--- title: "PV = nRT — AP Chem Ideal Gas Law Definition & Exam Guide" description: "PV = nRT is the ideal gas law linking pressure, volume, moles, and Kelvin temperature. See how AP Chem tests it in Topics 3.4 and 3.6, plus when it breaks down." canonical: "https://fiveable.me/ap-chem/key-terms/pv-nrt" type: "key-term" subject: "AP Chemistry" unit: "Unit 3" --- # PV = nRT — AP Chem Ideal Gas Law Definition & Exam Guide ## Definition PV = nRT is the ideal gas law, the equation relating a gas sample's pressure (P), volume (V), moles (n), and absolute temperature in Kelvin (T) through the gas constant R. In AP Chem it's the core tool of Topic 3.4 for predicting macroscopic gas behavior. ## What It Is PV = nRT is the [ideal gas law](/ap-chem/unit-3/ideal-gas-law/study-guide/XINb2AUU6e3c1rGlhBXg "fv-autolink"), the single equation that ties together the four macroscopic properties of a gas sample. P is [pressure](/ap-chem/key-terms/pressure "fv-autolink"), V is volume, n is the number of moles of gas particles, and T is absolute temperature (always Kelvin, never Celsius). R is the gas constant that makes the units work out, usually 0.08206 L·atm/(mol·K) on the AP exam. The big idea behind the equation is that an ideal gas doesn't care what it's made of. Helium, nitrogen, CO₂, whatever. If the particles take up negligible volume and don't attract each other, then pressure, volume, moles, and [temperature](/ap-chem/unit-5/reaction-rates/study-guide/4V94d3BwjoPaOOyQtDKQ "fv-autolink") lock together in this one relationship (EK 3.4.A.1). That assumption is also where the equation breaks. Real gases deviate from PV = nRT near condensation (attractions matter) and at extremely high pressures (particle volume matters), which is the whole point of Topic 3.6. ## Why It Matters PV = nRT lives in [Unit 3](/ap-chem/unit-3 "fv-autolink") (Properties of Substances and Mixtures) and directly supports two learning objectives. LO 3.4.A asks you to explain relationships between the macroscopic properties of a gas or gas [mixture](/ap-chem/key-terms/mixture "fv-autolink") using the ideal gas law, and LO 3.6.A asks you to explain why real gases deviate from it. So the exam wants two skills from you. First, use the equation, including its extensions like partial pressures and mole fractions (P_A = P_total × X_A). Second, know its limits, meaning you can explain when interparticle attractions or particle volumes make a real gas misbehave. The equation also shows up far beyond Unit 3, since any reaction that produces or consumes a gas (think stoichiometry FRQs) can hand you P, V, and T and expect moles back. ## Connections ### [Dalton's Law of Partial Pressure (Unit 3)](/ap-chem/key-terms/daltons-law-of-partial-pressure) Dalton's Law is just PV = nRT applied to a mixture. Each gas exerts pressure as if it were alone, so each component's [partial pressure](/ap-chem/key-terms/partial-pressure "fv-autolink") is its own little nRT/V, and the total pressure is the sum (EK 3.4.A.2). That's why adding 0.20 mol of He to a rigid container of N₂ raises total pressure without changing the N₂'s pressure at all. ### Deviation from Ideal Gas Law (Unit 3) Topic 3.6 is the fine print on PV = nRT. The equation assumes zero attractions and zero particle [volume](/ap-chem/key-terms/volume "fv-autolink"), so it fails near condensation conditions (attractions pull particles together, lowering measured pressure) and at very high pressures (particle volume stops being negligible). If an FRQ asks why a real gas's pressure is lower than the ideal prediction, intermolecular attractions are your answer. ### Moles of Gas and Molar Mass (Units 1 & 3) Since n = mass ÷ molar mass, you can rewrite the ideal gas law to find the molar mass of an unknown gas from P, V, T, and the sample's mass. This is a classic AP problem that fuses [Unit 1](/ap-chem/unit-1 "fv-autolink") mole math with Unit 3 gas behavior. ### Gas Stoichiometry in Reactions (Unit 4) When a reaction produces a gas, like CO₂ from sodium bicarbonate reacting with an acid, PV = nRT is the bridge between the gas you collect and the moles in your balanced equation. The 2024 FRQs used exactly this kind of setup, so expect the gas law to crash Unit 4's party. ## On the AP Exam PV = nRT is on the AP Chem equation sheet, so you don't memorize it, you apply it. MCQs often test it conceptually with no calculator, like asking what happens to P when T doubles at constant V and n (it doubles, since P and T are directly proportional). Others test whether you know n means moles of gas, or have you solve for an unknown variable. Heavier lifts include