Antoine Equation Calculator — Vapor Pressure from Temperature
Calculate vapor pressure for a pure substance from temperature using the Antoine equation. This page is designed for chemistry coursework, lab prep, and process work where you need checked constants, unit clarity, and one focused vapor-pressure answer.
Edited by Gail Joyce
Gail Joyce edits core chemistry calculator pages for formula clarity, unit consistency, and practical classroom and lab-use readability.
This calculator page is maintained by the Chemistry Calculators editorial team. The Antoine equation form, constant handling, worked examples, and temperature-range notes on this page are reviewed against standard chemistry and thermodynamics reference material before major updates.
Antoine Equation Calculator
Calculate vapor pressure using the Antoine equation: log₁₀(P) = A - B/(C + T). Enter Antoine constants (A, B, C) and temperature to find vapor pressure.
Use this page for pure-substance vapor pressure work with a valid Antoine constant set. It is not a mixture VLE solver, and its main job is vapor pressure from temperature rather than full boiling-point solving.
How to Use the Antoine Equation Calculator
Work in the same order you would in a vapor-pressure problem: choose a valid constant set, enter temperature with matching units, calculate, and then sanity-check the result against the substance and range you are using.
Choose a substance or enter a checked constant set
Use the quick-select list for common substances or enter your own A, B, and C values from a source such as NIST or a thermodynamics handbook.
Match temperature units to the constants
Enter temperature in the units expected by the constants, usually degrees Celsius, and stay inside the valid temperature range for that constant set.
Select the output pressure unit and calculate
Choose the pressure unit you want to report, then calculate to get the vapor pressure from the Antoine equation without rearranging the log expression by hand.
Review the result against known boiling behavior
Check whether the result makes physical sense for that substance. For example, water near 100°C should be close to 760 mmHg at standard pressure.
Table of Contents
Quickly navigate to different sections of this guide.
Understanding Antoine Equation
Ever wondered how engineers predict when a liquid will boil at different pressures? That's where the Antoine equation comes in. Developed back in 1888 by French engineer Louis Charles Antoine, this handy formula connects vapor pressure to temperature using just three constants (A, B, C) that are unique to each substance. What makes it special? It's accurate enough for real-world engineering work, yet simple enough that you don't need a supercomputer to run the calculations.
Here's why this matters: vapor pressure tells you when liquids boil, how efficiently distillation works, and how substances behave in different phases. The Antoine equation gives you reliable vapor pressure predictions over moderate temperature ranges—usually about 50-100°C wide. That sweet spot covers most practical applications, from designing distillation columns to predicting boiling points. Best part? It strikes a perfect balance between accuracy and simplicity, which is why it's still the go-to method after over 130 years.
While it's based on the Clausius-Clapeyron equation, Antoine's version uses empirical constants that come from real experimental data. You'll find these constants (A, B, and C) listed in databases like NIST for thousands of compounds. Researchers fit these constants to match actual vapor pressure measurements, and sometimes you'll find multiple sets for the same substance—each optimized for a different temperature range.
One crucial thing to remember: each set of constants only works within a specific temperature range. Go outside that range, and your results start getting unreliable. That's why checking the valid temperature range matters—it's the difference between accurate predictions and numbers that look right but are actually way off. Whether you're sizing a distillation column or figuring out evaporation rates, getting vapor pressure right is essential, and our calculator takes the math headaches out of it.
You'll see the equation written in different ways depending on what units and logarithm base someone prefers. The most common version uses base-10 logarithms with pressure in mmHg and temperature in °C, but you might also run into versions using natural logs or different units (kPa, bar, Kelvin, etc.). Whatever form you use, make absolutely sure your constants match your units—mixing them up is a surefire way to get completely wrong answers.
Key Concepts
Vapor Pressure
The pressure exerted by a vapor in equilibrium with its liquid phase at a given temperature. Higher temperatures increase vapor pressure.
Boiling Point
The temperature at which vapor pressure equals atmospheric pressure. The Antoine equation can predict boiling points at different pressures.
