Mixed heat

The heat of mixing h ^E (also referred to as mixing enthalpy or excess enthalpy ) is the heat that occurs when pure chemical substances are mixed :

• If the mixed heat is absorbed by the mixed substances from the environment , it is an endothermic course. ${\displaystyle \left(h^{E}>0\right)}$
• If the mixed heat is given off by the mixed substances to the environment , it is an exothermic course ${\displaystyle \left(h^{E}<0\right)}$

In this article, the symbol h ^E refers to the molar heat of mixing, i.e. H. the heat of mixing per amount of substance .

Examples

Depending on the mixing partner, the mixing of chloroform can be exothermic or endothermic (all examples for approx. 25 ° C.):

• Mixing with tetrahydrofuran is highly exothermic (about -2800 J / mol ).
• Mixing with ethanol takes place depending on the selected amount of source substance
  • either exothermic (20 mol% chloroform and 80 mol% ethanol: about -650 J / mol)
  • or endothermic (20 mol% ethanol and 80 mol% chloroform: approx. +400 J / mol)
• Mixing with cyclohexane is endothermic (approx. +700 J / mol).

• Mixing enthalpies at T = 25 ° C
• 

  Exothermic heat of mixing chloroform /
  tetrahydrofuran

• 

  Exothermic and endothermic heat of mixing chloroform / ethanol

• 

  Endothermic heat of mixing chloroform / cyclohexane

Modeling

Mixture heat curves of binary mixtures at a given temperature can be described with the equations according to Redlich-Kister (RK) and a sum of symmetrical functions (SSF). Both series developments are based on the following simple relationship, which, however, is only sufficiently precise for a few systems:

${\displaystyle {\frac {h^{E}}{x_{1}\cdot x_{2}}}=A}$

With

• ${\displaystyle x_{1}}$, : Molar fractions of the two components ${\displaystyle x_{2}}$
• ${\displaystyle A}$: Constant.

Redlich-Kister

${\displaystyle {\frac {h^{E}}{x_{1}\cdot x_{2}}}=\sum _{i=1}^{n}{A_{i}\left(2x_{1}-1\right)}^{i-1}}$

With

• A _i : adjustable parameter
• n = 1..6 (one to six parameters).

Sum of symmetric functions

${\displaystyle {\frac {h^{E}}{x_{1}\cdot x_{2}}}=\sum _{i=1}^{m}{\frac {A_{i}}{\left({\frac {x_{1}}{a_{i}}}+x_{2}a_{i}\right)^{2}}}}$

With

• A _i , a _i : adjustable parameters
• m = 1..3 (two, four or six parameters).

literature

1. ↑ Excess Enthalpy Data. DDBST GmbH, accessed on March 16, 2017 (English). 
2. ↑ Christensen C., Gmehling J., Rassmussen P., Weidlich U., Holderbaum T., "Heats of Mixing Data Collection", DECHEMA Chemistry Data Series Vol. III., DECHEMA , Frankfurt / M., 1984-1991.
3. ↑ Redlich O., Kister AT, "Algebraic Representation of Thermodynamic Properties and the Classification of Solutions", Ind.Eng.Chem., 40 (2), 345-348, 1948.

See also

• gE models
• Enthalpy of solution
• Activity coefficient
• The Dortmund database also contains mixed heats.