A. CHUGHTAI, R. MARSHALL, AND G. H. NANCOLLAS
208
Complexes in Calcium Phosphate Solutions1
by A. Chughtai, R. Marshall, and G. H. Nancollas Chemistry Department, State University of New York at Buffalo, Buffalo, New York 14.814 (Received July 3,1067)
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,2have 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 Coghlan4from 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 12 1. 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 The Journal of Physical Chemistry
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 Section AR 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 KCI-Hg2C12, Hg using a Beckman Research or Corning Model 12 pH meter and Beckman Type 41263 glass electrode; reproducibility was f 0.1 mv. Each cell incorporated a pair of glass electrodes so that any irregularity in the behavior of one of them was immediately apparent. The electrode systems were standardized before and after each experiment with NBS standard buffer solutions, prepared according to Bates 0.01 M hydrochloric acid 0.09 M potassium chloride, pH 2.098 at 25"; 0.05 M potassium tetroxalate, pH 1.679 at 25" and 1.690 a t 37"; 0.05 M potassium hydrogen phthalate, pH 4.008 at 25" and 4.028 at 37"; 0.025 M KH2P04 0.025 M iSa2HP04, pH 6.865 a t 25" and 6.841 at 37"; 0.01 J4 sodium borate, pH 9.180 at 25" and 9.08 a t 37". Considerable care was necessary in the standardization of the electrodes for CaH2PO4+measurements at low pH,
+
+
(1) These studies were aided by Contract N00014-66-CO227 (NR 105-419),between the office of Naval Research, Department of the Navy, and the State University of New York at Buffalo. (2) M. D.Francis, Ann. AT. Y . Acad. Sei., 131, 694 (1965). (3) I. Greenwald, J. Redish, and A. C. Kibrick, J . BioE. Chem., 135, 65 (1940). (4) R. E. Gosselin and E. R. Coghlan, Arch. Bwchem. Bwphys., 25,301 (1953). (5) C. W.Davies and B. E. Hoyle, J . Chem. Soc., 4134 (1953). ( 6 ) I. Greenwald, J . Phua. Chem., 67, 2853 (1963). (7) E.C. Moreno, T. M. Gregory, and W. E. Brown, J . Rea. Natl. Bur. Std., 70A, 545 (1966). (8) R. G. Bates, "Determination of pH," John Wiley and Sons, Inc., New York, N. Y.,1964.
COMPLEXES IN CALCIUM PHOSPHATE SOLUTIONS particularly in the design of calomel electrode junction, owing to the increased importance of the liquid junction potential under these conditions; both potassium tetroxalate and HCI-KC1 buffers were used in each experiment. I n order to achieve as wide a range of concentrations as possible, six separate titration systems were studied: KH2P04+ CaC12 titrated with NaH2P04; KH2P04 Na2HP04with CaC12; KH2P04 CaC12 with H3P04;Na2HP04with CaC1,; Na3P04with CaC12; NaOH H3P04with CaCI2.
+
+
+
+
Results and Discussion The results of the potentiometric measurements over the entire ranges of concentration could be interpreted in terms of the formation of three complex species, CaH2P04+,CaHP04, and Capo4- with thermodynamic association constants K f , KO, and K-, respectively. Although the existence of the ion pair NaHP04- has been proposed by Smith and Alberty,g Bates,lo in his extensive hydrogen electrode cell measurements with sodium phosphate buffers, could find no evidence for the presence of this species; in the present work, the interaction between Naf and HP042- ions was ignored. The concentrations of ionic species in the solutions were calculated from equations for total calcium ion concentration
+ [CaH2P04+]+ [CaHP04] + [CaPOd-] + [CaOH+]
209
3[C1-]
+
TP = [Hd'04] [HzP04-] [Pod3--] [CaH2P04+]
+
+ [HP042-l +
+ [CaHP04]+ [CaP04-]
and electroneu trality
+
+
+
+
EK+l [Na+l 2[Ca2+l [H+l [CaH2P04+] [CaOH+l = [OH-] [CI-1 [H2P04-l 2[HP042-] 3 [ P O P ] [CaP04-]
+ +
+
+ +
+
Values of the dissociation constants of phosphoric acid a t 25" and were those of BatesloJ1(ICla = 7.112 X 6.095 X a t 37"; ICza = 6.339 X 10-8 at 25" and 6.562 X at 37"), Vanderzee12 (ha= 4.3 X a t 25"), and .Bjerrum13 (ICaa = 6.6 X 10-13 a t 37"; K(CaOH+) = 20.014). At low pH the concentrations [Capo4-], [CaHP04], [CaOHf], [P043-],and [OH-] are negligible and [H2P04-]
+ El-1
TP - 2 7 ' ~
- 1K+1 - INa+l
+ IH+1
[H+1f12 k2a ~kla
[H+Ifz
Values of K f were obtained with the aid of an IBM 7044 computer by successive approximations of the ionic strength
[Hf]
-
[Na+] - [K+] - Tp}
using activity coefficients calculated from the equation -log f2 = h2[I1/1/(1 11/*)-0a31r].16The results of some typical experiments are given in Table I. The mean value of K f , 25.6 1. mole-l at 25", is appreciably larger than the value of 11-12 estimated by Davies and Hoyle6from colorimetric measurements.
