Gas Laws and the Behavior of Gases

Introduction to Gas Laws

The study of gases is fundamental in chemistry, as gases exhibit unique behaviors that are described by several physical laws. The Kinetic Molecular Theory provides a model for understanding the properties and behavior of gases, which are further quantified by the gas laws. These laws relate the pressure, volume, temperature, and amount of gas, allowing us to predict how gases will respond to changes in their environment.

Kinetic Molecular Theory of Gases

Basic Assumptions

• Random Motion: Gas particles move randomly with high velocity, resulting in no definite shape or volume.

• Negligible Attractive Forces: The forces between gas particles are minimal, so the particles are far apart.

• Compressibility: The actual volume of gas molecules is extremely small compared to the volume the gas occupies, making gases easy to compress and able to fill any container.

• Constant Motion: Gas particles move rapidly in straight paths and exert pressure when they collide with the walls of their container.

• Kinetic Energy and Temperature: The average kinetic energy of gas molecules is proportional to the Kelvin temperature; higher temperatures mean faster movement and greater pressure.

Properties of Gases

Four Basic Properties

When discussing gases, four main properties are considered:

• Pressure (P): The force exerted by gas particles colliding with the walls of a container. Heating increases particle speed and pressure.

• Volume (V): The space occupied by the gas, equal to the size of the container.

• Temperature (T): Related to the kinetic energy of particles; measured in Kelvin for calculations.

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

Atmospheric Pressure

• A column of air from the atmosphere to Earth's surface exerts a pressure of about 1 atm.

• Atmospheric pressure decreases with altitude due to fewer air particles.

• Units of Pressure: Atmosphere (atm), millimeters of mercury (mmHg), torr (Torr), kilopascals (kPa), pounds per square inch (psi).

Volume and Temperature

• Volume: Measured in liters (L) or milliliters (mL); equals the size of the container.

• Temperature: Directly related to kinetic energy; must use Kelvin (K) in calculations.

• Doubling the Kelvin temperature doubles the kinetic energy and pressure (if volume and amount are constant).

Amount of Gas (n)

• Measured in grams (g) but converted to moles (n) for calculations.

Measuring Gas Pressure

Barometers and Pressure Units

• Atmospheric pressure is measured with a barometer.

• Pressure decreases with increasing altitude.

• Pressure Formula:

• Pressure Equalities:

Gas Laws

Boyle’s Law: Pressure and Volume

Boyle’s Law describes the inverse relationship between the pressure and volume of a gas, provided temperature and amount of gas remain constant. If one increases, the other decreases proportionally.

• Mathematical Expression:

• Example: If a sample of oxygen gas has a volume of 12.0 L at 600 mmHg, what is the final pressure when the volume changes to 36.0 L (at constant T and n)?

Charles’ Law: Temperature and Volume

Charles’s Law states that the volume of a gas is directly proportional to its temperature (in Kelvin), provided pressure and amount of gas are constant. As temperature increases, so does volume.

• Mathematical Expression:

• Example: A sample of oxygen gas has a volume of 420 mL at 18°C. At what temperature (in °C) will the volume be 640 mL (P and n constant)?

Gay-Lussac’s Law: Temperature and Pressure

Gay-Lussac’s Law describes the direct relationship between the pressure and Kelvin temperature of a gas, with volume and amount constant. As temperature increases, pressure increases proportionally.

• Mathematical Expression:

• Example: A gas has a pressure of 645 Torr at 128°C. What is the temperature (in °C) if the pressure increases to 824 Torr (V and n constant)?

Application: Boiling Point of Water at Different Altitudes

Water boils at a lower temperature in the mountains than at sea level because atmospheric pressure is lower at higher altitudes. Lower pressure means water molecules require less energy (lower temperature) to escape into the gas phase.

References

• Timberlake, K. (2018). Chemistry: Introduction to general, organic and biological chemistry (13th ed.). Pearson Education.