How do you calculate dew point using the Antoine equation?

Rearrange the Antoine equation to solve for temperature: T = B/(A − log₁₀(P*)) − C, using the partial pressure of the condensable vapor as P*. The dew point is the temperature at which that partial pressure equals the saturation vapor pressure, i.e. condensation just begins.

What are Antoine constants for water?

For water (T in °C, P* in mmHg), commonly used Antoine constants are A = 8.07131, B = 1730.63, C = 233.426, valid over roughly 1–100°C. Different reference sources fit slightly different constants, so always confirm the valid range and units before using a set from elsewhere.

What units are used in the Antoine equation?

A, B, and C are regression coefficients fitted together as a package for specific units, most commonly T in °C and P* in mmHg, as used in this calculator. They aren't independent physical quantities, so always check what temperature and pressure units the source of your constants assumes before using them.

Can the Antoine equation be used for mixtures?

Not directly, it gives the vapor pressure of a pure component. For mixtures, you combine each component's Antoine-derived P* with a mixing rule like Raoult's law (or a modified form with activity coefficients for non-ideal systems).

What is the difference between the Antoine equation and Raoult's law?

The Antoine equation calculates a pure-component property, vapor pressure versus temperature. Raoult's law is a mixing rule that uses that vapor pressure, along with liquid composition, to predict phase equilibrium in a mixture.

Why does the Antoine equation only work over a limited temperature range?

The A, B, and C constants are fitted to experimental vapor pressure data over a specific range (26–104°C for Benzene, 1–100°C for Water in this calculator). Different sources also fit constants to different datasets or ranges, so no single "correct" triplet exists, outside its fitted range, a set of constants no longer matches real vapor pressure behavior.

Is the Antoine equation accurate near the critical point?

No. It is a good empirical fit over a moderate sub-critical range but breaks down as pressure approaches critical conditions, where vapor and liquid properties converge and the underlying simplifying assumptions stop holding.

Home/Calculators/Thermo & Air/Antoine Equation

GATE 2025, Q47

Antoine Equation
Calculator

Calculate vapor pressure P* and dew point temperature with step-by-step solutions, aligned with GATE 2025 Chemical Engineering.

Formula

$\log_{10}(P^{*}) = A - \dfrac{B}{C + T}$

Quick Answer

The Antoine equation calculates vapor pressure using log₁₀(P*) = A − B/(C+T), where A, B, and C are substance-specific constants and T is temperature. This calculator solves for vapor pressure instantly for Benzene and Water, the same relationship commonly tested in GATE Chemical Engineering, including dew point problems like GATE 2025 Q47.

Antoine Equation Calculator

$\log_{10}(P^{*}) = A - \dfrac{B}{C+T}$ · Vapor pressure from temperature

Temperature

Valid range: 26–104°C

Antoine Constants — $\log_{10}(P/\text{mmHg}) = A - \dfrac{B}{C + T},\ T\ \text{in} \ °C$

Benzene (26–104°C)

A = 6.90565

B = 1211.033

C = 220.79

Water (1–100°C)

A = 8.07131

B = 1730.63

C = 233.426

How to Use the Antoine Equation Calculator

1
Enter the temperature
Enter the temperature T and select °C or °F.
2
Set the Antoine constants A, B, and C
Select Benzene or Water to load its Antoine constants A, B, and C.
3
Click Calculate
Click the Calculate button to run the Antoine equation.
4
Read the vapor pressure result
Read the resulting vapor pressure P* in mmHg, bar, and kPa, along with the full step-by-step solution.

The GATE 2025 Q47 dew point problem, solved with this calculator, is below, or browse the full GATE ChemE previous year questions collection.

What Is the Antoine Equation?

The Antoine equation, $\log_{10}(P^{*}) = A - \dfrac{B}{C+T}$ , estimates the vapor pressure P* of a pure substance at a given temperature T using three constants, A, B, and C, fitted specifically to that substance. It's one of the most-used correlations in chemical engineering because it turns a property that's expensive to measure experimentally at every temperature into a two-second calculation, accurate to within a percent or so over the range it's fitted for.

Vapor pressure sits at the center of vapor-liquid equilibrium (VLE). In an ideal mixture obeying Raoult's law, the partial pressure a component exerts in the vapor phase equals its liquid mole fraction times its pure-component vapor pressure: $p_i = x_i P_i^{*}$ . That single relationship, combined with an Antoine correlation for P_i*, is what lets you compute bubble points, dew points, relative volatility, and distillation column behavior without ever running an experiment.

This calculator uses Antoine constants for benzene and water sourced from Perry's Chemical Engineers' Handbook, with T in °C and P* returned in mmHg (also converted to bar and kPa). Getting comfortable with this equation, and its constants' units and valid range, pays off directly on the GATE CH paper, where it shows up almost every year in some form.

