Ideal Gas Laws and Assumptions

Ideal Gas

• An ideal gas is composed of particles with negligible volume and no intermolecular forces.
• All collisions between particles are considered elastic.
• Real gases deviate from ideal behavior, especially at low temperatures and high pressures.

Ideal Gas Model Assumptions

• Constant random motion: Gas molecules move constantly in straight lines until colliding with each other or the container walls.
• Perfectly elastic collisions: Collisions between molecules do not result in any energy loss.
• No intermolecular forces: Forces of attraction between gas particles are negligible compared to their kinetic energy.

Ideal Gas Model Assumptions (continued)

• Negligible particle volume: The volume occupied by the gas particles themselves is much smaller than the container's volume.
• Kinetic energy and temperature: The kinetic energy of gas particles is directly proportional to the Kelvin temperature.

Pressure-Volume Relationships

• Boyle's Law: At constant temperature, the pressure of a fixed amount of gas is inversely proportional to its volume (pV = constant).
• Doubling the pressure of a gas, at a constant temperature, will halve its volume.

Pressure-Volume Relationships (continued)

• Graphs illustrating the relationship between pressure and volume in an ideal gas show an inverse relationship.
• Standard Temperature and Pressure (STP): 273.15 K and 100 kPa

Worked Example 1

• A weather balloon filled with 32.0 dm³ of helium at 100.0 kPa pressure at sea level.
• Reaches an altitude of 4500 m where atmospheric pressure is 57.7 kPa.
• The volume of the balloon at this altitude (assuming constant temperature) is approximately 55.5 dm³.

Practice Question 1

• A weather balloon at a certain altitude has a temperature of -35.0°C and a volume of 0.250 m³.
• The balloon contains 16.0 g of helium
• Calculate the pressure inside the balloon in kPa.
• Answer: 31.7 kPa

Real Gases vs Ideal Gases

• Deviation from ideal gas behavior arises when intermolecular forces become significant or when gas particle volume is no longer negligible.
• At low temperatures or high pressures, these conditions are often met.

Real Gases vs Ideal Gases (continued)

• The kinetic energy of gas molecules is reduced at low temperatures, increasing intermolecular forces.
• High pressures increase the proportion of space taken up by gas molecules. The volume of the molecules becomes significant compared to the space between them

Ideal Gas Conditions

• Low pressure and high temperature lead to ideal gas behavior.
• At low pressure, the space between molecules is large compared to the volume of the molecules themselves.
• High temperatures give gas particles enough kinetic energy to overcome intermolecular forces.

The Molar Volume of an Ideal Gas

• Equal volumes of any two gases, at the same temperature and pressure, contain equal numbers of particles.
• The molar volume of an ideal gas at STP (standard temperature and pressure) is 22.7 dm³.

Worked Example 2

• A 2.00 dm³ sample of an unknown gas at STP (standard temperature and pressure) has a mass of 2.47 g.
• Calculate the molar mass of the gas.
• Answer: 28.0 g/mol

Practice Question 2

• Determine the molar mass of an elemental diatomic gas with a density of 3.12 g/dm³ at STP.
• Answer: 70.9 g/mol; Cl₂

Combined Gas Law

• The combined gas law describes the relationship between pressure, volume, and temperature of a fixed amount of gas.
• pV/T = constant
• This can be used to relate properties at different conditions.

Worked Example 3

• Illustrates determining the volume of an ideal gas sample under altered pressure and temperature conditions from starting conditions, using combined gas law

Practice Question 3

• Calculate the volume in dm³ of an ideal gas sample with starting conditions of 1.00 dm³ at STP
• To be changed to conditions of 50.0°C and 50.0 kPa

Ideal Gas Equation

• The ideal gas equation (pV = nRT) relates pressure (p), volume (V), amount (n), temperature (T), and universal gas constant (R).
• Ideal gas law used to determine gas properties from others

Worked Example 4

• A 3.30 g sample of an unknown organic compound was vaporized at 150°C and 101.3 kPa to produce 1.91 dm³ of gas.
• The gas was combusted to produce...
• Determine the molar mass, empirical formula and molecular formula