Gas Laws and Properties of Gases

Kinetic Molecular Theory of Gases

The Kinetic Molecular Theory provides a model to explain the behavior of gases. It describes the motion and interactions of gas particles, which helps us understand gas properties and the relationships between them.

• Gases consist of small particles that move randomly with high velocity, resulting in no definite shape or volume.

• Attractive forces between particles are minimal, so gas particles are far apart from each other.

• The actual volume of gas molecules is extremely small compared to the total volume the gas occupies. This allows gases to fill any container and be easily compressed.

• Gas particles are in constant motion, moving rapidly in straight paths. Their collisions with the walls of a container create pressure.

• The average kinetic energy of gas molecules is proportional to the Kelvin temperature. Higher temperatures mean faster movement and greater pressure exerted by the gas.

Properties of Gases

Four Basic Properties

When studying gases, four fundamental properties are considered: pressure, volume, temperature, and amount of gas.

• Pressure (P): The force exerted by gas particles colliding with the walls of their container. Measured in units such as atmosphere (atm), millimeters of mercury (mmHg), torr (Torr), kilopascals (kPa), and pounds per square inch (psi).

• Volume (V): The space occupied by a gas, typically measured in liters (L) or milliliters (mL).

• Temperature (T): Related to the kinetic energy of gas particles. All gas law calculations use the Kelvin (K) scale.

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

Pressure and Atmospheric Pressure

Gas particles exert pressure when they collide with the walls of their container. In the atmosphere, this is called atmospheric pressure, which is the force exerted by air molecules (mainly O2 and N2) on Earth's surface.

• Atmospheric pressure at sea level is about 1 atm.

• At higher altitudes, atmospheric pressure decreases due to fewer air particles.

• Common pressure units: 1 atm = 760 mmHg = 760 Torr = 101.325 kPa = 14.7 psi.

Volume and Temperature

The volume of a gas is equal to the size of its container. The temperature of a gas is directly related to the average kinetic energy of its particles. Doubling the Kelvin temperature doubles the kinetic energy and, if volume and amount are constant, doubles the pressure.

• Volume units: liters (L), milliliters (mL).

• Temperature units: Kelvin (K) is always used in gas law calculations.

Amount of Gas (n)

The amount of gas is usually measured in grams, but for gas law calculations, it must be converted to moles (n).

Measuring Gas Pressure

Barometers and Pressure Calculations

Atmospheric pressure is measured with a barometer. The formula for pressure is:

$ \text{Pressure} = \frac{\text{Force}}{\text{Area}} $

• Pressure decreases with increasing altitude.

• Pressure units are interchangeable using the provided 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. As pressure increases, volume decreases, and vice versa.

Mathematical expression:

$ P_1 V_1 = P_2 V_2 $

• 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’s Law: Temperature and Volume

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

Mathematical expression:

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

• 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 states that the pressure of a gas is directly proportional to its Kelvin temperature, provided volume and amount of gas are constant. As temperature increases, pressure increases.

Mathematical expression:

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

• 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 and Atmospheric Pressure

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.

Additional info: The relationships described by the gas laws are foundational for understanding chemical reactions involving gases, respiratory physiology, and many industrial processes.