Thermodynamics of the System InCl 3 -HCl-H 2 O at 25 °C Kenneth S. Pitzer,* ,² Rabindra N. Roy, ‡ and Peiming Wang ² Department of Chemistry and Lawrence Berkeley National Laboratory, UniVersity of California, Berkeley, California 94720, and Hoffman Department of Chemistry, Drury College, Springfield, Missouri 65802 ReceiVed: December 9, 1996 X A comprehensive equation for the thermodynamic properties of the system InCl 3 -HCl-H 2 O at 25 °C in the ion-interaction (Pitzer) equation form is generated on the basis of a very recent and comprehensive array of electrochemical cell measurements of the HCl activity, together with older published measurements of the activity of InCl 3 in mixtures with 0.02 m HCl. Alternate equations with and without explicit consideration of the ion pair InCl 2+ as a separate species are tested. Excellent agreement is obtained on either formulation between calculated and measured activities, although considerable uncertainty remains concerning the standard potential for the In electrode. Suggestions are made for additional experiments to reduce this uncertainty. Introduction Aqueous InCl 3 differs markedly from other M 3+ -Cl - systems such as AlCl 3 , LaCl 3 , etc., in that In 3+ has a strong association with Cl - to InCl 2+ and a very strong tendency to hydrolyze to InOH 2+ . Also, if solid indium is present, possibly as an electrode, the reduction reaction forming In + must be considered. Thus, the thermodynamics of the In 3+ , Cl - ,H 2 O system is both interesting and challenging. By making measurements on the system InCl 3 -HCl-H 2 O the hydrolysis can be controlled or eliminated. Measurements were made and have been reported recently 1 for the electro- chemical cell Published 2,3 values are available for the cell The present paper presents an analysis of all these results in terms of the ion-interaction (Pitzer) equations. 4,5 Since the data for cell b extend only to an ionic strength of 0.33 mol kg -1 , the present equation has limitations for some properties outside of this range, but its refinement is straightforward when cell b is measured at larger molality. And the present range is sufficient to show clearly the tendency toward ion association to InCl 2+ . The results for cell b at the lowest molality are examined for possible deviation arising from the reaction Equilibrium constant values 6,7 reported for the hydrolysis reaction and for the association reaction I are considered in the calculations. Conductance data 8 are also considered and are found to be generally consistent with respect both to ion association and to hydrolysis effects. Several investigators have studied aqueous In 2 (SO 4 ) 3 . 9-12 This system is even more complex with more severe hydrolysis and complexation. Indeed, Leitzke and Stoughton 12 conclude that the species InSO 4 + and In(SO 4 ) 2 - dominate except at extreme dilution. But at high dilution InOH 2+ will be important. Thus, In 3+ may never be the dominant species, and little can be learned about its properties from the sulfate studies. Several structural methods have been applied to aqueous InCl 3. . At high concentration all indicate that the species InCl 2 + with a symmetrical linear structure is dominant. 13,14 Our equations are designed to represent this species, but it is not expected to be important at low concentrations. Equations The ion-interaction equations for a multisolute system as first proposed in 1974 4b and widely used since 5 are adopted. But the exact form to represent the association to InCl 2+ must be considered. If the maximum degree of association is moderate, the method 4c used for MgSO 4 and other +2 sulfates is simple; hence, it was tested and found to be satisfactory. No separate species is introduced, but a specially designed binary interaction term is added. The association is so strong, however, that it seemed worthwhile to make an alternate calculation with InCl 2+ as an explicit species and an equilibrium constant K for formation in reaction I. This pattern has been used for the HSO 4 - ion, along with H + and SO 4 2- in various treatments. 15,16 For the present system, this introduces ion-interaction terms that can indicate the amount of further association to InCl 2 + . Thus, the results of this alternate formulation indicate more clearly the actual proportions of In 3+ , InCl 2+ , and InCl 2 + present at various compositions. Formulation I without InCl 2+ as a Separate Species. For this calculation, the composition is expressed in terms of the unassociated ionic strength and ionic strength fractions as follows: m A ) m(HCl) (1a) m B ) m(InCl 3 ) (1b) I ) m A + 6m B (1c) Y A ) m A /I (1d) Y B ) 6m B /I (1e) The complete equations for ln γ HCl and ln γ InCl3 are given in the Appendix as eqs A1 and A2. For formulation I, all terms ² University of California. ‡ Drury College. X Abstract published in AdVance ACS Abstracts, May 1, 1997. Pt,H 2 |HCl(m A ), InCl 3 (m B ), H 2 O|AgCl,Ag (a) In(s)|HCl(m A ), InCl 3 (m B ), H 2 O|AgCl,Ag (b) In 3+ + Cl - ) InCl 2+ (I) In 3+ + 2In(s) ) 3In + (II) In 3+ + H 2 O ) InOH 2+ + H + (III) 4120 J. Phys. Chem. B 1997, 101, 4120-4126 S1089-5647(96)04026-6 CCC: $14.00 © 1997 American Chemical Society