STABILITY OF COMPLEX IONSWITH SPECIAL REFERENCE TO HYDRATION
Feb., 1954
121
THE STABILITY OF COMPLEX IONS WITH SPECIAL REFERENCE TO HYDRATION BY R. J. P. WILLIAMS Merton College, Oxford, England Received December 18, 1966
I
The principal factors controlling the stability of complex ions in aqueous solution are discussed. These factors are the charges and sizes of the reacting species and their electronegativities but they cannot be directly related to complex stability without consideration of the heats and entropies of hydration of the reactants and proddcts. Mention is also made of the less important influence of orbital contributions.
The stability of a complex ion in solution is measured by the equilibrium constant, K , for the reaction M(HzO)o
+ L(Hz0)b
ML(Hg0)c
+ + b - c)HzO (U
AFO,
(1)
where M is any metal ion and L is any ligand. (Charges are omitted for convenience.) Many authors have attempted to correlate such experimentally found equilibrium constants with properties of the metal ion involved. I n particular it has been pointed out that there is an empirical relationship between the ionic potential of the cation, z / r , (where r is the radius of the cation and z its charge) and log K for a limited number of simple complexes of the alkaline earth metals'; and that there is also a relationship between the ionization potential, Io2,2of the cation and log K for a large number of complexes of the divalent cations of the first transition series of the elements in the periodic table.a Other more extensive correlations have been suggested also but they are of limited applicability.'~~In order to further clarify the factors affecting the values of K a search of the literature has been made for the corresponding heats and entropies of complex formation. The values found are listed in Table I. The Entropy Changes upon Complex Formation The equilibrium constant for the formation of a complex, K , can be expressed in the form -2.303 RT log K
E.
A P
AHo
-
TAP
(1)
where AFO, A H o and ASo are the standard molar free energy, heat, entropy of formation of the (1) R. J. P. Williams, J . Chem. Soc., 3770 (1952). (2) The ionization potential for the stage M + M + + 2e, Ioz, will be used in this paper aE a rough measure of the electronegativity of a cation.$ Other authors have used the ionization potential for e, IO,^ and t h a t for the stage M + M e, the stage M -+ M I i a , S as measures of the electrou affinity of a divalent ion. It is possible t o defend the choice of IIIon the ground t h a t the charge on the central ion never falls below unity. The choice of I o 1 would appear t o be indefensible. IOZrepresents the total electron affinity of the divalent ion and is therefore the maximum interaction with a ligand by electron exchange-in keeping with Paulibg's theory of the essential neutrality of the central ion in complexes.~ T h e fact t h a t the heat of hydration increases much more slowly than the ionization potential, 1 0 2 , for a series of cations would suggest however t h a t the Pauling theory is incorrect. The use of either l o a or Iia would appear t o be equally admissible a t the present time. (3) H. Irving and R. J. P. Williams, Nature, 172, 746 (1948); Analyst, 7 7 , 813 (1952); J . Chem. Soc. 3192 (1953). (4) W.6. Fyfe, ibid., 2018,2023 (1952). (5) M. Calvin and N. C. Melchior, J. A m . Chem. Soc., 7 0 , 3270 (1948). (6) L. Pauling, "Victor Henri Memorial Volume," Liege, 1948,p. 1. (7) T. 0.Denny a n d C. B. Monk, Trans. Faraday Soc., 47, 992 (1951); C. B. Monk, ibid., 47,297 (1951). (8) D.P.Mellor and L. Maley, Nature, 161,436 (1948).
+
+
+
-
TABLE Is MOLARHEATS A N D ENTROPIESOF THE FORMATION OF COMPLEX IONS IN AQUEOUSSOLUTION
+ +
+
Reaction
kcal.
2c1CUI CNAg' CIAgI 31Ag' 2ssos-AgI 2CNh u l 2CNMg" Sod-Mg'I CHs(CO*)z-Barr S2OS-Znrl CH2(Cot)$-ZnII 4CNCdlI 2CN HgII 2C1Hgrl 3C1HgII 2BrHgII 4BrHgII 41HgT12CNHgT14CNLa1'' SO4-Cr"' OHCrrrI 2 0 H CrIII C1CrIII 2C1Crrrl 2BrU'" OHFell* OzHFerI1 OHFerI1 FFelIr C1Fer'' BrFer" N3FelIr GO4-N P 4CNSnIr OHSnl' C1SnlI BrCd" C1Ma1' 2a" ZnII 4NH3 CUI' 4NH3 N P 6NH3 CO" 6NH3 CdI' 4NH3 Hg'I 4NHa CU' 2a" Ag' 2a" CoTT1 5NH.7
-11.3
CUI
AH'
kcal.'
