How to Use This Gas Law Calculator
- Combined gas law: pick your units, fill in the initial and final conditions, and leave blank the one value you want. Leave both boxes of a quantity blank to hold it constant.
- Ideal gas law: choose what to solve for, enter the other three quantities in any units, and give the amount in moles or as grams with the gas’s formula.
Which Gas Law to Use
| Law | Equation | Held constant |
|---|---|---|
| Boyle’s law | P1V1 = P2V2 | Temperature and amount |
| Charles’s law | V1/T1 = V2/T2 | Pressure and amount |
| Gay-Lussac’s law | P1/T1 = P2/T2 | Volume and amount |
| Combined gas law | P1V1/T1 = P2V2/T2 | Amount |
| Ideal gas law | PV = nRT | Nothing; one set of conditions |
Every one of these comes from PV = nRT with some quantities held fixed. That connection, with a worked example for each law, is in AP Chemistry gas laws, and the ideal gas law itself is covered in AP Chemistry ideal gas law.
Why Gas Law Temperatures Must Be in Kelvin
Pressure and volume are proportional to absolute temperature, which is measured from absolute zero. Warming a gas from 10 °C to 20 °C does not double its volume; in kelvin it goes from 283 K to 293 K, an increase of about 3.5%. The calculator converts every temperature to kelvin before solving, keeping the decimal places of a Celsius value: 25.0 °C becomes 298.2 K. Pressure and volume can stay in any unit in the combined gas law, because the units cancel as long as both values use the same one. The reason temperature matters at the particle level is explained in AP Chemistry kinetic molecular theory.
Worked Example: Using the Combined Gas Law
A gas occupies 2.50 L at 1.00 atm and 25.0 °C. What is its volume at 2.00 atm and 100.0 °C?
Kelvin: T1 = 25.0 + 273.15 = 298.2 K; T2 = 100.0 + 273.15 = 373.2 K.
Rearrange: V2 = P1V1T2 / (T1P2).
Solve: V2 = (1.00)(2.50)(373.15) ÷ [(298.15)(2.00)] = 1.56 L.
Doubling the pressure alone would halve the volume to 1.25 L; heating the gas offsets part of that, so the answer lands in between.
Worked Example: Using the Ideal Gas Law With Grams
What volume does 16.0 g of O2 occupy at 1.00 atm and 0.0 °C?
Moles: 16.0 g ÷ 32.00 g/mol = 0.500 mol.
Kelvin: 0.0 + 273.15 = 273.2 K.
Solve: V = nRT / P = (0.500)(0.08206)(273.15) ÷ 1.00 = 11.2 L.
That is half of 22.4 L, the molar volume of an ideal gas at 0 °C and 1 atm, because 0.500 mol is half a mole. Converting grams to moles first is the same step used in AP Chemistry stoichiometry, and a mixture of gases is handled with AP Chemistry partial pressure.
Which Value of R to Use
| R | Use it when |
|---|---|
| 0.08206 L·atm/(mol·K) | Pressure in atm and volume in liters |
| 62.36 L·torr/(mol·K) | Pressure in torr or mmHg and volume in liters |
| 8.314 J/(mol·K) | Energy calculations, such as in thermodynamics |
All three values are printed on the exam’s formula sheet, described in the AP Chemistry reference sheet guide. The calculator uses 0.08206 after converting your units, so its answers carry at most four significant figures. To see how stronger free-response answers could move your overall estimate, try the AP Chem Score Calculator.
Related Resources
- AP Chem Score Calculator
- AP Chemistry Gas Laws
- AP Chemistry Ideal Gas Law
- AP Chemistry Partial Pressure
- AP Chemistry Kinetic Molecular Theory
- AP Chemistry Temperature Conversions
- Unit 3 Review: Properties of Substances and Mixtures
Frequently Asked Questions
What is the combined gas law formula?
P1V1/T1 = P2V2/T2, for a fixed amount of gas. Temperatures must be in kelvin. If one quantity stays constant it cancels, which gives Boyle's law (constant temperature), Charles's law (constant pressure), or Gay-Lussac's law (constant volume).
When do you use the ideal gas law instead of the combined gas law?
Use the ideal gas law, PV = nRT, when the problem involves the amount of gas in moles or grams, or describes a single set of conditions. Use the combined gas law when the same sample of gas changes from one set of conditions to another.
Why must temperature be in kelvin for gas law problems?
Gas volume and pressure are proportional to absolute temperature, and only the Kelvin scale starts at absolute zero. Doubling a temperature in degrees Celsius does not double the kinetic energy of the particles, so Celsius values give wrong answers.
What value of R should I use?
Match R to your units. With pressure in atmospheres and volume in liters, use R = 0.08206 L·atm/(mol·K). For energy in joules, use 8.314 J/(mol·K). With pressure in torr or mmHg, use 62.36 L·torr/(mol·K).
What is the molar volume of a gas at STP?
About 22.4 L per mole of an ideal gas at standard temperature and pressure, 0 °C (273.15 K) and 1 atm. You can check it with the calculator: 1.00 mol at 1.00 atm and 273 K gives 22.4 L.
This page is not affiliated with or endorsed by College Board. AP® is a trademark registered by the College Board.