A laboratory rotary evaporator, used to exploit vapor pressure at reduced pressure to distill a solvent at lower temperature — Vapor pressure in practice: a rotary evaporator lowers the system pressure so the solvent's vapor pressure reaches ambient at a much lower temperature. Walter Grassroot, Public domain, via Wikimedia Commons.

Derivation: From Clausius-Clapeyron to Antoine

The Antoine equation isn't arbitrary, it's a refinement of the Clausius-Clapeyron equation, which comes from equating the Gibbs free energy of the liquid and vapor phases at equilibrium:

\dfrac{dP}{dT} = \dfrac{\Delta H_{vap}}{T\,\Delta V}

Assuming the vapor behaves as an ideal gas and V_vapor ≫ V_liquid (so ΔV ≈ V_vapor = RT/P), this becomes $\dfrac{dP}{dT} = \dfrac{\Delta H_{vap}\,P}{RT^2}$ . Separating variables and integrating with ΔH_vap treated as constant gives the simple Clausius-Clapeyron form:

\ln(P^{*}) = -\dfrac{\Delta H_{vap}}{RT} + \text{constant}

This predicts a straight line when ln(P*) is plotted against 1/T, and real data roughly follows that trend, but not closely enough for engineering accuracy. The problem is that ΔH_vap actually decreases as temperature rises (it hits zero at the critical point), so the "constant ΔH_vap" assumption breaks down over any meaningful temperature span.

Antoine's fix was empirical rather than theoretical: replace T with (T+C) in the denominator. This third constant acts as a temperature offset that absorbs most of the curvature Clausius-Clapeyron misses, without requiring a more complex functional form. The result fits real vapor pressure data to within about 1% over a substance-specific range (typically spanning its normal boiling point), which is why every A, B, C triplet only works over the range it was regressed against.

The Vapor Pressure Curve

Plotted rather than just stated: how sharply P* climbs with temperature, and exactly where it crosses 760 mmHg, the normal boiling point, computed live from the same equation above.

log₁₀P = A − B/(C+T) plotted over water's fitted range — vapor pressure climbs far faster than linearly with temperature, which is the whole reason boiling at 20°C takes real effort.

When You'll Need It in GATE Chemical Engineering

The Antoine equation rarely appears as a standalone question, it's usually the tool a bigger problem needs you to reach for:

Dew point / bubble point problems, finding the temperature or pressure at which a vapor starts condensing or a liquid starts boiling requires P_i* at the unknown condition, which means solving the Antoine equation (often iteratively, since T appears on both sides once you're solving for temperature).
Raoult's law and VLE problems, any y-x-T-P relationship for an ideal binary system reduces to Antoine equations for each component plus $p_i = x_i P_i^{*}$ .
Distillation, relative volatility ( $\alpha = P_A^{*}/P_B^{*}$ ) and McCabe-Thiele-style equilibrium curves are built directly from Antoine-derived vapor pressures.
Humidity and psychrometry, dew point of moist air, wet-bulb temperature, and humidity chart calculations all require the vapor pressure of water at various temperatures, exactly the GATE 2025 Q47 style of question.

Three Fully Worked Examples

Example 1: Dew Point from Absolute Humidity

Problem: Moist air has an absolute humidity of 0.02 kg water/kg dry air at 1 bar total pressure. Find the dew point temperature.

Given: H = 0.02 kg/kg dry air, P = 1 bar = 750.062 mmHg, M_water = 18, M_air = 29, Antoine (water): A=8.07131, B=1730.63, C=233.426.

Approach: Convert humidity to a mole fraction, get the partial pressure of water, then invert the Antoine equation to solve for T, the dew point is where the current partial pressure of water equals its saturation pressure.

n_{water} = \dfrac{0.02}{18} = 0.001111\ \text{mol}, \quad n_{air} = \dfrac{1}{29} = 0.034483\ \text{mol}

y_{water} = \dfrac{0.001111}{0.001111+0.034483} = 0.03122

p_{water} = 0.03122 \times 750.062 = 23.41\ \text{mmHg}

\log_{10}(23.41) = 1.3696

T = \dfrac{B}{A - \log_{10}P^{*}} - C = \dfrac{1730.63}{8.07131 - 1.3696} - 233.426 = 258.23 - 233.43

Answer: T_dew ≈ 24.8°C (298.0 K)

Example 2: Bubble Point Pressure, Benzene-Toluene Mixture

Problem: A liquid mixture is 40 mol% benzene, 60 mol% toluene at 90°C. Find the bubble point pressure and vapor composition.

Given: x_B = 0.4, x_T = 0.6, T = 90°C. Antoine (benzene): A=6.90565, B=1211.033, C=220.79. Antoine (toluene): A=6.95464, B=1344.800, C=219.482.

Approach: At the bubble point, total pressure equals the sum of Raoult's law partial pressures: P = x_B·P_B* + x_T·P_T*.

