Gases and Pressure Summary

Gases and Pressure

Kinetic-Molecular Theory of Gases

• Gases consist of small, widely separated particles.
• Gas particles behave independently.
• Particles move rapidly in straight lines until collision.
• Gas pressure is due to particle collisions with container walls.
• Average kinetic energy depends on absolute temperature: KE{ave} \propto T{Kelvin}

Gas Pressure

• Pressure (P) is force (F) per unit area (A): P = \frac{F}{A}
• Conversions:
  • 1 atm = 760 mmHg = 760 torr = 14.7 psi = 101325 Pa = 101.325 kPa

Boyle’s Law

• For a fixed amount of gas at constant temperature, pressure and volume are inversely related: P \times V = k
• P1V1 = P2V2
• Inhalation: Volume increases, pressure decreases, air flows in.
• Exhalation: Volume decreases, pressure increases, air flows out.

Charles’s Law

• For a fixed amount of gas at constant pressure, volume is proportional to Kelvin temperature: \frac{V}{T} = k
• \frac{V1}{T1} = \frac{V2}{T2}

Gay-Lussac’s Law

• For a fixed amount of gas at constant volume, pressure is proportional to Kelvin temperature: \frac{P}{T} = k
• \frac{P1}{T1} = \frac{P2}{T2}

Combined Gas Law

• Combines Boyle's, Charles's, and Gay-Lussac's laws: \frac{P1V1}{T1} = \frac{P2V2}{T2}

Avogadro’s Law

• At constant pressure and temperature, volume is proportional to the number of moles: \frac{V}{n} = k
• \frac{V1}{n1} = \frac{V2}{n2}
• STP conditions: 1 atm (760 mm Hg) and 273 K (0°C).
• Standard molar volume: 22.4 L/mol at STP.

Ideal Gas Law

• PV = nRT
• R (universal gas constant) = 0.0821 \frac{L \cdot atm}{mol \cdot K}
• n = \frac{PV}{RT}, V = \frac{nRT}{P}, P = \frac{nRT}{V}

Dalton’s Law of Partial Pressures

• The total pressure of a gas mixture is the sum of the partial pressures.
• P{total} = PA + PB + PC