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Daily Dose of Utilities

Ideal Gas Law Calculator (PV = nRT)

The ideal gas law is PV = nRT. With R = 0.082057 L·atm/(mol·K), one mole of gas at 0 °C (273.15 K) and 1 atm takes up 1 × 0.082057 × 273.15 ÷ 1 = 22.41 L.

mol

Volume

22.414 L

Uses R = 0.082057 L·atm/(mol·K) (8.314 J/(mol·K)). Real gases depart from this at high pressure or low temperature.

Show the math

  1. 1

    Convert to atm, liters and kelvin

    0 °C = 273.15 K

    R = 0.082057 L·atm/(mol·K) only works with these units. Temperature must be absolute (kelvin), never °C or °F.

Read the steps as text
  1. Convert to atm, liters and kelvin. 0 °C = 273.15 K R = 0.082057 L·atm/(mol·K) only works with these units. Temperature must be absolute (kelvin), never °C or °F.
  2. V = nRT ÷ P. 1 × 0.082057 × 273.15 ÷ 1 = 22.414 L

Using PV = nRT

The ideal gas law links a gas's pressure (P), volume (V), amount in moles (n) and absolute temperature (T) through the gas constant R. Rearrange it to find whichever is missing: P = nRT ÷ V, V = nRT ÷ P, n = PV ÷ RT or T = PV ÷ nR.

R's value depends on the units, so the calculator converts everything to atmospheres, liters and kelvin and uses R = 0.082057 L·atm/(mol·K), then converts the answer back to the unit you picked. In SI units the same constant is 8.314 J/(mol·K).

Why temperature must be in kelvin

The gas law needs absolute temperature, measured from absolute zero. At 0 °C a gas still has plenty of molecular motion and pressure, so plugging in 0 would wrongly predict zero volume. Adding 273.15 converts Celsius to kelvin.

Real gases follow the ideal gas law closely at everyday temperatures and pressures. It becomes less accurate at very high pressures or very low temperatures, where the size of the molecules and the attraction between them start to matter.

Frequently asked questions

What is the value of R in the ideal gas law?
0.082057 L·atm/(mol·K), 8.314 J/(mol·K) or 62.36 L·mmHg/(mol·K). They are the same constant in different units.
What is the molar volume of a gas at STP?
22.41 L at 0 °C and 1 atm. Since 1982 IUPAC has defined STP as 0 °C and 1 bar, which gives 22.71 L.
What pressure do 2 moles of gas exert in a 10 L container at 25 °C?
P = nRT ÷ V = 2 × 0.082057 × 298.15 ÷ 10 = 4.89 atm, or about 496 kPa.
Can I use grams instead of moles?
Convert grams to moles first by dividing by the gas's molar mass. The grams to moles calculator does this from the formula, for example 44.009 g/mol for CO2.

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