Chapter 8: Gases – Properties, Laws, and Applications

Chapter 8: Gases

Fundamental Properties of Gases

Gases are described by four key properties that determine their behavior in chemical and physical processes:

• Pressure (P): The force exerted by gas particles per unit area.

• Volume (V): The space occupied by the gas.

• Temperature (T): A measure of the average kinetic energy of gas particles, expressed in Kelvin.

• Amount (n): The quantity of gas, measured in moles.

These properties are interrelated through several gas laws, which describe how changes in one property affect the others.

Pressure and Its Measurement

Definition of Pressure

Pressure is defined as the force applied per unit area:

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

• Units of Pressure: 1 atm = 760 mm Hg = 760 torr = 14.7 lb/in2 (psi) = 101,325 Pa

Pressure is commonly measured using barometers and manometers.

Atmospheric Pressure

Atmospheric pressure is the pressure exerted by the weight of air above the Earth's surface. It is measured using a mercury barometer, where the height of mercury (in mm) indicates the atmospheric pressure.

• Composition of air: 21% O2, 78% N2, 1% other gases

• Standard atmospheric pressure: 760 mm Hg

Kinetic Molecular Theory

Basic Principles

The Kinetic Molecular Theory explains the behavior of gases based on the motion of their particles:

• Gas particles are in constant, random motion.

• Collisions between particles and container walls create pressure.

• The average kinetic energy of particles is proportional to temperature (in Kelvin).

This theory provides the foundation for understanding gas laws.

Gas Laws

Boyle's Law

Boyle's Law describes the relationship between pressure and volume at constant temperature and moles:

• Statement: Pressure and volume are inversely related.

• Formula: $P_1 V_1 = P_2 V_2$

• Example: Decreasing the volume of a gas increases its pressure.

Charles's Law

Charles's Law describes the relationship between volume and temperature at constant pressure and moles:

• Statement: Volume and temperature (in Kelvin) are directly related.

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

• Example: Heating a gas increases its volume.

Avogadro's Law

Avogadro's Law describes the relationship between volume and amount (moles) at constant temperature and pressure:

• Statement: Volume and moles are directly related.

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

• Example: Adding more gas increases the volume.

Combined Gas Law

The Combined Gas Law integrates Boyle's, Charles's, and Gay-Lussac's laws to relate pressure, volume, and temperature when the amount of gas is constant:

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

• Application: Used when more than one property changes simultaneously.

Ideal Gas Law

The Ideal Gas Law combines all four properties into a single equation:

• Formula: $PV = nRT$

• R (Gas Constant): 0.082058 L·atm/(mol·K)

• Application: Used to calculate any property of a gas when the other three are known.

Dalton's Law of Partial Pressures

Dalton's Law states that the total pressure of a mixture of gases is the sum of the partial pressures of each individual gas:

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

• Application: Used to determine the pressure contribution of each gas in a mixture.

Standard Temperature and Pressure (STP)

Definition and Application

STP refers to a temperature of 0°C (273 K) and a pressure of 1 atm. At STP, one mole of any ideal gas occupies 22.4 L.

• Formula: 1 mol gas at STP = 22.4 L

• Example: Calculate the volume of 4.00 g of CH4 at STP.

Worked Examples

Example 1: Boyle's Law

• Oxygen gas has a volume of 12.0 L at 600 mmHg. What is the new pressure when the volume changes to 36.0 L at constant T and n?

• Solution: Use $P_1 V_1 = P_2 V_2$ to solve for $P_2$.

Example 2: Charles's Law

• A balloon has a volume of 785 mL at 21°C. If the temperature drops to 0.0°C, what is the new volume at constant pressure and moles?

• Solution: Use $\frac{V_1}{T_1} = \frac{V_2}{T_2}$ (convert temperatures to Kelvin).

Example 3: Avogadro's Law at STP

• What is the volume of 4.00 g of CH4 at STP?

• Solution: Calculate moles of CH4, then multiply by 22.4 L/mol.

Example 4: Dalton's Law

• What is the partial pressure of oxygen gas if the molar composition of air is 80% N2 and 20% O2?

• Solution: $P_{O_2} = 0.20 \times P_{\text{total}}$

Summary Table: Gas Laws

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	$P_1 V_1 = P_2 V_2$	Boyle's law
$\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$	P, n	$\frac{V_1}{T_1} = \frac{V_2}{T_2}$	Charles's law
$\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$	V, n	$\frac{P_1}{T_1} = \frac{P_2}{T_2}$	Gay-Lussac's law

Additional info:

• Gay-Lussac's Law relates pressure and temperature at constant volume and moles: $\frac{P_1}{T_1} = \frac{P_2}{T_2}$

• Always convert temperatures to Kelvin when using gas laws.

• Real gases deviate from ideal behavior at high pressures and low temperatures.