AP Chemistry Ideal Gas Law

PV = nRT explained, and three full worked examples.

The ideal gas law relates a gas sample's pressure, volume, temperature, and number of moles in a single equation. It's provided on the exam's reference sheet, so the actual skill being tested isn't memorization, it's correctly rearranging the formula and keeping units consistent.

The Formula

PV = nRT, where P is pressure (atm), V is volume (L), n is moles, T is temperature (K), and R = 0.08206 L·atm/(mol·K) is the gas constant given on the AP Chemistry reference sheet. Start from this exact form every time and solve algebraically for whichever variable the question asks for, rather than memorizing separate rearranged versions.

Unit check first: temperature must be in Kelvin (add 273 to a Celsius value) and pressure must be in atm to match R's units, or the answer will be wrong by a consistent factor.

Worked Example 1: Solving for Pressure

A 5.00 L container holds 0.250 mol of gas at 298 K. What is the pressure?

P = nRT/V = (0.250 mol)(0.08206 L·atm/mol·K)(298 K) / 5.00 L = 1.22 atm

Worked Example 2: Solving for Volume

A 1.50 mol gas sample is at 2.00 atm and 310 K. What volume does it occupy?

V = nRT/P = (1.50 mol)(0.08206 L·atm/mol·K)(310 K) / 2.00 atm = 19.1 L

Worked Example 3: Combined with Stoichiometry

CaCO₃(s) → CaO(s) + CO₂(g). If 5.00 g of CaCO₃ decomposes completely, what volume of CO₂ gas is produced at 1.00 atm and 298 K?

Molar mass of CaCO₃ = 100.09 g/mol.
5.00 g ÷ 100.09 g/mol = 0.0500 mol CaCO₃
Mole ratio CaCO₃ to CO₂ is 1:1, so 0.0500 mol CO₂ forms.
V = nRT/P = (0.0500 mol)(0.08206 L·atm/mol·K)(298 K) / 1.00 atm = 1.22 L

This is a two-part problem: a stoichiometry calculation to find moles of gas, then the ideal gas law to convert those moles to a volume.

Common Mistakes

Using Celsius instead of Kelvin. Always convert (K = °C + 273) before plugging into PV = nRT.
Mismatched pressure units. If a problem gives pressure in mmHg or kPa, convert to atm first, or use a different value of R, never mix units.
Treating the ideal gas law as a stoichiometry shortcut. It converts between a gas's own P, V, n, and T, it doesn't relate two different substances. A reaction between two different gases still needs the mole ratio from a balanced equation first.
Forgetting to find total moles in a gas mixture. When a problem gives several gases in one container, n in PV = nRT is the total moles of all gases combined, not just one component's moles.

Frequently Asked Questions

What is the ideal gas law?

PV = nRT, relating a gas sample's pressure (P), volume (V), moles (n), and temperature (T) through the gas constant R. It's one of the most frequently tested equations on the AP Chemistry exam, and it's provided on the exam's reference sheet, you don't need to memorize R's value.

What value of R do I use, and what units?

R = 0.08206 L·atm/(mol·K) is the version provided on the AP Chemistry reference sheet. Using it means pressure must be in atm, volume in liters, and temperature in Kelvin, always convert Celsius to Kelvin before plugging in.

Do I need to memorize the rearranged forms of PV = nRT?

No. Start from PV = nRT every time and solve algebraically for whatever variable you need. Memorizing separate rearranged versions (V = nRT/P, and so on) just creates more formulas to mix up under exam pressure.

What's the most common mistake with this formula?

Forgetting to convert temperature to Kelvin, or using a pressure unit (like mmHg or kPa) that doesn't match the units built into R = 0.08206 L·atm/(mol·K). Both errors silently make every answer wrong by a consistent, easy-to-miss factor.

Can the ideal gas law combine with stoichiometry?

Yes, this is a common multi-step question type. Use a balanced equation and mole ratios to find moles of a gas produced or consumed, then use PV = nRT to convert those moles to a volume, pressure, or temperature (or the reverse, starting from a measured gas volume to find moles for a stoichiometry calculation).

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