Gas Laws Study Guide
Gas-law problems are among the most predictable in chemistry: the same handful of relationships, in the same forms, on nearly every exam. The traps are always in the units — Celsius versus Kelvin, mismatched pressure units, the wrong R. This guide organizes every law around the combined relationship, shows how density and molar mass drop out of PV = nRT, and ends with partial pressures and real-gas behavior.
Key formulas
PV = nRT, with R = 0.08206 L·atm/(mol·K) = 8.314 J/(mol·K); P in matching pressure units, V in liters, T in Kelvin
P1V1/T1 = P2V2/T2 (combined gas law; T must be in Kelvin)
P1V1 = P2V2 at constant T (Boyle's law)
V1/T1 = V2/T2 at constant P (Charles's law)
P_total = P1 + P2 + ... = sum of partial pressures (Dalton's law); P_i = X_i x P_total
d = PM/RT, where d is gas density in g/L and M is molar mass in g/mol
Topic checklist
Units and conditions
Pressure units: 1 atm = 760 mmHg = 760 torr = 101.325 kPa = 14.7 psi; convert to match the R you use.
Temperature must be in Kelvin for every gas-law calculation: K = °C + 273.15.
Amount of gas is always in moles for PV = nRT.
The simple gas laws
Boyle's law: at constant temperature, pressure and volume are inversely proportional (P1V1 = P2V2).
Charles's law: at constant pressure, volume is directly proportional to absolute temperature (V1/T1 = V2/T2).
Gay-Lussac's law: at constant volume, pressure is directly proportional to absolute temperature (P1/T1 = P2/T2).
Combined gas law and STP
The combined gas law P1V1/T1 = P2V2/T2 handles simultaneous changes in P, V, and T.
STP is defined as 0 °C (273.15 K) and 1 atm; one mole of an ideal gas occupies 22.4 L at STP.
Cancel variables held constant to reduce the combined law to the simple laws you need.
The ideal gas law
PV = nRT is the workhorse; choose R to match your units (0.08206 L·atm/mol·K or 8.314 J/mol·K).
Rearrange before plugging in: solve algebraically for the unknown first.
Check that the answer's magnitude is plausible — a liter of gas cannot weigh 500 g.
Partial pressures and mixtures
Dalton's law: P_total = P1 + P2 + ..., and each gas behaves as if alone (P_i = X_i x P_total).
Collecting a gas over water requires subtracting the vapor pressure of water from the measured total.
Mole fraction X_i = n_i / n_total applies to both pressure and composition.
Real gases
Real gases deviate from ideal behavior at high pressure and low temperature.
The van der Waals equation adds corrections: 'a' for intermolecular attractions, 'b' for particle volume.
Gases closest to ideal: small, nonpolar, and at high temperature with low pressure.
Common mistakes
Mistake: Plugging Celsius temperatures directly into gas laws
Fix:
Convert first: T(K) = T(°C) + 273.15. A Charles's law problem at 27 °C uses 300.15 K, never 27. This single mistake is the most common point-loss in gas-law exams.
Mistake: Using the wrong value of R for the given pressure/volume units
Fix:
Pair R with the units you have: use 0.08206 L·atm/(mol·K) when pressure is in atm and volume in liters; use 8.314 J/(mol·K) when working in SI units. Convert pressure or volume first if they don't match.
Mistake: Assuming STP means room temperature or mixing STP with SATP
Fix:
STP for gas calculations is 0 °C and 1 atm (22.4 L/mol). Do not confuse it with SATP (25 °C, 100 kPa) or with room temperature unless the problem says so.
Mistake: Memorizing gas density as a separate formula instead of deriving it from PV = nRT
Fix:
Density follows from d = m/V = PM/RT. Derive it, don't memorize it: start from n = m/M in PV = nRT and solve for m/V.
Exam tips
Drill mixed problems in gas-laws-practice until the correct law is obvious within five seconds of reading the question.
Write a 'given and unknown' box before every calculation; gas-law errors are almost always unit errors caught there.
Keep a mini conversion table (atm, mmHg, kPa, torr, K) on your scratch sheet during the test.
When a problem mentions 'collected over water,' immediately write down the water vapor pressure correction.
If time is short, PV = nRT plus the combined law covers roughly 80 percent of exam questions.