The four variables and their units
Every gas law relates the same four variables: pressure (P), volume (V), temperature (T), and moles (n). The individual gas laws (Boyle's, Charles's, Gay-Lussac's) each hold two of these constant and relate the other two. The ideal gas law, PV = nRT, ties all four together at once. The gas itself is assumed to behave as an ideal gas — particles with negligible volume and no intermolecular attractions, which is a good approximation for most real gases (O₂, N₂, CO₂, He) at ordinary classroom pressures and temperatures.
| Variable | Symbol | Common units | Also seen |
|---|---|---|---|
| Pressure | P | atm | kPa, mmHg, torr |
| Volume | V | L | mL, cm³ |
| Temperature | T | K (kelvin) | — |
| Amount | n | mol | — |
Temperature MUST be in kelvin
Every gas law equation requires absolute temperature (K), never °C. Convert first: K = °C + 273 (use 273.15 for extra precision). Plugging in Celsius directly is the single most common gas-law error, and it can throw an answer wildly off or even produce a physically impossible result such as a negative volume or pressure.
Boyle's Law — pressure and volume
At constant temperature and moles, pressure and volume are inversely proportional — squeeze a gas into a smaller space and its pressure rises. This gives: P₁V₁ = P₂V₂ Held constant: T, n. Changing: P, V.
Worked example: A gas occupies 6.0 L at 2.0 atm. What is the new volume if the pressure increases to 3.0 atm (temperature constant)? P₁V₁ = P₂V₂ → (2.0 atm)(6.0 L) = (3.0 atm)(V₂) → V₂ = 12.0 ÷ 3.0 = 4.0 L Pressure went up, so volume went down — consistent with the inverse relationship.
Charles's Law — volume and temperature
At constant pressure and moles, volume and absolute temperature are directly proportional — heat a gas and it expands. This gives: V₁ / T₁ = V₂ / T₂ Held constant: P, n. Changing: V, T (in kelvin).
Worked example: A balloon holds 2.50 L of gas at 20.0 °C. What volume does it occupy at 80.0 °C (pressure constant)? Convert first: T₁ = 20.0 + 273 = 293 K, T₂ = 80.0 + 273 = 353 K V₁ / T₁ = V₂ / T₂ → 2.50 / 293 = V₂ / 353 → V₂ = 2.50 × (353 / 293) = 3.01 L
Gay-Lussac's Law — pressure and temperature
At constant volume and moles, pressure and absolute temperature are directly proportional — heat a sealed rigid container and the pressure climbs (this is why an aerosol can warns against heat). This gives: P₁ / T₁ = P₂ / T₂ Held constant: V, n. Changing: P, T (in kelvin).
Worked example: A rigid tank holds gas at 1.20 atm and 300 K. What is the pressure if the tank is heated to 450 K (volume constant)? P₁ / T₁ = P₂ / T₂ → 1.20 / 300 = P₂ / 450 → P₂ = 1.20 × (450 / 300) = 1.80 atm
Same shape, different pair
All three individual laws are the same idea — one variable held constant, the other two related as a ratio equal to itself before and after. Notice which letter is missing from each equation to identify which law applies: no T → Boyle's, no P → Charles's, no V → Gay-Lussac's.
The combined gas law
When only moles (n) are held constant and P, V, and T all change, use the combined gas law, which merges the three laws above into one relationship: P₁V₁ / T₁ = P₂V₂ / T₂ Setting P constant recovers Charles's Law, setting T constant recovers Boyle's Law, and setting V constant recovers Gay-Lussac's Law — the combined law is the general case.
