Gas Laws and Equations

Overview

This lecture covers essential gas law formulas and equations in electrochemistry, including definitions, conversions, and applications of the major gas laws.

Pressure and Unit Conversions

• Pressure is defined as force divided by area (P = F/A), standard unit is Pascal (Pa = N/m²).
• In chemistry, common units: 1 atm = 101.3 kPa = 760 mmHg = 14.7 psi.

Ideal Gas Law and Gas Constant (R)

• Ideal gas law: PV = nRT.
• R = 0.08206 L·atm/(mol·K) for chemistry; use pressure in atm, volume in liters, T in Kelvin.
• R = 8.3145 J/(mol·K) for physics; use pressure in Pa, volume in m³, T in Kelvin.
• To convert Celsius to Kelvin: K = °C + 273.15.

Combined Gas Law & Related Equations

• Combined gas law: (P₁V₁)/(n₁T₁) = (P₂V₂)/(n₂T₂).
• If moles (n) constant: (P₁V₁)/T₁ = (P₂V₂)/T₂.
• Keep all units consistent (e.g., both pressures in atm, both volumes in liters, temperatures in K).

Specific Gas Laws

• Boyle’s Law (T, n constant): P₁V₁ = P₂V₂ (inverse relationship).
• Charles’ 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).
• PV = (mass/MW)·RT; rearranged to MW = (mass·RT)/(PV).
• Density: d = (P·MW)/(RT).

Standard Temperature and Pressure (STP)

• STP: 0°C (273.15 K), 1 atm (760 mmHg).
• At STP, 1 mol of gas occupies 22.4 L.

Dalton's Law of Partial Pressures

• Total pressure = sum of partial pressures: P_total = P₁ + P₂ + ...
• Partial pressure: P_A = mole fraction of A × total pressure.
• Mole fraction = moles of A / total moles; sum of all mole fractions = 1.

Kinetic Molecular Theory

• Average kinetic energy of a gas ∝ temperature (in Kelvin).
• Use R = 8.3145 J/(mol·K) for calculations.

Root Mean Square Velocity

• u_rms = sqrt(3RT/MW); MW in kg/mol, R = 8.3145 J/(mol·K), u_rms in m/s.

Graham’s Law of Effusion

• Rate₁/Rate₂ = sqrt(MW₂/MW₁) (rate is inversely proportional to square root of molar mass).
• Time is inversely proportional to rate: Rate₁/Rate₂ = Time₂/Time₁.

Key Terms & Definitions

• Pressure (P) — Force per unit area exerted on a surface.
• Ideal Gas Law — Relationship among pressure, volume, temperature, and moles: PV = nRT.
• Mole Fraction — Proportion of moles of one component to total moles in a mixture.
• Effusion — Process of gas escaping through a small hole.
• Root Mean Square Velocity — Measure of average speed of gas particles.

Action Items / Next Steps

• Review and memorize all listed formulas and their conditions.
• Practice unit conversions for pressure, volume, and temperature.
• Complete practice problems related to gas laws, especially on stoichiometry and effusion.