Ideal Gas Law Calculator
Solve PV = nRT for any variable. Supports combined gas law, gas density, Van der Waals real gas correction, Dalton's law of partial pressures, and RMS velocity.
atm
L
mol
K
Solved Variable
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Variable —
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atm
L
mol
K
Result
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mol
L
K
L²·atm/mol²
Pressure Comparison
Ideal Gas Pressure —
Van der Waals Pressure —
Compressibility Factor Z —
Molecular Speed
RMS Velocity —
How to Use This Calculator
- Select what to solve for (P, V, n, or T).
- Enter the other three known values.
- Use Gas at Two States tab for combined gas law (P₁V₁/T₁ = P₂V₂/T₂).
- Use Density tab to find gas density from molar mass and conditions.
- The Professional tab applies Van der Waals correction for real gases.
Formula
PV = nRT | R = 0.08206 L·atm/(mol·K)
Combined: P₁V₁/T₁ = P₂V₂/T₂
Density: ρ = PM/(RT) g/L (M = molar mass g/mol)
Example
Find V for 2 mol N₂ at 1 atm, 298 K: V = nRT/P = 2 × 0.08206 × 298 / 1 = 48.9 L.
Frequently Asked Questions
- PV = nRT, where P = pressure (atm), V = volume (L), n = moles, R = 0.08206 L·atm/(mol·K), T = temperature (K). It describes the behavior of an ideal gas under various conditions.
- K = °C + 273.15. For example, 25°C = 298.15 K. Always use Kelvin in gas law calculations — using Celsius or Fahrenheit gives wrong results.
- P₁V₁/T₁ = P₂V₂/T₂. It combines Boyle's, Charles's, and Gay-Lussac's laws to relate a gas at two different states.
- The Van der Waals equation corrects for intermolecular attractions (a) and molecular volume (b): (P + an²/V²)(V − nb) = nRT. Real gases deviate from ideal behavior at high pressure and low temperature.
- RMS velocity = √(3RT/M), where M is molar mass in kg/mol and R = 8.314 J/(mol·K). This is the root-mean-square speed of gas molecules at temperature T.