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Potentiometric measurements have been used to determine the association constants for the formation of the complexes CaH2P04+, CaHP04, and Capo4-in solutions of calcium phosphate a t 25.0 and 37.0". Approximate values of the thermodynamic functions for the association reactions are presented.The solubilities of the various forms of calcium phosphate have been the subject of frequent study, but surprisingly little detailed work has been done in order to characterize the complex species present in solutions of this important biological mineral. A number of surface complexes, proposed from the results of solubility studied with hydroxyapatite,2 have been invoked in an attempt to learn more about the growth and dissolution of bone and tooth enamel. The interpretation of such solubility data, however, is markedly dependent upon the nature and concentrations of the species present in the solutions.Greenwald and co-workersa were the first to recognize that the pH of solutions containing hydrogen phosphates was lowered upon the addition of calcium ions, and they calculated an association constant, K" = [CaHP04]/[Ca2+][HP04z--], of 300 1. mole-' at an ionic strength of 0.006 and at about 22". The existence of the species CaHP04 was later confirmed by Gosselin and Coghlan4 from ion-exchange studies involving Ca45. Davies and Hoyle5 proposed CaH2P04+ as the major species in calcium phosphate solutions at pH 4.54-5.17 with a thermodynamic association constant, K + = [CaH2PO4+]/ [Ca2+] [H2P04-], lying between 11 and 121. mole-'; their value for K" was 471-625 1. mole-' and the pH measurements were made colorimetrically. Greenwald recalculated these results6 and obtained K" = 230-982 1. mole-'. The results of recent solubility studies a t 37.5", by nforeno, Gregory, and Brownl, of dicalcium phosphate, CaHP04 2Hz0, in phosphoric acid solutions at pH values between 3.5 and 6.8 have been interpreted in terms of K" = 588 f 31 1. mole-' at this temperature.I n view of the lack of agreement in the reported association constants, it was thought desirable to study the system by means of a precise potentiometric method over a wide range of pH. By careful control of concentrations and experimental technique, it has been possible to prepare solutions of calcium phosphate which are appreciably supersaturated and stable for at least 1 day. This has enabled potentiometric measurements to be made over a much wider range of concentration than was previously thought possible, and, for the firs time, the species Capo4-has been characterized from the results of measurements a t high pH. Experimental SectionAR reagents and grade A glassware were used, and carbon dioxide was excluded from all solutions by bubbling nitrogen through the solution. Calcium chloride solutions were standardized by passing through Dowex 50-W ion-exchange resin in the hydrogen form and titrating the liberated hydrochloric acid with sodium. hydroxide. Emf measurements were made at 25 f 0.02 and 37 f 0.03" with cells of the type glass electrode-solution under study-1.0 M KC...

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Undisplaced fractures of the axis are not always stable. The transoral route allows good access for stabilization of displaced hangman's fractures. In special circumstances, a locking plate may prove useful in securing the bone graft. The cervical spine locking plate can be inserted transorally with no complications and by using standard instrumentation.