The ideal gas law, , links the pressure, volume, moles, and temperature of a gas so you can solve for any one variable when you know the others. For gas mixtures, each gas contributes its own partial pressure, and those partial pressures add up to the total pressure by Dalton's law. For AP Chemistry, convert temperature to Kelvin before using gas-law equations.
What Is the Ideal Gas Law?
The ideal gas law is PV = nRT, where pressure, volume, moles, and temperature describe the macroscopic behavior of an ideal gas sample. In AP Chemistry, you use it to solve for a missing gas variable, explain how gas variables change, and connect gas mixtures to partial pressure and mole fraction.
Why This Matters for the AP Chemistry Exam
This topic is about explaining and predicting how a gas sample responds when you change one of its properties. You should be able to describe how P, V, T, and n connect through PV = nRT, and explain what happens to one variable when another changes while the rest are held constant. That reasoning shows up in both the multiple-choice and free-response sections, often paired with stoichiometry or asking you to interpret a graph of gas behavior. Partial pressures and mole fractions also matter when you work with gas mixtures, so being fluent with both the math and the particle-level reasoning behind it pays off.
Key Takeaways
- PV = nRT relates pressure, volume, moles, and temperature; if you know any three, you can solve for the fourth.
- Pressure comes from gas particles colliding with the container walls, so explanations about pressure should mention collision frequency and force.
- Always use Kelvin for temperature, liters for volume, and atm for pressure when R = 0.08206 L·atm·mol⁻¹·K⁻¹. Match your units to R.
- Boyle's, Charles's, Gay-Lussac's, and Avogadro's laws each describe how two variables relate when the others are constant; the combined gas law ties three of them together.
- In a mixture, each gas exerts a partial pressure proportional to its mole fraction, and the total pressure is the sum of the partial pressures.
- Graphs of P, V, T, and n relationships are fair game, so know what a P vs. V curve or a V vs. T line should look like.
Pressure and Temperature
Gases exert pressure on their surroundings. The phrase to connect with pressure is "the number of times particles hit the walls of the container." If a question asks you to explain any relationship involving pressure, work that idea in.
Standard pressure is the pressure exerted by the weight of Earth's atmosphere at a given location, often called atmospheric pressure. Here it is in four common units:
Standard Pressure: 1.00 atm = 760 mm Hg = 760 torr = 101.3 kPa
Temperature is treated as the average kinetic energy of the particles in a substance. The higher the temperature, the greater the average kinetic energy, which means particles are moving faster.
Standard Temperature: 0 °C = 273.15 K (°C + 273.15 = K)
STP, or Standard Temperature and Pressure, refers to conditions of 1 atm and 273.15 K. This term shows up often, so recognize it on sight.
Gas Laws and Relationships
Gas laws describe how pressure, volume, temperature, and moles of a gas relate to each other. The relationships below hold when the amount of gas is constant.
Boyle's Law
Boyle's law describes the relationship between pressure and volume at constant temperature. It is an inverse relationship: P1V1 = P2V2, where P is pressure, V is volume, and the numbers refer to initial and final conditions.
When volume decreases, particles collide with the container walls more often, which increases pressure.
Charles's Law
Charles's law describes the relationship between volume and temperature at constant pressure. It is a direct relationship: V1/T1 = V2/T2, where V is volume, T is temperature, and the numbers refer to initial and final conditions.
When temperature (average kinetic energy) increases, particles move faster and collide with the walls more often and harder. Volume increases to keep the pressure constant.
Gay-Lussac's Law
Gay-Lussac's law describes the relationship between pressure and temperature at constant volume. It is a direct relationship: P1/T1 = P2/T2, where P is pressure, T is temperature, and the numbers refer to initial and final conditions.
As temperature increases, particles move faster and collisions with the walls become more frequent and stronger, which raises the pressure.
Avogadro's Law
Avogadro's law describes the relationship between volume and moles of gas. It is a direct relationship: V1/n1 = V2/n2, where V is volume, n is moles of gas, and the numbers refer to initial and final conditions.
Adding more particles to a container causes more collisions with the walls, so volume increases to keep pressure constant.
Avogadro also found that equal volumes of gases at the same temperature and pressure contain the same number of particles. For example, 5 L of H2 and 5 L of He at STP contain the same number of particles.
The Combined Gas Law
Three of these laws combine into the combined gas law: P1V1/T1 = P2V2/T2. When solving problems, you can drop any variable that does not change. For example, in a pressure-volume problem at constant temperature, T cancels and you are left with P1V1 = P2V2, which is just Boyle's law.
If you remember the combined gas law, you can recover the others, but you should still understand the reasoning behind each relationship.
Ideal Gas Law
The ideal gas law brings all four variables together: PV = nRT. The values below are on the AP Chemistry reference table, and they are quick to memorize:
- P = pressure in atm
- V = volume in L
- n = moles of gas
- R = universal gas constant (0.08206 L·atm·mol⁻¹·K⁻¹)
- T = temperature in Kelvin
Convert temperature to Kelvin, volume to liters, and pressure to atm in every problem. If you forget which units to use, check the units of R on the reference sheet and match them.