Temperature Range
Each substance has a valid temperature range for its Antoine constants. Outside this range, accuracy decreases significantly.
Common Antoine Constants (for log₁₀(P) = A - B/(C + T), P in mmHg, T in °C)
| Substance | A | B | C | Temp Range (°C) |
|---|---|---|---|---|
| Water | 8.07131 | 1730.63 | 233.426 | 1-100 |
| Ethanol | 8.11220 | 1592.86 | 226.184 | -2 to 100 |
| Benzene | 6.90565 | 1211.033 | 220.790 | -36 to 81 |
| Methanol | 8.08097 | 1582.271 | 239.726 | -14 to 65 |
| Acetone | 7.02447 | 1161.0 | 224.0 | -59 to 56 |
| Toluene | 6.95464 | 1344.8 | 219.48 | -27 to 111 |
| Hexane | 6.87776 | 1171.53 | 224.366 | -49 to 69 |
| Heptane | 6.90240 | 1268.636 | 216.432 | -25 to 98 |
| Octane | 6.92374 | 1355.126 | 209.517 | -13 to 126 |
| Chloroform | 6.95464 | 1170.875 | 226.448 | -35 to 62 |
Note: Constants are from NIST Chemistry WebBook. Always verify constants match your temperature range and units.
Formulas and Equations
The Antoine Equation Calculator uses the Antoine equation, a semi-empirical correlation derived from the Clausius-Clapeyron equation. Understanding these formulas helps verify calculations and troubleshoot when needed. The equation provides accurate vapor pressure predictions over moderate temperature ranges for pure substances.
Antoine Equation (Base-10 Logarithm Form)
Where P is vapor pressure, T is temperature, and A, B, C are substance-specific constants. This is the most common form, using base-10 logarithms. Pressure is typically in mmHg, temperature in °C.
Physical Meaning: Constant A represents the intercept, B relates to the heat of vaporization, and C is a temperature offset. The term B/(C + T) accounts for the temperature dependence of vapor pressure.
Solving for Vapor Pressure
Raise 10 to the power of (A - B/(C + T)) to get vapor pressure. This is the explicit form used by the calculator.
Calculation Steps: (1) Calculate C + T, (2) Divide B by (C + T), (3) Subtract from A, (4) Raise 10 to this power.
Alternative Forms
The Antoine equation exists in several forms depending on units and logarithm base:
Natural Logarithm Form: ln(P) = A - B/(C + T) (less common, uses natural log)
Different Units: Constants change with units. For kPa: different A, B, C values. For Kelvin: C values differ.
Extended Antoine Equation: Some sources use extended forms with additional terms for wider temperature ranges.
Boiling Point Calculation
To find boiling point at a given pressure, set P equal to that pressure and solve for T:
This requires iterative solution or algebraic manipulation. At standard atmospheric pressure (760 mmHg), this gives the normal boiling point.
Worked Examples
Step-by-step examples demonstrating Antoine equation calculations across various scenarios. These examples cover common applications in chemical engineering, process design, and laboratory work.
Example 1: Water Vapor Pressure at 100°C
Scenario: Calculate vapor pressure of water at 100°C using A=8.07131, B=1730.63, C=233.426 (constants for mmHg and °C).
Solution:
Step 1: Calculate C + T = 233.426 + 100 = 333.426
Step 2: Calculate B/(C + T) = 1730.63 / 333.426 = 5.192
Step 3: Calculate A - B/(C + T) = 8.07131 - 5.192 = 2.879
Step 4: Calculate log₁₀(P) = 2.879
Step 5: Calculate P = 10^2.879 = 757.6 mmHg
Answer: Vapor pressure = 757.6 mmHg ≈ 760 mmHg (1 atm). Water boils at 100°C when P = 760 mmHg (atmospheric pressure), confirming the calculation is correct.
Example 2: Ethanol Vapor Pressure at 25°C
Scenario: Calculate vapor pressure of ethanol at 25°C using A=8.11220, B=1592.86, C=226.184. This is useful for understanding evaporation rates.
