July 20, 1957
COMPLEXES OF TRIPHOSPHATE IONWITH ALKALIMETALIONS [CONTRIBUTION FROM
MCPHERSON CHEMICAL. LABORATORY, THEOHIO STATE
3651
UNIVERSITY]
The Complexes of Triphosphate Ion with Alkali Metal Ions1 BY JAMES I. WATTERS,SHELDON M. LAMBERT AND E. DANLOUGHRAN RECEIVED MARCH6 , 1957 The stabilities of the complexes of triphosphate ion with sodium, potassium and lithium ions have been calculated from the p H lowering during titrations of triphosphate ion with hydrogen ion. In one M tetramethylammonium chloride a t 25". formulas of the complexes and the values of their formation constant are: KP30104-, O.Oe; NaP30104-, * 0.08; LiP30104-,l O 0 . * 7 0.06. Sodium and lithium ions also form acidic complexes with HP030104-, having the following formulas * and L ~ ( H P S O ~ Oloo." ) ~ - , * 0.06. and values for their formation constants: Na(HP0301o)~-,
Introduction Since Huber's2 preparation and investigations, sodium triphosphate has become an important commercial product. Triphosphate ion forms complexes with most metal ions including those of the alkali group. As a consequence of the biological and commercial importance of triphosphates, several author^^-^ have studied the lowering of pH of triphosphate buffers by the addition of alkali and particularly alkaline earth metal ions. In most of the studies the effect was ascribed to complex formation, but no quantitative evaluations of the stability constants were made. Recently, Martell and Schwarzenbach6 have evaluated the stability constants of magnesium and calcium complexes with triphosphate by treating the data obtained in the titration of triphosphoric acid in a manner similar to that used in this study. Schendewolf and Bonhoeffer' in a study of polyphosphates by membrane potentials observed that the order of increasing stability for the alkali metal complexes was K + < Na+ < Li+ and that the stability increased with polyphosphate chain length. On the basis of conductivity measurements Monks obtained a value of 102.5for the first formation constant of the sodium complex. Van Wazer and Campanellag obtained a somewhat smaller complexity constant for sodium with several condensed polyphosphate glasses. They also investigated the complexes of other metal ions. Theoretical If an acid can be titrated in the presence of a relatively large excess of metal ion without precipitate formation, i t is possible to investigate complex formation by the lowering of the pH. When the inflections a t the various equivalence points persist for the stepwise addition or removal of hydrogen ions, the calculations are greatly simplified. I n this case, i t is evident that each ligand adds one hydrogen ion in a stepwise manner even though the ligand niay also be bound to a metal (1) Presented before the Division of Physical and Inorganic Chemistry, 131st Meeting of the American Chemical Society, Miami, Florida, 1957. ( 2 ) H. Huber, AIzgev. Chem., 5 0 , 323 (1937). (3) L. Frankenthal, THIS J O U R N A L , 66, 2124 (1946). (4) H. Rudy, Angew. Chem.. 6 4 , 447 (1941). (5) M. Bobtelsky and S. Kertes, J . A p p l . C h e m (Lundoiz), 4 , 410 (1954). (6) A. E. Martell and G. Schmarzenbach, Helu. Chim. Acta, 39, 653 (1956). (7) U. Schendewolf and K. F. Bonhoeffer, Z . Eieklroclienz., 6 7 , 216 (1953). (8) C. B. Monk, J . Chem. Soc., 427 (1949). (9) J. R. Van Wazer and D. Campanella, T H r s J O U R N A L , 72, 655 (1950).
ion. Under these conditions it is expedient to define a function which is called the apparent acidity constant,6 K6'-,,, for this stepwise addition of hydrogen ion as
where m, n and q indicate the number of metal, hydrogen and triphosphate ions in any particular species. I n this paper parentheses indicate concentrations and brackets indicate activities. n has a single value from zero to five if the addition of hydrogen ion is stepwise while m and q may have several values if several complex species and the uncomplexed ligand, as well, are in equilibrium. The general equation for the stepwise addition of hydrogen ion to triphosphate ion and the corresponding acidity constant are H + -I- HnPd&(5-n)-
Hn+~PaOio(~-")- ( 2 )
The general equation for the formation of any complex ion and the corresponding complexity constant, PM~H,,L~, are mM
+
+ qH,P3010Q(~-~)-
M,(H,P~OIO)~(~Q-"P-~)(3)
where the subscript L indicates the ligand P3OlO5-. The calculations are further simplified if the maximum values of m and q are unity. This assumption can be tested by calculations based on varied concentrations and ratios of metal ion and triphosphate ion. I n this case eq. 3 reduces to Mf
+ H ~ P ~ O ~ O ( Jc ~ - " ) -MH,PaOlo('-")-
(4)
A high concentration of an essentially non-complexing electrolyte such as tetramethylammonium chloride and relatively low concentrations of metal ion and triphosphate ion are used in order to minimize the effect of the varied concentrations of the reacting species on the various activity coeficients. Under these conditions a lowering of the fiH in the titration curve indicates complex formation since the presence of metal ion in an acid enhances its acidity. I n regions where no pH lowering occurs, one may conclude that complex formation does not occur to an appreciable extent. Since no pH lowering occurred in the triphosphate curves for n values larger than 2 , when the concentrations of the reactants were relatively small
3652
JAMES
I. WATTERS,SHELDON AI. L A ~ I U EAKNTD 15. DANLOUGIIKAN
the following equations were derived by substituting equations having the fornis of ( 2 ) and (3) into (1) with m and q equal to unity in the metal complex.
VOl. 79
Experimental
T h e sodium triphosphate, tetramethylammonium chloride arid tetramethylammonium hydroxide were prepared according t o a procedure described in a previous paper.1° Carbonate-free potassium and sodium hydroxide solutions IH+] [(HP30i04-) f (MI-IPaOrc3-)1 were prepared from Baker Analyzed pellets and stored in K’, = (H2P30103-)--paraffin-lined bottles. All water used in preparing soluK4 KMHLKa(h1 ‘) (5) tions and washing the columns was demineralized, doubly distilled, and purged with nitrogen t o remove t h e dissolved carbon dioxide. Mallinckrodt reagent grade salts were used. Ks KbILK5(M+) The potassium and lithium triphosphate solutions were 1 KMEL(MT prepared by passing a 0.03 M solution of the recrystallized I
