Difficulty: Introductory | Prerequisites: Basic algebra, unit conversions
Source: General Chemistry, Purdue University
Tags: gas laws, Boyle's law, Charles's law, Gay-Lussac's law, ideal gas law, PV=nRT, combined gas law, Graham's law, kinetic energy, CHEM 101, general chemistry
Gas laws describe how pressure, volume, temperature, and the amount of gas relate to one another. They sit near the middle of a general chemistry sequence, after stoichiometry and before thermodynamics, and they come back in equilibrium and reaction kinetics later in the course.
You will need comfortable algebra (solving for one variable, rearranging fractions) and an understanding of the mole concept. If you can convert between Celsius and Kelvin and know what a mole is, you have the prerequisites.
Four named laws (Boyle, Charles, Gay-Lussac, and the combined law) each hold one or two gas variables constant and describe what happens to the rest. The ideal gas law (PV = nRT) wraps all four into a single equation. Graham's law then connects molar mass to how quickly a gas escapes through a tiny opening. Nearly every exam problem in this unit is an algebra exercise: identify which variables change, pick the right law, plug in, and solve.
Pressure (P)
Force per unit area exerted by gas particles colliding with the walls of their container. Measured in atm, mmHg (torr), or kPa.
In simple terms, this means how hard the gas pushes on whatever holds it.
Volume (V)
The space a gas occupies, typically measured in litres (L).
Temperature (T)
A measure of the average kinetic energy of gas particles. In gas law calculations, always expressed in Kelvin (K = °C + 273.15).
Think of it as how fast the particles are moving on average.
Moles (n)
The amount of substance, where 1 mole = 6.022 × 10²³ particles (Avogadro's number). Calculated as mass divided by molar mass.
Boyle's Law
At constant temperature, the pressure and volume of a gas are inversely proportional: P₁V₁ = P₂V₂.
In simple terms, squeeze a gas into a smaller space and the pressure goes up.
Charles's Law
At constant pressure, the volume of a gas is directly proportional to its absolute temperature: V₁/T₁ = V₂/T₂.
Think of it as "heat it up, it expands."
Gay-Lussac's Law
At constant volume, the pressure of a gas is directly proportional to its absolute temperature: P₁/T₁ = P₂/T₂.
Same container, more heat, more pressure.
Combined Gas Law
Merges Boyle, Charles, and Gay-Lussac into one expression: (P₁V₁)/T₁ = (P₂V₂)/T₂. Use it when none of the three variables is held constant.
Ideal Gas Law
PV = nRT. Relates all four gas variables through the universal gas constant R. Works well at moderate temperatures and low pressures.
Universal Gas Constant (R)
The proportionality constant in PV = nRT. Its numerical value depends on the pressure unit: 0.0821 L·atm/(mol·K), 62.4 L·mmHg/(mol·K), or 8.314 L·kPa/(mol·K).
Graham's Law of Effusion
The rate of effusion of a gas is inversely proportional to the square root of its molar mass. Lighter gases escape faster.
Kinetic Energy (KE) of a Gas
Average KE = ½mv², where m is the mass of a particle and v is its velocity. At a given temperature, all ideal gases have the same average kinetic energy, regardless of identity.
Holds temperature constant.
P₁V₁ = P₂V₂.
Pressure and volume are inversely proportional: double the pressure, halve the volume.
Mnemonic from the source: "Boyle Tea" (Boyle, Temperature constant).
Example: A gas at 2.0 atm occupies 3.0 L. Compress it to 1.0 L at constant temperature and the pressure rises to 6.0 atm.
Holds pressure constant.
V₁/T₁ = V₂/T₂.
Volume and temperature are directly proportional: heat a balloon and it expands.
Temperature must be in Kelvin. Using Celsius here is the single most common calculation error in this unit.
Mnemonic: "Charles Peed" (Charles, Pressure constant).
Holds volume constant.
P₁/T₁ = P₂/T₂.
Pressure and temperature are directly proportional: a sealed container heats up, pressure rises.
Again, temperature in Kelvin only.
(P₁V₁)/T₁ = (P₂V₂)/T₂.
Use this when more than one variable changes and you are comparing two states of the same sample of gas.
If you hold one variable constant, the combined law simplifies back to Boyle, Charles, or Gay-Lussac.
PV = nRT.
R values (pick the one that matches your pressure unit):
R = 0.0821 L·atm/(mol·K) when pressure is in atm.
R = 62.4 L·mmHg/(mol·K) when pressure is in mmHg.
R = 8.314 L·kPa/(mol·K) when pressure is in kPa.
Assumes ideal behaviour: particles have no volume and exert no intermolecular forces on each other.
Real gases deviate from ideal behaviour at high pressures and low temperatures, where particles are close together and intermolecular forces matter.
n = mass / molar mass (MM), so PV = (mass/MM) × RT.
Density (d) = mass / volume, which can be rearranged from the ideal gas law to d = (P × MM) / (RT).
Rate of effusion of gas A / Rate of effusion of gas B = √(MM_B / MM_A).