The ideal gas law is one of the most useful equations in this course. Many problems are a matter of plugging in values, but some pair it with stoichiometry, so be ready to combine the two.
Dalton's Law of Partial Pressure
In a mixture of ideal gases, the pressure each gas exerts (its partial pressure) is independent of the other gases. According to Dalton's law of partial pressure, the total pressure equals the sum of the partial pressures of every gas in the mixture:
P_total = P_A + P_B + P_C + ...
To find a single gas's partial pressure, use its mole fraction. The mole fraction of gas A is written X_A and equals moles A / total moles. For example, in a mixture of 3 mol O2 and 4 mol H2, the mole fraction of O2 is 3/(3+4) = 3/7. Then:
P_A = X_A × P_total
Going straight to P_A = X_A × P_total is usually faster than calculating each step separately, so get comfortable with that form.
How to Use This on the AP Chemistry Exam
Problem Solving
- Identify which variables are given and which one you are solving for, then choose the right equation. If three of P, V, T, and n are known, use PV = nRT. If only two variables change, use the matching simple gas law or the combined gas law.
- Convert units before plugging in. Temperature must be in Kelvin, and your pressure and volume units must match R.
- For mixtures, find the mole fraction first, then multiply by total pressure to get a partial pressure.
Free Response
- When asked to explain a change, connect the variables at the particle level. For anything involving pressure, mention collision frequency and force, not just "pressure goes up."
- State which variables are held constant. A clear explanation names the constant variable and then explains the direct or inverse relationship between the two that change.
Graphs
- Be ready to read or sketch plots of P, V, T, and n. A P vs. V graph at constant temperature curves (inverse relationship), while V vs. T or P vs. T at the right conditions is a straight line (direct relationship).
Common Trap
- Forgetting to convert Celsius to Kelvin is the fastest way to lose points on gas problems. Check temperature units first.
Common Misconceptions
- Pressure and volume are not directly related. At constant temperature, they are inverse. Squeezing a gas into a smaller volume raises the pressure because collisions happen more often.
- Temperature must be in Kelvin, not Celsius. Gas law ratios break down with Celsius because Celsius can be zero or negative, which would give nonsense results.
- Mole fraction is not a percent of mass or volume. It is moles of one component divided by total moles of all components.
- Each gas in a mixture acts independently. A gas's partial pressure depends only on its own moles and the conditions, not on what other gases are present.
- The combined gas law and PV = nRT are different tools. Use the combined gas law to compare two states of the same gas sample; use PV = nRT to find an absolute value of one variable at a single set of conditions.
- "Standard temperature" is 273.15 K, not room temperature. STP conditions are 1 atm and 0 °C, which is colder than a typical room.
Related AP Chemistry Guides
Vocabulary
The following words are mentioned explicitly in the College Board Course and Exam Description for this topic.Term | Definition |
|---|---|
Dalton's Law of Partial Pressures | The principle that the total pressure of a gas mixture equals the sum of the partial pressures of the individual gas components. |
ideal gas law | The equation PV = nRT that relates pressure, volume, number of moles, and temperature of an ideal gas. |
macroscopic properties | Observable physical and chemical characteristics of a substance that can be measured at the bulk level, such as melting point, boiling point, and vapor pressure. |
mole fraction | The ratio of the number of moles of one component to the total number of moles in a mixture, used to relate partial pressure to total pressure. |
partial pressure | The pressure exerted by a single gas in a mixture of gases, used in equilibrium expressions for gas-phase reactions. |
Frequently Asked Questions
What is the ideal gas law in AP Chemistry?
The ideal gas law is PV = nRT. It relates pressure, volume, moles, and Kelvin temperature for an ideal gas sample, so you can solve for one variable when the others are known.
What does each variable in PV = nRT mean?
P is pressure, V is volume, n is moles of gas, R is the gas constant, and T is temperature in Kelvin. Match pressure and volume units to the R value you use.
Why must temperature be in Kelvin for gas laws?
Gas-law relationships depend on absolute temperature. Celsius can be zero or negative, which breaks proportional reasoning, so AP Chemistry gas-law calculations should use Kelvin.
What is partial pressure?
Partial pressure is the pressure a single gas would exert in a mixture. For ideal gases, each gas acts independently, and total pressure equals the sum of all partial pressures.
How do mole fraction and partial pressure connect?
A gas's partial pressure equals its mole fraction times the total pressure: PA = XA x Ptotal. Mole fraction is moles of that gas divided by total moles of gas in the mixture.
What gas-law graphs should I know for AP Chemistry?
Know the direct and inverse relationships among P, V, T, and n. For example, P vs. V at constant temperature is inverse, while V vs. T at constant pressure is direct when temperature is in Kelvin.