The Solubility of Octacalcium Phosphate at 37°C
in the System Ca(OH)2-H3PO4-KNO3-H20
L.J. SHYU, L. PEREZ, S.J. ZAWACKI, J.C. HEUGHEBAERT,* and G.H. NANCOLLAS
Chemistry Department, State University of New York at Buffalo, Buffalo, New York 14214
The
octacalcium
solubility
product
of
phosphate
acid against potassium hydroxide solution. Potassium di/Ca4H(P04)3 * 2.5H20] has been determined in the system
hydrogen phosphate solutions were standardized by titratCa(OH)2H3PO4KNO3-H20 at 37°C in experiments involving a
ing against potassium hydroxide both potentiometrically
range of hydrodynamics, ionic strength, and equilibration time. A
and using thymolphthalein blue as indicator.
value of pKg,= 49.3 + 0.2 was obtained for three different solid
preparations by considering activity coefficients and ion-pair correcOne sample of OCP (preparation A), prepared in acetate
tions.
buffer,5 was kindly donated by Dr. W.E. Brown. A second
preparation (B) was made by hydrolyzing dicalcium phosJ Dent Res 62(3):398400, March 1983
Introduction.
Octacalcium phosphate [Ca4H(PO4)3-2.5H2O, hereafter
referred to as OCP] was identified as a separate calcium
phosphate phase almost 100 yr ago.1 The importance of
OCP stems from the ease with which it can be transformed
into the thermodynamically more stable hydroxyapatite
[Ca5 (PO4)3(OH), hereafter referred to as HAP]. The structural and chemical characteristics of OCP have been described, and it has been shown that the rate of conversion to
HAP increases with increasing pH and temperature.2 The
solubility of OCP has been measured at 250C,3 and, hitherto,
it has usually been assumed that, as in the case of some
other calcium phosphate phases, the same value would be
applicable at the physiological temperature, 370C. Recently, however, constant composition crystal growth experiments in supersaturated solutions of calcium phosphate
have suggested that the retrograde temperature coefficient
of solubility of OCP may be substantial.4 Since calcium
phosphate precipitation is of importance not only in biological mineralization, but also in the formation of destructive scale in cooling-towers, this finding may result in a
much greater enthalpic driving force for the precipitation of
OCP. An increasing awareness of the importance of this
phase in such systems prompted the present detailed solubility study.
Materials and methods.
Deionized, triply distilled water, pretreated with
saturated nitrogen gas to exclude carbon dioxide, was used
to prepare solutions. Potassium hydroxide was prepared
from "Dilut-it" reagent solutionst and was standardized
against potassium hydrogen phthalate.t Solutions of
calcium nitrate,+ potassium dihydrogen phosphate,t and
potassium nitrate+ were prepared from the ultra-pure
grade salts. Calcium and potassium ion determinations
were made by passing aliquots of the solutions through an
ion-exchanger in the H formt and titrating the eluted
Received for publication June 2, 1982
Accepted for publication August 16, 1982
This research was supported by the Stauffer Chemical Company
and by a grant from the National Institute of Dental Research
(DE-03223).
*Laboratoire de Physico-Chimie des Solides, ERA CNRS n°263,
38 Rue des Trente-Six Ponts, Toulouse 31400, France
tJ.T. Baker Co.
NY
+Ventron Co., Alfa Division
+70/30, He/N2 mixture Quantasorb, Quantachrome, Greenvale,
tDowex 50W-XB
398
phate dihydrate (DCPD) at a pH of 6.40 and 370C, using a
pH-stat to control the hydrogen ion activity. The conversion process, DCPD-+OCP, was monitored from time to
time by x-ray,++ infrared spectroscopy,' and chemical
analysis, and was shown to be complete in less than 24 h
under these conditions. A third sample (C) was prepared by
a constant composition method.4 The solid phases were
washed thoroughly with triply distilled water and were
filtered through a 0.22 gm filter.** The specific surface
area of the crystals, 14.7 m2g-1, 25.3 m2g- , and 8.6
m2g-1 for samples A, B, and C, respectively, was determined by a single-point BET method.+
The solubility of OCP was determined by allowing OCP
crystal growth and dissolution experiments to proceed to
equilibrium in solutions initially supersaturated or undersaturated with respect to OCP. Approximately 30 mg of
crystals A, B, or C were added to solutions containing
calcium nitrate, potassium dihydrogen phosphate, and
potassium nitrate, in the pH range 6.0-6.5. The suspensions
were either sealed in Pyrex vessels and shaken in a
thermostat at 37 0C, or stirred in a covered Pyrex glass
vessel surrounded by a jacket through which thermostated
water was circulated. In the latter experiments, presaturated nitrogen was bubbled through the solutions to
avoid contamination by carbon dioxide. The equilibration
experiments were allowed to proceed for four, ten, 30, or
40 d under different conditions of stirring, concentration,
and ionic strength. At the end of these time periods, the
pH was measured using glasst and silver/silver chloride
electrodes. Calcium and phosphate were analyzed by a
method modified from that described previously,6 using
atomic absorption spectroscopy for calcium and a spectrophotometrico method for phosphate. It was important
to verify, by chemical analysis, x-ray diffraction, and
infrared spectroscopy, the absence of solid phases other
than OCP in the experiments.
