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General Chemistry I · Core Concept

The Gas Laws

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On this page 7 sections
  1. In 30 seconds
  2. Why this matters
  3. The college version
  4. Eli explains
  5. Worked example
  6. Key takeaway
  7. Study tools

In 30 seconds

The simple gas laws describe how a gas responds when one variable changes while the others are held constant: says pressure and volume are inversely related at constant temperature, says volume is directly proportional to Kelvin temperature at constant pressure, and says volume is directly proportional to the number of moles at constant temperature and pressure. All three combine into the , PV = nRT, which can also be rearranged to find gas (d = PM/RT) or molar mass.

Why this matters

The gas laws govern lung function: breathing changes thoracic volume, and by Boyle's law this changes the pressure inside the lungs, drawing air in and pushing it out. Anesthesia delivery and ventilator settings depend on pressure–volume–temperature relationships. In the laboratory, the ideal gas law lets chemists determine the molar mass of an unknown volatile liquid by vaporizing it, measuring its mass, volume, temperature, and pressure, and solving for M. Scuba diving safety is a direct application — a diver ascending (pressure dropping) causes gas in the lungs to expand per Boyle's law, which is why divers must exhale continuously during ascent.

The college version

1. Boyle's, Charles's, and Avogadro's Laws

Boyle's law (constant T and n): pressure and volume are inversely proportional.

P1 V1 = P2 V2

Charles's law (constant P and n): volume is directly proportional to absolute temperature.

V1T1 = V2T2

Avogadro's law (constant T and P): volume is directly proportional to the number of moles.

V1n1 = V2n2

A critical consequence of Avogadro's law is the : at standard temperature and pressure (0 °C = 273.15 K and 1 atm), one mole of any ideal gas occupies about 22.4 L.

2. The Ideal Gas Law

Combining all three laws gives the ideal gas law:

PV = nRT

where P is pressure, V is volume, n is moles, T is absolute temperature in kelvin, and R is the . The value of R depends on the units of pressure and volume:

R = 0.08206 L·atm·mol-1·K-1 = 8.314 J·mol-1·K-1 = 8.314 kPa·L·mol-1·K-1

The handles problems where P, V, and T all change while n stays fixed:

P1 V1T1 = P2 V2T2

3. Density and Molar Mass from the Ideal Gas Law

Substituting n = m/M (mass over molar mass) into PV = nRT gives:

PV = mM RT   ⇒  M = mRTPV = dRTP

where d = m/V is density. Rearranged for density:

d = PMRT

This shows gas density is directly proportional to molar mass at fixed T and P — heavier gases are denser.

How it works

  1. Identify which variables change and which stay constant.
  2. Choose the law: Boyle's (constant T, n), Charles's (constant P, n), Avogadro's (constant T, P), combined (three variables change), or ideal (need n or a single-state value).
  3. Convert every temperature to kelvin and make all pressure units consistent.
  4. Write the formula first, then substitute numbers with units.
  5. Cancel units to confirm the answer's units, then round to the correct significant figures.

Common confusions

Do not confuseWithDifference
Boyle's lawCharles's lawBoyle's: P vs V (inverse, constant T); Charles's: V vs T (direct, constant P)
°CKOnly Kelvin is proportional to particle energy; use K
Ideal gasReal gasIdeal assumes zero particle volume and no attractions; real gases deviate at high P, low T
DensityMolar massDensity d = m/V depends on conditions; molar mass M is fixed per substance
22.4 L22.4 L at any condition22.4 L applies only at STP (0 °C, 1 atm)

Memory aids

"Be Careful Always" — Boyle (inverse), Charles (direct), Avogadro (direct) — plus "K first!" to remember to convert temperatures to Kelvin before touching any gas-law equation.

Quick review

Topic Recap

Boyle's, Charles's, and Avogadro's laws each describe how a gas responds when one variable changes at a time; together they form the ideal gas law, PV = nRT. Kelvin temperatures and consistent units are non-negotiable. Rearranging the ideal gas law yields the density and molar-mass equations, d = PM/RT and M = dRT/P, which connect measurable gas properties to chemical identity.

Knowledge Check

  1. A gas occupies 4.0 L at 1.0 atm and constant temperature. If the pressure is increased to 2.0 atm, what is the new volume?
  2. A gas at 300 K has a volume of 2.0 L. At constant pressure, what volume does it occupy at 450 K?
  3. What volume does 0.500 mol of an ideal gas occupy at 273.15 K and 1.00 atm?
  4. A gas has a density of 1.25 g/L at 0 °C and 1 atm. What is its molar mass?
  5. Using the ideal gas law, find the pressure of 0.750 mol of gas in a 12.0 L flask at 25.0 °C.