Solution:
Step 1: C + T = 226.184 + 25 = 251.184
Step 2: B/(C + T) = 1592.86 / 251.184 = 6.342
Step 3: A - B/(C + T) = 8.11220 - 6.342 = 1.770
Step 4: P = 10^1.770 = 58.9 mmHg
Answer: Vapor pressure = 58.9 mmHg at 25°C. This relatively high vapor pressure explains why ethanol evaporates quickly at room temperature.
Example 3: Benzene Vapor Pressure at 80°C
Scenario: Calculate vapor pressure of benzene at 80°C using A=6.90565, B=1211.033, C=220.790. This is important for distillation design.
Solution:
Step 1: C + T = 220.790 + 80 = 300.790
Step 2: B/(C + T) = 1211.033 / 300.790 = 4.026
Step 3: A - B/(C + T) = 6.90565 - 4.026 = 2.880
Step 4: P = 10^2.880 = 759.0 mmHg
Answer: Vapor pressure = 759.0 mmHg at 80°C. Benzene's normal boiling point is 80.1°C, so this result is consistent with vapor pressure equaling atmospheric pressure at the boiling point.
Example 4: Methanol at 50°C
Scenario: Calculate vapor pressure of methanol at 50°C using A=8.08097, B=1582.271, C=239.726.
Solution:
Step 1: C + T = 239.726 + 50 = 289.726
Step 2: B/(C + T) = 1582.271 / 289.726 = 5.463
Step 3: A - B/(C + T) = 8.08097 - 5.463 = 2.618
Step 4: P = 10^2.618 = 414.7 mmHg
Answer: Vapor pressure = 414.7 mmHg at 50°C. Methanol has a high vapor pressure, making it volatile and requiring careful handling.
Example 5: Comparing Vapor Pressures
Scenario: Compare vapor pressures of water and ethanol at 25°C to understand their relative volatilities.
Solution:
Water (A=8.07131, B=1730.63, C=233.426):
P_water = 10^(8.07131 - 1730.63/(233.426 + 25)) = 10^(8.07131 - 6.696) = 10^1.375 = 23.8 mmHg
Ethanol (from Example 2): P_ethanol = 58.9 mmHg
Ratio: P_ethanol / P_water = 58.9 / 23.8 = 2.47
Answer: At 25°C, ethanol has 2.47 times higher vapor pressure than water. This explains why ethanol evaporates faster and why it can be separated from water by distillation.
Frequently Asked Questions (FAQs)
Got questions? We've got answers. Here are the most common things people ask about the Antoine equation and vapor pressure calculations.
What is the Antoine equation?
It's a formula that connects vapor pressure to temperature: log₁₀(P) = A - B/(C + T). The three constants (A, B, C) are unique to each substance and come from experimental data. French engineer Louis Charles Antoine came up with this back in 1888, and it's still the go-to method today because it's simple, accurate, and works well for most practical applications.
Where do I find Antoine constants?
Your best bets are NIST Chemistry WebBook, the DIPPR database, or Perry's Chemical Engineers' Handbook. You'll also find them in various chemical engineering handbooks and online resources. Here's the catch: constants can vary between sources, so pick one source and stick with it. Always double-check the units (mmHg vs kPa, °C vs K) and make sure you know the valid temperature range.
What units are used in the Antoine equation?
Most commonly, pressure is in mmHg and temperature is in °C, but you'll also see kPa for pressure and Kelvin for temperature. The key thing? Your constants must match your units. If your constants are for mmHg and °C, use mmHg and °C—don't mix and match. Mixing units is a surefire way to get completely wrong answers, so always check your source's unit requirements.
What is the temperature range validity?
Each set of constants works best over a specific temperature range—usually about 50-100°C wide. Go outside that range, and your accuracy starts dropping fast. If you need to work outside the range, look for a different set of constants optimized for your temperature. Extrapolating beyond the valid range can give you errors of 10% or more, so it's worth finding the right constants.
Can I use the Antoine equation for mixtures?
