What is Antoine Equation ?

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Antoine Equation

Antoine equation was developed by a French engineer, Louis Charles Antoine in 1888. The mathematical expression was derived from Clausius-Clayperon equation which describes the relationship between temperature and vapour pressure for pure components.

Antoine Equation

where p is the vapor pressure, T is temperature (in °C or in K according to the value of C) and A, B and C are component-specific constants.

Closely related equation with C set as zero was also developed by Ernest Fedinard August. The August equation can be written as
Antoine Equation_Ernest Fedinard August Eqution
The Ernest Fedinard August shows that a linear relationship exits between logarithm of the vapour pressure and the inverse of temperature (you can compare this with the Arrhenius equation). Values of the constants, A, B and C for water and ethanol are given in Table below.

Parameterisation for T in °C and P in mmHg
A B C T min. (°C) T max. (°C)
Water 8.07131 1730.63 233.426 1 100
Water 8.14019 1810.94 244.485 99 374
Ethanol 8.20417 1642.89 230.300 −57 80
Ethanol 7.68117 1332.04 199.200 77 243

The Antoine equation can also be transformed in a temperature-explicit form with simple algebraic manipulations:
Antoine Equation_Ernest Fedinard August Eqution

The normal boiling point of ethanol is 78.32°C. Calculate the expected atmospheric pressure in mm/Hg by using the Antoine equation.

From the above Table,
When A = 8.20417, B = 1642.89, C = 230.300 and T = 78.32°C
Pressure from Antoine equation
P = 10(A − (B / (C + T)))
P = 760 mmHg.
Similarly,
When A = 7.68117, B = 1332.04, C = 199.200 and T = 78.32°C
P = 761 mmHg.

Use the Antoine equation and the data given in the above table, calculate the normal boiling point of water.


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