Unit 5A – Pressure and Gas Laws

Overview

This unit covers the fundamental concepts of gases, including the kinetic molecular theory, pressure and its measurement, the ideal gas law, and the application of gas laws to solve quantitative problems. Understanding these principles is essential for predicting and explaining the behavior of gases under various conditions.

Kinetic Molecular Theory (KMT)

Basic Postulates of KMT

• Constant Motion: Gas molecules are in continuous, random motion.

• Negligible Volume: The volume of individual gas molecules is extremely small compared to the total volume of the container.

• Elastic Collisions: Collisions between gas molecules and with the walls of the container are perfectly elastic (no net loss of kinetic energy).

• No Intermolecular Forces: There are no attractive or repulsive forces between the molecules (ideal gas assumption).

Interactions such as phase changes or chemical reactions are not considered in KMT.

Key Terms and Definitions

• Pressure (P): The force exerted by gas molecules colliding with the walls of their container. Units: atm, bar, mmHg, kPa.

• Volume (V): The space that the gas occupies. Units: L, m3.

• Moles (n): The amount of substance, measured in moles (mol).

• Temperature (T): A measure of the average kinetic energy of the molecules. Units: K (Kelvin).

• Molecular Mass (m): The mass of a single molecule.

• Velocity (u): The speed of a molecule.

Relationship: The kinetic energy of a molecule is given by .

Additional info: As temperature increases, the average kinetic energy and velocity of gas molecules increase.

Pressure and Pressure Conversions

Pressure Units and Conversions

• 1 atm = 101.325 kPa = 1.01325 bar

• 1 atm = 760 mm Hg = 760 torr

• 1 atm = 14.696 psi

Physicists and chemists may use different units; always check which units are required for calculations.

Gas Constant (R) Values

Manometers and Barometers

• Manometer: Measures pressure by the difference in liquid height (usually mercury) in a U-shaped tube. Used to measure the pressure of a gas sample.

• Barometer: Measures atmospheric pressure by the height of mercury in a column.

Open Manometer: Compares gas pressure to atmospheric pressure. If the mercury column rises, sample pressure > atmospheric pressure. If it falls, sample pressure < atmospheric pressure.

Closed Manometer: Measures the absolute pressure of a gas (vacuum on one side).

The Ideal Gas Law

Equation and Variables

The ideal gas law relates pressure, volume, temperature, and moles of a gas:

• P: Pressure

• V: Volume

• n: Number of moles

• R: Gas constant (see table above)

• T: Temperature (Kelvin)

Use this law when only one set of conditions is given for a gas. Ensure all units are consistent with the value of R used.

Standard Temperature and Pressure (STP)

• Standard Temperature: 0°C = 273 K

• Standard Pressure: 1 atm

• At STP, 1 mol of an ideal gas occupies 22.4 L.

Calculating Moles from Mass

Combined Gas Law

Changing Conditions for a Gas

When a gas changes from one set of conditions to another, use the combined gas law:

• Cancel any variable that is not changing.

• Units must be consistent on both sides.

• Temperatures must be in Kelvin.

Notes: For a container with rigid walls, volume is constant. For elastic walls, pressure is constant. Unless specified, assume a variable is held constant.

Partial Pressure and Dalton’s Law

Partial Pressure

The partial pressure of a gas is the pressure it would exert if it alone occupied the container.

Dalton’s Law of Partial Pressures

The total pressure in a mixture of gases is the sum of the partial pressures of each component:

Mole Fraction (χ)

The mole fraction of a component is the ratio of its moles to the total moles in the mixture:

The partial pressure of a gas can be calculated as:

Example Calculation

• If 45% of molecules are nitrogen () and 55% are oxygen () in a tank at 1 atm:

• Total pressure:

Using Dalton’s Law with the Ideal Gas Law

Application

The ideal gas law can be applied to the total moles and total pressure, or to the moles and partial pressure of a single gas in a mixture.

For a mixture of gases:

Sample problem: If a 12.0 L tank at 30.0°C has a total pressure of 1.75 atm and the partial pressure of O2 is 0.350 atm, the moles of O2 are:

Total moles can be found using the total pressure:

Alternatively, using mole fraction:

Practice Problems and Applications

Sample Problems

• Calculate the pressure exerted by a given amount of gas at a specific temperature and volume.

• Determine the mass of gas remaining in a container given pressure, volume, and temperature.

• Predict how changes in volume, temperature, or moles affect pressure using the combined gas law.

• Apply Dalton’s Law to mixtures of gases to find partial pressures and mole fractions.

Conceptual Questions

• What causes pressure in a gas?

• How does decreasing volume affect pressure?

• How do containers with rigid vs. elastic walls behave when temperature changes?

• How does adding moles of gas affect pressure if volume is constant?

Summary Table: Gas Laws and Their Applications

Additional info: These laws assume ideal gas behavior, which is a good approximation under most conditions except at very high pressures or low temperatures, where real gases deviate from ideality.