Gas Law Formulas and Concepts

Overview

This lecture covers essential gas law formulas, units, and their applications in electrochemistry, focusing on key equations and conversions used in chemistry.

Pressure: Definitions and Units

• Pressure is defined as force divided by area (P = F/A).
• Standard unit in physics: pascal (Pa) = 1 newton/m².
• Chemistry commonly uses atmospheres (atm): 1 atm = 101.3 kPa = 760 mmHg = 14.7 psi.

Gas Law Formulas

• Ideal Gas Law: PV = nRT.
  • R (gas constant): 0.08206 L·atm/(mol·K) for chemistry or 8.3145 J/(mol·K) for physics.
  • Use atm and liters with R = 0.08206; use Pa and m³ with R = 8.3145.
• Convert temperature to Kelvin: K = °C + 273.15.
• Convert Fahrenheit to Celsius: °C = (°F - 32) × 5/9.

Gas Law Variants

• Combined Gas Law: (P₁V₁)/(n₁T₁) = (P₂V₂)/(n₂T₂); if n is constant: (P₁V₁)/T₁ = (P₂V₂)/T₂.
  • Use matching units for pressure and volume; temperature must be in Kelvin.
• Boyle’s Law (T, n constant): P₁V₁ = P₂V₂ (inverse relationship).
• Charles’s Law (P, n constant): V₁/T₁ = V₂/T₂ (direct relationship).
• Gay-Lussac’s Law (V, n constant): P₁/T₁ = P₂/T₂ (direct relationship).
• Avogadro’s Law (P, T constant): V₁/n₁ = V₂/n₂ (direct relationship).

Molar Mass and Density of Gases

• Moles: n = mass/molar mass (MW).
• Alternate ideal gas equation: PV = (mass/MW)RT.
• Density of gas: d = (P × MW)/(RT).

Standard Temperature and Pressure (STP)

• STP: 273 K (0°C), 1 atm (760 mmHg).
• 1 mole of gas at STP occupies 22.4 L.

Dalton’s Law of Partial Pressures

• Total pressure: P_total = P₁ + P₂ + P₃ + ...
• Partial pressure: P_a = (mole fraction of a) × P_total.
• Mole fraction: χ_a = n_a / n_total = P_a / P_total.
• Sum of all mole fractions equals 1.

Kinetic Energy and Gas Velocity

• Average kinetic energy ∝ absolute temperature (use R = 8.3145 J/mol·K).
• Root Mean Square (rms) velocity: u_rms = √(3RT/MW) (MW in kg/mol).
• Higher temperature or lighter molecules = higher velocity.

Graham’s Law of Effusion

• Rate ratio: (rate₁/rate₂) = √(MW₂/MW₁).
• Heavier gases effuse slower than lighter gases.
• Time for effusion is inversely proportional to rate: (rate₁/rate₂) = (t₂/t₁).

Key Terms & Definitions

• Pressure (P) — Force per unit area exerted by a gas.
• Mole Fraction — Ratio of moles of a component to total moles in mixture.
• STP — Standard Temperature (273 K) and Pressure (1 atm) conditions.
• Partial Pressure — Pressure contributed by a single gas in a mixture.
• Root Mean Square Velocity (u_rms) — Average speed of gas molecules.
• Effusion — Movement of gas particles through a small hole.

Action Items / Next Steps

• Practice problems on gas laws and Graham’s Law.
• Review formulas and ensure unit consistency in calculations.
• Refer to any provided practice links or videos for applied examples.