Computerized Calculation of Stepwise Formation Constants of Transition Metal Ions with Tetradentate Ligands Bjerrum9smethod of calculation ( I ) of stepwise stability constants was devised for systems which contain up to six ligands per metal ion. Later, Block and McIntyre ( 2 ) developed a method which uses simultaneous equations to solve formation functiuns for eases where there are no more than three bidentate or two terdentate ligands per metal ion, thus eliminating the successive approximation method introduced by Bjerrum (I). In contrast, the algebraic solutions far the protonation and metallation reactions with tetradentate ligands are exceedingly complex and cumbersome to use. As an outgrowth of our work with tetradentate ligands (3).*Fortran IVcomputer program has been written tocalculate protonation constants and stepwise formation constants for the divalent metal ion complexes with tetradentate ligsnds in aqueous and 50 vol. % dhxane-water solutions. T h e dioxane-water mixture was chosen because of its usefulness in the t i t r n t ~ mo i writer-in.c,luhle ligaudr and c~,mplpre\arnd hpwuir true thernmdynnm~cdata rather thnn mrrclt nwleril\, quotlent, can hr ohtainrd ,4r T h e pmttnionwtr~vt i t r a r ~ mprucrdtrrt docrihrd by t i o h l h r q 5 i.3 rmpluyed Fur the i U ~ 1 " .dioxnnewa1c.r m l r t u n j , ns wvlird hy Van i'ilrrt end i.'rrndu\ ( t i , , a lmrar intrrpolllim o i m a l r r ~ t ydata l i uicd in order t o determine the activity cb&icie"t functions. In aqueous solutions, logy* is equal t o -0.03 i 0.005 units (7.8) for the concentration of divalent metal ions called for in the arocedure (5).The o r o m m s are easily modified to accommodate
since structural similarities in their metal complexes model a~numberof biologically important compounds (9).A copy of the listings of these programs is available upon request from the authors.
Literature Cited (11 Bjerrum. J.. "Metal Ammine Formation in Aqueous Solutinn? P. Haaspand Sons. Coponhagen, 1941. (2) Rock, B.P., and Mclntyre. Jr.. G. H..J. Amer Chem.Sur..,75,5667 (19531. 131 Nelron.H.C..andGoldher~.D.E..lnorx. Chim. A d o . 19.L21119761. 141 Van Uifert.L.G..snd H8aa.C. G., J A m e r Chrm Snc.. 75.451 (19611. 15) Goldberg, D.E.,J.CHEM. F.DUC.39,828(1962). (6) Van liit4rt.L. G.end Ferncliu%W.C., J. Amsr. Chrm S o r . 76,5887 (19%). (71 Berbch.C. R..Ph.D. Disse~tation.ThePcnnrylvanisStatDUniversity. 1955. 181 Mclntyre.J~.,C. H.. PhD. Disser~ltion,TheP~nnaylvaniaStateUniversity, 1954. (9) Bulch. D. H..Farmery, K..Geadken, V. L.. KaMie,V.. Melnyk.A.C.,Spsrsti.C.R.,andTakel.N.,Adu.Chrm. S e r , 100.44
David E. Goldbere
(18711 Harold C. Nelson
The University of Texas a t Austin Austin, 78712
162 / Journal of Chemical Education