+
Table I
T M X 108, M
2.673 4.174 5.473 6.245 6.544 6.659 8.092
TM = [Ca2+]
total phosphate concentration
-
2.336 3.699 4.914 5.999 6.277 6.425
TP X 108,
M
PH
Ionic strength x 102,
[CaHzPOd t1
M
1M
x
104,
At 25" 5.935 3.273 1.322 1.891 5.954 3.140 1.742 2.99Q 6.049 3.023 2.114 3.709 6.301 2.965 2.351 4.228 5.449 3.295 2.396 4.152 6.023 2.970 2.452 4.201 10.880 2.728 3.202 6.369 Mean K + = 25.6 1. mole-'; mean deviation k l . 7 (48 determinations) At 37" 5.345 3.262 1.157 2.027 5.277 3.195 1.538 2.900 5.290 3.115 1.885 3.483 6.558 2.902 2.266 4.921 5.754 3.127 2.312 4.831 5.575 2.953 2.318 4.901 Mean K + = 31.9 1. mble-1; mean deviation -Ir 1.6 (36 determinations)
K +, 1. mole-]
22.5 24.7 25.1 25.2 25.9 24.8 19.9
31.3 30.9 29.7 31.5 31.9 34.3
I n the intermediate pH range, the concentrations [Capo4-], [P043--],and [OH-] could be ignored, and [HP042-] was calculated by solving the quadratic equation
[Cl-I
+ [H+l + [Na+] + [K+l = 0
(9) R.M.Smith and R. A. Alberty, J . Phys. Chem., 60, 180 (1956). (10) R. G. Bates and S. F. Acree, J . Res. Natl. Bur. Std.. 30. '21 (1943). (11) R.G.Bates, ibid., 47,127 (1951). (12) C. E. Vanderiee and A. S. Quist, J . Phys. Chem., 65, 118 (1961). Volume 73, Number 1 January 1968
A. CHUGHTAI, R. MARSHALL, AND G. H. NANCOLLAS
210 Table I1 : CaHP04 Complex Formatian T M X 101,
TP X 108,
M
M
I
PH
x
108,
M
[CaHzPOb+I, x 104, M
ICaHPO41, x 104, M
KO,
1. mole-1
4 697 6.110 6.990 7.906 9.076 10.42 11.47 11.71
1.076 1.108 1,119 1* 098 1.106 1.098 1,094 1.051
25", K + = 25.6 1. mole-1 5.576 2.403 5.700 2.342 5.726 2.833 6.513 4.028 5.603 3.076 7.554 3.508 3.314 5.682 8.029 4.428 3.640 5.561 9.259 3.842 5.537 4.010 10.26 3.985 5.664 4.302 10.61 5.554 4.327 5.222 11.30 2.693 Mean K" = 548 1. mole-'; mean deviation f2.8 (61 determinations)
546 550 545 548 549 546 552 549
3.407 4.341 5.978 7.544 8.937 10.21 11.85 12,21
1.107 1.101 1.092 1.111 1.103 1.085 1.102 1.087
37", K + = 31.9 1. mole-' 5.566 2.062 4.857 2.178 5.529 2.302 6.013 2.452 5.475 2,732 7.872 2.798 5 * 435 3.175 9.667 3.096 5.404 3.552 11.00 3.253 5.379 3.890 12.02 3.339 5.473 4.361 13.20 4.582 5.086 4,450 14.21 2,025 Mean K" = 681 1. mole-'; mean deviation &2.8 (57 determinations)
683 681 679 679 678 678 683 689
I
Table I11 : CaPOa- Complex Formation
x
K - X 10-8,
At 25' 1.40 4.54 1.45 4.63 1.00 5.76 1.51 4.82 1.58 4.80 1.66 4.77 1.67 4.84 1.73 4.83 1.73 4.90 1.85 4.78 Mean K - = 2.9 & 0.1 X 106 1. mole-'
6.50 6.65 6.39 6.94 7.12 7.30 7.44 7.61 7.75 7.95
1.95 2.06 1.94 2.26 2.38 2.52 2.60 2.71 2.79 2.91
2.93 2.94 2.89 3.06 2.93 2.80 2.87 2.81 2.88 2.86
At 37" 2.88 3.54 3.00 3.55 3.45 3.18 3.57 3.21 3.38 3.48 3.44 3.54 3.49 3.58 3.56 3.59 0.2 X 1O81. mole-' Mean K - = 3.46
6.16 6.34 6.54 6.69 6.89 7.05 7.21 7.39
6.52 6.84 7.11 7.40 7.63 7.94 8.10 8.33
3.71 3.64 3.40 3.53 3.33 3.36 3.41 3.35
[ H + ] X 1011, M
1.304 1.379 1.452 1.525 1.596 1.666 1.735 1.803 1.870 1.935
8.95 8.87 8.80 8.72 8.65 8.58 8.51 8.44 8.37 8.30
8.11 8.27 8.43 8.59 8.69 8.76 8.93 9.04 9.18 9.29
1,452 1.525 1.596 1.666 1.735 1.803 1.870 1.935
8.80 8.72 8.65 8.58 8.51 8.44 8.37 8.30
3.10 3.15 3.22 3.26 3.33 3.36 3.44 3.49
Values of
KO
[CaHPOd], x 108, M
were calculated as for K + using
s2) + 2[C1-] + 2TM - 2 T p ) h a
Table 11summarizes the results of some typical experThe Journal of Physical Chemiatry
