Gas Laws and Key Concepts - Jason Cameron
1. Kinetic Molecular Theory (KMT)
- Gases consist of small particles in constant, random motion.
- Particles are far apart, have negligible volume, and no intermolecular forces (ideal gas).
- Kinetic Energy (KE): Depends on temperature (KE = ½mv²).
- Temperature: Measures average KE of particles.
- Absolute Zero: 0 K (-273.15°C), where molecular motion stops.
- Kelvin Scale: K = °C + 273.15.
2. Pressure
- Units: kPa (kilopascals), atm (atmospheres), mm Hg (millimeters of mercury), Torr, psi (pounds per square inch).
- Conversions:
- 1 atm = 101.325 kPa = 760 mm Hg = 760 Torr = 14.7 psi.
- Atmospheric Pressure: Decreases with altitude.
3. Standard Conditions
- STP (Standard Temperature and Pressure): 0°C (273.15 K) and 1 atm (101.325 kPa).
- Molar Volume at STP = 22.4 L/mol.
- SATP (Standard Ambient Temperature and Pressure): 25°C (298.15 K) and 1 atm.
- Molar Volume at SATP = 24.8 L/mol.
4. Gas Laws
- Boyle’s Law: P₁V₁ = P₂V₂ (constant n, T).
- Inverse relationship: Pressure ↑, Volume ↓.
- Charles’s Law: V₁/T₁ = V₂/T₂ (constant n, P).
- Direct relationship: Temperature ↑, Volume ↑.
- Gay-Lussac’s Law: P₁/T₁ = P₂/T₂ (constant n, V).
- Direct relationship: Temperature ↑, Pressure ↑.
- Combined Gas Law: P₁V₁/T₁ = P₂V₂/T₂ (constant n).
5. Avogadro’s Law
- V₁/n₁ = V₂/n₂ (constant P, T).
- Direct relationship: Moles ↑, Volume ↑.
6. Ideal Gas Law
- Formula: PV = nRT.
- P = pressure (kPa), V = volume (L), n = moles, R = gas constant (8.314 L·kPa/mol·K), T = temperature (K).
- Ideal Gas: Follows PV = nRT under all conditions.
- Real Gas: Deviates at high P and low T due to intermolecular forces and particle volume.
1. Dalton’s Law of Partial Pressures
- Formula: Pₜₒₜₐₗ = P₁ + P₂ + P₃ + …
- Total pressure of a gas mixture = sum of partial pressures of individual gases.
- Collecting Gas Over Water:
- Pₐₜₘ = P₉ₐₛ + Pᵥₐₚₒᵣ.
- P₉ₐₛ = Pₐₜₘ - Pᵥₐₚₒᵣ (use water vapor pressure table).
2. Gas Stoichiometry
- Use mole ratios from balanced equations.
- Combine stoichiometry with gas laws:
- Example: Use PV = nRT to find moles of gas, then use mole ratio to find other quantities.
- Density of Gases:
- d = m/V = (PM)/(RT).
- M = molar mass, P = pressure, T = temperature.
3. Graham’s Law of Effusion
- Formula: Rate₁/Rate₂ = √(M₂/M₁).
- Lighter gases effuse faster than heavier gases.
- M₁ and M₂ are molar masses of gases.
4. Limiting Reagent Review
- Identify the limiting reagent in gas reactions using stoichiometry.
- Use mole ratios to determine which reactant runs out first.
- Combined Gas Law: P₁V₁/T₁ = P₂V₂/T₂.
- Ideal Gas Law: PV = nRT.
- Density: d = m/V = (PM)/(RT).
- Graham’s Law: Rate₁/Rate₂ = √(M₂/M₁).
- Dalton’s Law: Pₜₒₜₐₗ = P₁ + P₂ + P₃ + …
6. Practice Tips
- Always convert temperature to Kelvin (K = °C + 273.15).
- Use consistent units for pressure, volume, and temperature.
- Indicate mole ratios in stoichiometry, even if 1:1.
- Practice graphing relationships (e.g., P vs. V, V vs. T, P vs. T).