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Antoine Equation Vapor Pressure Calculator

Calculate the exact vapor pressure of pure liquids at specific temperatures using the Antoine Equation. Essential for chemical engineering, distillation, and HVAC refrigerant mechanics.

Antoine Equation Vapor Pressure Calculator

The Antoine Equation predicts the saturated vapor pressure of a pure liquid at any temperature using three empirically-derived constants (A, B, C) specific to each chemical compound. When vapor pressure equals atmospheric pressure, the liquid boils.

Fluid Presets (NIST Antoine Constants)

log10 intercept

slope numerator

offset (°C)

log₁₀(P) = A − B/(C + T_C) = 8.07131 − 1730.63/(233.426 + 20.00) = 8.07131 − 1730.63/253.43 = 1.24237
P = 10^1.24237 = 17.473 mmHg
Vapor Pressure
17.473
mmHg
Atmospheres
0.02299
atm
Kilopascals
2.3296
kPa
PSI
0.33788
psi
Predicted normal boiling point (P=760 mmHg): 100.0°C— Moderate volatility
Vapor Pressure vs. Temperature (Current Constants)
-10°C
2.12 mmHg
0°C
4.54 mmHg
20°C
17.47 mmHg
50°C
92.30 mmHg
100°C
760.09 mmHg

Practical Example

A chemical engineer calculates the vapor pressure of water at 100°C to confirm the standard boiling point:

log₁₀(P) = 8.07131 − 1730.63 / (233.426 + 100) = 8.07131 − 1730.63/333.426 = 8.07131 − 5.1906 = 2.8807
P = 10^2.8807 = 759.5 mmHg ≈ 760 mmHg = 1.000 atm.

This confirms that at exactly 1 atmosphere of pressure, water begins to boil at precisely 100°C — the vapor pressure equals the atmospheric pressure, and the liquid-to-gas phase transition occurs throughout the bulk of the liquid (boiling), not just at the surface (evaporation). At higher altitudes (e.g., Denver, 0.83 atm), the boiling point drops to approximately 94°C — which is why pasta takes longer to cook in the mountains.

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What is Vapor Pressure, Phase Equilibria, and the Clausius-Clapeyron Equation: Why Liquids Boil?

Vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its liquid phase at a given temperature. Every liquid continuously evaporates from its surface; vapor molecules continuously recondense. At equilibrium, the rate of evaporation equals the rate of condensation — the pressure at this equilibrium is the vapor pressure. When vapor pressure exactly equals external atmospheric pressure, boiling occurs: vapor bubbles form and grow throughout the bulk liquid. This is why boiling point varies with altitude — the external pressure is lower, so the vapor pressure threshold is reached at a lower temperature.

Mathematical Foundation

Antoine Equation — Vapor Pressure from Temperature
log⁡10(P)=A−BC+T∴P=10(A−BC+T)\log_{10}(P) = A - \frac{B}{C + T} \quad \therefore \quad P = 10^{\left(A - \frac{B}{C+T}\right)}
PP= Saturated vapor pressure at temperature T [mmHg]. This is the pressure that the vapor phase of the liquid exerts when the liquid and vapor are in thermodynamic equilibrium (coexisting at the same temperature). Vapor pressure is a purely temperature-dependent property for a given pure substance — it does not depend on the amount of liquid or vapor present. As temperature increases, molecules have more kinetic energy, more escape to the vapor phase, and equilibrium vapor pressure rises exponentially. This exponential temperature dependence is exactly what the Antoine equation captures via the 10^x (exponential) mathematical form.
A,B,CA, B, C= Empirically-determined Antoine constants specific to each pure compound and temperature range. A is a dimensionless intercept constant that scales the overall vapor pressure magnitude. B (units of temperature × log10 pressure) captures the energy barrier for vaporization — proportional to the heat of vaporization. C (units of temperature) is an offset added to temperature to account for the non-ideal behavior of real gases near their boiling points. Antoine constants are tabulated by NIST (National Institute of Standards and Technology) and are valid only within specific temperature ranges — using constants outside their designed range can produce significant errors.
TT= Temperature in Celsius [°C]. CRITICAL: Antoine constants are almost universally tabulated for T in degrees Celsius, not Kelvin or Fahrenheit. Always convert to Celsius before applying the equation. The consequence of using the wrong temperature scale is catastrophic: using T=212 (°F) when the equation expects T=100 (°C) for water's boiling point would compute ln10(P) = 8.07131 − 1730.63/(233.426+212) = 8.07131 − 3.888 = 4.183, giving P = 10^4.183 = 15,241 mmHg — completely wrong. The C+T denominator also prevents evaluation at T = −C, where the equation has a vertical asymptote (undefined). For water, C=233.426, so the denominator is zero at T=−233°C — far below physically meaningful conditions.

