Gas Laws in Electrochemistry

Overview

This lecture provides essential formulas and key concepts related to gas laws in electrochemistry, focusing on pressure, the ideal gas law, specific gas laws, and related calculations.

Pressure & Units

• Pressure (P) = Force (F) / Area (A); SI unit is pascal (Pa), where 1 Pa = 1 N/m².
• Common chemistry pressure units: 1 atm = 101.3 kPa = 760 mm Hg (torr) = 14.7 psi.

Ideal Gas Law & R Values

• Ideal Gas Law: PV = nRT (P in atm, V in L, n in moles, T in K).
• Gas constant R = 0.08206 L·atm/mol·K (use atm & L) or 8.3145 J/mol·K (use Pa & m³).
• Temperature conversion: K = °C + 273.15; °C = (°F - 32) × 5/9.

Combined & Specific Gas Laws

• Combined Gas Law: (P₁V₁)/(n₁T₁) = (P₂V₂)/(n₂T₂).
• Boyle’s Law (constant n & T): P₁V₁ = P₂V₂ (P and V are inversely related).
• Charles’s Law (constant P & n): V₁/T₁ = V₂/T₂ (V and T are directly related).
• Gay-Lussac’s Law (constant V & n): P₁/T₁ = P₂/T₂ (P and T are directly related).
• Avogadro’s Law (constant P & T): V₁/n₁ = V₂/n₂ (V and n are directly related).

Molar Mass & Density of Gases

• n = mass (m) / molar mass (M).
• Rearranged Ideal Gas Law: PV = (m/M)RT → M = mRT/(PV).
• Gas density: d = PM/RT.

Standard Temperature and Pressure (STP)

• STP: 273 K (0°C) and 1 atm (760 mm Hg).
• At STP, 1 mol of gas occupies 22.4 L.

Dalton’s Law of Partial Pressures

• Total Pressure = sum of individual gas partial pressures.
• Partial pressure: Pₐ = (mole fraction of A) × (total pressure).
• Mole fraction = moles of gas / total moles; sum of all mole fractions = 1.

Kinetic Molecular Theory & RMS Speed

• Average kinetic energy ∝ temperature (use R = 8.3145 J/mol·K).
• Root Mean Square velocity: u = √(3RT/M); M in kg/mol, u in m/s.

Graham’s Law of Effusion

• Rate of effusion ∝ 1/√(molecular weight); formula: Rate₁/Rate₂ = √(M₂/M₁).
• Time for effusion is inversely related to rate: Rate₁/Rate₂ = Time₂/Time₁.

Key Terms & Definitions

• Pressure (P) — the force exerted per unit area.
• Mole (n) — amount of substance in moles.
• Molar mass (M) — mass of one mole of a substance.
• STP — standard temperature and pressure (273 K, 1 atm).
• Partial pressure — pressure from an individual gas in a mixture.
• Mole fraction — ratio of moles of one gas to total moles in mixture.

Action Items / Next Steps

• Review and memorize all listed formulas and unit conversions.
• Complete practice problems on gas laws and Graham’s law.
• Check any provided links or resources for additional sample questions.