Formula for Calculating Partial Pressure with Antoine Equation
Use this interactive calculator to estimate saturation vapor pressure with Antoine constants and convert it to component partial pressure using Raoult-style liquid fraction input.
Expert Guide: Formula for Calculating Partial Pressure with Antoine Equation
The Antoine equation is one of the most practical tools in thermodynamics and chemical engineering when you need vapor pressure as a function of temperature. Once vapor pressure is known, you can move directly into partial pressure calculations for evaporation, distillation, humidification, solvent recovery, and many environmental modeling tasks. In plain terms, the Antoine equation helps you estimate how strongly a liquid wants to enter the vapor phase at a specific temperature. That value then feeds into partial pressure relationships such as Raoult type calculations or direct saturation estimates.
The standard Antoine form is: log10(Psat) = A – B/(C + T), where Psat is saturation pressure, T is temperature in °C, and A, B, C are empirical constants for a specific chemical over a valid temperature range. Most published constants generate pressure in mmHg, though you must always check the source. This is a key point because unit mismatches are one of the most common reasons professionals get unrealistic answers.
How Antoine and Partial Pressure Connect
Partial pressure is the pressure contribution of one component in a gas mixture. If your component is in equilibrium with a liquid phase, Antoine gives you the saturation pressure, then you can calculate a component partial pressure using the physical model you need:
- Saturation estimate: p_i = Psat,i (for pure component vapor in equilibrium).
- Ideal liquid mixture estimate (Raoult style): p_i = x_i * Psat,i, where x_i is liquid mole fraction.
- Gas phase composition from Dalton law: y_i = p_i / P_total.
The calculator above combines these steps so you can compute Psat, then component partial pressure, and finally gas phase mole fraction y at a defined total pressure. This is often enough for early design checks, educational use, and screening calculations before applying activity coefficient models.
Step by Step Formula Workflow
- Select compound constants A, B, C from a trusted source.
- Verify the temperature is within the valid published range.
- Compute saturation pressure with Antoine in its original pressure unit.
- Convert pressure to your engineering unit (kPa, bar, atm) as needed.
- If mixture behavior is needed, apply p_i = x_i * Psat,i.
- Find vapor composition with y_i = p_i / P_total.
- Sanity check: y_i should usually be between 0 and 1.
Comparison Table: Typical Antoine Constants and Normal Boiling Points
The table below lists widely used Antoine coefficient sets (mmHg, T in °C) and common normal boiling points. These values are representative and should be confirmed against your exact source and range before regulatory or design-critical use.
| Compound | A | B | C | Typical Valid Range (°C) | Normal Boiling Point (°C) |
|---|---|---|---|---|---|
| Water | 8.07131 | 1730.63 | 233.426 | 1 to 100 | 100.0 |
| Ethanol | 8.20417 | 1642.89 | 230.300 | 0 to 78 | 78.37 |
| Acetone | 7.02447 | 1161.00 | 224.000 | -9 to 95 | 56.05 |
| Benzene | 6.90565 | 1211.033 | 220.790 | 7 to 80 | 80.10 |
| Methanol | 8.08097 | 1582.271 | 239.726 | 10 to 90 | 64.70 |
Comparison Table: Example Vapor Pressures at Different Temperatures
The following example values (kPa) are consistent with common Antoine data sets and illustrate how quickly pressure rises with temperature. This non-linear rise is why vapor containment, condenser sizing, and vent design can change dramatically over modest temperature shifts.
| Compound | Psat at 25°C (kPa) | Psat at 50°C (kPa) | Psat at 75°C (kPa) | Approximate Increase 25 to 75°C |
|---|---|---|---|---|
| Water | 3.17 | 12.35 | 38.56 | ~12.2x |
| Ethanol | 7.87 | 29.45 | 72.10 | ~9.2x |
| Acetone | 30.70 | 80.80 | 180.00 | ~5.9x |
Practical Engineering Interpretation
When engineers ask for the formula for calculating partial pressure with Antoine, they are usually solving one of three practical problems: estimating solvent losses, predicting vapor phase composition, or checking whether a process operates near saturation. The Antoine equation itself gives saturation pressure only. The partial pressure formula depends on the physical assumption around your system. In ideal binary liquid mixtures, multiplying by liquid mole fraction is a common first-pass approach. In gas-phase mixtures, Dalton law translates partial pressure into gas composition and vice versa.
In real production systems, especially those involving polar compounds, electrolytes, high pressure, or strongly non-ideal mixtures, you may need improved models such as NRTL, UNIQUAC, or equations of state. Even then, Antoine remains useful as a reliable base expression for pure component vapor pressure before activity corrections are applied.
Common Mistakes and How to Avoid Them
- Using constants outside valid ranges: coefficients are range-specific and may produce large error if extrapolated.
- Ignoring pressure units: mmHg, kPa, and bar are not interchangeable without conversion.
- Confusing x and y: x is liquid mole fraction, y is vapor mole fraction.
- Mixing temperature scales: Antoine sets typically use °C, but other equations may use K.
- Assuming ideality everywhere: high concentration or strongly interacting species often need activity coefficients.
Worked Example
Suppose you have ethanol at 60°C in a liquid mixture with x_ethanol = 0.40 and total pressure 101.325 kPa. Using the constants in this page: log10(Psat) = 8.20417 – 1642.89/(230.3 + 60). This gives Psat around 46.8 kPa (after mmHg to kPa conversion). Then partial pressure from Raoult style relation is p = x * Psat = 0.40 * 46.8 = 18.7 kPa. Vapor mole fraction is y = p/P_total = 18.7/101.325 = 0.184. This indicates ethanol contributes about 18.4 percent of the gas phase pressure under the assumed ideal framework.
If the same mixture is heated, Psat rises non-linearly and p rises proportionally for fixed x. This is why small temperature increases can rapidly increase VOC emissions, vent loading, and flammability concern in solvent systems.
Data Quality and Trusted References
For professional work, always source Antoine constants and thermophysical properties from authoritative databases. Good starting points include:
- NIST Chemistry WebBook (.gov)
- NIST ThermoData Engine Antoine Equation Notes (.gov)
- Purdue University Vapor Pressure Learning Resource (.edu)
Cross-checking constants against at least two independent references is a strong quality habit. If your process is safety-critical, document the source, date, temperature range, and unit assumptions used in your calculations.
When to Move Beyond Antoine
Antoine is excellent for pure-component saturation pressure in moderate ranges, but use caution for broad extrapolation, near critical conditions, or high-accuracy design. In those cases, specialized correlations such as Wagner equations, or full property packages in process simulators, provide better consistency. For multicomponent non-ideal systems, combine Antoine with activity coefficient models and verify with measured VLE data when possible.
Final Takeaway
The formula for calculating partial pressure with Antoine is straightforward once the workflow is clear: calculate Psat from temperature, then apply the appropriate partial pressure relationship for your physical model. This page gives you a practical calculator and a repeatable method that is useful for laboratory estimates, process troubleshooting, and early-stage design decisions. If you keep units consistent, stay within constant validity ranges, and validate assumptions about ideality, Antoine-based partial pressure calculations are fast, reliable, and highly actionable.