The lighter gas effuses faster.
Example: Hydrogen (MM = 2) effuses four times faster than oxygen (MM = 32) because √(32/2) = √16 = 4.
KE = ½mv².
At a given temperature, all ideal gas particles have the same average kinetic energy regardless of their identity.
Lighter particles must therefore move faster to have the same KE as heavier ones.
Boyle's Law: P₁V₁ = P₂V₂ (T constant)
Charles's Law: V₁/T₁ = V₂/T₂ (P constant)
Gay-Lussac's Law: P₁/T₁ = P₂/T₂ (V constant)
Combined Gas Law: (P₁V₁)/T₁ = (P₂V₂)/T₂
Ideal Gas Law: PV = nRT
Graham's Law: Rate_A / Rate_B = √(MM_B / MM_A)
Average Kinetic Energy: KE = ½mv²
Moles: n = mass / molar mass
Density from Ideal Gas Law: d = (P × MM) / (RT)
Boyle's law explains why your ears pop on an aeroplane: as cabin pressure drops, the air trapped in your inner ear expands until it escapes through the Eustachian tube.
Charles's law is why a hot-air balloon rises. Heating the air inside the envelope increases its volume relative to the cooler air outside, lowering its density and producing lift.
Graham's law is the reason a hydrogen leak is harder to contain than a propane leak: hydrogen, being much lighter, effuses through tiny gaps far more quickly.
Students often use Celsius in gas law calculations. Every gas law formula requires Kelvin. Add 273.15 (or 273 for quick work) to convert.
Students sometimes confuse effusion with diffusion. Effusion is gas escaping through a tiny hole into a vacuum. Diffusion is gas spreading through another gas.
Students assume all gases behave ideally. Real gases deviate significantly at high pressures and low temperatures. The ideal gas law is an approximation, not a universal truth.
Students mix up which law applies when. If the question says temperature is constant, you want Boyle. Pressure constant, Charles. Volume constant, Gay-Lussac. If two variables change, use the combined law. If moles appear, use the ideal gas law.
⚠️ Unit matching is tested constantly. If pressure is in atm, use R = 0.0821. If in kPa, use R = 8.314. A wrong R value gives a wrong answer even if the algebra is perfect.
⚠️ Questions that give temperature in Celsius are testing whether you remember to convert to Kelvin.
⚠️ Graham's law problems often ask you to compare two gases. Set up the ratio carefully: the heavier gas goes under the square root on top, the lighter on the bottom.
⚠️ "At STP" means 0 °C (273.15 K) and 1 atm. One mole of an ideal gas at STP occupies 22.4 L. This fact appears in multiple-choice questions regularly.
⚠️ Expect at least one problem asking you to derive density or molar mass from the ideal gas law by rearranging PV = nRT.
True or false: Boyle's law applies when pressure is held constant. (False, temperature is held constant.)
Fill in the blank: In PV = nRT, temperature must always be in ______. (Kelvin)
True or false: A lighter gas effuses more slowly than a heavier gas. (False, lighter gases effuse faster.)
Fill in the blank: At STP, one mole of an ideal gas occupies ______ litres. (22.4)
True or false: Real gases behave most like ideal gases at high pressures and low temperatures. (False, they behave most ideally at low pressures and high temperatures.)
Q: A 4.0 L sample of gas is at 2.0 atm and constant temperature. What is the new pressure if the volume is compressed to 1.0 L?
A: Use Boyle's law. P₁V₁ = P₂V₂. (2.0)(4.0) = P₂(1.0). P₂ = 8.0 atm.
Q: A gas occupies 500 mL at 300 K and constant pressure. What volume does it occupy at 600 K?
A: Use Charles's law. V₁/T₁ = V₂/T₂. 500/300 = V₂/600. V₂ = 1000 mL.
Q: How many moles of an ideal gas occupy 10.0 L at 2.00 atm and 350 K?
A: PV = nRT. n = PV/(RT) = (2.00)(10.0) / (0.0821 × 350) = 20.0 / 28.735 ≈ 0.696 mol.
Q: Gas A has a molar mass of 4 g/mol and Gas B has a molar mass of 36 g/mol. How many times faster does Gas A effuse compared to Gas B?
A: Rate_A / Rate_B = √(MM_B / MM_A) = √(36/4) = √9 = 3. Gas A effuses 3 times faster.
Q: What is the density of O₂ (MM = 32.0 g/mol) at STP (1 atm, 273.15 K)?
A: d = (P × MM) / (RT) = (1.00 × 32.0) / (0.0821 × 273.15) = 32.0 / 22.43 ≈ 1.43 g/L.
Gas laws connect directly to stoichiometry: once you know PV = nRT, you can find moles of a gas produced in a reaction and convert to litres at any conditions, not just STP.
They also lead into thermodynamics. The kinetic molecular theory, which underpins these laws, reappears when you study enthalpy, entropy, and the Boltzmann distribution.
Dalton's law of partial pressures (covered separately) extends the ideal gas law to mixtures and is essential for equilibrium calculations involving gaseous reactions.
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