Answers and Rationales

  1. 2.0 L. Boyle's law: V2 = 4.0 L × (1.0/2.0) = 2.0 L. Doubling pressure halves volume.
  2. 3.0 L. Charles's law: V2 = 2.0 L × (450/300) = 3.0 L. Volume rises in proportion to Kelvin temperature.
  3. 11.2 L. V = nRT/P = (0.500)(0.08206)(273.15)/1.00 = 11.2 L — half the 22.4 L molar volume because there is half a mole.
  4. 28.0 g/mol. M = dRT/P = (1.25)(0.08206)(273.15)/1.00 = 28.0 g/mol, matching N₂.
  5. 1.53 atm. P = nRT/V = (0.750)(0.08206)(298.15)/12.0 = 1.53 atm.
Eli, the EliExplains learning guide

Eli explains

The same idea, in plain words

Explain it like I’m 10

Think of gas particles as a swarm of tiny cars on an invisible track. Boyle's law says that if you shrink the track (smaller volume) without changing how fast the cars drive (temperature), they crash into the walls more often, so pressure rises — squeeze the container and pressure climbs. Charles's law says that if you heat the cars so they drive faster, they push the walls outward, so the gas takes up more space — warm a balloon and it inflates. Avogadro's law says that if you add more cars (more moles) at the same speed, the crowd needs a bigger track — more gas means more volume. The ideal gas law bundles all of this into one equation: pressure times volume equals the amount of gas times a constant times temperature. This picture stops being exact for real gases at very high pressure (when the particles get so crowded that their own size and their stickiness start to matter) — that is why we call it the ideal gas law.

Simple Example

A sealed syringe of air at constant temperature has its plunger pushed in to halve the volume. By Boyle's law, the pressure doubles. If the same gas is instead warmed (at constant pressure), Charles's law predicts its volume grows in direct proportion to its Kelvin temperature.

Worked example

Worked Example 1 — Boyle's law. A balloon holds 2.50 L of gas at 745 mmHg. At constant temperature, the pressure is raised to 1.20 atm. What is the new volume?

First put both pressures in the same unit:

1.20 atm × 760 mmHg1 atm = 912 mmHg

V2 = V1 × P1P2 = 2.50 L × 745 mmHg912 mmHg = 2.04 L

Worked Example 2 — Charles's law. A sample of gas occupies 3.00 L at 27.0 °C. At constant pressure, to what volume does it expand when heated to 127 °C?

Convert both temperatures to kelvin first:

T1 = 27.0 + 273.15 = 300.15 K, T2 = 127 + 273.15 = 400.15 K

V2 = V1 × T2T1 = 3.00 L × 400.15 K300.15 K = 4.00 L

Worked Example 3 — Ideal gas law. How many moles of gas are in a 5.00 L container at 22.0 °C and 0.950 atm?

T = 22.0 + 273.15 = 295.15 K

n = PVRT = (0.950 atm)(5.00 L)(0.08206 L·atm·mol-1·K-1)(295.15 K) = 0.196 mol

Worked Example 4 — Density and molar mass. An unknown gas has a density of 1.78 g/L at 25.0 °C and 1.00 atm. Find its molar mass.

T = 298.15 K

M = dRTP = (1.78 g/L)(0.08206 L·atm·mol-1·K-1)(298.15 K)1.00 atm = 43.5 g/mol

This molar mass is close to that of CO₂ (44.0 g/mol).

Common setup errors. (1) Using Celsius instead of Kelvin — the most frequent error, and it destroys every gas-law answer. (2) Mixing pressure units with the wrong R: use R = 0.08206 only with L and atm, or R = 8.314 with L and kPa. (3) Forgetting that Boyle's law requires constant temperature and moles. (4) Rounding intermediate values too early; keep extra digits until the final answer.

Key takeaways

  • High yield: Always convert °C to Kelvin (+273.15) before any gas-law calculation.
  • High yield: PV = nRT with R = 0.08206 L·atm/(mol·K); keep pressure in atm and volume in L with this R.
  • High yield: Boyle's law is inverse (P ↑ means V ↓); Charles's and Avogadro's laws are direct.
  • One mole of ideal gas occupies 22.4 L at STP.
  • Gas density increases with molar mass at constant T and P: d = PM/RT.
  • The combined gas law reduces to each simple law when the appropriate variable is held constant.
  • Charles's law predicts a temperature of absolute zero (−273.15 °C) where volume would vanish.
  • Never change subscripts in any formula; only adjust coefficients in reactions (not directly relevant here but a habit).

Keep learning

Ready to build on this? Continue to the next lesson.

Practice General Chemistry I

This lesson has no separate scored set. Practice draws from the subject’s question bank.

Study tools & related lessonsYou’ll learn to · Key vocabulary · Related

You’ll learn to

  • State Boyle's, Charles's, and Avogadro's laws and the conditions held constant in each.
  • Use the ideal gas law PV = nRT to solve for any one variable given the others.
  • Derive and use the combined gas law for changes in P, V, and T.
  • Calculate gas density and molar mass from the ideal gas law.

Key vocabulary

Boyle's law
P and V are inversely proportional at constant T, n
Charles's law
V is proportional to Kelvin T at constant P, n
Avogadro's law
V is proportional to n at constant T, P
Ideal gas law
PV = nRT
Universal gas constant
R = 0.08206 L·atm/(mol·K) (or 8.314 J/(mol·K))
Combined gas law
P1V1/T1 = P2V2/T2
STP
0 °C (273.15 K) and 1 atm
Molar volume
22.4 L occupied by 1 mol of ideal gas at STP
Density
Mass per unit volume, d = PM/RT for a gas

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