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The relation between the Margules and van Laar equations: The square‐root equation
Author(s) -
Otterstedt J.E. A.,
Missen R. W.
Publication year - 1962
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.5450400105
Subject(s) - thermodynamics , extrapolation , activity coefficient , mole fraction , chemistry , square root , mathematics , physics , organic chemistry , mathematical analysis , geometry , aqueous solution
The excess free energy of mixing (ΔG E ) has been used to show that the Margules and van Laar equations are reciprocally related. Thus if the Margules equation is written as χ G = ΔG E /x 1 x 2 = Σa k x 1 k , then the van Laar equation can be written as χ G −1 = Σb k x 1 k . It is known from previous work that the Margules equation does not adequately represent the thermodynamic properties of solutions of alcohols in non‐polar solvents over the whole range of composition, and it is pointed out that the van Laar equation cannot be used if the excess function changes sign. In such cases the use of a square‐root analogue of the Margules equation, χ G = Σc k x 1 (k‐2)/2 , is proposed. This equation satisfactorily accounts for the rapid increase in χ as the mole fraction of alcohol becomes small and is empirically useful. However, it has theoretical disadvantages; it cannot be used to determine by extrapolation the value of the partial molar excess thermodynamic property for component 1 in an infinitely dilute solution; furthermore, it predicts a violation of the second law in the case of free energy of mixing for solutions dilute in component 1, but the region of violation lies outside the experimental range for x 1 as low as 0.01.