Gas Laws and Properties: Study Notes for GOB Chemistry

Gas Laws and Properties

Kinetic Molecular Theory of Gases

The Kinetic Molecular Theory provides a model for understanding the behavior of gases. It explains how gas particles move and interact, and forms the basis for the gas laws.

• Random Motion: Gas consists of small particles moving randomly with high velocity, resulting in no definite shape.

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

• Volume: The actual volume occupied by gas molecules is very small compared to the total volume of the gas, allowing gases to fill any container and be easily compressed.

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

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

Four Basic Properties of Gases

When studying gases, four fundamental properties are considered: pressure, volume, temperature, and amount of gas. Each property has specific units and significance in gas law calculations.

Property	Description	Units of Measurement
Pressure (P)	The force exerted by a gas against the walls of the container	atmosphere (atm); millimeter of mercury (mmHg); torr (Torr); pascal (Pa)
Volume (V)	The space occupied by a gas	liter (L); milliliter (mL)
Temperature (T)	The determining factor of the kinetic energy of gas particles	degree Celsius (°C); kelvin (K) (K is required in calculations)
Amount (n)	The quantity of gas present in a container	gram (g); mole (n) (n is required in calculations)

Pressure

Pressure is the result of gas particles colliding with the walls of their container. Heating the container increases the speed and frequency of collisions, raising the pressure. Atmospheric pressure is the force exerted by air particles (mainly O2 and N2) on us.

• Atmospheric Pressure: At sea level, atmospheric pressure is about 1 atm. It decreases at higher altitudes due to fewer air particles.

• Units: Common units include atmosphere (atm), millimeters of mercury (mmHg), torr (Torr), kilopascals (kPa), and pounds per square inch (psi).

• Pressure Equalities:

  • 1 atm = 760 mmHg = 760 Torr

  • 1 mmHg = 1 Torr

  • 1 atm = 101.325 kPa

  • 1 atm = 14.7 psi

• Formula: Pressure is calculated as: $\text{Pressure} = \frac{\text{Force}}{\text{Area}}$

Volume and Temperature

Volume is the space a gas occupies, equal to the size of its container. Temperature is related to the kinetic energy of gas particles and must be measured in Kelvin for gas law calculations.

• Volume Units: Liters (L) and milliliters (mL).

• Temperature Units: Kelvin (K) is required for calculations; Celsius (°C) may be used for reporting.

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

Amount of Gas (n)

The amount of gas is typically measured by mass (grams), but gas law calculations require the use of moles (n).

• Mole (n): The standard unit for the amount of gas in calculations.

• Conversion: Grams must be converted to moles using the molar mass.

Measuring Gas Pressure

Atmospheric pressure is measured with a barometer. As altitude increases, atmospheric pressure decreases due to fewer air particles.

• Barometer: Instrument used to measure atmospheric pressure.

• Pressure Units: See previous section for equalities.

Gas Laws

Boyle’s Law: Pressure & Volume

Boyle’s Law describes the inverse relationship between the pressure and volume of a gas, provided temperature and amount remain constant.

• Inverse Relationship: As pressure increases, volume decreases, and vice versa.

• Formula: $P_1 V_1 = P_2 V_2$

• 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 (T and n constant)?

Charles’ Law: Temperature & Volume

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

• Direct Relationship: As temperature increases, volume increases.

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

• 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 & Pressure

Gay-Lussac’s Law describes the direct relationship between the pressure and temperature (in Kelvin) of a gas, provided volume and amount remain constant.

• Direct Relationship: As temperature increases, pressure increases.

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

• 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)?

Atmospheric Pressure and Boiling Point

Atmospheric pressure affects the boiling point of liquids. At higher altitudes, atmospheric pressure is lower, so water boils at a lower temperature than at sea level.

• Explanation: Lower atmospheric pressure means less energy is required for water molecules to escape into the gas phase, resulting in a lower boiling point.

• Application: Cooking times may be longer at high altitudes due to lower boiling temperatures.

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