Worked example: A gas has a volume of 4.00 L at 1.00 atm and 273 K. What is its volume at 2.50 atm and 373 K? P₁V₁ / T₁ = P₂V₂ / T₂ → (1.00)(4.00) / 273 = (2.50)(V₂) / 373 V₂ = [(1.00)(4.00)(373)] / [(273)(2.50)] = 1492 / 682.5 = 2.19 L
The ideal gas law: PV = nRT
The ideal gas law relates all four variables at once for a single state of a gas (no "before/after" needed): PV = nRT R is the ideal gas constant. Its numeric value depends entirely on which pressure and volume units you're using — pick the R that matches your units, or convert your units to match a familiar R.
| Value of R | Use when P is in… | Use when V is in… |
|---|---|---|
| 0.0821 L·atm/(mol·K) | atm | L |
| 8.314 J/(mol·K) | Pa | m³ |
| 8.314 L·kPa/(mol·K) | kPa | L |
| 62.4 L·mmHg/(mol·K) | mmHg or torr | L |
Worked example: How many moles of gas are in a 5.00 L tank at 2.00 atm and 350 K? n = PV / RT = (2.00 atm)(5.00 L) / [(0.0821 L·atm/(mol·K))(350 K)] = 10.0 / 28.7 = 0.348 mol
Ideal gas law vs. the individual laws
Boyle's, Charles's, and Gay-Lussac's laws all fall out of PV = nRT when n and one other variable are fixed — they're special cases, not separate physics. If a problem gives you moles (or asks for them) and only one state of the gas, reach for PV = nRT. If it gives two states of the SAME sample of gas changing conditions, use the combined law instead.
STP and molar volume
STP (Standard Temperature and Pressure) is a reference condition chemists use so gas volumes can be compared on equal footing. The definition used in nearly all US high school and AP Chemistry courses is: T = 0 °C (273 K), P = 1 atm (101.3 kPa) At STP, one mole of ANY ideal gas occupies 22.4 L — this is the molar volume of a gas at STP, and it doesn't depend on which gas it is (that's the point of the ideal gas approximation).
A newer IUPAC definition exists — know which one your course uses
In 1982 IUPAC redefined standard pressure as 1 bar (100 kPa) instead of 1 atm (101.325 kPa), which changes molar volume to 22.7 L/mol. Most US general chemistry courses, textbooks, and the AP Chemistry exam still use the older 1 atm / 22.4 L/mol convention — that's the one used throughout this sheet. If a problem specifies "IUPAC STP" or gives pressure in bar, use 22.7 L/mol instead.
Worked example: What volume does 3.50 mol of CO₂ gas occupy at STP? V = n × 22.4 L/mol = 3.50 × 22.4 = 78.4 L Worked example (reverse): A sample of N₂ gas occupies 11.2 L at STP. How many moles is that? n = V ÷ 22.4 L/mol = 11.2 ÷ 22.4 = 0.500 mol
Try it yourself
gas-lab-trials.csvDownload gas-lab-trials.csv: https://restedteacher.com/practice-files/chemistry/gas-lab-trials.csv
Nine gas-sample measurements. Most rows are paired with another row (same sample, two states); one row stands alone for the ideal gas law. Each pair or single row is missing exactly one quantity, marked "unknown".
Open it in Google Sheets or Excel
You'll need a calculator. For a paired row (paired_with names the other trialid), compare the two states first: whichever of P, V, or T is the SAME in both rows tells you which individual law applies — no T change → Boyle's, no P change → Charles's, no V change → Gay-Lussac's, and all three changing means the combined gas law. A row with paired_with set to "none" is a single state — use the ideal gas law, PV = nRT.
1. A gas occupies 4.0 L at 1.0 atm and constant temperature. What volume does it occupy at 2.5 atm?
2. A gas sample has a volume of 2.0 L at 300 K and constant pressure. What is its volume at 450 K?
3. How many moles of gas fill a 5.0 L container at 2.0 atm and 350 K?
Using gas-lab-trials.csv:
4. For each paired trial (GL1/GL2, GL3/GL4, GL5/GL6, GL7/GL8), state which gas law applies and calculate the value marked "unknown."
5. For the single-state trial (GL9), use the ideal gas law to calculate the value marked "unknown." Use R = 0.0821 L·atm/(mol·K).
6. Round every answer to 3 significant figures.