The gas laws are not the hard part — the algebra is two lines. The hard part is the moment before that, when you have four named equations and have to pick one. Choose wrong and the numbers still compute; they just compute the wrong answer. This guide gives you a single decision rule for telling the gas law equations apart.
The Decision Rule: Count What Changes
Every basic gas problem involves four quantities: pressure (P), volume (V), temperature (T), and amount in moles (n). The equation you need depends on two questions:
- Is this one state, or a before-and-after?
- Which quantities are changing, and which are held constant?
If the problem describes a gas at a single set of conditions, use the ideal gas law. If it describes a gas changing from one state to another, use a combined-style law, and which one depends on what stays fixed. Answer those two questions first and the equation picks itself.
The Single-State Law: PV = nRT
The ideal gas law is PV = nRT, where R is the gas constant, 0.0821 L·atm/(mol·K).
Reach for it when the problem gives you one condition and asks for a missing variable — no "before" and "after." Telltale phrasings: "what volume does 2.0 mol of gas occupy at..." or "find the pressure of a sample at...". You are solving for one unknown in one snapshot.
Example: What volume does 0.500 mol of gas occupy at 1.00 atm and 300 K? Solve PV = nRT for V: V = nRT/P = (0.500)(0.0821)(300)/(1.00) = 12.3 L. One state, one equation.
The Before-and-After Laws
When a gas moves between two states, use a law in the form (state 1) = (state 2). The amount of gas (n) is almost always constant — the same sealed sample — so the choice is about which of P, V, T is also held constant.
- Boyle's law — P₁V₁ = P₂V₂. Temperature constant; pressure and volume trade off. Use it when T is unchanged. Squeeze a gas, pressure rises.
- Charles's law — V₁/T₁ = V₂/T₂. Pressure constant; volume and temperature move together. Use it when P is unchanged. Heat a gas at fixed pressure, it expands.
- Gay-Lussac's law — P₁/T₁ = P₂/T₂. Volume constant (a rigid container); pressure rises with temperature.
- Combined gas law — P₁V₁/T₁ = P₂V₂/T₂. Nothing is held constant except n. Use it when P, V, and T all change. The other three laws are just this one with a term cancelled.
The combined gas law is the safe default for any two-state problem: if a quantity does not change, it appears identically on both sides and cancels, collapsing the combined law into Boyle's, Charles's, or Gay-Lussac's automatically.
The non-negotiable: temperature in Kelvin
Every gas law uses absolute temperature. Convert Celsius to Kelvin (K = °C + 273.15) before plugging in. Using 25 instead of 298 does not produce a small error — it produces a meaningless one, because the laws assume zero means zero molecular motion. This single conversion is the most common gas-law mistake.
When the amount of gas changes
The four laws above all assume a sealed, constant amount of gas. Two situations break that assumption. Avogadro's law — V₁/n₁ = V₂/n₂ — applies when the amount of gas changes at constant temperature and pressure: volume is proportional to moles, which is why equal volumes of any gas at the same T and P hold equal numbers of molecules. And if a problem involves a chemical reaction producing or consuming gas, the moles change as the reaction runs, so no before-and-after law covers it — use stoichiometry to find the moles of gas, then apply PV = nRT. Recognizing a problem as a stoichiometry-plus-gas-law hybrid keeps you from forcing a pure gas law onto it.
Worked Comparison
Same gas, two problems, to show the rule in action.
"A 2.0 L gas at 1.0 atm is compressed to 0.50 L at constant temperature. New pressure?" Two states, temperature constant — Boyle's law. P₂ = P₁V₁/V₂ = (1.0)(2.0)/(0.50) = 4.0 atm.
"A 2.0 L gas at 1.0 atm and 300 K is heated to 400 K and 1.5 atm. New volume?" Two states, P and T both change — combined gas law. V₂ = P₁V₁T₂/(T₁P₂) = (1.0)(2.0)(400)/[(300)(1.5)] = 1.8 L. The only difference between the two problems is how many quantities changed.
Getting Help
Gas-law problems are dimensional-analysis problems once the equation is chosen, so the same unit-tracking habit pays off across chemistry — browse the General Chemistry study guides for more worked methods.
Conclusion
Choosing the right gas law equation is a two-question decision: one state or two, and what is held constant. One state means PV = nRT. Two states mean a before-and-after law — Boyle's if temperature is fixed, Charles's if pressure is fixed, Gay-Lussac's if volume is fixed, and the combined gas law if everything moves. Convert every temperature to Kelvin first, and the algebra takes care of itself.
