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Ideal Gas Law Calculator

PV = nRT, solved for pressure, volume, moles or temperature, in the units you already have.

Solve for

mol

Converted to kelvin before use — PV = nRT is only true in kelvin.

Volume

22.414 L

P
1 atm
V
22.414 L
n
1 mol
T
273.15 K

Working

  1. V = nRT ÷ P = (1 × 0.082057366 × 273.15) ÷ 1 = 22.4140 L
  2. R = 0.082057366 L·atm·K⁻¹·mol⁻¹

One law, four questions

Every ideal gas problem is the same equation rearranged. Choose the quantity you want, supply the other three, and the algebra is fixed. The working shown under the answer is the rearrangement itself, which is the part worth copying into an exam answer.

The two traps

The first is temperature: always kelvin, no exceptions. The second is mixing unit systems — pressure in kilopascals with a gas constant in litre-atmospheres gives an answer wrong by a factor of about a hundred. Converting on the way in, as this does, removes both.

Related: molar mass calculator, chemical equation balancer, periodic table.

How it works

PV = nRT ties together the four things you can measure about a gas. It describes a hypothetical gas whose particles have no volume and no attraction to each other, which turns out to be a very good approximation at ordinary pressures.

Ideal gas law

PV = nRT

P = nRT ÷ V     V = nRT ÷ P     n = PV ÷ RT     T = PV ÷ nR

R = 0.08206 L·atm·K⁻¹·mol⁻¹  =  8.314 J·K⁻¹·mol⁻¹
P
pressure
V
volume
n
amount of gas, in moles
R
the gas constant — its value depends on the units used
T
absolute temperature, in kelvin, always

One mole of gas at 1 atm and 0 °C

  • P = 1 atm
  • n = 1 mol
  • T = 0 °C = 273.15 K
  1. V = nRT ÷ P
  2. V = (1 × 0.08206 × 273.15) ÷ 1

V = 22.41 L — the molar volume of an ideal gas at 1 atm and 0 °C.

Good to know

  • Temperature must be in kelvin. A proportionality needs a scale that starts at zero, and a gas at 0 °C plainly has volume. Entering celsius is the single most common error in these problems.
  • Match R to your units. Pressure in kilopascals with a litre-atmosphere R gives an answer wrong by about a hundredfold.
  • Boyle's, Charles's and Gay-Lussac's laws are all this equation with one variable held constant — they are not separate physics.
  • Real gases deviate at high pressure and low temperature, where molecular volume and attraction stop being negligible. An equation such as van der Waals is needed there.

Kalkulator Terkait

Pertanyaan yang Sering Ditanyakan

What is the ideal gas law?

PV = nRT relates the pressure, volume, amount and temperature of a gas through the gas constant R. It describes a hypothetical gas whose particles have no volume and no attraction to each other — a very good approximation for real gases at ordinary pressures.

Why must temperature be in kelvin?

Because the law is a proportionality, and proportionalities need a scale that starts at zero. At 0 °C a gas plainly has volume, so celsius cannot be proportional to anything. Kelvin starts at absolute zero, where an ideal gas would have no volume at all. Entering celsius is the single most common error in these problems.

What value of R should I use?

It depends on the units. With pressure in atmospheres and volume in litres, R is 0.08206 L·atm·K⁻¹·mol⁻¹. With SI units of pascals and cubic metres it is 8.314 J·K⁻¹·mol⁻¹. This calculator converts your inputs and uses the matching value.

When does the ideal gas law stop working?

At high pressure and low temperature, where molecules are close enough for their own volume and their mutual attraction to matter. Real gases then deviate, and an equation such as van der Waals is needed.

What is STP?

Standard temperature and pressure: 0 °C and 100 kPa under the current IUPAC definition, where one mole of ideal gas occupies 22.71 L. Older textbooks use 1 atm and give 22.4 L, which is why the two numbers both circulate.