Not directly—the Antoine equation is for pure substances only. For mixtures, you'll need Raoult's law or other vapor-liquid equilibrium models. The idea is to calculate vapor pressure for each component separately using the Antoine equation, then combine them using mole fractions: P_total = Σ(x_i × P_i). Each component gets its own Antoine constants.
How accurate is the Antoine equation?
Within the valid temperature range, you can typically expect accuracy within 1-5% for most compounds. It's most accurate in the middle of the temperature range and starts getting less reliable near the edges. Near the critical point or at very low temperatures, accuracy drops off significantly. For mission-critical applications, always verify against experimental data if possible.
What's the difference between Antoine constants from different sources?
Different sources might give you different constants for the same substance. Why? They could be using different experimental data, different fitting methods, or optimizing for different temperature ranges. The important thing is to use all three constants (A, B, C) from the same source. If you switch sources, test that you get similar results in your temperature range before trusting them.
Can I convert Antoine constants between different unit systems?
Technically yes, but it's tricky and easy to mess up. You're better off finding constants in your desired units directly from a reliable source. If you absolutely must convert, know that A changes with pressure units, B changes with both pressure and temperature units, and C changes with temperature units. Unless you're really confident with the math, stick to finding constants in the units you need.
How do I calculate boiling point using the Antoine equation?
Set vapor pressure equal to your operating pressure and solve for temperature: T = B/(A - log₁₀(P)) - C. For standard atmospheric pressure (760 mmHg), this gives you the normal boiling point. Most of the time, you'll need to solve this iteratively or use numerical methods. Some calculators can handle this automatically, but it's more complex than just calculating vapor pressure from temperature.
What should I do if my temperature is outside the valid range?
First, see if you can find constants for a different temperature range that covers your needs. Many substances have multiple sets of constants for different ranges. If that doesn't work, consider alternative equations like the Wagner equation or extended Antoine equation. As a last resort, go straight to experimental data. Whatever you do, don't extrapolate beyond the valid range—you'll get unreliable results.
Common Mistakes and How to Avoid Them
We've all been there—you run a calculation and something just doesn't look right. Here are the most common slip-ups people make with the Antoine equation, plus how to dodge them:
Mistake 1: Mixing Units
This is probably the #1 mistake. Using constants meant for mmHg and °C with values in kPa and Kelvin will give you completely wrong results—we're talking orders of magnitude off. How to avoid it: Before you even start, check what units your constants expect. If they're for mmHg and °C, stick with mmHg and °C throughout. Convert everything upfront if you need different units.
Mistake 2: Using Temperature Outside Valid Range
Those constants aren't magic—they only work well within a specific temperature range. Push beyond that range, and your accuracy tanks. We're talking errors of 10% or more, which can completely mess up your design calculations. How to avoid it: Always check the temperature range that comes with your constants. If your temperature is outside that range, hunt down constants optimized for your temperature instead of forcing it.
Mistake 3: Mixing Constants from Different Sources
Grabbing constant A from NIST, B from Perry's, and C from some random website? Bad idea. Those three constants are fitted together as a set, so mixing and matching gives you garbage results. How to avoid it: Get all three constants (A, B, C) from the same source and make sure they're for the same temperature range. Don't cherry-pick—use the complete set.
Mistake 4: Using the Equation for Mixtures
The Antoine equation is built for pure substances. Toss a mixture at it directly, and you'll get nonsense. How to avoid it: For mixtures, calculate vapor pressure for each component separately using the Antoine equation, then combine them using Raoult's law or another vapor-liquid equilibrium model. Each component needs its own set of Antoine constants.
Mistake 5: Wrong Logarithm Base
Using natural log (ln) when your constants expect base-10 log (log₁₀), or vice versa, will give you completely wrong answers. How to avoid it: Check what logarithm base your constants use. Most sources use log₁₀, but some use natural log. If you're not sure, look it up—your source should tell you.
References and Further Reading
For more information about the Antoine equation:
| Resource | Description | Category |
|---|---|---|
| NIST | Thermodynamic databases with Antoine constants | Official |
| LibreTexts Chemistry | Open chemistry reference material covering vapor pressure, phase equilibrium, and thermodynamic relationships | Educational |