finding the molar mass of an unknown gas from mass, P, V, and T, or finding total pressure after gas is added to a rigid container using partial pressures. On FRQs, the gas law usually appears inside a bigger problem. The 2024 long FRQ involved a reaction producing CO₂ gas, where you connect collected gas back to reaction stoichiometry. Topic 3.6 questions flip the script and ask you to explain in words why a real gas deviates from the ideal prediction. The two acceptable reasons are interparticle attractions (near condensation) and particle volume (at extremely high pressure). Watch the classic traps of Celsius instead of Kelvin and mL instead of L. ## PV = nRT vs Combined gas law (P₁V₁/T₁ = P₂V₂/T₂) The combined gas law compares one gas sample at two different conditions, with moles held constant. PV = nRT describes a sample at a single set of conditions and explicitly includes n. Use the combined form for 'a gas changes from state 1 to state 2' problems, and the full ideal gas law whenever moles are unknown, changing, or the thing you're solving for. They're really the same physics, since the combined law is just PV = nRT written twice with nR canceled out. ## Key Takeaways - PV = nRT relates a gas's pressure, volume, moles, and absolute temperature, and temperature must always be in Kelvin. - The equation is on the AP formula sheet along with R = 0.08206 L·atm/(mol·K), so the test rewards application and unit care, not memorization. - If volume and moles are constant, pressure and Kelvin temperature are directly proportional, so doubling T doubles P. - In gas mixtures, each component obeys PV = nRT independently, which is why partial pressures add up to the total pressure (Dalton's Law). - Real gases deviate from PV = nRT for exactly two reasons the CED names, which are interparticle attractions near condensation and particle volume at extremely high pressures. - You can find an unknown gas's molar mass by solving PV = nRT for n and dividing the sample's mass by that mole value. ## FAQs ### What is PV = nRT in AP Chem? It's the ideal gas law from Topic 3.4, relating a gas's pressure (P), volume (V), moles (n), and Kelvin temperature (T) through the gas constant R. It lets you solve for any one of those properties if you know the other three. ### Do I have to memorize PV = nRT for the AP exam? No. The equation and the value of R (0.08206 L·atm/(mol·K)) are both printed on the AP Chemistry equations and constants sheet. What you do need to memorize is the workflow, like converting Celsius to Kelvin and mL to L before plugging in. ### Does PV = nRT work for real gases? Not perfectly. Real gases deviate from the ideal gas law near condensation conditions, where interparticle attractions lower the measured pressure, and at extremely high pressures, where particle volume becomes significant. Topic 3.6 (LO 3.6.A) tests exactly these two explanations. ### What's the difference between PV = nRT and the combined gas law? PV = nRT describes one gas sample at one set of conditions and includes moles. The combined gas law (P₁V₁/T₁ = P₂V₂/T₂) compares the same fixed amount of gas before and after a change. Use PV = nRT whenever moles are unknown or changing. ### What does n stand for in PV = nRT? n is the number of moles of gas particles in the sample. It's not mass, so for an unknown gas you can substitute n = mass ÷ molar mass and solve for molar mass, a common AP calculation. ## Related Study Guides - [3.4 Ideal Gas Law](/ap-chem/unit-3/ideal-gas-law/study-guide/XINb2AUU6e3c1rGlhBXg) ## Structured Data ```json {"@context":"https://schema.org","@graph":[{"@type":"LearningResource","@id":"https://fiveable.me/ap-chem/key-terms/pv-nrt#resource","name":"PV = nRT — AP Chem Ideal Gas Law Definition & Exam Guide","url":"https://fiveable.me/ap-chem/key-terms/pv-nrt","learningResourceType":"Concept explainer","educationalLevel":"AP® / High School","about":{"@id":"https://fiveable.me/ap-chem/key-terms/pv-nrt#term"},"audience":{"@type":"EducationalAudience","educationalRole":"student"},"dateModified":"2026-06-11T05:27:15.366Z","isPartOf":{"@type":"Collection","name":"AP Chemistry Key Terms","url":"https://fiveable.me/ap-chem/key-terms"},"publisher":{"@type":"Organization","name":"Fiveable","url":"https://fiveable.me"}},{"@type":"DefinedTerm","@id":"https://fiveable.me/ap-chem/key-terms/pv-nrt#term","name":"PV = nRT","description":"PV = nRT is the ideal gas law, the equation relating a gas sample's pressure (P), volume (V), moles (n), and absolute temperature in Kelvin (T) through the gas constant R. 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