What is the value of R?

R = 8.314 J/(mol·K) in SI units. It is also commonly written as 0.0821 L·atm/(mol·K) and 0.08314 L·bar/(mol·K). Use the form whose units match your other inputs.

How does the ideal gas law relate to Charles' law?

Holding n and P constant in PV = nRT gives V/T = nR/P = constant, which is Charles' law. Holding n and T constant gives Boyle's law; holding n and V constant gives Gay-Lussac's law.

When does the ideal gas law fail?

At very high pressures (molecules forced close together) and very low temperatures (near condensation), real gases deviate from PV = nRT. The Van der Waals equation provides corrections for these regimes.

Standard Temperature and Pressure: traditionally 0 °C (273.15 K) and 1 atm. One mole of an ideal gas at STP occupies 22.4 L (molar volume).

Can I use Celsius for temperature?

No. T must be in Kelvin because the law depends on absolute temperature.

How many moles are in 1 litre of gas at STP?

0.0446 mol. One mole of an ideal gas occupies 22.4 L at STP (0 °C, 1 atm), so 1 L holds 1 / 22.4 = 0.0446 mol.

Ideal Gas Law Calculator: PV = nRT

Enter any three of P, V, n, or T and the calculator computes the fourth using PV = nRT with R = 8.314 J/(mol·K).

Ideal Gas Law Calculator (PV = nRT)

R = 8.314 J/(mol·K). Enter 3 of 4 values.

P (Pressure)

V (Volume)

n (Moles)

T (Temperature)

24.46 L

V = nRT/P = 1×8.314×298.1 / 101300 = 24.46 L

What Is the Ideal Gas Law?

The ideal gas law PV = nRT is the single equation that captures the macroscopic behaviour of an ideal gas. It states that the product of pressure and volume equals the number of moles times the universal gas constant R times the absolute temperature.

Each variable has a clear role: P is pressure (Pa, kPa, atm, etc.), V is volume (L, m³), n is the amount of substance in moles, R is the universal gas constant 8.314 J/(mol·K), and T is the absolute temperature in Kelvin. The equation was assembled from the earlier work of Boyle, Charles, Gay-Lussac, and Avogadro by Émile Clapeyron in 1834.

An ideal gas is a theoretical construct: point-like particles with no intermolecular forces and no volume of their own. Real gases approximate this behaviour well at moderate temperatures and low-to-moderate pressures.

Common Values of R

R	Units	Use with
8.314	J/(mol·K)	SI: Pa, m³, K
0.08206	L·atm/(mol·K)	atm, L, K
0.08314	L·bar/(mol·K)	bar, L, K
62.36	L·mmHg/(mol·K)	mmHg, L, K

Special Cases: Charles', Boyle's and Gay-Lussac's Laws

Fix two variables in PV = nRT and you recover one of the simple gas laws. Fixing n and P gives V ∝ T, Charles' law. Fixing n and T gives PV = constant, Boyle's law. Fixing n and V gives P ∝ T, Gay-Lussac's law. Fixing n alone gives the combined gas law P₁V₁/T₁ = P₂V₂/T₂.

Worked Example 1: Moles at STP

How many moles of gas occupy 5.0 L at STP (273.15 K, 101.325 kPa)? n = PV/(RT) = (101325 × 0.005) / (8.314 × 273.15) = 0.223 mol. As a check: 5.0 L / 22.4 L per mol = 0.223 mol.

Worked Example 2: Pressure of CO₂ in a Tank

A 10 L tank holds 0.5 mol of CO₂ at 350 K. The pressure: P = nRT/V = (0.5 × 8.314 × 350) / 0.010 = 145,495 Pa ≈ 1.44 atm.

Real Gases and Van der Waals

For very dense gases or low-temperature gases, replace PV = nRT with the Van der Waals equation which adds corrections for molecular volume (b) and intermolecular attraction (a). Real gases such as air, nitrogen, and oxygen follow PV = nRT closely at moderate pressure and temperature, which is why the ideal gas law remains the default tool for everyday chemistry and engineering problems.

What Makes a Gas Ideal

An ideal gas is a model built on three assumptions: its molecules take up no volume of their own, they exert no attractive or repulsive forces on each other, and every collision between them is perfectly elastic. No real gas fully meets these conditions, but light, non-polar molecules such as helium, hydrogen, and nitrogen come close under normal conditions. Heavier or polar molecules, such as water vapour or ammonia, deviate more, especially as pressure rises or temperature falls toward the point where the gas would condense into a liquid.