GasWorks

Pressure, Boyle, Charles, Gay-Lussac, Avogadro, the combined and ideal gas laws, mixtures, gas stoichiometry and kinetic theory.
Every law has a live model you can drag. Each tab has Hint, Reset and Skip, 3 levels and a crown to win.

Track 0 · Introductory Chemistry · part of ChemTracks

Start here: why gases are different

A gas is mostly empty space with particles in fast, random motion. Four things describe it: pressure (P), volume (V), temperature (T) and amount (n). Change one and the others respond. Every tab has a live model: a cylinder, a piston and moving particles. Drag the slider, see the law happen, then practise it.

Law	Constant	Changing	Relationship	Equation
Boyle	T, n	P, V	Inverse	P₁V₁ = P₂V₂
Charles	P, n	V, T	Direct	V₁/T₁ = V₂/T₂
Gay-Lussac	V, n	P, T	Direct	P₁/T₁ = P₂/T₂
Avogadro	P, T	V, n	Direct	V₁/n₁ = V₂/n₂

Build it, test it, own it

Read the idea, move the model, then practise. Every tab has Hint, Reset and Skip, 3 levels, and a crown to win. You never need to memorize: the model shows you why.

Sense check

Before you press Check, ask: does this make chemical sense? Squeezed gas should have a higher pressure. Hotter gas (in kelvin) should take more room.

Step 1. Pressure: what a gas does to its walls

Gas particles fly around and hit the walls. All those hits together are the pressure (force ÷ area). Units: 1 atm = 760 mmHg = 760 torr = 101.325 kPa = 14.7 psi. A smaller unit means a bigger number for the same pressure.

Worked example. Convert 912 mmHg to atm: 912 ÷ 760 = 1.20 atm.

Step 2. Boyle's law: P and V (inverse)

Squeeze a gas into less room and the particles hit the walls more often. At constant T and n, P × V = constant: P₁V₁ = P₂V₂. Slide the piston in the live model and watch P × V stay the same.

Worked example. A gas at 2.0 atm fills 6.0 L. Compressed to 3.0 L: P₂ = 2.0 × 6.0 ÷ 3.0 = 4.0 atm.

Step 3. Charles's law: V and T (direct, kelvin)

Heat a gas and the particles move faster, pushing a flexible container out. At constant P and n, V ÷ T = constant. Always use kelvin: K = °C + 273.15.

Worked example. A balloon is 2.00 L at 27 °C (300 K). At 87 °C (360 K): V₂ = 2.00 × 360 ÷ 300 = 2.40 L.

Step 4. Gay-Lussac's law: P and T (direct, kelvin)

In a rigid container the volume cannot change, so heating the gas raises the pressure. At constant V and n, P ÷ T = constant (kelvin again).

Worked example. A sealed can at 1.0 atm and 300 K is heated to 450 K: P₂ = 1.0 × 450 ÷ 300 = 1.5 atm.

Step 5. Avogadro's law: V and n (direct)

More gas particles need more room. At constant T and P, V ÷ n = constant. At STP (0 °C, 1 atm) one mole of any gas occupies 22.4 L.

Worked example. How much room does 0.50 mol of gas take at STP? 0.50 × 22.4 = 11.2 L.

Step 6. The combined gas law

Join the three laws: P₁V₁/T₁ = P₂V₂/T₂ (n constant). If one variable stays the same, it cancels and you are back to a simple law. Always use kelvin and matching units.

Worked example. 2.0 L at 1.0 atm and 300 K goes to 2.0 atm and 600 K: V₂ = 2.0 × (1.0/2.0) × (600/300) = 2.0 L.

Step 7. The ideal gas law: PV = nRT

All four variables in one equation with R = 0.08206 L·atm/(mol·K). Use atm, L, mol, K. From it come the molar mass M = mRT/(PV) and the density d = PM/(RT).

Worked example. 1.00 mol at 300 K in 10.0 L: P = nRT/V = 1.00 × 0.08206 × 300 ÷ 10.0 = 2.46 atm.

Step 8. Mixtures: Dalton's law

In a mixture every gas pushes as if it were alone: P_total = P₁ + P₂ + … and P_i = χ_i P_total. A gas collected over water is mixed with water vapor, so subtract the vapor pressure.

Worked example. Gas collected over water at 25 °C, barometer 760 mmHg: P_gas = 760 − 23.8 = 736 mmHg.

Step 9. Gases in reactions

Coefficients are mole ratios, and at the same T and P they are volume ratios too. Otherwise: grams → moles → mole ratio → V = nRT/P.

Worked example. 2 H₂ + O₂ → 2 H₂O(g): 10 L of H₂ needs 5 L of O₂ (same T and P).

The two nevers of chemistry

NEVER work with mass ratios, only with mole ratios.

NEVER work with unbalanced reactions, always balance first.

Step 10. Why it all works: kinetic theory and Graham's law

Tiny particles, huge gaps, constant random motion. Temperature is the average kinetic energy, so at the same T light molecules move faster: u_rms = √(3RT/M). Lighter gases also effuse faster: rate₁/rate₂ = √(M₂/M₁).

Worked example. H₂ (2.02 g/mol) effuses √(32.00/2.02) = 3.98 times faster than O₂.

Practice the gas laws

GasWorks is Track 0 of ChemTracks. Every law has a live model, a short lesson, three levels of randomly generated problems with hints and worked solutions, and a crown for mastering it. Earn all eleven crowns for a certificate.

Topics covered

Pressure units: atm, mmHg, torr, kPa and psi, barometers and manometers
Boyle's, Charles's, Gay-Lussac's and Avogadro's laws
The combined gas law and the ideal gas law PV = nRT
Molar mass and density of gases
Dalton's law, mole fraction and gases collected over water
Gas stoichiometry and kinetic molecular theory, Graham's law
The Gas Law Table Builder challenge

Frequently asked questions

What does GasWorks cover?

Pressure and its units, Boyle's, Charles's, Gay-Lussac's and Avogadro's laws, the combined gas law, the ideal gas law, Dalton's law of partial pressures, gas stoichiometry, kinetic molecular theory and Graham's law.

Why must gas law temperatures be in kelvin?

Gas volume and pressure are proportional to absolute temperature. Celsius has an arbitrary zero, so convert with K = degrees C + 273.15 before using any gas law.

Which track is GasWorks in?

Track 0 (Introductory Chemistry) of ChemTracks. Each law has a live model with a piston and moving particles you can drag.

Do I get a certificate?

Yes. Earn every crown in GasWorks and you can claim a free certificate of completion as a PDF. Finish all six Track 0 Works to also earn the Track 0 badge and certificate, which anyone can verify.

Do I need an account to use GasWorks?

No. It runs in your browser and saves your progress on your own device.