AS

310105h Laws of Perfect Gases 2024 TF (1)

Laws of Perfect Gases

  • Objectives:

    • Describe Boyle’s Law, Charles’s Law, and the general gas law in relation to pressure.

    • Solve problems involving gas laws.

    • Describe the principles of gas compressibility.

Ideal Gases

  • Definition of Ideal Gases:

    • Exhibits theoretical properties that include:

      • Obeys all gas laws under all conditions.

      • Does not condense into a liquid when cooled.

      • Shows straight lines when plotting volume (V) vs. temperature (T) or pressure (P) vs. temperature (T).

Boyle’s Law (Pressure and Volume)

  • Principle:

    • Absolute pressure exerted by a mass of an ideal gas is inversely proportional to the volume it occupies at constant temperature.

    • As volume decreases, pressure increases, given constant temperature and gas amount.

Boyle’s Law Formula

  • Formula:

    • P1V1 = P2V2

  • Terms:

    • P = absolute pressure.

    • V = absolute volume.

  • Conditions:

    • Valid at moderate temperatures and pressures with no leakage in containment.

Charles’s Law (Temperature and Volume)

  • Principle:

    • An increase in gas temperature leads to an increase in gas volume if the volume is allowed to increase (flexible system) while pressure remains constant.

Charles’s Law Formula

  • Formula:

    • V1/T1 = V2/T2

  • Terms:

    • V = volume, T = absolute temperature; must be in Kelvin (°K) or Rankine (°R).

Gay-Lussac’s Law (Pressure and Temperature)

  • Principle:

    • An increase in gas temperature causes an increase in gas pressure in a constant volume system.

    • Pressure increases proportionally with temperature when gas cannot expand.

Gay-Lussac’s Law Formula

  • Formula:

    • P1/T1 = P2/T2

  • Terms:

    • P = absolute pressure, T = absolute temperature; must be in Kelvin (°K).

Avogadro’s Law (Volume and Number of Molecules)

  • Principle:

    • The number of moles of gas is directly proportional to the volume of gas, provided the temperature remains constant.

  • Mole Definition:

    • A mole is a unit representing a specific number of molecules.

Avogadro’s Law Formula

  • Formula:

    • V1/n1 = V2/n2

  • Terms:

    • V = volume, n = number of molecules (moles).

Combined and Ideal Gas Law

  • Formula:

    • P1V1/T1 = P2V2/T2

  • Conditions and Terms:

    • Valid at Kelvin (°K) and absolute pressure; no leakage; constant volume.

Real Gas

  • Definition:

    • Real gases do not follow ideal gas laws.

    • Characteristics include:

      • Molecules stick together and occupy more total volume, unlike ideal gases.

Compressibility Factor

  • Formula:

    • PV = ZnRT

  • Terms:

    • P = pressure, V = volume, Z = compressibility factor, n = number of gas molecules, R = universal gas constant (8314.51 J/kmol•K), T = temperature in Kelvin (K).

Liquefaction of Gas

  • Critical Temperature:

    • The temperature above which a gas cannot be liquefied. Below this temperature, gas can be liquefied.

  • Critical Pressure:

    • The pressure required to liquefy gas at or below its critical temperature.