Gas laws
- Ideal gas law: PV = nRT. R = 0.0821 L·atm/(mol·K) = 8.314 J/(mol·K). Temperature must be in kelvin (K = °C + 273).
- Boyle: P₁V₁ = P₂V₂ (T, n constant). Charles: V₁/T₁ = V₂/T₂. Gay-Lussac: P₁/T₁ = P₂/T₂. Avogadro: V ∝ n.
- Combined: P₁V₁/T₁ = P₂V₂/T₂.
- STP = 0 °C (273 K) and 1 atm: 1 mol of ideal gas occupies 22.4 L.
- Density d = PM / RT (M = molar mass). Molar mass M = dRT / P.
- Pressure units: 1 atm = 760 mmHg = 760 torr = 101.325 kPa.
Mixtures
- Dalton: P_total = P₁ + P₂ + …; partial pressure Pᵢ = Xᵢ × P_total (X = mole fraction).
- Gas collected over water: P_gas = P_total − vapor pressure of water at that temperature.
Kinetic molecular theory
- Assumptions: point particles with no volume, no attractions, perfectly elastic collisions, average kinetic energy ∝ absolute temperature.
- Average kinetic energy per mole = (3/2)RT: it depends only on T, not on the identity of the gas.
- Root-mean-square speed u = √(3RT / M): lighter gases move faster at the same T.
- Graham's law: rate₁ / rate₂ = √(M₂ / M₁).
Real gases
- Real gases deviate most at HIGH pressure (molecular volume matters) and LOW temperature (attractions matter).
- Van der Waals: (P + an²/V²)(V − nb) = nRT. The a term corrects for attractions; b corrects for molecular volume.
- Gases behave most ideally when small, nonpolar (He, H₂) and at high T and low P.
⚠️ Common traps
- Using °C in a gas law.
- Assuming heavier gases have more kinetic energy at the same temperature (they have the same average KE but move slower).
- Forgetting to subtract water's vapor pressure for gas collected over water.
- Saying real gases are most ideal at high pressure.
Mini-quiz
- What volume do 2.0 mol of an ideal gas occupy at STP?
- At the same temperature, how does the effusion rate of helium (4 g/mol) compare with methane (16 g/mol)?
- A gas occupies 2.0 L at 27 °C. At constant pressure it is heated to 327 °C. What is its new volume?
- A container holds 2 mol N₂, 1 mol O₂ and 1 mol Ar at a total pressure of 2.0 atm. What is the partial pressure of N₂?
- Under which conditions does a real gas deviate MOST from ideal behavior?
Answer key: 1 C · 2 D · 3 B · 4 B · 5 C