The gas laws all describe relationships between the same four variables: pressure, volume, temperature in Kelvin, and moles. Boyle’s Law (P1V1 = P2V2) relates pressure and volume. Charles’s Law (V1/T1 = V2/T2) relates volume and temperature. Gay-Lussac’s Law (P1/T1 = P2/T2) relates pressure and temperature. The Ideal Gas Law (PV = nRT) combines all of them into one equation for a single set of conditions.
What are the variables every gas law uses?
Every gas law in this unit is really just a relationship between the same handful of variables: pressure (P), volume (V), temperature (T, always in Kelvin), and moles (n).
The individual gas laws are special cases where one or two of these are held constant, which is exactly why students confuse them. They all describe the same underlying behavior from different angles. Learn the four variables and which ones each law freezes, and the formulas stop needing to be memorized separately.
One rule before anything else: temperature always goes in Kelvin. Add 273.15 to a Celsius value. Using Celsius in a gas law is the most common wrong answer in the entire unit, because a ratio built on Celsius is meaningless.
What is Boyle’s Law?
Boyle’s Law holds temperature and moles constant and says pressure and volume are inversely related. As volume decreases, pressure increases, and the other way around. The formula is P1V1 = P2V2.
Picture squeezing a sealed syringe. As you push the plunger in and shrink the volume, the gas pushes back harder, so pressure goes up. That is Boyle’s Law in one image. See Boyle’s Law.
What is Charles’s Law?
Charles’s Law holds pressure and moles constant and says volume and temperature are directly related. As temperature increases, volume increases. The formula is V1/T1 = V2/T2.
This is why a balloon left in a hot car expands and a balloon left outside on a cold day shrinks. The gas inside is responding directly to the temperature change while the pressure stays roughly constant. See Charles and Combined Gas Law.
What is Gay-Lussac’s Law?
Gay-Lussac’s Law holds volume and moles constant and says pressure and temperature are directly related. As temperature increases, pressure increases. The formula is P1/T1 = P2/T2.
This is the law behind the warning on an aerosol can about heat. The volume of a sealed can cannot change, so rising temperature drives the internal pressure up until the can fails.
What is the combined gas law?
When moles stay constant but pressure, volume and temperature all change at once, you do not need three separate laws. Use P1V1/T1 = P2V2/T2.
Boyle, Charles and Gay-Lussac are each just the combined gas law with one variable cancelled out. If you only memorize one before-and-after formula, memorize this one and cancel what stays constant.
What is the Ideal Gas Law and when do you use it?
The Ideal Gas Law, PV = nRT, combines all of the individual gas laws into a single equation that works for one set of conditions, not a before-and-after comparison. R is the ideal gas constant, 0.0821 L atm per mol K when pressure is in atmospheres.
Here is the decision rule students most need:
- One set of conditions, and the problem gives you three of the four variables and asks for the fourth? Use PV = nRT.
- Two sets of conditions, a before and an after for the same sample of gas? Use the combined gas law or the relevant individual law.
See The Ideal Gas Law.
A worked ideal gas law example
What volume does 2.5 moles of gas occupy at 300 K and 1.2 atm?
Rearrange PV = nRT to solve for V, which gives V = nRT / P. Plugging in: V = (2.5 mol)(0.0821 L atm/mol K)(300 K) divided by 1.2 atm, which works out to about 51.3 liters.
Notice that every unit cancels except liters. That unit check is a fast way to catch a setup mistake before you even finish the arithmetic. If your units do not cancel down to what the question asked for, your setup is wrong, not your calculator.
What is Dalton’s Law of partial pressures?
In a mixture of gases, each gas exerts pressure independently, and the total pressure is the sum of the individual partial pressures. Each gas behaves as though the others are not there.
This shows up constantly in gas collection problems, especially gas collected over water, where you have to subtract the vapor pressure of water to get the pressure of the gas you actually care about. Other Derived Gas Laws covers this group.
When do gases stop behaving ideally?
The Ideal Gas Law assumes gas particles have no volume of their own and do not attract or repel each other. That is a useful approximation, not a literal truth.
Real gases deviate most from ideal behavior in two conditions:
- High pressure, because particles are forced close together and their actual volume starts to matter.
- Low temperature, because particles slow down enough for intermolecular attractions to matter.
The AP exam usually expects you to recognize these conditions and explain in words why a real gas would deviate from the ideal prediction, not just calculate a new number. See Deviations from Ideal Gases.
Frequently asked questions
What are the four main gas laws?
Boyle’s Law relates pressure and volume at constant temperature. Charles’s Law relates volume and temperature at constant pressure. Gay-Lussac’s Law relates pressure and temperature at constant volume. The Ideal Gas Law, PV = nRT, ties pressure, volume, moles and temperature together for a single set of conditions.
Why does temperature have to be in Kelvin for gas law problems?
Because the gas laws use ratios, and a ratio only works on an absolute scale where zero means zero. Celsius has an arbitrary zero, so doubling from 10 to 20 degrees Celsius is not doubling the thermal energy. Kelvin starts at absolute zero, so the ratios are real. Convert with K = C + 273.15.
When do you use PV = nRT instead of the combined gas law?
Use PV = nRT when the problem describes a single set of conditions and gives you three of the four variables. Use the combined gas law when the problem describes the same gas sample before and after a change, and asks what happens to one variable.
What is the value of R in the ideal gas law?
R is 0.0821 L atm per mol K when pressure is measured in atmospheres and volume in liters. It is 8.314 J per mol K when working in energy units. Pick the version whose units match the rest of your problem, then check that everything cancels.
Why do real gases deviate from ideal behavior?
Because the ideal model assumes particles occupy no volume and exert no forces on each other. At high pressure the particles are crowded and their own volume matters. At low temperature they move slowly enough that intermolecular attractions pull them together. Both cause measurable departure from PV = nRT.
Gas laws come back constantly later in the course, especially in kinetic molecular theory and thermodynamics, so it is worth being solid on all of these formulas now. They are covered with guided practice in the full AP and Honors Chemistry course.