Gas Laws
Start here if gas-law problems all blur together. Building from thermochemistry, this unit helps you sort them by one key question first: what stays constant, what changes, and do you need a simple gas law or PV = nRT — setting up solutions.
What you'll learn
12.1 Start Here: How Gases Behave and What Pressure Really Means
Gases are the most spread-out state of matter. Their particles are far apart, move quickly in random directions, and collide with every surface around them.
Gas pressure is not a vague push. It comes from particle collisions with the container walls. That particle picture is what makes the gas laws make sense later.
Pressure is force per unit area (P = F/A). Gas pressure comes from all of those collisions with the walls of a container.
This is also why a sharp knife cuts better than a dull one: the same force applied over a smaller area creates greater pressure.
In chemistry, 1 atmosphere (1 atm) is the standard reference pressure. Real atmospheric pressure can change with weather and altitude, but many chemistry problems use 1 atm as the starting reference. A barometer measures atmospheric pressure by the height of mercury it can support, and the SI unit of pressure is the pascal (Pa = N/m²).
These five pressure units all measure the same thing. Recognize which unit a problem gives you and convert before setting up any gas law equation.
| Unit | Symbol | = 1 atm | Common Use |
|---|---|---|---|
| Atmosphere | atm | 1.000 | Standard chemistry problems |
| Millimeters mercury | mmHg | 760.0 | Barometers, medical settings |
| Torr | torr | 760.0 | Equivalent to mmHg |
| Kilopascal | kPa | 101.325 | SI unit, international use |
| Pascal | Pa | 101,325 | Formal SI calculations |
12.2 Boyle's Law: Pressure and Volume Move Opposite Ways
At constant temperature and constant amount of gas, pressure and volume are inversely proportional.
Do not miss the condition words here. If temperature is not constant, Boyle's Law is not the right shortcut anymore.
If pressure doubles, volume is cut in half. The product P × V stays constant.
Real-world example: A scuba diver exhales air bubbles at depth (~3 atm). As the bubbles rise toward the surface (~1 atm), the pressure drops to about one-third, so the volume triples.
The P vs. V graph for Boyle's Law always forms a hyperbola.
Exam Tip
- Boyle's Law only works when T and n are both constant.
- The phrase "constant temperature" or "isothermal" is your signal to use Boyle's Law.
- A pressure increase must compress the gas (decrease volume), and vice versa.
12.3 Charles's Law: Volume and Temperature Rise Together
At constant pressure and constant amount of gas, volume is directly proportional to absolute temperature in Kelvin. Double the Kelvin temperature → double the volume. The V vs. T graph is a straight line through the origin when T is in Kelvin.
The most common mistake in this whole unit happens here: leaving temperature in Celsius. Do not do that. Gas-law temperature must be in Kelvin.
Why Kelvin? At absolute zero (0 K = −273°C), gas volume theoretically reaches zero. Kelvin starts at this true zero point, making the proportional relationship mathematically valid. Using Celsius gives wrong answers.
12.4 Gay-Lussac's Law: Pressure Changes When a Rigid Container Is Heated
At constant volume and constant amount of gas, pressure is directly proportional to absolute temperature in Kelvin. This applies to any rigid container. Heating → higher pressure.
Start here when the problem mentions a rigid can, sealed tank, or fixed-volume container. That is the clue that volume is constant and pressure is the thing that responds.
Real-world example: An aerosol spray can in a hot car can explode. The rigid metal walls prevent volume change, so the rising temperature directly drives up the internal pressure — sometimes past the structural limit of the can.
12.5 Avogadro's Law and Molar Volume at STP
At constant temperature and pressure, volume is directly proportional to moles. At the same temperature and pressure, equal volumes of gases contain the same number of molecules.
Notice the wording carefully: equal volumes mean equal numbers of molecules, not automatically equal numbers of atoms.
Classic trap
- "Does 1 L of CH₄ or 1 L of H₂ contain more hydrogen atoms at STP?" Both contain the same number of molecules by Avogadro's Law.
- But CH₄ has 4 H atoms per molecule while H₂ has only 2.
- So 1 L of CH₄ contains twice as many hydrogen atoms.
- Equal molecules does not mean equal atoms. Always distinguish atoms from molecules.
12.6 The Combined Gas Law: One Gas Sample, Two Sets of Conditions
Use the Combined Gas Law when one sample of gas changes from an initial state to a final state and the amount of gas stays constant. This law is useful when pressure, volume, and temperature are connected across two sets of conditions.
If this feels shaky, look for the story structure: before and after, same gas sample, no gas added or lost. That is your cue.
Use this table to see all five laws side by side. The 'Held Constant' column is what you check first when reading a gas law problem.
| Law | Held Constant | Equation | Graph of | Shape |
|---|---|---|---|---|
| Boyle's | T, n | P₁V₁ = P₂V₂ | P vs. V | Hyperbola |
| Charles's | P, n | V₁T₁ = V₂T₂ | V vs. T | Straight line |
| Gay-Lussac's | V, n | P₁T₁ = P₂T₂ | P vs. T | Straight line |
| Combined | n only | P₁V₁T₁ = P₂V₂T₂ | — | — |
| Avogadro's | T, P | V₁n₁ = V₂n₂ | V vs. n | Straight line |
12.7 The Ideal Gas Law: When PV = nRT Is the Better Tool
Combines all four gas variables into one equation for one set of conditions. Unlike the Combined Gas Law, you do not need before-and-after conditions — just what is true right now. Solve for whichever variable is unknown.
The temptation is to avoid PV = nRT or reach for it too early. Use it when you have one state, not two, and when pressure, volume, temperature, and moles all matter together.
Exam Tip
- Ideal gas behavior assumes no intermolecular forces and negligible molecular volume.
- Real gases deviate most at very high pressure or very low temperature.
- For introductory chemistry, always assume ideal behavior unless the problem states otherwise.
12.8 Dalton's Law: Total Pressure and Gas Collected Over Water
In a mixture of non-reacting gases, each gas exerts its own pressure independently. The partial pressure of each gas equals the pressure it would exert alone at the same T and V. Total pressure is the sum of all partial pressures.
Do not miss the classic trap here: if the gas is collected over water, the measured pressure is not just your gas. You have to subtract water vapor first.
When a gas is collected over water, the measured pressure includes both the gas you want and water vapor. Subtract the water vapor pressure first to get the pressure of the dry gas. Then use that dry gas pressure in the Ideal Gas Law.
- Water vapor pressure at common temperatures: 20°C → 17.5 mmHg | 25°C → 23.8 mmHg | 30°C → 31.8 mmHg | 37°C → 47.1 mmHg.
- These must be looked up in a table — they cannot be calculated from the gas laws.
12.9 Kinetic Molecular Theory: Why the Gas Laws Work
The gas laws arise from the behavior of molecules described by the Kinetic Molecular Theory (KMT):
This section ties the whole unit together. If the formulas start to feel memorized instead of understood, come back here and connect each law to particle motion.
The actual volume of molecules is negligible compared to the container. This is why gases are almost entirely empty space and are easily compressed.
They travel in straight lines between collisions. This motion produces pressure when molecules hit container walls.
No kinetic energy is lost in collisions. Total kinetic energy stays constant at constant temperature.
Ideal gas molecules move completely independently between collisions.
KEavg = 32kBT. This directly explains Charles's Law (T↑ → molecules move faster → push walls harder → volume expands at constant P) and Gay-Lussac's Law (T↑ → harder wall collisions → P increases at constant V).
Next step after Unit 12
Gas laws connect particles to measurable changes in pressure, volume, and temperature. The next move is to study solutions, where concentration and dissolved particles become the new focus.