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.
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
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.
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:
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.