Difficulty: Introductory | Prerequisites: Basic algebra, unit conversions, mole concept.
This topic covers the behaviour of gases at the molecular level and the mathematical laws that describe how pressure, volume, temperature and amount of gas relate to one another. It sits at the foundation of physical chemistry and comes back in thermodynamics, equilibrium and electrochemistry. You should already be comfortable converting between Celsius and Kelvin and working with moles.
Gases are compressible, spread to fill their containers and exert pressure on the walls. A handful of laws (Boyle's, Charles's, Gay-Lussac's, Avogadro's) each hold one or two variables constant and describe how the rest change, and the ideal gas law PV = nRT rolls them all into a single equation. These laws assume "ideal" behaviour, meaning no intermolecular forces and no molecular volume, which works well at ordinary temperatures and pressures.
Pressure (P)
Force per unit area exerted by gas particles colliding with the walls of their container. Measured in atm, mmHg, torr, kPa or psi. Think of it as how hard the gas pushes outward.
Volume (V)
The space a gas occupies, expressed in litres (L) or millilitres (mL).
Temperature (T)
A measure of the average kinetic energy of gas particles. Always expressed in Kelvin (K) for gas law calculations. In simple terms, hotter gas means faster-moving particles.
STP (Standard Temperature and Pressure)
273 K (0 °C) and 1 atm. The reference conditions used for gas law calculations. Do not confuse this with standard state conditions (298 K, 1 atm, 1 M), which are used for thermodynamic quantities such as enthalpy and free energy.
Ideal gas
A hypothetical gas whose particles have no intermolecular forces and occupy no volume. Real gases approximate ideal behaviour at high temperature and low pressure. Think of it as a simplified model that makes the maths clean.
Molar volume
The volume occupied by one mole of an ideal gas at STP: 22.4 L.
Ideal gas constant (R)
8.21 x 10⁻² L·atm·mol⁻¹·K⁻¹, or equivalently 8.314 J·K⁻¹·mol⁻¹ in SI units.
Molar mass (M)
The mass of one mole of a substance, in g/mol (or kg/mol when used in the root-mean-square speed formula).
Gases have very weak intermolecular forces between particles.
They are easily compressible, unlike liquids and solids.
A gas expands to fill its entire container and exerts pressure on the container walls.
Pressure: atm, mmHg (torr), kPa, psi. Conversion: 1 atm = 760 mmHg = 760 torr = 101.3 kPa = 14.7 psi.
Volume: litres (L) or millilitres (mL).
Temperature: always Kelvin for gas law work. Convert from Celsius by adding 273.
Amount: moles (n).
STP: 273 K, 0 °C, 1 atm. Used in gas law problems.
Standard state: 298 K, 1 atm, 1 M. Used for thermodynamic quantities (enthalpy, entropy, free energy, cell voltage). These two are not the same, and mixing them up is a common exam error.
A mercury barometer measures atmospheric pressure by the height of a mercury column.
When atmospheric pressure increases, the mercury column rises. This also happens at elevations below sea level.
When atmospheric pressure decreases, the column falls. This also happens at high elevation.
PV = nRT, where P is pressure, V is volume, n is moles, R is the gas constant and T is temperature in Kelvin.
This single equation relates all four gas variables. Every other named gas law is a special case of it with one or two variables held constant.
P₁V₁ / T₁ = P₂V₂ / T₂
Used when moles are constant but pressure, volume and temperature all change between state 1 and state 2.
Density = PM / RT, where M is the molar mass of the gas.
One mole of any ideal gas occupies 22.4 L at STP, regardless of the gas's identity.
At constant temperature and pressure, the volume of a gas is directly proportional to the number of moles.
V₁/n₁ = V₂/n₂, or equivalently V₁n₂ = V₂n₁.
Equal moles of any gas at the same T and P occupy the same volume. One mole at STP = 22.4 L.
Volume is inversely proportional to pressure.
P₁V₁ = P₂V₂.
Double the pressure on a gas and its volume halves, provided temperature stays constant.
Volume is directly proportional to temperature in Kelvin.
V₁/T₁ = V₂/T₂.
Heat a gas and it expands; cool it and it contracts.
Pressure is directly proportional to temperature in Kelvin.
P₁/T₁ = P₂/T₂.
Heat a sealed rigid container and the pressure inside rises.