Laws & Principles

  • The Boiling Point Principle — When Vapor Pressure Equals Atmospheric Pressure: A liquid boils when its vapor pressure equals the surrounding atmospheric pressure. At sea level (P_atm = 760 mmHg = 1.000 atm = 101.325 kPa), water boils at exactly 100°C — the temperature at which its Antoine equation computes P = 760 mmHg. At Denver's altitude (5,280 ft, P_atm ≈ 630 mmHg = 0.83 atm), water boils at approximately 94°C. At the summit of Mt. Everest (29,032 ft, P_atm ≈ 253 mmHg = 0.33 atm), water boils at only 70°C — too low to cook pasta or safely sterilize water by boiling alone. In a pressure cooker at 2 atm (1,520 mmHg), water boils at 120°C — cooking food significantly faster.
  • Raoult's Law and Vapor-Liquid Equilibrium (VLE) for Mixtures: For an ideal binary mixture, the vapor pressure of each component is reduced by its liquid mole fraction: P_i = x_i × P_i_sat (where P_i_sat is the pure-component vapor pressure from the Antoine equation). The total system pressure is the sum: P_total = x_A × P_A_sat + x_B × P_B_sat. The vapor composition (y_A = x_A × P_A_sat / P_total) is always richer in the more volatile component (higher P_sat). This is the thermodynamic foundation of distillation — successive vapor-liquid equilibrium stages (theoretical plates) progressively enrich the vapor in the more volatile component. Industrial distillation columns (petroleum refining, ethanol production, air separation) are all designed from VLE calculations using Antoine equation vapor pressures.
  • The Clausius-Clapeyron Equation — Physical Basis for Antoine's Form: The rigorous thermodynamic relationship between vapor pressure and temperature is given by the Clausius-Clapeyron equation: d(ln P)/dT = ΔH_vap / (R × T²), where ΔH_vap is the latent heat of vaporization and R is the universal gas constant. Integrating this equation with a constant ΔH_vap (ideal gas approximation) gives: ln(P) = A' − ΔH_vap/(R×T). The Antoine equation is a practical semi-empirical improvement: adding the constant C to the denominator accounts for the temperature dependence of ΔH_vap and the non-ideal compressibility of real vapors, significantly extending the valid temperature range without requiring rigorous thermodynamic integration.
  • Temperature Range Validity — When Antoine Constants Break Down: Each set of Antoine constants (A, B, C) is valid only within a specific temperature range defined by NIST. Outside this range: (1) The exponential extrapolation diverges rapidly from reality. (2) The liquid may undergo phase changes that invalidate the equation (solid-liquid transition near the melting point, super-critical conditions near the critical point). (3) For refrigerants near their critical point (high pressure operations), more sophisticated equations of state (Peng-Robinson, Redlich-Kwong-Soave) are required. Always verify that your operating temperature is within the tabulated valid range before trusting the calculation for engineering design.

Step-by-Step Example Walkthrough

" A chemical plant engineer needs to verify the vapor pressure of water at 100°C to confirm it will boil under standard atmospheric conditions before commissioning a steam generator. "

