Antoine equation

Antoine equation describes the functional relationship between the temperature and the saturation vapor pressure of pure substances and is derived by the Clausius -Clapeyron equation.

  • 3.1 Example calculation

The equation

Today common form

With

  • P: pressure, usually given in mmHg
  • T: temperature, usually given in ° C
  • A, B, C, empirical, material-specific parameters.

The simplified form with

Ie August- equation after the German physicist Ernst Ferdinand August ( 1795-1870 ). Describes a purely linear relationship between the logarithm of the pressure and the reciprocal of the temperature, while the Antoine equation may already describe a curvature of this curve.

Temperature - explicit form

The Antoine equation can be rearranged so that the temperature can be calculated as a function of pressure:

Original equation

Antoine used the form

It turns out that the conversions

The form used today corresponds to the original equation.

With the given values ​​for benzene by Antoine Aorig = 1.1650, D = 5.8524 and C = 216 is obtained for 80 ° C, a vapor pressure of benzene to

And thus approximately atmospheric pressure.

Scope

The Antoine equation can not describe the overall saturation vapor pressure curve between the triple point and the critical point correctly with its three parameters. Therefore, in most cases two sets of parameters for a component to be used. As a rule, a set of parameters below the normal boiling point is valid and a second for the range from the normal boiling point to the critical point. Since then result in inconsistencies at the crossing point, the application of the Antoine equation is no longer appropriate today.

  • Typical deviation of a parameter adjustment over the entire range (experimental data for benzene )

Deviation of an adaptation of the Antoine equation (3 parameters )

Deviation of an adaptation of the DIPPR 101 equation (4 parameters)

Examples

[ p] = mmHg

Example calculation

For ethanol, the normal boiling point is tB = 78.32 ° C. Thus, the following statement:

Units

The coefficients of the Antoine equation are usually given in mmHg and ° C - even today, where the unit system SI is preferred and thus the pressure unit Pascal and the temperature unit Kelvin. The use of the pre- SI units shall have exclusive historical reasons and comes directly from Antoine's original publication.

However, it is easy to convert the Antoine parameters in other pressure and temperature units. To change from degrees Celsius Kelvin, 273.15 be subtracted from the C parameters. To change from millimeters of mercury to Pascal, it is sufficient hinzuzuaddieren the decadic logarithm of the factor between the units to the output parameter:

( 101325 Pa 760 mmHg)

The parameters in ° C and ethanol mmHg

Be converted for K and Pa to

The first Calculation example for TB = 351.47 K to

A similar simple transformation can be used when the decadal to be exchanged for the natural logarithm. It is sufficient to multiply the parameters A and B ln ( 10) = 2.302585.

The sample calculation with the converted parameters (for K and Pa)

Will

( The small differences in the results are driven solely by the limited accuracy of the coefficients used. )

Extensions of the equation

To circumvent the limitations of the Antoine equation, there are simple extensions to further terms.

The other parameters to increase the flexibility of the equations, and thus allow for the description of the entire steam pressure of the triple point curve to the critical point. Moreover, the equations to the original extended Antoine equation by setting of the other parameters D, E and F can be reduced to 0.

A difference to the original form is also that the extended equations use the exponential function and the natural logarithm. However, this has no effect on the equation form.

Swell

  • NIST Chemistry WebBook
  • Dortmund Data Bank
  • Various reference books and publications, for example, Lange's Handbook of Chemistry, McGraw -Hill Professional
  • I. Wichterle, J. Linek, " Antoine Vapor Pressure Constants of Pure Compounds"
  • Yaws CL, Yang H.-C., " To Estimate Vapor Pressure Easily. Antoine Coefficients Relate Vapor Pressure to Temperature for Almost 700 Major Organic Compounds ", Hydrocarbon Processing, 68 (10 ), pages 65-68, 1989
69762
de