Unit 3 Properties of Substances and Mixtures

AP Chemistry Gas Laws

Boyle's, Charles's, Gay-Lussac's, and the combined gas law, with the Kelvin rule and the graphs behind them, in four worked examples.

Many gas questions describe a sample before and after a change: a balloon rises, a can is heated, a syringe is pushed in. For those, a two-state equation is quicker than solving PV = nRT twice, because the gas constant and the amount of gas cancel. This page shows where those equations come from, how to choose the right one, and how to avoid the Kelvin mistake that costs the most points. The official reference sheet lists the combined gas law among its equations.

The Gas Laws as Special Cases of PV = nRT

For a fixed amount of gas, PV/T = nR is constant, so the same sample in two states obeys P₁V₁/T₁ = P₂V₂/T₂, the combined gas law. Hold one variable constant and it simplifies to a named law:

Boyle's law (T and n constant): P₁V₁ = P₂V₂. Pressure and volume are inversely proportional.
Charles's law (P and n constant): V₁/T₁ = V₂/T₂. Volume is proportional to the Kelvin temperature.
Gay-Lussac's law (V and n constant): P₁/T₁ = P₂/T₂. Pressure is proportional to the Kelvin temperature.
Avogadro's law (P and T constant): V₁/n₁ = V₂/n₂. Volume is proportional to the moles of gas.

The particle explanation is the same in each case: pressure comes from collisions with the walls, and the average kinetic energy of the particles is proportional to the Kelvin temperature, as described in kinetic molecular theory. The graphs show each relationship with the points used in the examples below.

To check an answer, the gas law calculator solves the combined gas law or any of these special cases, converts the units, and shows each step.

Fig. 1 · The three simple gas laws as graphs

Worked Example 1: Compressing a Gas at Constant Temperature With Boyle's Law

A gas occupies 5.00 L at 1.00 atm. It is compressed to 2.00 L at the same temperature. What is the new pressure?

Setup: T and n are constant, so P₁V₁ = P₂V₂.
Solve: P₂ = P₁V₁/V₂ = (1.00 atm)(5.00 L) ÷ (2.00 L) = 2.50 atm.

The volume fell by a factor of 2.5, so the pressure rose by a factor of 2.5. Check direction first: less volume means more frequent wall collisions, so the pressure must go up. No temperature conversion is needed because temperature does not appear.

Worked Example 2: Heating a Balloon at Constant Pressure With Charles's Law

A balloon holds 3.00 L of air at 25°C. It is warmed to 75°C at constant pressure. What is its volume?

Convert to kelvins: T₁ = 25 + 273 = 298 K and T₂ = 75 + 273 = 348 K.
Solve: V₂ = V₁T₂/T₁ = (3.00 L)(348 K) ÷ (298 K) = 3.50 L.

Using Celsius values would give (3.00)(75/25) = 9.0 L, a threefold error caused by a temperature ratio that is not physical. The Kelvin scale starts at the point where the particles have the least energy, so doubling the Kelvin temperature really does double the volume. This is the unit check stated on the ideal gas law page.

The conversion formulas, plus when a temperature change needs no conversion at all, are in AP Chemistry temperature conversions.

Worked Example 3: Changing Pressure and Temperature Together With the Combined Gas Law

A weather balloon holds 5.0 L at 1.0 atm and 20°C. It rises to where the pressure is 0.40 atm and the temperature is −40°C. Find the new volume.

Kelvins: T₁ = 20 + 273 = 293 K and T₂ = −40 + 273 = 233 K.
Solve: V₂ = V₁ (P₁/P₂)(T₂/T₁) = (5.0 L)(1.0/0.40)(233/293) = 9.9 L.

The two changes pull in opposite directions. The pressure drop by a factor of 2.5 would raise the volume to 12.5 L, and the cooling by a factor of 233/293 = 0.795 lowers it back to 9.9 L, so a quick estimate between the two effects is a useful check. Use the combined form whenever more than one of P, V, and T changes, and the amount of gas has not changed.

