ANTOINE CONSTANTS: FORMULAS, EQUATIONS, EXAMPLES - PHYSICAL - 2025

The constants Antoine are three parameters that appear on an empirical relationship between saturation vapor pressure and temperature for pure substances. They depend on each substance and are assumed to be constant in a certain range of temperatures.

Outside of that range, Antoine's constants change their value. The constants are related by an equation created in 1888 by the French engineer Louis Charles Antoine (1825–1897).

Figure 1. Vapor pressure as a function of temperature. Source: wikimedia commons

Formulas and equations

The most common way to express the Antoine function is:

In this formula P represents the saturation vapor pressure expressed in millimeters of mercury (mmHg), T is the temperature that has been the independent variable and is expressed in ℃.

A, B and C are the constants or parameters of Antoine's formula.

The importance of this formula, which despite being empirical, gives a simple analytical expression that can be easily used in thermodynamic calculations.

Antoine's formula is not unique, there are more precise expressions that are extensions of this formula, but with the disadvantage that they have six or more parameters and their mathematical expression is more complex, which makes them impractical to use in thermodynamic calculations.

Saturation steam

Since Antoine's formula measures saturation vapor pressure, it is necessary to explain what it consists of.

A liquid is placed in a glass ampoule or other container. All air is removed from the blister. The assembly is placed in a thermal bath until equilibrium is reached.

At the beginning everything is liquid, but because there is a vacuum, the faster molecules begin to leave the liquid forming a gas of the same substance as the liquid.

The previous process is evaporation and as it occurs the vapor pressure increases.

Some of the vapor molecules lose energy and rejoin the liquid phase of the substance, this is the condensation process.

Then two processes occur simultaneously, evaporation and condensation. When an equal number of molecules come out of the liquid to which they are incorporated into it, a dynamic equilibrium is reached and at this moment the maximum vapor pressure known as saturation pressure occurs.

It is this vapor saturation pressure that Antoine's formula predicts for each substance and each temperature.

In some solids a similar phenomenon occurs when going from the solid to the gaseous phase directly without going through the liquid phase, in these cases a saturation vapor pressure can also be measured.

It is not easy to establish a theoretical model starting from first principles since changes in molecular kinetic energy are involved, which can be of the translational, rotational and vibrational type, with the internal energy of molecular bonding. It is for this reason that in practice empirical formulas are used.

How are Antoine's constants calculated?

There is no theoretical method to obtain Antoine's constants, since it is an empirical relationship.

They are obtained from the experimental data of each substance and adjusting the three parameters A, B and C, so that they minimize the quadratic difference (least squares method) of the prediction with the experimental data.

For the end user, who are generally chemical engineers, there are tables in the chemistry manuals where these constants are given for each substance indicating the maximum and minimum temperature ranges in which they are applicable.

There are also available online services that give the values ​​of the constants A, B and C as is the case of DDBST GmbH Onlines Services.

For the same substance there may be more than one valid temperature range. Then depending on the working range, one or another group of constants is chosen.

Difficulties may appear if the working range of temperatures is between two ranges of validity of the constants, due to the fact that the pressure predictions of the formula do not coincide in the boundary zone.

Examples

Example 1

Find the vapor pressure of water at 25 ℃.

Solution

Let's first calculate the exponent: 1.374499

P = 10 ^ 1.374499 = 23.686 mmHg = 0.031166 atm

Results analysis

These results are interpreted like this:

Suppose pure water is placed in an airtight container from which air has been removed by a vacuum pump.

The container with the water is placed in a thermal bath at a temperature of 25 ℃ until it reaches thermal equilibrium.

The water in the hermetic container partially evaporates until it reaches the saturation vapor pressure, which is nothing other than the pressure at which the dynamic equilibrium between the liquid phase of water and the vapor phase is established.

That pressure in this case turned out to be 0.031166 atm at 25 ℃.

Example 2

Find the vapor pressure of water at 100 ℃.

Solution

We consult the tables to determine Antoine's constants. There are two ranges for water:

Between 1 ℃ and 100 ℃ and between 99 ℃ up to 374 ℃.

In this case, the temperature of interest is in both ranges.

We use the first of the ranges

A = 8.07131

B = 1730.63

C = 233.426

P = 10 ^ (8.07131 - 1730.63 / (100 + 233.426))

Exponent calculation

Let's first calculate the exponent: 2.8808

P = 10 ^ 1.374499 = 760.09 mmHg = 1,0001 atm

Next we use the second of the ranges

In this case the constants are

A = 8.14019

B = 1810.94

C = 244.485

P = 10 ^ (8.14019 - 1810.94 / (100 + 244.485))

Let's first calculate the exponent: 2.88324

P = 10 ^ 2.88324 = 764.2602 mmHg = 1.0056 atm

There is a percentage difference between the two results of 0.55%.

References

1. Application of the laws of Raoult and Dalton and of Antoine's equation. Recovered from: misapuntesyantación.wordpress.com
2. Antoine's formula online calculator. Recovered from: ddbonline.ddbst.de/AntoineCalculation/AntoineCalculationCGI.exe
3. Gecousb. Thermodynamics and steam tables / Antoine's constants. Recovered from: gecousb.com.ve
4. Thermal properties of matter. Recovered from: webserver.dmt.upm.es
5. Yaws and Yang. Antoine's constant tables for over 700 organic compounds. Recovered from: user.eng.umd.edu
6. Wikipedia. Antoine's equation. Recovered from wikipedia.com
7. Wikipedia. Clausius-Clapeyron equation. Recovered from wikipedia.com
8. Wisniak J. Historical development of the vapor pressure equation from dalton to antoine. Recovered from: link.springer.com