-26.3 2.7 -29.2 -19.3 -33.0 -55.4 5.7 3.2 2.6 3.1 -26.0 -24.6 -13.4 -15.3 -20.9 -25.9 -43.0 -46.9 -59.6 2.5 - 1.0 4.5 5.0 $10.0 +11.6 2.1 1.8 - 1.2 7.5 8.5 6.1 - 4.3 - 0.3 -42.0 -10.0 2.6 1.4 0.6 - 1.2 -14.0 -19.7 -19.0 -13.0 -13.0 -28.5 -16.0 -13.3 -49.4
A80 oal./ok.
- 4.5 -
+ 6.0
-11.5 -40.5 -60.5 3.6 4.0 3.1 5.0 -23.8 -14.3 -18.2 -19.4 -23.9 -29.0 -38.9
-26.0 f25.1 +17.0 +31 .O +24.0 $19.0 +27.0 7.3 +30.0 +16.0 $13.7 f10.0 +10.3 -13.7
-
-40.5 5.3 -14.0
-
- 2.0 - '2.6 -17.2 -12.5 -16.0 6.9 - 2.0 0.8 5.7 -13.2
-
-17.0 - 1.6 - 1.0 - 1.9 - 0.3 -12.0 -16.6 -11.3 7.9 - 9.1 -26.2 -15.2 -10.0 -42.4
-
+ + + +
+ +
+ -
+ + + +
+ +
+
-
-15.3 $26.0 $43.3 +23.3 +40.2
Ref,
9 9 10 9 9 9 9 11 11 11 11 9 9 9 9 9 9 0
9 9 11 9 9 9 9 0
+50.5 f49.0 $50.0 $49.0 +35.0 +23.0 5.0 +43.0
+
$23.0 +14.0 8.0 8.0 - 3.0 - 6.7 -10.0 -25.7 -17.0 -13.0 - 7.7 - 2.7 -11.0 -23.3
+
+
9 12 12 12 12 12 12 12 9 13 13 13 14 9 15 15 15 15 16 16 16 16 0
R. J. P. WILLIAMS
122
Vol. 58
of reactions. In the first group the reactions are between cations and anions with a resulting reducReaction kcal,’ cal./’C. Ref. tion in the total number of ions in solution and a COIII4NH3 2CI- (cis) -33.3 9 concomitant neutralization of charge. I n the CoII’ 2En 2C1- (cis) -40.6 9 second group the complex is formed from a cation Cur1 En -15.0 -14.2 17 -18.9 and a neutral molecule and there is no net reduction CUI’ 2En + 3 . 3 18 of the sum of the positive and negative charges in -27. 1 -26.1 N P En -12.0 17 -12.6 - 9.9 the solution. In all but four of the thirty-one - 7 . 0 17 Co“ En - 6.3 - 8.4 examples in the first group ASo favors complex ZnII E n - 7 . 7 - 9 . 8 - 7 . 0 17 formation. I n all but six of the twenty-eight re19 CuII Trien -22.0 +22.0 -28.7 actions in the second group the entropy change 19 NiII Trien +23.0 -19.9 -13.0 does not favor the formation of the complex. Five 19 Cor’ Trien -15.6 - 9 . 0 +22.0 of the unusual examples in the latter group are FelI Trien -11.5 - 9 . 0 + 8 . 0 19 taken from one reference and it would appear to be 19 MnII Trien - 7 . 5 - 4 . 0 $12.0 advisable to check these data. A reasonable exFeII Dipy 0 . 0 20 - 7.5 - 7.5 planation of the difference between the entropy Fe“ 3Dipy 0.0 20 -24.5 -24.5 changes in the two groups of reactions suggests AgI Pyridine - 2 . 8 - 4.7 - 6.3 21 itself. Agl a-Picoline - 3 . 1 - 4.2 - 3 . 7 21 Frank and Evansz4have suggested that ions in Agl yPicoline - 3 . 1 - 4 . 2 - 3 . 7 21 aqueous solution order the water molecules around AgI Butylamine - 4.7 - 6.2 - 5 . 3 21 them so as to form an “iceberg,” the process being AgI Ethylamine - 4.7 - 6.2 - 5 . 3 21 similar to a partial freezing of the liquid. On this AgI Tolylamine - 4 . 5 - 6 . 2 - 5 . 8 21 picture the removal of ions from solution, as in the HI CH3C02- 6.5 - 0 . 1 +22,1 22 process of complex formation between oppositely 22 +29.2 HI OH-13.4 -19.0 charged ions, will lead to the break-down of the (‘ice22 H’ SO,-- 2.6 5 . 2 $26.3 bergs” and a resulting entropy change favoring HI - 5.8 + 1 . 7 +25.0 22 complex formation. Qualitatively the data in + 1 . 0 23 HI NH3 -12.1 -12.6 Table I agree with this picture. A quantitative H‘ CHaNHz + 4 . 5 23 -13.1 -14.5 approach can also be made as Evans and Uril2 HI Pyridine - 7 . 2 - 4 . 7 + 8 . 