas Law

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

• Each law describes the relationship between two variables while keeping the others constant.

Boyle's Law (P and V Relationship)

• At constant n and T, the volume of an ideal gas is inversely proportional to its pressure:

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

$P_1 V_1 = P_2 V_2$

Example:

• If $V_1 = 8.0$ L at $P_1 = 2.0$ atm, and $P_2 = 8.0$ atm, then $V_2 = \frac{2.0\ \text{atm} \times 8.0\ \text{L}}{8.0\ \text{atm}} = 2.0$ L

Practice Problems and Applications

• Practice converting between pressure units, using the ideal gas law, and applying the combined gas law to solve for unknowns.

• Understand how changes in temperature, pressure, or volume affect a gas sample using the appropriate law.

Summary Table: Gas Laws and Their Relationships

Combined Gas Law	Properties That Do Not Change	Relationship	Name of Gas Law
$\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$	n	All variables	Combined Gas Law
$P_1 V_1 = P_2 V_2$	n, T	P and V	Boyle's Law
$\frac{V_1}{T_1} = \frac{V_2}{T_2}$	n, P	V and T	Charles's Law
$\frac{P_1}{T_1} = \frac{P_2}{T_2}$	n, V	P and T	Gay-Lussac's Law
$\frac{V_1}{n_1} = \frac{V_2}{n_2}$	P, T	V and n	Avogadro's Law

Additional info: These notes are based on lecture slides and include both conceptual explanations and worked examples. For further practice, students are encouraged to use online simulations and adaptive learning tools as referenced in the slides.