80.828162
0.999994
atm
22.413935
L
1.000002
mol
273.150397
K
1.292494
g/L
28.970056
g
80.828162
0.999994
atm
22.413935
L
1.000002
mol
273.150397
K
1.292494
g/L
28.970056
g
The Ideal Gas Law Calculator solves PV = nRT for any one of the four variables: pressure, volume, amount (moles), or temperature. Simply select which variable to solve for, enter the known values, and get an instant result. This is the most fundamental equation in gas chemistry and is used daily by chemists, physicists, engineers, and students worldwide.
The ideal gas law combines Boyle's law, Charles's law, and Avogadro's law into a single unified equation. While it assumes idealized behavior (no intermolecular forces, zero molecular volume), it provides excellent approximations for most gases under ordinary conditions of temperature and pressure.
The ideal gas law is expressed as:
$$PV = nRT$$
where:
Rearranging to solve for each variable:
$$P = \frac{nRT}{V} \qquad V = \frac{nRT}{P} \qquad n = \frac{PV}{RT} \qquad T = \frac{PV}{nR}$$
The gas density can be derived by combining PV=nRT with n=m/M (where M is molar mass):
$$\rho = \frac{PM}{RT}$$
The ideal gas constant R has different values depending on the unit system: R = 8.314 J/(mol·K) = 0.08206 L·atm/(mol·K) = 62.36 L·mmHg/(mol·K). This calculator uses 0.08206 for atm-liter units. The ideal gas approximation works well when the gas is far from its condensation point and at moderate pressures (generally below 10 atm).
The calculated value gives you the unknown gas property. Pressure in atm indicates the force per unit area; volume in liters is the space occupied; moles represent the amount of gas; temperature in Kelvin reflects the average kinetic energy. The density estimate assumes a molar mass of 29 g/mol (approximately air). For other gases, multiply the density by (actual molar mass / 29).
Inputs
Results
Two moles of an ideal gas in a 10-liter container at 300 K exerts about 4.92 atm of pressure. This is nearly 5 times atmospheric pressure.
Inputs
Results
One mole of any ideal gas at STP occupies exactly 22.414 liters — the molar volume. This is one of the most important reference values in gas chemistry.
The ideal gas law (PV = nRT) is a fundamental equation of state that relates the pressure, volume, amount, and temperature of an ideal gas. It assumes gas molecules have no intermolecular forces and negligible volume. It combines the experimental gas laws of Boyle, Charles, and Avogadro into one equation.
R is the ideal (universal) gas constant. Its value depends on the units: R = 8.314 J/(mol·K) for SI units, R = 0.08206 L·atm/(mol·K) for atmosphere-liter units, R = 62.36 L·mmHg/(mol·K) for mmHg-liter units. All represent the same physical constant in different unit systems.
The ideal gas law requires absolute temperature because gas volume and pressure are directly proportional to absolute temperature. At 0 K (absolute zero), an ideal gas would have zero volume and zero pressure. Using Celsius would give negative values that break the proportionality.
The ideal gas law becomes inaccurate at high pressures (molecules are close together and intermolecular forces matter), low temperatures (near condensation), and for gases with strong intermolecular forces (like water vapor, NH₃). In these cases, the van der Waals equation or other equations of state are more accurate.
STP (Standard Temperature and Pressure) is 0°C (273.15 K) and 1 atm (101.325 kPa). At STP, one mole of an ideal gas occupies 22.414 liters (the molar volume). IUPAC's newer definition uses 0°C and 1 bar, giving a molar volume of 22.711 L.
Rearranging PV = nRT with n = m/M gives density ρ = PM/(RT), where M is molar mass. For air (average M ≈ 29 g/mol) at STP: ρ = 1 × 29/(0.08206 × 273.15) ≈ 1.29 g/L.
Yes, the ideal gas law applies to mixtures using the total number of moles. Dalton's law states that each gas in a mixture behaves independently, so PV = n_total × RT. The partial pressure of each component is P_i = (n_i/n_total) × P_total.
The kinetic molecular theory derives PV = nRT from statistical mechanics: gas molecules move randomly, collisions are elastic, molecules have negligible volume compared to the container, and there are no intermolecular forces. The pressure arises from molecular collisions with container walls.
Real gas molecules have finite volume and experience attractive forces (van der Waals forces). At high pressure, finite volume makes real gas volume larger than predicted. At moderate pressure, attractive forces make real gas volume smaller. The compressibility factor Z = PV/(nRT) measures deviation from ideality (Z = 1 for ideal gas).
The compressibility factor Z = PV/(nRT) quantifies how much a real gas deviates from ideal behavior. Z = 1 means ideal behavior. Z < 1 means attractive forces dominate (gas is more compressible than ideal). Z > 1 means molecular volume effects dominate (gas is less compressible). Most gases approach Z = 1 at low pressures and high temperatures.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
How helpful was this calculator?
Be the first to rate!
Combined Gas Law Calculator
Gas Laws Calculators
Charles's Law Calculator
Gas Laws Calculators
Gay-Lussac's Law Calculator
Gas Laws Calculators
Graham's Law of Effusion Calculator
Gas Laws Calculators
Van der Waals Equation Calculator
Gas Laws Calculators
STP Calculator (Standard Temperature and Pressure)
Gas Laws Calculators