4 21 have shown. If the entropy change upon the formation of a complex is due to the loss of hydration a The symbol “En” in the table refers to a molecule of ethylenediamine while the symbol “Trien” refers to the of the components of the complex, then for a series molecule NHzCHZCH~NH.CK~CH~NH.CH~CHZNHZ. It of anion complexes with one cation the entropy should be noted that whereas the data for the formation of complexes with anions are often available for the first stage change of complex formation should be proportional to the entropy of hydration of anions. Table of complex formation only, the data for the complexes with neutral molecules more frequently refer to the reaction be- I1 lists some of the molar entropies of hydration of tween a metal ion and several molecules or combining groups. gas ions as given by Latimer and Powe1LZ5 A The entropy and the heat changes in the latter reactions are therefore disproportionately large. The heats and entro- simple comparison between the entropies of hypies of formation of undissociated acid molecules are in- dration of the anions fluoride, hydroxyl, chloride, cluded so as to show the similarity between the formation of bromide and oxalate and the entropies of formation hydrogen ion complexes and complexes of other cations. of the ferric, chromic and stannous complexes of All the free energies and heats are given in kilocalories. these anions which have been measured, will show complex from its components in aqueous solution that the two quantities are roughly proportional. a t 25’. The values of ASo given in Table I will be A similar comparison should be possible for the discussed first. The table consists of two groups formation of complexes of different cations with the same anion and in this case the entropy of (9) ”Selected Values of Chemical Thermodynamio Properties,” formation of the complex should be proportional to National Bureau of Standards, Circular 500, Washington, 1952. tjhe entropy of hydration of the cation. Although (10) J. N. Jonte and D. S. Martin, J . Am. Chem. Soc., 74, 2052 there are some exceptions to this generalization the (1952). (11) I. J. Evans and C. B . Monk, T r a n s . Faraday Soc., 48, 934 following comparisons do confirm this suggestion (1952). for the most part. For the hydroxides the entropy (12) M. G. Evans and N. Uri. S.E.B. Symposium, No. 5, Cambridge, change on complex formation follows the order, 1951. UIV (50.5), FeIII (50.0), (43.3), SnII (23.0); (13) C. E. Vanderzee, J . A m . Chem. Soc., 74, 3552, 4806 (1952). (14) E. L. King, ibdd., 71, 319 (1949). for the chlorides the order is FeIII (35.0), CrlI1 (15) J. Bjerrum, “Metal Ammine Formation in Aqueous Solution,” (23.3), SnII (14.0), CdII (8.0), AgI (6.0); for the P. Haase and Sons, Copenhagen, 1941. formation of the chlorides of formula MClZ, CrTI1 (i6) W. S. Fyfe, J . Chem. Soc., 2318, 2323 (1952). (40.2), HgII (16.0); for the monobromides, FeIII (17) H. Irving and R. J. P. Williams (rinpub.); R. J. P. Williams, D.Phil. Thesis, Oxford, 1960. (23.0), SnII (8.0); for the formation of cyanides of (18) J. Bjerrum and E. J. Nielsen, Acta Chem. Seand., 2, 297 formula M(CN)2, CdII (30.0), AgI (25.1), Au‘ (1948). (17.0); and for the tetracyanide complexes ZnII (19) H. B. Jonassen, G. G. Hurst, R. B. LeBlanc and A. W. Mei(-7.3) and HgII (-15.3). The order of the bohm, THIS JOURNAL, 66, 16 (1952). (20) J. H. Baxendale and P. George, T r a n s . Paraday Sac., 46, 736 molar entropies of hydration of the cations is (1950). UTV> CrIII > FeIII > ZnII > CdII > Sn’I > (21) G. A. Carlson, J. P. McReynolds and F. €1. Verhoek, J . A m . HgII > AgI > AuI.5 In their paper Latimer and Chem. Soc., 67, 1334 (1945). TABLE I (Continued) AFO
AHo kcal.
ASo
+
(22) W. M. Latimer, Chem. Reus., 18, 349 (1936). (23) D. H. Everett and W. F. I
