Why must temperature be in kelvin for the ideal gas law?

PV = nRT is derived assuming temperature is measured from absolute zero, where a gas's volume or pressure would theoretically hit zero. Using Celsius (which is offset by 273.15 from that zero point) would give wrong answers, and could even produce a negative or zero volume for a positive Celsius temperature, kelvin is the only scale where the proportionality actually holds.

Why does R change value depending on the units used?

R is a physical constant, but its numeric value depends on which units express pressure and volume. R = 0.08206 L·atm/(mol·K) works when pressure is in atmospheres and volume in liters; R = 8.314 J/(mol·K) works in SI units (pascals and cubic meters). Mixing a unit set with the wrong R value is one of the most common gas-law mistakes.

What is STP and why does 1 mole occupy 22.4 L there?

STP (standard temperature and pressure) is the reference condition 0°C (273.15 K) and 1 atm. Plugging n = 1, T = 273.15 K, and P = 1 atm into V = nRT/P gives V ≈ 22.4 L, a commonly memorized number, but it's really just one specific case of the same PV = nRT relationship, not a separate rule.

Does the ideal gas law work for real gases?

It's a good approximation at low pressure and high temperature, where gas molecules are far apart and their own volume and intermolecular attractions are negligible. It becomes less accurate at high pressure or low temperature, where molecular volume and intermolecular forces matter, the van der Waals equation adds correction terms for exactly those effects.

V = nRT / P: Solving the Ideal Gas Law for Volume

V = nRT / P

Start from PV = nRT and divide both sides by whatever is sitting next to V. Everything else stays where it is. This is the molar volume at STP, and getting 22.4 L back is a good check that your units and your R agree.

Worked example

What volume does 1.00 mol of an ideal gas occupy at 1.00 atm and 273.15 K?

V = nRT / P

V = (1.00 mol x 0.08206 L·atm/mol·K x 273.15 K) / 1.00 atm

V = 22.414 / 1.00

V = 22.41 L

Why the rearrangement works

PV = nRT is one equation with four variables and a constant, so knowing any three gives you the fourth. To isolate V, divide both sides by everything that shares its side of the equals sign. Nothing else moves, and no term changes sign, because there is no addition anywhere in the equation. That is why all four rearrangements look so similar.

The same problem in different units

One mole of gas at body temperature, 310 K, still at 1.00 atm.

V = nRT / P

V = (1.00 mol x 0.08206 L·atm/mol·K x 310 K) / 1.00 atm

V = 25.44 L

Warmer gas takes more room. Up from 22.41 L at 0 °C to over 25 L at body temperature, for the same one mole.

Which R to use

R only looks like several different constants because it carries units. Pick the one that matches the units you already have, and do not convert anything afterwards.

R	Units	Use when
0.08206	L·atm / mol·K	pressure in atm, volume in litres
8.314	J / mol·K	pressure in pascals, volume in cubic metres
62.36	L·mmHg / mol·K	pressure in mmHg or torr

Where this goes wrong

Temperature must be in kelvin. Celsius is the single most common reason an ideal gas answer comes out wrong, and it is silent: the arithmetic still works, the number is just false. Add 273.15.

R has to match your units. Using 0.08206 with pressure in kilopascals gives an answer that is out by a factor of about a hundred.

Volume in litres, not millilitres, when you are using 0.08206. A 250 mL flask is 0.250 L.

Practice

Answers are underneath each one. Use R = 0.08206 and keep temperature in kelvin.

What volume does 0.250 mol occupy at 2.00 atm and 300 K?
3.08 L
And the same 0.250 mol at 0.500 atm, same temperature?
12.31 L

The other rearrangements

n = PV / RT, for moles
P = nRT / V, for pressure
T = PV / nR, for temperature

Or use the ideal gas law calculator, which solves for whichever one you leave blank and shows the working.