Ix
[CaOHt], X lOS, M
M
104,
Tp X lOS,
M
M
TM
[CaPOa-], X 106 J4
104,
1. mole-1
iments a t intermediate pH, and it is seen that the variation in KO over the range of accessible concentrations is very small. In experiments under supersaturated con(13) N. Bjerrum and A. Unmack, Kgl. Danske Videnskab. Selskab, Mat. F y s . Medd., 9, 141 (1929). (14) C.W. Davies and B. E. Hoyle, J . Chem. Soc., 233 (1951). (15) C. W. Davies, "Ion Association," Butterworth and Co., Ltd., London, 1962.
COMPLEXES IN CALCIUM PHOSPHATE SOLUTIONS
211
ditions at high pH, [HaP04]and [CaH2P04+]were negligible and [HPOZ2-]was calculated by successive approximations for I from the quadratic equation
+
100
1
1
.
1
,
.
,
,
+
~ T M 3Tp [Naf] [H+] - [Cl-]
-
[OH-] = 0
The constancy of the K - values given in Table I11 provides supporting evidence for the presence of two complexes, CaHPO4 and Capo4-, at high pH. It was not possible to interpret the experimental data in terms of the presence of any other species such as Ca3(P04)z. I n his calculation of K" from Bjerrum's data, Greenwaldesubstitutedvalues for log [HI [CaP04-]/ [CaHP04] of 8.0, 8.5, and 9.0. The best consistency was obtained with the value 8.5, which can be compared with the value 8.64 of the present work. The agreement is remarkably good, in view of the differences in pH involved and of the wide range of choice of values for the dissociation of CaHP04 made by Greenwald. The association constant values a t 25" have been used to construct the complex composition diagram given as a function of pH in Figure 1, in which the concentrations of complexes are calculated for a hypothetical system M in both total calcium and total phosphate and at an ionic strength 0.15 M, close to the physiological value. The values obtained for the association constants a t 25 and 37" have been used to calculate approximate thermodynamic functions for the reactions and these are given in Table IV together with estimated uncertainties. Although direct calorimetric determination of AH is to be preferred to the temperature coefficient method, in these calcium phosphate systems, the range of accessible concentrations is such that the complexes, particularly CaPO4- at high pH, are present in too small amounts
PH
Figure 1. Concentrations of ionic species present in solutions of calcium phosphate as a function of p H for T M = T p = 10-8 M : (1) total complexes; (2) [CaHzP04+]; (3) [CaHP04]; (4) [CaPOa-I.
Table IV : Thermodynamic Functions a t 25" Reaotion
+ +
Cat+ H2PO4C a s + + HPOaaCat+ PO,*-
- AU, koa1 mole -1
AH,koal mole-1
1.92 f 0.04 3.7 f 0.01 8.81 zk 0.03
3.4 zk 1 . 7 3.3 f0.6 3 . 1 j=2.0
A 8 , oal mole-'
deg-1
18 6 23 f 0.5 40 f 4
for accurate enthalpy change measurement. As is to be expected for interactions which are essentially electrostatic in nature,lB complex formation is accompanied by endothermic' enthalpy changes. The complexes are stabilized through the positive entropy changes reflecting the release of solvent molecules from the cospheres of the free ions when association takes place. The AS values increase with increasing negative charge on the anion. (16) G. H. Nancollas, "Interactions in Electrolyte Solutions," Elsevier Publishing Co., Amsterdam, 1966.
Volume 7.9, Number 1 January 1968
