Estimate real-gas critical constants using reliable equations. Switch modes, validate inputs, and export results quickly. Clear outputs help compare and interpret measurements.
Choose a mode, enter values, and calculate. The layout adapts to large, small, and mobile screens.
This calculator uses the van der Waals equation of state to estimate the thermodynamic critical point. For a real gas approximated by van der Waals parameters a and b, the critical constants are:
In the reverse mode, the calculator estimates b from Vc (or from Tc and Pc if Vc is omitted), then computes two independent estimates of a from Tc and Pc and reports their agreement.
Sample inputs below use common reference-style values (for demonstration). Try them in either mode to verify the workflow and compare outputs.
| Scenario | a | b | Tc | Pc | Notes |
|---|---|---|---|---|---|
| Example A | 0.364 L²·bar/mol² | 0.0427 L/mol | ≈ 304 K | ≈ 73.9 bar | Good for checking conversions. |
| Example B | 0.550 L²·bar/mol² | 0.0500 L/mol | ≈ 352 K | ≈ 81.5 bar | Higher attraction raises Tc. |
| Example C | 0.300 L²·bar/mol² | 0.0350 L/mol | ≈ 275 K | ≈ 70.0 bar | Lower b reduces Vc. |
A fluid reaches its critical point when the liquid–vapor boundary disappears and both phases become one. The critical temperature (Tc) and pressure (Pc) anchor phase envelopes and reduced-property scaling, using Tr = T/Tc and Pr = P/Pc for quick comparisons across substances.
The attraction parameter a summarizes cohesive forces, while b represents excluded volume. If a and b come from fitted P–V–T data, they provide a convenient route to estimate critical constants without a property table lookup.
The calculator applies closed-form van der Waals critical relations: Tc = 8a/(27Rb), Pc = a/(27b²), and Vc = 3b. Analytic formulas keep the computation fast and numerically stable.
Tc is a temperature scale for condensation limits, Pc is the minimum pressure needed to liquefy at Tc, and Vc is the molar volume at that point. Use Vc to build reduced volume Vr = V/Vc and to compare “tight” versus “loose” fluids in packing behavior across datasets or simulation runs.
Zc = PcVc/(RTc) measures non-ideality at the critical point. For van der Waals, Zc equals 0.375 (3/8). Real fluids often fall near 0.27–0.30, so Zc is a useful reasonableness check when your estimate seems surprising.
Pc scales as 1/b², so small errors in b or unit conversion can strongly affect Pc. This tool converts common lab units (L²·bar/mol², L/mol) to SI internally and then reports Pc in Pa, bar, or atm and Vc in m³/mol or L/mol. Keep R at 8.314462618 J/(mol·K) for SI conversions.
In reverse mode, b is taken from Vc/3 (or estimated from Tc and Pc if Vc is blank). Two values of a are computed independently from Tc and Pc, and their percent difference is reported. For CO₂, values near Tc ≈ 304.13 K and Pc ≈ 73.77 bar typically agree well.
Treat outputs as estimates: the van der Waals model is intentionally simple and may mispredict strongly polar or associating fluids. Use the agreement metric, compare Zc to expected ranges, and validate against reference data when design decisions depend on critical accuracy. Export CSV for records and share PDF in reports.
It estimates Tc, Pc, and Vc using van der Waals relations, or estimates van der Waals parameters from critical constants, with an agreement check for consistency.
Because Pc = a/(27b²). A small change in b is squared, so volume-unit errors or rounding in b can shift Pc noticeably.
Only for the van der Waals model. Real fluids have different Zc values, so deviations can indicate the model is not matching the substance closely.
Yes. The calculator estimates b from Tc and Pc, then computes Vc = 3b. Providing Vc can improve b when you have reliable molar-volume data.
It compares a derived from Pc versus a derived from Tc. A small value suggests your Tc and Pc inputs are mutually consistent within this framework.
Use R = 8.314462618 J/(mol·K) with SI conversions. If you work outside SI, keep R consistent with your units or rely on the built-in unit conversions.
Use a more advanced equation of state for mixtures, near-critical design, or strongly polar fluids. This tool is best for fast estimation, screening, and input validation.
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.