Published and original data on the stability of complexes formed by bivalent ions of the first transition series have been collected and examined critically. The order Mn < Fe < Co < Ni < Cu > Zn has been found to hold for the stability of nearly all such complexes irrespective of the nature of the co-ordinated ligand or of the number of ligand molecules involved.A theoretical justification for this stability order follows from consideratioiis of the reciprocal of the ionic radii and the second ionisation potentials of the metals concerned, and it is shown why other (empirical) orders, or stability orders which include other elements, can have no general validity.The extent to which variations in characteristic co-ordination number, stereochemical considerations, and entropy factors may affect such a stability order is discussed theoretically and illustrated by examples. Changes in bonding orbitals concomitant with changes in the nature of the ligand are shown to lead to certain complexes of anomalously high stability, notably in the case of ferrous ions.

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Methods suitable for determining the step-stability constants of very stable complexes of transition metals with 1,lO-phenanthroline and its analogues are reviewed. Partition coefficients for 2,2'-bipyridyl and l , 10-phenanthroline between aqueous buffers of ionic strength 0 . 1~ and chloroform, carbon tetrachloride, and n-hexane have been measured at 25'.From measurements of the distribution of the two ligand bases between these solvents and aqueous buffers containing known concentrations of various cations, step-stability constants, valid for 25" and 0. 1M-potassium chloride (or nitrate) have been determined for bivalent ions of manganese, iron, cobalt, nickel, copper, zinc, and cadmium.The stabilities of the 1 : 1 complexes follow the Irving-Williams order in each case and they increase in the order Mn < Cd < Fe < Zn < Co < Ni < Cu. For the 3 : 1 complexes, however, the order becomes Mn < Cd < Zn < Co < Cu < Fe < Ni. The anomalous stability of the ferrous triscomplex is shown to arise because K , is greater than both K , and K,, owing to formation of a spin-paired complex.THIS series of papers form part of an extensive study of the quantitative aspects of steric hindrance to chelation with the immediate goal of seeking an interpretation of the I' singular " reactions 1 between certain heterocyclic bases and ferrous or cuprous ions which form the basis of the " ferroin '' and the ' I cuproin " reaction. To this end the stability constants of complexes of zinc, cadmium, and the transition metals manganese, iron, cobalt, nickel, and copper with 2,2'-bipyridyl, 1,lO-phenanthroline, 2-methyl-, 5-methyl-, and 2,9-dimethyl-phenanthroline have been determined. Most of this work was completed by 19M2 but publication was delayed in order to include values for 5-methylphenanthroline. The present paper (Part I) deals with complexes of 2,2'-bipyridyl and 1,lO-phenanthroline. Part I1 reports work with the ligands 2-methyl-and 2,9-dimethyl-l,lO-phenanthroline which differ from the parent base in carrying one or more substituents adjacent to the nitrogen atoms and thus presenting steric hindrance to co-ordination. In Part I11 the theory of the method is elaborated somewhat and results are reported for 5-methyl-1,lO-phenanthroline in which the electron-repelling substituent is so located as to cause no steric hindrance to co-ordination. In Part IV some calorimetric measurements will be reported. Tris-complexes of 2,2'-bipyridyl (bipy) and 1,lO-phenanthroline (phenan) with ferrous iron are known to be remarkably stable, with overall formation constants of about lo1' and 1021, respectively. The " robust " character of such transition-metal complexes is further exemplified by the considerable optical stability of the antipodes of the triscomplexes of nickel and ferrous iron.3 If the Irving-Williams order of stabilities

Attention is drawn to the approximations implicit in existing methods for computing, from experimental data, the successive stability constants governing the formation of complexes in step-equilibria. A new " correction term " method is described. This makes use of the symmetry properties of the formation curve for the particular case N = 2.best" set of stability constants from inconsistent experimental data is shown to be soluble by a least-squares treatment after an algebraic transformation. This procedure is applicable to systems of higher complexity. The effects of improved methods of computation are illustrated by examples taken from the literature. The problem of computing the Note onSymbolism.-Following Bjerrum most authors have used k n to represent the stability constant of a complex MLn relative to MLn -1. Schwarzenbach uses KML. Now K is customarily used for equilibrium constants, and k for velocity constants, and to avoid confusion we shall use Kn for the above stability constant. The overall constant [ML,]/[M] [L]" (see p. 3399) has been variously designated EL&&, (Schwarzenbach), K , (Bjenum), and fin (Fronaeus and other Scandinavian authors). We prefer the last, so that the expression fin = K1K2K3 . . . K, in our terminology corresponds to Kn = klk,k, . . . kn in Bjerrum's.THE formation of a complex species ML, from a central atom or ion M, and molecules or ions of a Zigad L, is assumed to be governed by a series of thermodynamic equilibrium constants defined by where K , is the classical (concentration) equilibrium constant, F , = fnn;,-, .fL/'f-, and charges are omitted for the sake of generality. If L is uncharged, ML, and MLncarry the same ionic charge, so that, provided measurements are made in solutions of constant, and not too high, ionic strength, F, may be set equal to unity, and the convenient approximation Kn Bjerrum (KgZ. Danske Videnskab. SeZsk., 1946, 22, Nr. 18) used a single average value of Fn in his studies of complexes formed by cupric and chloride ions. The same author (" Metal Ammine Formation in Aqueous Solution," P. Haase, Copenhagen, 1941) introduced the concept of the degree of formation, or ligand number, E, which he defined as the average number of ligand molecules or ions per molecule of M, and showed that for all systems in which only mononuclear complexes occur, values of Z, and of [L], the concentration of free ligand, are related by the equation where Pn = K1K2 . . . K,, and Po = 1, by definition. Experimental methods for the determination of stability constants, developed by Leden, Bjerrum, and Fronaeus, have recently been discussed by Sullivan and Hindman KnT = (MLn)/(MLn-1)(L) = KnIFn KnT is valid.