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Ideal Gas Law Calculator (PV = nRT)

Solve PV = nRT for pressure, volume, moles or temperature in any units, with the gas constant and temperature conversions handled for you.

Find

The ideal gas law ties together the four things you can measure about a gas: its pressure, volume, amount and temperature. Know three and this calculator finds the fourth, in whatever units your problem uses, converting to kelvin and matching the gas constant for you.

How to Use It

  1. Choose what to Find: Pressure, Volume, Moles or Temperature.
  2. Enter the other three values and pick each one’s unit.
  3. Choose the unit for the answer in Answer In.
  4. Press Calculate.

How It Works

P V=n R T\vA{P}\,\vB{V} = \vC{n}\,R\,\vD{T}

R is the gas constant, 8.314 J/(mol·K). The calculator converts pressure to pascals, volume to cubic meters and temperature to kelvin, solves the equation for the unknown, then converts the answer to the unit you chose:

P=nRTVV=nRTPn=PVRTT=PVnRP = \frac{nRT}{V} \qquad V = \frac{nRT}{P} \qquad n = \frac{PV}{RT} \qquad T = \frac{PV}{nR}

Worked Example

What volume does 1 mol of gas fill at 0 °C (273.15 K) and 1 atm (101,325 Pa)?

V=1×8.314×273.15101,325≈0.0224 m3=22.4 LV = \frac{1 \times 8.314 \times 273.15}{101{,}325} \approx 0.0224 \text{ m}^3 = 22.4 \text{ L}

That’s the standard molar volume chemistry classes use for gases at STP.

Tips and Common Mistakes

  • Always use kelvin. 25 °C is 298.15 K; plugging in 25 gives an answer over ten times too small.
  • Match R to your units when working by hand: 0.08206 L·atm/(mol·K) or 8.314 J/(mol·K).
  • Moles, not grams. Divide a mass by the molar mass first.
  • Watch which STP. 0 °C and 1 atm gives 22.4 L per mole; IUPAC’s 1 bar gives about 22.7 L.
  • Real gases differ at high pressure or low temperature, where molecules crowd and attract.

Frequently Asked Questions

What is the ideal gas law?

PV = nRT: pressure times volume equals moles times the gas constant times the absolute temperature. It links the four properties of a gas.

Why must temperature be in kelvin?

The law needs a scale that starts at absolute zero. Celsius and Fahrenheit don't, so the calculator converts to kelvin for you.

Which value of R should I use?

It depends on the units: 8.314 J/(mol·K) in SI, or 0.08206 L·atm/(mol·K). The calculator works in SI, so any units you pick give the same answer.

What is STP?

Standard temperature and pressure. Using 0 °C and 1 atm, one mole of an ideal gas fills about 22.4 L. (IUPAC's current STP uses 1 bar, giving about 22.7 L.)

When isn't a gas ideal?

At high pressure or low temperature, when molecules are close together and attract each other. Real gases then differ from PV = nRT.

How do I find moles from grams of gas?

Divide the mass by the molar mass. 32 g of O₂ is 1 mol.

Sources

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