  1. 1. Use NIST Antoine constants for water (1–100°C range): A = 8.07131, B = 1730.63, C = 233.426.
  2. 2. Temperature T = 100°C (already in Celsius — no conversion needed).
  3. 3. Compute denominator: C + T = 233.426 + 100 = 333.426.
  4. 4. Compute log₁₀(P) = 8.07131 − 1730.63 / 333.426 = 8.07131 − 5.1906 = 2.8807.
  5. 5. Compute P = 10^2.8807 = 759.5 mmHg.
  6. 6. Compare to atmospheric pressure: 760 mmHg. Difference: 0.07% — within experimental error.
  7. 7. Conclusion: Water boils at 100°C at 1 atm. The steam generator will function as designed.
  8. 8. Bonus check: At 20°C, P = 10^(8.07131 − 1730.63/253.426) = 10^1.2423 = 17.47 mmHg.
  9. 9. This explains why puddles evaporate at room temperature — the vapor pressure is non-zero.
  10. 10. At −10°C (supercooled water): P = 10^(8.07131 − 1730.63/223.426) = 2.15 mmHg — very low volatility.
Final Result: Vapor pressure of water at 100°C = 759.5 mmHg ≈ 760 mmHg (1.000 atm). Confirmed: water boils at 100°C at sea level. The half-percent error vs. the theoretical 760 mmHg reflects the inherent accuracy of the Antoine equation's temperature range boundary at exactly 100°C.

Quick Answer: What is the Antoine equation and what does it calculate?

The Antoine equation calculates the saturated vapor pressure of a pure liquid at a given temperature: log10(P) = A − B ÷ (C + T), where P is vapor pressure (usually in mmHg) and T is temperature in °C. The three constants A, B, C are substance-specific, empirically fit to experimental data, and tabulated by NIST (National Institute of Standards and Technology) for hundreds of compounds. The equation is the workhorse of chemical engineering vapor-liquid equilibrium (VLE) calculations for distillation design, flash calculations, process safety (flammability limit analysis), HVAC refrigerant cycle sizing, and any application where the boiling/condensation behavior of a pure component must be predicted without running exhaustive experiments.

NIST Antoine Constants — Common Substances Reference

Substance A B C T range (°C) P unit
Water (H2O) 8.07131 1730.63 233.426 1–100 mmHg
Ethanol (C2H5OH) 8.20417 1642.89 230.300 −57 to 80 mmHg
Methanol (CH3OH) 7.87863 1473.11 230.000 −14 to 65 mmHg
Acetone (C3H6O) 7.11714 1210.595 229.664 −32 to 77 mmHg
Benzene (C6H6) 6.87987 1196.76 219.161 8–103 mmHg
Toluene (C7H8) 6.95334 1343.943 219.377 6–137 mmHg
Ammonia (NH3) 7.36050 926.132 240.170 −83 to 60 mmHg
Source: NIST Chemistry WebBook — log10 form. Always verify constants and T range from NIST before engineering use.

Water Boiling Point vs Altitude — Antoine Equation Applied

Location Altitude (ft) Atm Pressure Water Boiling Point
Sea level0760 mmHg (1.00 atm)100.0°C
Denver, CO5,280630 mmHg (0.83 atm)94.0°C
Mexico City7,350585 mmHg (0.77 atm)91.5°C
Quito, Ecuador9,350544 mmHg (0.72 atm)89.2°C
Mt. Everest summit29,032253 mmHg (0.33 atm)70.0°C
Pressure cooker (2 atm)—1,520 mmHg (2.00 atm)120.4°C
Boiling point is where Antoine equation P equals local atmospheric pressure. At Everest, water at 70°C cannot kill pathogens requiring 100°C sterilization.

Pro Tips & Critical Antoine Equation Mistakes

Do This

  • ✓Always verify which logarithm base the tabulated constants were fit to — log10 vs ln (loge). NIST primarily publishes constants for the base-10 form (log10 P = A − B/(C+T)). However, many European chemical engineering textbooks and older Perry’s tables use the natural logarithm form (ln P = A − B/(C+T)). The A, B, C values are completely different between the two forms — applying log10 constants to the ln version overestimates the vapor pressure by a factor of ln(10) = 2.303 in the exponent. For water at 100°C: log10 constants give P = 759.5 mmHg (correct). If mistakenly used with ln: P = 102.8807 × 2.303 exponent shift → catastrophically wrong result.
  • ✓Use compound-specific constants from NIST — never guess or interpolate between substances. Antoine B closely tracks the heat of vaporization (ΔHvap ≈ 2.303 × R × B). For water B = 1730.63 (ΔHvap = 40.7 kJ/mol). For acetone B = 1210.6 (ΔHvap = 30.2 kJ/mol). Benzene and toluene have similar B values not because their molecular weights match, but because their aromatic ring structures give similar C–C bond enthalpies. Never interpolate constants between similar chemicals — a 5% error in B propagates to >10% error in P via the exponential.

