Chapter 5.2 : Gases and Gas Laws – General Chemistry Study Notes

Gases and Gas Laws

Introduction to Gases

Gases are one of the fundamental states of matter, characterized by their ability to expand and fill any container. The behavior of gases is governed by several physical laws that relate pressure, volume, temperature, and amount of gas.

Factors Influencing the Pressure of a Gas

Understanding Gas Pressure

Gas pressure results from collisions between gas molecules and the walls of their container. The frequency and force of these collisions determine the pressure exerted by the gas.

• Volume: Increasing the volume of the container allows gas molecules to spread out, decreasing the frequency of collisions and thus lowering the pressure.

• Amount (Number of Molecules): Adding more gas increases the number of collisions, raising the pressure.

• Temperature: Higher temperature means gas molecules move faster, leading to more frequent and forceful collisions, which increases pressure.

Boyle’s Law: Volume-Pressure Relationship

Definition and Mathematical Formulation

Boyle’s Law describes the relationship between the pressure and volume of a fixed amount of gas at constant temperature. It states that the pressure of a gas is inversely proportional to its volume.

• Mathematical Expression: $P \propto \frac{1}{V}$ $P V = k$ (where k is a constant for a given amount of gas at constant temperature)

• Equation for Two States: $P_1 V_1 = P_2 V_2$

• Example: If the volume of a gas decreases, its pressure increases, provided temperature and amount of gas remain constant.

Application Example

A scuba diver inhales air at 3 bar pressure deep underwater and swims quickly to the surface while holding her breath. According to Boyle’s Law, the volume of air in her lungs would increase by a factor of 3 as the pressure decreases from 3 bar to 1 bar.

Sample Calculation

Given: 1 mole of oxygen at 25.00°C occupies 24.47 L at 1.000 atm. What volume will the same amount of oxygen occupy at 298.2 K when the pressure increases to 22.00 psi?

• Use: $V_2 = \frac{V_1 P_1}{P_2}$

• Calculation: $V_2 = \frac{24.47 \text{ L} \times 14.70 \text{ psi}}{22.00 \text{ psi}} = 16.35 \text{ L}$

Charles’ Law: Volume-Temperature Relationship

Definition and Mathematical Formulation

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

• Mathematical Expression: $V \propto T$ $\frac{V}{T} = k$

• Equation for Two States: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$

• Example: Heating a gas at constant pressure causes its volume to increase.

Sample Calculation

A container with 500 mL of gas at 300 K. What is the final volume at standard temperature and pressure (STP)?

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

• Calculation: $V_2 = \frac{500 \text{ mL} \times 300 \text{ K}}{273 \text{ K}} = 549 \text{ mL}$

Gay-Lussac’s Law: Pressure-Temperature Relationship

Definition and Mathematical Formulation

Gay-Lussac’s Law states that for a fixed amount of gas in a container with constant volume, the pressure is directly proportional to the absolute temperature.

• Mathematical Expression: $P \propto T$ $\frac{P}{T} = k$

• Equation for Two States: $\frac{P_1}{T_1} = \frac{P_2}{T_2}$

• Example: If the temperature of a gas doubles, its pressure also doubles (at constant volume).

Avogadro’s Law: Volume-Amount Relationship

Definition and Mathematical Formulation

Avogadro’s Law states that at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles (amount) of gas present. Equal volumes of any gases at the same temperature and pressure contain the same number of molecules.

• Mathematical Expression: $V \propto n$ $\frac{V}{n} = k$

• Equation for Two States: $\frac{V_1}{n_1} = \frac{V_2}{n_2}$

• Example: Doubling the amount of gas (in moles) doubles the volume at constant temperature and pressure.

Sample Calculation

If 1.00 mol of O2 occupies 22.4 L at STP, what volume will 0.10 mol O2 occupy at STP?

• Use: $V_2 = \frac{n_2}{n_1} V_1$

• Calculation: $V_2 = \frac{0.10}{1.00} \times 22.4 \text{ L} = 2.24 \text{ L}$

Application Example

To blow up a balloon to 1.2 L, and each breath supplies 0.060 mol of exhaled air, how many moles of air are in 30 balloons?

• Total moles: $0.060 \text{ mol} \times 30 = 1.80 \text{ mol}$

Summary Table: Gas Laws

Law	Relationship	Equation
Boyle’s Law	Pressure vs. Volume (inverse)	$P_1 V_1 = P_2 V_2$
Charles’ Law	Volume vs. Temperature (direct)	$\frac{V_1}{T_1} = \frac{V_2}{T_2}$
Gay-Lussac’s Law	Pressure vs. Temperature (direct)	$\frac{P_1}{T_1} = \frac{P_2}{T_2}$
Avogadro’s Law	Volume vs. Amount (direct)	$\frac{V_1}{n_1} = \frac{V_2}{n_2}$

Historical Context: The Study of Gases

Hot Air Balloons and the Development of Gas Laws

The first passenger flight in a hot air balloon in 1783 spurred scientific interest in understanding the behavior of gases, especially at high altitudes. This led to the development of the gas laws and their applications in transportation, meteorology, and physiology.

Key Concepts: The gas laws are essential for understanding phenomena such as breathing under water, balloon flight, and the behavior of gases in various scientific and industrial contexts.

Additional info: Some calculations and examples have been expanded for clarity and completeness.