Worked Example 4: Heating a Sealed Container at Constant Volume

A sealed aerosol can at 25°C holds gas at 2.0 atm. It is heated to 100°C. What is the pressure, and what would a Celsius-based calculation wrongly give?

Kelvins: 298 K and 373 K.
Solve: P₂ = P₁T₂/T₁ = (2.0 atm)(373 K) ÷ (298 K) = 2.5 atm.
The Celsius mistake: (2.0)(100/25) = 8.0 atm, more than three times too large.

A rigid container keeps the volume fixed, so only temperature changes the pressure. The same reasoning is why sealed cans carry a warning about heat. If gas is released or added, the amount changes and Avogadro's law, or the full ideal gas law, is needed instead.

Five Gas Law Practice Questions With Answers

A gas has a volume of 4.0 L at 760 torr. What is the volume at 380 torr and the same temperature?
Show answer
V₂ = (760 × 4.0) ÷ 380 = 8.0 L. Torr can be used directly because the pressure appears on both sides as a ratio.
A 2.0 L sample at 27°C is heated to 127°C at constant pressure. What is its volume?
Show answer
T₁ = 300 K and T₂ = 400 K, so V₂ = 2.0 × 400/300 = 2.7 L.
Why must temperature be in kelvins in these equations?
Show answer
Volume and pressure are proportional to absolute temperature, which is zero at 0 K. Celsius values do not give correct ratios, and they can even be zero or negative.
A sample of 10.0 L at 2.0 atm and 300 K changes to 5.0 atm and 450 K. What is the new volume?
Show answer
V₂ = 10.0 × (2.0/5.0) × (450/300) = 6.0 L.
For a fixed amount of gas at constant temperature, what do you get by plotting P against 1/V?
Show answer
A straight line through the origin, because P = (constant)(1/V). A plot of P against V is a curve called a hyperbola.

Common Gas Law Mistakes

Using Celsius. Convert every temperature to kelvins before forming a ratio.
Inverting a ratio. Pressure and volume are inversely related, so P and V go on opposite sides in Boyle's law; check that the answer moves in the expected direction.
Applying a two-state law when the amount of gas changes. Use PV = nRT, or Avogadro's law, if gas is added or removed.
Converting units unnecessarily. In a ratio, pressure in torr or volume in mL works if both states use the same unit; only temperature needs kelvins.
Holding the wrong variable constant. Read whether the container is rigid, flexible, or open before choosing a law.
Ignoring vapor pressure or a second gas. If the gas is collected over water or mixed with others, find the pressure of the gas alone first, as in partial pressure.

Gas questions are among the quickest to score once the setup is automatic. To see how a stronger Unit 3 would shift your overall estimate, the AP Chem Score Calculator turns section scores into a 1–5 range.

Frequently Asked Questions

What is Boyle's law?

At constant temperature and amount of gas, the pressure of a gas is inversely proportional to its volume: P₁V₁ = P₂V₂. Halving the volume doubles the pressure.

What is Charles's law?

At constant pressure and amount of gas, volume is directly proportional to the Kelvin temperature: V₁/T₁ = V₂/T₂. Doubling the Kelvin temperature doubles the volume.

What is the combined gas law?

For a fixed amount of gas, P₁V₁/T₁ = P₂V₂/T₂. It combines Boyle's, Charles's, and Gay-Lussac's laws, and it follows from the ideal gas law because n and R cancel.

Why must temperature be in kelvins in gas law problems?

Volume and pressure are proportional to absolute temperature, which is zero at 0 K, so the proportions only work on the Kelvin scale. A Celsius value would give wrong ratios and can even be zero or negative.

Do I need to convert pressure and volume units in the combined gas law?

Only to be consistent. Because each side is a ratio of the same quantity, any pressure unit or volume unit works as long as both states use it. Temperature is the exception and must always be in kelvins.

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