Avoid This

  • ✗Don't use °F or Kelvin for T — the constants assume T in °C. NIST Antoine constants are almost universally tabulated with T in °C. Entering T in Kelvin adds 273.15 to the denominator, equivalent to using a wildly incorrect C value. At T = 373.15 K (water’s boiling point in Kelvin) with water’s °C constants in the denominator: log10(P) = 8.07131 − 1730.63/(233.426+373.15) = 8.07131 − 2.853 = 5.218, giving P = 105.218 = 165,000 mmHg — 217× the correct value and physically impossible.
  • ✗Don't extrapolate beyond the NIST-tabulated temperature range. Water’s common constants are valid 1–100°C. At 150°C (above the tabulated range), the extrapolated Antoine answer is 3,568 mmHg — but the true value (from steam tables) is 3,583 mmHg, only 0.4% error in this case. For other substances near their critical temperature, extrapolation can fail catastrophically: accuracy degrades rapidly above ~0.7×Tc (reduced temperature). Always use the NIST extended-range constants for super-atmospheric conditions, or switch to more rigorous equations of state (Peng-Robinson, SRK) for pressures exceeding 10 atm.

Frequently Asked Questions

Why does the Antoine equation use log10 instead of a direct polynomial?

The logarithmic form is physically motivated by the Clausius-Clapeyron equation, which shows that ln(P) varies approximately linearly with 1/T (from thermodynamics: d(ln P)/dT = ΔHvap/(RT2)). Because vapor pressure spans orders of magnitude with temperature (water: 4.6 mmHg at 0°C, 760 mmHg at 100°C, 17,535 mmHg at 200°C), a polynomial in P would require extremely high-order terms to capture this range. The log form compresses the massive range into a nearly linear function, making three constants (A, B, C) sufficient for high accuracy over a 100+°C temperature range — a remarkable feat of curve-fitting efficiency. Direct polynomial fits in P would require 6–8 terms to achieve comparable accuracy.

How is the Antoine equation used in distillation column design?

Distillation design begins with vapor-liquid equilibrium (VLE) calculations to determine the relative volatility α between components: α = PAsat ÷ PBsat, where both Psat values come from the Antoine equation at the column’s operating temperature. For the ethanol-water system at 80°C: PEtOHsat (Antoine) = 760 mmHg, PH2Osat = 355 mmHg, so α = 2.14 (ethanol is 2.14× more volatile than water). The number of theoretical distillation stages needed is then estimated using the Fenske equation (Nmin = log(xD/xB × (1−xB)/(1−xD)) ÷ log(α)). Industrial ethanol production to 95% purity from a 10% feed requires approximately 30–40 theoretical stages.

What is the difference between vapor pressure and partial pressure?

Vapor pressure (Psat, from the Antoine equation) is a pure-component thermodynamic property — the equilibrium pressure of the substance’s vapor over its pure liquid at a given temperature. It depends only on temperature and the identity of the substance, not on the presence of other gases. Partial pressure (pA) is the contribution of component A to the total pressure in a gas mixture: pA = yA × Ptotal, where yA is the vapor mole fraction. For an ideal solution (Raoult’s law), the partial pressure equals the vapor pressure times the liquid mole fraction: pA = xA × PAsat. The distinction matters hugely in process safety: the explosion hazard of a flammable substance depends on its partial pressure (concentration in the gas phase), not its pure vapor pressure — diluting with nitrogen reduces partial pressure even though vapor pressure stays constant.

When should I use the Antoine equation vs more sophisticated equations of state?

Use the Antoine equation for: pure components, subcritical temperatures (T < 0.9 × Tc), pressures below ~50 bar, and vapor fractions between 0 and 1 (two-phase region). Switch to equations of state (Peng-Robinson, SRK, PC-SAFT) when: (1) operating near or above the critical point (supercritical fluids); (2) handling gas mixtures with strong non-ideal interactions (H2, CO2, polar + non-polar mixtures requiring activity coefficient models); (3) pressures exceeding 50–100 bar where compressibility effects are significant; (4) needing liquid-phase density alongside vapor pressure. For HVAC refrigerants (R-134a, R-410a), manufacturer tables or REFPROP (NIST’s reference fluid property software) are preferred over Antoine constants because modern refrigerants are near-critical under typical operating conditions.

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