Law / Relationship | Formula | What is held constant |
|---|---|---|
Ideal gas law | PV = nRT | (none, general) |
Combined gas law | P₁V₁/T₁ = P₂V₂/T₂ | n |
Boyle's law | P₁V₁ = P₂V₂ | T, n |
Charles's law | V₁/T₁ = V₂/T₂ | P, n |
Gay-Lussac's law | P₁/T₁ = P₂/T₂ | V, n |
Avogadro's principle | V₁/n₁ = V₂/n₂ | T, P |
Gas density | ρ = PM/RT | (derived from PV = nRT) |
Constants: R = 8.21 x 10⁻² L·atm·mol⁻¹·K⁻¹ = 8.314 J·K⁻¹·mol⁻¹. Molar volume at STP = 22.4 L/mol. 1 atm = 760 mmHg = 760 torr = 101.3 kPa.
Boyle's law is why a balloon expands as you take it up a mountain: the external pressure drops, so the gas inside pushes out further. Charles's law explains why a hot-air balloon rises: heating the air inside increases its volume, which lowers the density of that air below the density of the cooler air outside. Gay-Lussac's law is the reason aerosol cans carry warnings about heat: the gas inside a rigid can builds pressure as it warms and can rupture the container.
Students often confuse STP (273 K, 1 atm) with standard state conditions (298 K, 1 atm, 1 M). STP is for gas law calculations. Standard state is for thermodynamic quantities such as enthalpy and Gibbs free energy.
Students sometimes plug Celsius into gas law equations. Temperature must always be in Kelvin. Forgetting the conversion will give a wildly wrong answer.
Boyle's law is an inverse relationship (P up, V down), but Charles's and Gay-Lussac's are direct relationships. Students mix up which is which, especially under time pressure.
The 22.4 L molar volume applies only at STP. Using it at other conditions is a common error.
⚠️ Be able to identify which gas law applies to a problem from the variables given and what is held constant.
⚠️ Know the difference between STP and standard state conditions. This distinction is a favourite exam trap.
⚠️ Problems often ask you to rearrange PV = nRT to find density (ρ = PM/RT). Practise this manipulation.
⚠️ Unit conversions (atm to kPa, °C to K, mL to L) are frequently where marks are lost. Write units at every step.
True or false: STP is 298 K and 1 atm. (False. STP is 273 K and 1 atm.)
Fill in the blank: At STP, one mole of any ideal gas occupies ______ L. (22.4 L)
True or false: In Boyle's law, pressure and volume are directly proportional. (False. They are inversely proportional.)
Fill in the blank: In Charles's law, the variable held constant is ______. (Pressure)
True or false: Gay-Lussac's law applies when volume is held constant. (True.)
Q: A gas occupies 2.0 L at 1.0 atm. If the temperature is held constant and the pressure is increased to 4.0 atm, what is the new volume?
A: Use Boyle's law. P₁V₁ = P₂V₂. (1.0)(2.0) = (4.0)(V₂). V₂ = 0.50 L.
Q: A balloon has a volume of 3.0 L at 300 K. If the pressure stays constant and the temperature rises to 450 K, what is the new volume?
A: Use Charles's law. V₁/T₁ = V₂/T₂. 3.0/300 = V₂/450. V₂ = 4.5 L.
Q: What is the density of O₂ gas (M = 32 g/mol) at STP?
A: ρ = PM/RT = (1.0 atm)(32 g/mol) / (0.0821 L·atm·mol⁻¹·K⁻¹)(273 K) = 1.43 g/L.
Q: A rigid steel tank holds gas at 2.0 atm and 300 K. If the tank is heated to 600 K, what is the new pressure?
A: Use Gay-Lussac's law. P₁/T₁ = P₂/T₂. 2.0/300 = P₂/600. P₂ = 4.0 atm.
Q: 0.50 mol of gas at STP occupies what volume?
A: At STP, 1 mol = 22.4 L. So 0.50 mol = 0.50 x 22.4 = 11.2 L.
This material connects directly to kinetic molecular theory (covered in the companion notes), which explains why gas laws work at the particle level. It also feeds into Dalton's law of partial pressures and Henry's law of gas solubility. Later in the course, the ideal gas law reappears in chemical equilibrium (Kp expressions), thermodynamics (work done by expanding gases) and electrochemistry (cell potentials under non-standard conditions via the Nernst equation).
Ideal gas law, PV = nRT, Boyle's law, Charles's law, Gay-Lussac's law, Avogadro's principle, combined gas law, gas density, molar volume, STP, standard temperature and pressure, gas constant R, pressure-volume relationship, temperature-volume relationship, gas phase chemistry, CHEM 101, general chemistry gases, mercury barometer, atmospheric pressure, unit conversions atm kPa torr mmHg