Gases & Gas Laws
Pressure units, the gas laws, PV=nRT, partial pressures, molecular speeds, and gas stoichiometry.
Pressure units
REFERENCE1 atm = 101,325 Pa = 760 mmHg = 760 torr ≈ 1.01325 bar ≈ 14.696 psi. torr ≡ mmHg; 1 bar = 100,000 Pa exactly. Chain conversions by dimensional analysis.
Always use Kelvin
WATCH OUTEvery gas-law plug-in needs absolute T: T(K) = T(°C) + 273.15. Never put °C or °F into a gas-law equation. STP here = 0 °C (273.15 K) and 1 atm.
The simple gas laws
REFERENCE| Law | Held constant | Relation |
|---|---|---|
| Boyle | T, n | P₁V₁ = P₂V₂ |
| Charles | P, n | V₁/T₁ = V₂/T₂ |
| Gay-Lussac | V, n | P₁/T₁ = P₂/T₂ |
| Avogadro | T, P | V₁/n₁ = V₂/n₂ |
Combined gas law
CORE RULEP₁V₁/T₁ = P₂V₂/T₂ when P, V, and T all change (n fixed). T in Kelvin; P and V units just have to match between the two states.
Ideal gas law
CORE RULEPV = nRT for a single state with 3 of 4 knowns. T in Kelvin. P = nRT/V, V = nRT/P, n = PV/RT, T = PV/nR. Pick the R whose units match P and V.
Choosing R
REFERENCE| R value | Use when |
|---|---|
| 0.08206 L·atm/(mol·K) | P in atm, V in L |
| 8.314 J/(mol·K) | SI; and all u_rms / KMT speeds |
| 0.08314 L·bar/(mol·K) | P in bar, V in L |
| 62.36 L·torr/(mol·K) | P in torr, V in L |
Molar mass & density
CORE RULEM = mRT/(VP); density ρ = PM/(RT). At STP one mole occupies 22.4 L, so ρ_STP = M / 22.4 (g/L). Match R to the pressure unit.
Partial pressures (Dalton)
CORE RULEP_total = Σ P_partial. Mole fraction X_A = n_A/n_total = P_A/P_total, so P_A = X_A·P_total. Gas over water: P_gas = P_total − P_H₂O(T) (supplied).
Molecular speeds
CORE RULEu_rms = √(3RT/M), with M in kg/mol and R = 8.314 to get m/s. Ratio (same T): u_rms,A / u_rms,B = √(M_B/M_A). (Mean = √(8RT/πM); most probable = √(2RT/M).)
Graham's law
CORE RULEEffusion/diffusion: rate_A / rate_B = √(M_B/M_A): lighter gases move faster. Time scales the other way: time_A / time_B = √(M_A/M_B). Same temperature required.
Gas stoichiometry
METHODmass → moles → mole ratio → moles of gas → V via PV=nRT (or 22.4 L/mol at STP). If reactants and products are all gases at the same T, P, mole ratios equal volume ratios directly.