Ideal Gases

Ideal Gases

  • Kinetic Theory of Gases: Describes gas molecules that are in constant motion with the following assumptions:

    • Molecules move rapidly and randomly.

    • Molecules have negligible volume.

    • No intermolecular forces exist (no attraction/repulsion).

    • Collisions between gas molecules are elastic, meaning kinetic energy is conserved.

    • Temperature directly relates to average kinetic energy of molecules.

  • Gases that mostly fit these assumptions are termed ideal gases, while those that do not are known as real gases.

Molar Gas Volume

  • Gases exert pressure by colliding with container walls, and volume affects collision frequency.

  • Boyle's Law: Describes the inverse relationship between pressure and volume at constant temperature:

    • Mathematically: P ∝ 1/V or PV = constant.

    • Graphical Representations:

      • Pressure vs. 1/Volume yields a straight line.

      • Pressure vs. Volume yields a curve.

      • PV vs. P yields a straight line.

Changing Gas Temperature

  • Heating a gas (at constant pressure) results in increased kinetic energy and collision frequency, leading to increased volume:

    • Charles' Law: Volume is directly proportional to temperature (in Kelvin) at constant pressure:

      • Mathematically: V ∝ T or V/T = constant.

      • A graph of volume vs. temperature produces a straight line.

Changing Gas Pressure

  • Heating a gas (at constant volume) increases kinetic energy, particle speed, and collision frequency, causing pressure to rise:

    • Pressure-Temperature Relationship:

      • Temperature is directly proportional to pressure at constant volume:

      • Mathematically: P ∝ T or P/T = constant.

Combining Relationships

  • The relationships from Boyle's Law, Charles' Law, and pressure-temperature interactions can be combined:

    • PV/T = constant suggests the formation of the Ideal Gas Equation: PV = nRT.

Ideal Gas Equation

  • The relationship among pressure (P), volume (V), temperature (T), and moles of gas (n) is given by:

    • P = pressure in Pa

    • V = volume in mᶴ

    • n = moles of gas (mol)

    • R = gas constant (8.31 J/(K·mol))

    • T = temperature in Kelvin (K)

  • Can be rearranged to find unknown variables, calculate molar mass, etc.

Worked Examples

  • Example: Calculate temperature after volume changes at constant pressure using:

    • T₂ = (V₂ * T₁) / V₁.

  • Example: Calculate final pressure when conditions change:

    • Rearrangement of ideal gas equation.

Real Gases

  • Real gases exhibit deviations from ideal behavior at:

    • Low temperatures and high pressures.

  • Key Assumptions:

    • Volume of gas molecules becomes significant compared to total volume.

    • Attractive forces between molecules begin to influence behavior.

Conclusion

  • The ideal gas equation is provided in the IB Chemistry Data Booklet and should be applied carefully noting conditions of pressure, volume, and temperature.