Physics, — "On the Heat of Mixing of Normal and Associating 

 Liquids." By Dr. J. J. van Laar. (Communicated by Prof. 



H. A. LORENTZ). 



{Communicated at the meeting of September 30, 1922). 



1. In connection with a study by J. R. Katz (published in „Ver- 

 slag der Wis- en Natuurk. Afdeeling Kon. Akad. v. Wetensch." 

 Vol. XXXI, nos 5/6, p. 333 — 336) I wish to make a few remarks 

 on the heat of mixing of liquids, also in reference to the quantity 

 ''A' (or «/62). 



Different authors, among others van der Waals and myself, made 

 use of approximations some time ago, which seemed permissible ; 

 but which gave no account, not even in approximation, of the heat- 

 effect, which is sometimes very slight, especially for normal substances. 

 For here the case presented itself that the neglected quantities 

 {{v — by by the side of ?;*, p by that of "1^"^) would give a term of 

 higher order of magnitude in the results than that which results 

 from the not neglected part. The latter term appears to be of the 

 order of magnitude {h^]/a.^ — èl^/a,)^ whereas that of the neglected 

 part — yielding a term with (p -|- "/„a) Av — is of the order 

 b^V^a^ — biY^a^ on account of hv; hence, when the difference of the 

 critical pressures of the components is small, the neglected part 

 will have a much greater value than the not neglected part. 



And besides: While the first part — • referring to the change of 

 the potential energy without reference to the contraction — will 

 always be positive, the second (neglected) part — which is in con- 

 nection with the volume contraction Av — is nearly always n^(/a^2W. 

 In "quasi-ideal" mixtures of two liquids (i.e. liquids the critical 

 pressures of which are about equal), the effect will nearly always 

 be negative (i.e. heat is liberated), and not positive, as the earlier 

 theoretical derivation indicated. In liquids the critical pressures of 

 which are not about equal, sometiuies differ even considerably, it 

 will entirely depend on circumstances (relation of the a's and b's 

 inter se, value of the mixing ratio x) whether the result will be 

 positive or negative. 



In associated components, where Aj; can become much greater 

 than in mixtures of normal components (generally the critical pres- 

 sures also differ much more from each other), the above ratios will 



20 

 Proceedings Royal Acad. Amsterdam. Vol. XXV. 



