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.