Dec., 1954
THERMODYNAMIC FORMATION CONSTANTS OF COORDINATED COMPOUNDS
can be made, but the calculated values do appear to be reasonable. By applying the treatment to other systems, it may be possible to classify them accord-
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ing to certain models, e.g., a radiation and conduction model or a conduction only model. Work of this type is planned.
STUDIES ON COORDINATION COMPOUNDS. XII. CALCULATION O F THERMODYNAMIC FORMATION CONSTANTS AT VARYING IONIC STRENGTHS1 BY REEDM. IZATT, CHARLES G. HAAS,JR.,B. P. BLOCK AND W. CONARD FERNELIUS Contribution from the College of Chemistry and Physics, The Pennsylvania State University, State College, Pa. Received June 16, 1864
Molarity quotients determined potentiometrically a t varying ionic strengths have been converted to stepwise thermodynamic formation constants in aqueous solution for the reactions of Zn++, Ni++, Cea+, and Pr3+(as the perchlorates) with the acetylacetonate ion a t 30” by means of activity coefficients calculated from the Debye-Huckel equation. Agreement of the several thermodynamic constants calculated for each metal ion is good. The molarity quotients in the lit,eraturefor the Pb++-citrates and the Cu++-, Ni++-, Cd++-, and Mg++-malonate4 systems may be satisfactorily converted to thermodynamic constants by the same procedure.
Introduction Much of the quantitative work in the determination of formation “constants” of coordination compounds has been done in solutions containing a large excess of neutral salt, which was added to maintain the activity coefficients of the various species constant throughout the determination. This procedure allows comparisons to be made among different metal ions, if the same medium is employed in each case. Unfortunately, however, work on different coordination systems has been done a t various ionic strengths and often with different anions. It would be more desirable if the “constants” were true thermodynamic constants and therefore theoretically comparable. The present investigation was undertaken to determine for a given chelating agent, the acetylacetonate ion, the practicability of obtaining thermodynamic constants by correcting molarity quotients with theoretically calculated activity coefficients. The data obtained also indicate the range of ionic concentration in which such a calculation procedure yields concordant values. A further object of the investigation was to illustrate the desirability of the use of the method by applying it to data for molarity quotients already available in the literature and noting the agreement obtained. Theoretical.-The calculation of thermodynamic formation constants requires that the activity coefficient term of equation 1 be known.
where K f = the thermodynamic formation constant,
Qr = the molarity quotient y = the molar activity coefficient of the ionic species, a s indicated, present in the soln. x and y refer to the number of ligands, Ch, attached to Mn+ and the charge on the ligand, respectively
It may be learned by (i) making determinations (1) From a dissertation presented by Reed M . Izatt in partial fulfillment of the requirements for the degree of Doctor of Philosophy, August, 1954.
near infinite dilution (as in conductivity methods) , (ii) determining Qf a t several ionic strengths and extrapolating the plot of ionic strength or square root of ionic strength os. Qf to infinite dilution, or (iii) calculating activity coefficients from theoretical relationships (e.g., the Debye-Huckel theory). Procedure (i) yields thermodynamic constants so that no correction is necessary. Procedure (ii) gives accurate values if one is able to determine the &I values a t sufficiently dilute concentrations so that the error involved in the extrapolation from the last point to infinite dilution is minimized. This error is usually large since the curve is steepest at the last points measured. Procedure (iii) eliminates the necessity of making the large number of determinations required to define the curve because the activity coefficients enable one to determine the value of the thermodynamic constant from the molarity quotient a t some concentration, C. Ionic strength is defined by Lewis and Randall2 as 1.1 = ‘/aZmiZi2
Harned and Owen3 give the expression for the activity coefficient of an ion, f j , based on the DebyeHuckel theory as where (a) all terms have their usual significance (for a complete definition of terms see ref. 3) (b) the expression in the parentheses is constant for a given solvent and temperature, and is referred to hereafter as H (c)
r
= 2p
Equation 2, then, makes possible the calculation of the activity coefficient of an ion in dilute solutions. Since the work reported in this paper was performed in fairly concentrated solutions, it was (2) G. N . Lewis and M . Randall, “Thermodynamics and The Free Energy of Chemical Substances,” 1st ed., McGraiv-Hill Book Co., Inc., New York, N. Y . ,1923, pp. 373-74. (3) H. S. Harned and B. B.Owen, “Physical Chemistry of Electrolytic Solutions,” 2nd Ed., Reinhold Publ. Corp., New York, N. Y., 1950, pp. 35-42, equation 3-4-4, 117-121.
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R. M. IZATT, C. G. HAAS,JR.,B. P. BLOCK AND W. C. FERNELIUS
necessary to introduce a term, A , which takes into account the effect of the diameter of the ions on the activity coefficient. This has been done in equation 3, below, which was used to calculate all constants reported in this paper.
Vol. 58
and the temperature was maintained at 30.0 =k 0.1” during the titrations.
Calculations.-The formation molarity quotients were calculated by means of simultaneous equati ons, The thermodynamic dissociation constant of Zj2H fi acetylacetone, K D = (H+)(Ch-)/(HCh), was logfj = (3) l+A
