Ideal Gas Law
What is the Ideal Gas Law?
The ideal gas law combines three earlier relationships — Boyle's law, Charles's law, and Avogadro's law — into a single equation that holds for an idealized gas: point-like molecules with no intermolecular forces.
Real gases follow this closely at ordinary temperatures and pressures, which is why it's the default tool for gas calculations in an introductory chemistry course. The formula can be rearranged to solve for any one variable once the other three (plus the constant R) are known.
What Each Variable Means
Units
| Quantity | Symbol | Unit |
|---|---|---|
| Pressure | P | atmosphere (atm) |
| Volume | V | liter (L) |
| Amount | n | mole (mol) |
| Temperature | T | kelvin (K) |
When to Use It
- Finding one gas property (P, V, n, or T) when the other three are known
- Predicting how a gas sample behaves when conditions change
- Checking whether a real gas is behaving approximately ideally
Where This Formula Comes From
At constant temperature and amount, pressure and volume are inversely proportional.
P ∝ 1/VAt constant pressure and amount, volume is directly proportional to temperature.
V ∝ TAt constant pressure and temperature, volume is directly proportional to the amount of gas.
V ∝ nMerging them into one relationship and introducing a proportionality constant, R, to make it an equation gives the ideal gas law.
PV = nRTStep-by-Step Examples
Example 1: Solving for pressure
Problem: Find the pressure of 2 mol of gas in a 10 L container at 300 K.
List the given values and confirm temperature is already in Kelvin.
n = 2 mol, V = 10 L, T = 300 K, R = 0.0821 L·atm/(mol·K)Solve PV = nRT for pressure.
P = nRT / VPlug in the known values.
P = (2 × 0.0821 × 300) / 10 = 4.926Example 2: Solving for volume
Problem: Find the volume of 0.5 mol of gas at 1.5 atm and 350 K.
List the given values.
n = 0.5 mol, P = 1.5 atm, T = 350 KSolve PV = nRT for volume.
V = nRT / PPlug in the known values.
V = (0.5 × 0.0821 × 350) / 1.5 ≈ 9.58Interactive Calculator
Solving for Other Variables
V = nRT / PSolve for volume when pressure, amount, and temperature are known.n = PV / RTSolve for the amount of gas when pressure, volume, and temperature are known.T = PV / nRSolve for temperature when pressure, volume, and amount are known.Common Mistakes
Mistake: Using Celsius instead of Kelvin for temperature.
Fix: Always convert first: K = °C + 273.15. The ideal gas law only works with absolute temperature.
Mistake: Mismatching R's units with the units used for P, V, and T.
Fix: R = 0.0821 L·atm/(mol·K) requires atm, liters, and Kelvin. If your problem uses different units, either convert first or use a version of R matching those units.
Practice Questions
What is the volume of 1 mol of gas at 1 atm and 273 K?
Hint: This is the standard molar volume of a gas at STP.
A gas sample has P = 2 atm, V = 5 L, and T = 250 K. How many moles are present?
Hint: Rearrange PV = nRT to solve for n.
Frequently Asked Questions
Why must temperature be in Kelvin?
The gas law relies on temperature being an absolute measure of molecular motion. Celsius and Fahrenheit have arbitrary zero points that would make the proportionality break down — Kelvin's zero is absolute zero, where molecular motion theoretically stops.
What does "ideal" mean in ideal gas law?
It assumes gas molecules take up no volume themselves and have no attractive or repulsive forces between them. Real gases only approximate this, most closely at low pressure and high temperature.
Does the ideal gas law work for all gases?
It's a good approximation for most gases under normal conditions, but breaks down at very high pressure or very low temperature, where real intermolecular forces and molecular volume start to matter — that's when a more complex model like the van der Waals equation is used instead.
References
- OpenStax Chemistry 2e — The Ideal Gas Law