Ideal Gas Law Calculator

Common Examples

Input	Result
n = 1 mol, T = 273.15 K, P = 1 atm	V = 22.41 L
P = 2 atm, n = 0.5 mol, T = 300 K	V = 6.15 L
V = 10 L, n = 0.5 mol, T = 350 K	P = 1.44 atm
P = 1 atm, V = 5 L, T = 298 K	n = 0.2044 mol
P = 3 atm, V = 8.2 L, n = 1 mol	T = 299.73 K

How It Works

The Ideal Gas Law

PV = nRT

Where:

P = pressure in atmospheres (atm)
V = volume in liters (L)
n = amount of substance in moles (mol)
R = ideal gas constant = 0.08206 L atm / (mol K)
T = absolute temperature in Kelvin (K)

Rearranged forms:

Pressure: P = nRT / V
Volume: V = nRT / P
Moles: n = PV / (RT)
Temperature: T = PV / (nR)

The Gas Constant

The value of R depends on the units used. Common values:

R = 0.08206 L atm / (mol K) (when using atm and liters)
R = 8.314 J / (mol K) (when using pascals and cubic meters)
R = 62.36 L mmHg / (mol K) (when using mmHg and liters)

This calculator uses R = 0.08206 L atm / (mol K).

Standard Temperature and Pressure (STP)

At STP (0 degrees C = 273.15 K, 1 atm), one mole of any ideal gas occupies 22.414 liters. This value is called the molar volume at STP and is useful for quick conversions between moles and volume.

Converting to Kelvin

Temperature must be in Kelvin. To convert: K = C + 273.15. For Fahrenheit: K = (F - 32) x 5/9 + 273.15. Common reference points: water freezes at 273.15 K (0 C), room temperature is approximately 293 to 298 K (20 to 25 C), and water boils at 373.15 K (100 C).

Limitations

The ideal gas law assumes gas molecules have no volume and no intermolecular forces. It is most accurate at low pressures and high temperatures. For real gases at high pressures or low temperatures, the van der Waals equation or other corrections provide better results.

Worked Example

A sealed container holds 2.0 moles of nitrogen gas at 25 C (298.15 K) and 1.5 atm. What is the volume?

V = nRT / P = (2.0 x 0.08206 x 298.15) / 1.5 = 48.91 / 1.5 = 32.61 L

The gas occupies 32.61 liters under these conditions.

Related Calculators

Moles Calculator

Convert between mass, moles, and molar mass using the mole formula n = mass / molar mass.

Molar Mass Calculator

Calculate the molar mass of any chemical compound by entering its formula. Shows element breakdown with atomic masses.

Frequently Asked Questions

What is an ideal gas?

An ideal gas is a theoretical model where gas molecules are point particles with no volume and no intermolecular attractions or repulsions. Real gases approximate ideal behavior at low pressures and high temperatures. Common gases like nitrogen, oxygen, and helium behave very close to ideal at standard conditions.

Why must temperature be in Kelvin?

The ideal gas law requires absolute temperature (Kelvin) because the relationship between gas properties and temperature is directly proportional only on the absolute scale. At 0 K (absolute zero), an ideal gas would have zero volume and zero pressure. Using Celsius or Fahrenheit would give incorrect results because these scales have arbitrary zero points.

What are common pressure units and conversions?

1 atm = 101,325 Pa = 101.325 kPa = 760 mmHg = 760 torr = 14.696 psi. This calculator uses atmospheres (atm). If your problem uses different units, convert to atm first: divide kPa by 101.325, divide mmHg by 760, or divide psi by 14.696.

How do I find the number of moles?

Moles can be calculated as mass (grams) divided by molar mass (g/mol). For example, 32 g of O2 (molar mass 32 g/mol) is 1 mole. Alternatively, at STP, moles = volume in liters / 22.414. The moles calculator on this site can help with this conversion.

When does the ideal gas law break down?

The ideal gas law becomes inaccurate at very high pressures (above about 10 atm for most gases), very low temperatures (near the condensation point), and for gases with strong intermolecular forces (like water vapor or ammonia). In these cases, the van der Waals equation or other real gas models provide better accuracy.