Model real gases beyond the ideal law. Use flexible units for constants, volume, and temperature. Get corrected pressure, Z factor, and insights quickly today.
The Van der Waals equation (for n moles) is: P = nRT/(V − n b) − a n² / V²
Example inputs use n = 1 mol, T = 300 K, V = 1 L, and constants in bar·L²/mol² and L/mol.
| Gas (example) | a (bar·L²/mol²) | b (L/mol) | Ideal pressure (bar) | Van der Waals pressure (bar) |
|---|---|---|---|---|
| CO₂ | 3.592 | 0.04267 | 24.9434 | 22.4632 |
| N₂ | 1.352 | 0.03870 | 24.9434 | 24.5956 |
| CH₄ | 2.253 | 0.04278 | 24.9434 | 23.8052 |
Real gases deviate from the ideal law when molecules interact and occupy finite space. The Van der Waals model estimates pressure by adding a repulsive volume correction and subtracting an attraction correction. For 1 mol at 300 K in 1 L, the ideal estimate is about 24.94 bar, while the corrected value depends on the constants.
The constant a measures how strongly molecules attract; larger a usually lowers predicted pressure at the same T and V. The constant b represents excluded volume per mole and increases effective crowding. In the example table, CO₂ has a higher a than N₂, so its corrected pressure drops more.
Handbooks often list a in bar·L²/mol² and b in L/mol, while many calculations use SI units. Typical b values for simple gases cluster around 0.038–0.043 L/mol, and a values vary widely (for example, N₂ ≈ 1.352 and CO₂ ≈ 3.592 in bar·L²/mol²). Match units to your source.
The repulsive term uses V − n b. If V approaches n b, the denominator shrinks and pressure rises quickly, reflecting limited free volume. This calculator blocks cases where V ≤ n b. For 1 mol with b = 0.0427 L/mol, total volume must exceed 0.0427 L.
The attractive term a n²/V² reduces pressure and becomes significant at high density (small V) and with strongly interacting gases. The compressibility factor Z = PV/(nRT) summarizes deviation: Z < 1 often indicates attractions dominating, while Z > 1 suggests repulsions are more important at that state. Tracking Z across conditions is a fast sanity check.
Reviewing ideal and corrected pressures side by side helps validate assumptions. At low pressures and large molar volumes, both models converge. As density increases, the corrected pressure can differ by several percent, which matters for equipment sizing, load estimates, and quick process checks. It also highlights which term drives the deviation.
The Van der Waals equation is best for trends and moderate departures from ideality. Near saturation, close to the critical region, or at very high pressures, more accurate equations of state may be required. Use measured data when safety or compliance depends on the result.
Select known a and b values, choose consistent units, and enter n, T, and V. Confirm that V is comfortably above n b, then review P, Z, and the repulsive/attractive breakdown. Export CSV or PDF to document assumptions and repeat for sensitivity checks across conditions and unit choices.
Enter moles n, temperature, total volume, and the constants a and b for your gas. Choose the correct unit system for a and b, then select your preferred output pressure unit before calculating.
Use a reputable thermodynamics handbook, data sheet, or engineering reference for your gas. Ensure the constants are reported in the same units you select. Constants can vary slightly across sources and fitted temperature ranges.
The model treats b as excluded volume per mole. If V ≤ n·b, the available free volume becomes zero or negative, which is unphysical and causes the repulsive term to blow up. Increase V or reduce n to proceed.
Z compares real-gas behavior to the ideal law. Values near 1 indicate near‑ideal behavior. Z below 1 often signals attractions dominating, while Z above 1 suggests repulsions dominate. Use it as a quick check on plausibility.
It captures trends but can be noticeably inaccurate near saturation and critical conditions. For design-grade work in those regions, use a more accurate equation of state and validate against experimental property data.
The calculator converts temperature to Kelvin and volume to cubic meters internally. It also converts a and b from common bar–liter units to SI when selected. Results are then converted to your chosen pressure unit.
The repulsive term increases pressure because molecules occupy space, effectively reducing free volume. The attractive term reduces pressure because intermolecular forces pull molecules inward. Their balance determines whether the corrected pressure is above or below the ideal estimate.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.