Abstract
A computer program has been designed to calculate the ionic activities of calcium and orthophosphate in a wide variety of solutions. In the case of synthetic solutions the calculations were checked by comparing the computed pH values with those observed experimentally. Tests of this type with solutions having the concentrations of calcium and orthophosphate found in biological fluids and with pH values ranging from pH 3.0–10.0 indicated that the program was suitable for biological applications. The program was not effective for solutions in which the bromide ion was a principal source of ionic strength probably because of the failure of the extended Debye-Hückel equation under those circumstances. No evidence for the formation of any sodium phosphate complex at normal biological concentrations could be found.
Résumé
Un programme d'ordinateur a été mis au point pour calculer les activités ioniques du calcium et l'orthophosphate dans un grand nombre de solutions. Dans le cas de solutions synthétiques, les calculs sont vérifiés en comparant les valeurs de pH, obtenues par ordinateur, avec celles observées expérimentalement. Des essais de ce type, avec des solutions possèdant des concentrations de calcium et d'orthophosphate trouvées dans les liquides biologiques et à des valeurs de pH variant de 3.00 à 10.00, indiquent que le programme est adapté pour des applications biologiques. Le programme n'est pas effectif pour des solutions, dans les lesquelles l'ion bromure est la source principale de la force ionique, sans doute, par manque d'équation étendue de Debye-Hückel dans ces circonstances. Aucune formation de complexe de phosphate de sodium n'a été notée à des concentrations biologiques normales.
Zusammenfassung
Es wurde ein Computer-Programm ausgearbeitet, um die Ionenaktivitäten von Calcium und Orthophosphat in einer breiten Varietät von Lösungen zu berechnen. Die Berechnungen wurden bei synthetischen Lösungen durch Vergleiche zwischen den auf diese Weise errechneten pH-Werten und den experimentell gefundenen kontrolliert. Diese Art Kontrollen mit Calcium-und Orthophosphatkonzentrationen, wie sie in biologischen Flüssigkeiten gefunden werden, und mit pH-Werten zwischen 3,0 und 10,0 wies darauf hin, daß das Programm für biologische Anwendungen geeignet war. Das Programm konnte nicht benützt werden für solche Lösungen, bei welchen hauptsächlich das Bromidion zur Einstellung der Ionenstärke verwendet wurde, vermutlich weil die erweiterte Debye-Hückel-Gleichung unter diesen Umständen nicht anwendbar ist. Die Bildung eines Natriumphosphat-Komplexes unter normalen biologischen Konzentrationen konnte nicht nachgewiesen werden.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barrow, G. M.: Physical chemistry. New York: The McGraw-Hill Book Co. 1966.
Bates, R. G.: First dissociation constant of phosphoric acid from 0°C to 60°C. Limitations of the electromotive force method for moderately strong acids. J. Res. nat. Bur. Stand.47, 127–134 (1951).
—: Determination of pH. New York: John Wiley & Sons 1954.
—, Acree, S. F.: pH of aqueous mixtures of potassium dihydrogen phosphate and disodium hydrogen phosphate at 0°C. J. Res. nat. Bur. Stand.34, 373–394 (1945).
Bjerrum, N., Unmack, A.: Electrometrische Messungen mit Wasserstoffelektroden. K. danske. Vidensk. Selsk. Skr.9, 5 (1929).
Brown, W. E.: Behaviour of slightly soluble calcium phosphates as revealed by phase-equilibrium calculations. Soil Sci.90, 51–57 (1960).
Chen, P. S., Toribara, T. Y., Warner, H.: Microdeterminations of phosphorus. Analyt. Chem.28, 1756–1758 (1956).
Chugtai, A., Marshall, R., Nancollas, G. H.: Complexes in calcium phosphate solutions. J. phys. Chem.72, 208–211 (1968).
Davies, C. W., Hoyle, B. E.: The dissociation constant of calcium hydroxyde. J. chem. Soc. 233–234 (1951).
Finlayson, B., Miller, G. H.: Urine ion equilibria. A numerical approach demonstrated by application to antistone therapy. Invest. Urol.6, 428–440 (1969).
Gregory, T. M., Moreno, E. C., Brown, W. E.: Solubility of CaHPO4·2 H2O in the system Ca(OH)2−H3PO4−H2O at 5, 15, 25 and 37.5° C. J. Res. nat. Bur. Stand70A, 545–552 (1970).
Harned, H. S., Robinson, R. A.: A note on the temperature variation of the ionisation constants of weak electrolytes. Trans. Faraday Soc.36, 973–978 (1940).
Kielland, J.: Individual activity coefficients of ions in aqueous solutions. J. Amer. chem. Soc.59, 1675–1678 (1937).
Manov, G. C., Bates, R. G., Hamer, W. J., Acree, S. F.: Values of the constants in the Debye-Hückel equation for activity coefficients. J. Amer. chem. Soc.65, 1765–1767 (1943).
Mattock, G.: pH measurement and titration. London: Heywood Co. Ltd. 1961.
Nims, L. F.: The first dissociation constant of phosphoric acid. J. Amer. chem. Soc.56, 1110 (1934).
Pak, C. Y.: The physico-chemical basis for the formation of renal stones of calcium phosphate origin. J. clin. Invest.48, 1914–1922 (1969).
Pedersen, K. O.: Determination of calcium fractions of serum. II. Investigation of calcium ion activity and stability of important calcium complexes by an improved semimicro method. Scand. J. clin. Lab. Invest.25, 199–209 (1970).
Robertson, W. G., Peacock, M.: New techniques for the separation and measurement of the calcium fractions of normal human serum. Clin. chim. Acta20, 315–326 (1968).
——, Nordin, B. E. C.: Activity products in stone-forming and non-stone-forming urine. Clin. Sci.34, 579–594 (1968).
Smith, R. M., Alberty, R. A.: The apparent stability constants of ionic complexes of various adenosine phosphates with monovalent cations. J. phys. Chem.60, 180–184 (1956).
Walser, M.: Determination of free magnesium ions in body fluids. Analyt. Chem.32, 711–717 (1960).
—: Ion association. 6. Interactions between calcium, magnesium, inorganic phosphate, citrate and protein in normal human plasma. J. clin. Invest40, 723–730 (1961).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Smales, F.C. A computer program for calculating the activities of calcium and orthophosphate ions in biological fluids and related synthetic solutions. Calc. Tis Res. 8, 304–319 (1971). https://doi.org/10.1007/BF02010149
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02010149