Chemistry · Unit 3: Intermolecular Forces and Properties · 14 min read · Updated 2026-05-11
Ideal Gas Law — AP Chemistry
AP Chemistry · Unit 3: Intermolecular Forces and Properties · 14 min read
1. Core Ideal Gas Law ($PV = nRT$)★★☆☆☆⏱ 4 min
The ideal gas law is a combined equation of state that relates the four measurable properties of an ideal gas: pressure ($P$), volume ($V$), temperature ($T$), and amount of gas in moles ($n$). An ideal gas is defined as a gas where intermolecular forces are negligible and gas molecules have no volume relative to their container, an approximation that holds for most AP exam problems.
Unlike individual empirical gas laws that only relate two variables while holding others constant, the ideal gas law relates all four variables at once, making it applicable to nearly all introductory gas problems. It accounts for 5-10% of your total AP Chemistry exam score directly.
PV = nRT
Where $R$ is the universal gas constant. For almost all AP Chemistry problems, you will use $R = 0.0821 \frac{L \cdot atm}{mol \cdot K}$, which matches the most common units of pressure (atmospheres) and volume (liters) on the exam. The non-negotiable requirement of the ideal gas law is that temperature *must* be in Kelvin, the absolute temperature scale. All other units must match the units of $R$.
Exam tip: Always write down units for every variable and cancel units as you go. If your final units do not match what the question asks for, you know you rearranged the formula incorrectly before you calculate a wrong numerical answer.
2. Derived Relationships: Molar Mass and Gas Density★★★☆☆⏱ 4 min
The ideal gas law can be rearranged to solve for two extremely useful properties for unknown gases: molar mass ($M$) and density ($d$). Recall that moles are defined as $n = \frac{m}{M}$, where $m$ is mass of the gas in grams, and $M$ is molar mass in g/mol. Substituting into the core ideal gas law gives:
PV = \left(\frac{m}{M}\right)RT
M = \frac{mRT}{PV}
Since density $d = \frac{m}{V}$, we can substitute this into the equation to get a direct relationship between density, molar mass, pressure, and temperature:
d = \frac{PM}{RT}
These derivations are very common on AP FRQs, where you may be asked to derive the relationship yourself or use it to find the molar mass of an unknown gas from experimental data.
3. Dalton's Law of Partial Pressures★★☆☆☆⏱ 3 min
For mixtures of non-reacting ideal gases, the ideal gas law applies to the mixture as a whole and to each individual gas in the mixture. Dalton’s law of partial pressures states that the total pressure of a mixture is equal to the sum of the partial pressures of each individual gas, where the partial pressure of a gas is the pressure it would exert if it occupied the entire container alone.
P_{total} = P_1 + P_2 + P_3 + ... + P_n
Since all gases in the same mixture share the same volume and temperature, partial pressure is proportional to the mole fraction of the gas $\chi_i = \frac{n_i}{n_{total}}$, giving the useful relationship:
P_i = \chi_i P_{total}
One of the most common AP exam applications of Dalton’s law is for gases collected over water: the total pressure in the collection vessel is the sum of the pressure of the collected gas and the vapor pressure of water at the experimental temperature:
P_{gas} = P_{total} - P_{water}
4. AP-Style Practice Problems★★★☆☆⏱ 3 min
Common Pitfalls
Why: Most problems give experimental temperatures in Celsius for realism, and students forget the ideal gas law requires absolute temperature.
Why: Students memorize $R = 0.0821$ but forget it requires liters and atmospheres; they leave volume in mL or pressure in kPa and get the wrong order of magnitude.
Why: Students only use the total pressure given in the problem, ignoring that water contributes to the total pressure.
Why: Many older textbooks teach the pre-1982 IUPAC STP definition; the AP CED uses the current IUPAC definition.
Why: Students confuse mass percent with mole percent and use mass fractions to calculate partial pressure.
Why: Students memorize $d = PM/RT$ but forget density depends on P and T, so two gases with different molar masses can have the same density at different conditions.