P_B^{*} = 10^{(6.90565 - 1211.033/310.79)} = 10^{3.0090} = 1020.7\ \text{mmHg}

P_T^{*} = 10^{(6.95464 - 1344.8/309.482)} = 10^{2.6092} = 406.7\ \text{mmHg}

P = 0.4(1020.7) + 0.6(406.7) = 408.3 + 244.0

Answer: P ≈ 652.3 mmHg (0.870 bar, 87.0 kPa), y_benzene ≈ 0.626

Example 3: Water Vapor Pressure Applied in Raoult's Law

Problem: Find the vapor pressure of pure water at 60°C, then find water's partial pressure above a solution where its liquid mole fraction is 0.9.

Given: T = 60°C, x_water = 0.9, Antoine (water): A=8.07131, B=1730.63, C=233.426.

\log_{10}(P^{*}) = 8.07131 - 1730.63/293.426 = 8.07131 - 5.8977 = 2.1736

P^{*} = 10^{2.1736} = 149.1\ \text{mmHg}\ (19.88\ \text{kPa})

p_{water} = x_{water} \times P^{*} = 0.9 \times 149.1

Answer: P* = 149.1 mmHg (19.9 kPa); p_water ≈ 134.2 mmHg (17.9 kPa)

Common Mistakes GATE Students Make

°C vs K mix-ups. These Antoine constants are fit for T in °C. Plugging in Kelvin directly (a very easy slip under exam pressure) throws the answer off by hundreds of degrees in the denominator, always check what temperature unit a specific A/B/C set expects.
Extrapolating past the valid range.Benzene's constants here are only valid 26–104°C, water's 1–100°C. The equation still returns a number outside that range, it just won't be accurate, and nothing warns you.
Confusing dew point with bubble point. Bubble point (liquid → first vapor) uses $\sum x_i P_i^{*} = P$ . Dew point (vapor → first liquid) uses $\sum \dfrac{y_i P}{P_i^{*}} = 1$ . Using the wrong summation is one of the most common VLE errors on GATE.
Silent unit mismatches.These constants output mmHg. Forgetting to convert before comparing against a pressure given in kPa or bar, or before using it in a formula that expects SI units, produces answers off by a constant factor that's easy to miss.

Key Takeaways

$\log_{10}(P^{*}) = A - \dfrac{B}{C+T}$ is an empirical refinement of Clausius-Clapeyron, with C added purely to improve curve fit.
Each A/B/C set is only valid over the temperature range it was regressed against, check that range before trusting an answer.
Match temperature and pressure units exactly to what the constants expect (commonly °C and mmHg).
Dew point uses a vapor-phase summation; bubble point uses a liquid-phase summation, don't swap them.
For mixtures, Antoine gives you P_i*; Raoult's law (or a non-ideal extension) turns that into phase equilibrium behavior.

GATE 2025, Validate Your Answer

Q47 uses the Antoine equation directly. Pre-filled with GATE values, click Calculate to verify.

Q47Antoine Equation★ Antoine2m · Psychrometry

Moist air has an absolute humidity of 0.02 kg moisture/kg dry air at 1 bar. MW_water = 18, MW_air = 29. Using the Antoine equation for water, find the dew point temperature.

Answer: ≈ 26°C (299 K) $T = \dfrac{B}{A - \log_{10}P} - C$

Frequently Asked Questions

Whenever a problem needs vapor pressure at a specific temperature rather than just at the normal boiling point, dew/bubble point calculations, distillation relative volatility, Raoult's law VLE, humidity and psychrometry, all of them start here, including GATE 2025 Q47. See the derivation below for why this particular curve fit became the default over the more rigorous alternative.

Further reading: The Antoine Equation, Explained

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How to Use the Antoine Equation Calculator

What Is the Antoine Equation?

Derivation: From Clausius-Clapeyron to Antoine

The Vapor Pressure Curve

When You'll Need It in GATE Chemical Engineering

Three Fully Worked Examples

Example 1: Dew Point from Absolute Humidity

Example 2: Bubble Point Pressure, Benzene-Toluene Mixture

Example 3: Water Vapor Pressure Applied in Raoult's Law

Common Mistakes GATE Students Make

Key Takeaways

GATE 2025, Validate Your Answer

Frequently Asked Questions

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Derivation: From Clausius-Clapeyron to Antoine

The Vapor Pressure Curve

When You'll Need It in GATE Chemical Engineering

Three Fully Worked Examples

Example 1: Dew Point from Absolute Humidity

Example 2: Bubble Point Pressure, Benzene-Toluene Mixture

Example 3: Water Vapor Pressure Applied in Raoult's Law

Common Mistakes GATE Students Make

Key Takeaways

GATE 2025, Validate Your Answer

Frequently Asked Questions

Related

Mass Transfer

Psychrometric Calculator

GATE CH Formula Sheet

GATE Practice Tests by Year

Antoine Equation
Calculator