Results and discussion.
Concentrations of ionic species in the equilibrated
calcium phosphate solutions were computed using mass
balance, electroneutrality, and available protonation7,8
and ion-pair9'10 equilibrium data. The calculations were
made by successive approximations for the ionic strength,
++XRG 3000 Philips Diffractometer, Cu-Ka, radiation, Ni filter
°Perkin-Elmer, Model 467
**Millipore, Bedford, MA
¶ Beckmann Model 531085, glass electrode
'Perkin-Elmer, Model 503
'Varian Model Cary 210
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lo-,
0
I* .
SOLUBILITY OF OCTA CALCIUMPHOSPHATE
V64 62 No. 3
106 *
Ionic
Strength
I
.05
,
.03
399
where A is the temperature-dependent Debye-Hiickel
constant. The thermodynamic solubility product of OCP,
KSo, may be expressed in terms of the conditional value,
K'So, by Equation 1:
0.1
I
Ky4 3(E.1
1+4[+IPO3 1 Y2Y3Y1 =Ky2y3y(Eq. 1)
:
Kso [Ca24]4[H+](P04
3 43
a.47
0
4
45
431
.16
.12
.0w
.04
0
i"/ul"'s+ 11- 0-3
I
Fig. 1 - Plots of pK'So (OCP) against [I/2/(1 + I1/2)-0.3I].
0, sample B, stirred cell, initial pH = 6.40, ten d equilibration;
O, sample A, pH = 6.00, shaken for 40 d; and L , sample A,
shaken for 30 d, pH = 6.00.
in which square brackets enclose molar concentrations.
Introduction of activity coefficients results in Equation 2:
(Eq. 2)
pK'so = pKso- 44A[I1½/(1 + I'/2) - 0.311
Typical experimental conditions are summarized in
the Table, in which [KOH] represents the concentration of
base required to bring the calcium phosphate solutions to
the desired pH values. At the end of the experiments, the
solid phase in equilibrium with the solutions was confirmed
as OCP by x-ray diffraction, infrared spectroscopy, and
chemical analysis. The results of the solubility determinations are shown in the Table, and pK'so is plotted as a function of ionic strength (Eq. 2) in Fig. 1. The temperaturedependent constant, A, calculated from the slope of the
straight line (linear regression coefficient, 0.977), was 0.57,
in good agreement with the calculated value, 0.52.12 The
corresponding thermodynamic solubility product, pKso,
was 49.3 ± 0.2 - some two orders of magnitude lower
than the value 47.08 at 250 C.3
On the assumption that complete hydrolysis of DCPD
to OCP had occurred, Madsen13 reported concentration
data for the solubility of the latter phase. A re-calculation
of these results gave pKso = 48.46 for OCP at 370C. A
decreasing solubility with increasing temperature has been
noted for many metal phosphate systems.14 The difference
between 250C and 37 C for OCP in the present work is
I
23
I~
'C
4
IC)
2 F
05
-J
I
3
64
7
\
r
K 5
~~~~~~~~~~~~~A
c
9
~~~~~~-p
I
-~~~~~~~~~~~~~
8
34 5
6
7
8
o
0
4
3
5
6
7
8
9
pH
Fig. 2 Solubility isotherms of OCP at 37°C. Curves A, B, and
C calculated for constant TCa/Tp and I. A, TCa/Tp = 1.33, I = 0.5
mol L-1; B, TCa/Tp = 0.10, I = 0.05; C, TCa/Tp = 1.33, 1 =0.05;
D, TCa/Tp varying from 1.35 -0.49 and I from 3 x 10-4 -2.5
mol L-1.
-
17
8
9
Io
and the activity coefficients of z-valent species, yz, were
calculated from the extended form of the Debye-Hiickel
equation proposed by Davies,11
I,
-log yz
=
Az2 [1/2 /( I+ I1 /2) -0.311
DC PD
6
~~~~~~~~~~9
0
oc P
HAP
8
7
9
6
H
Fig. 3 -Solubility isotherms for calcium phosphates at 37°C.
Calculated at I = 0.1 mol L- I and (TCa/Tp) 1.00, 1.33, and 1.67
for DCPD, OCP, and HAP, respectively.
3
4
5
p
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=
400
SHYUETAL.
J Dent Res March 1983
TABLE
OCP SOLUBILITY EXPERIMENTS AT 370C
Expt. No.t
1A
6A
11A
17A
18B
19B
20B
21B
22B
24C
30C
32C
27C
TCa
103mol L-1
Initial Conditions*
KOHl
3
[KNO3
Tp
mol L104 mol L-1
103mol L-1
3.00
2.25
1.50
3.00
2.14
2.29
2.60
2.81
2.94
0.546
0.265
0.528
3.00
4.00
3.00
2.00
2.00
1.25
1.48
1.98
2.35
2.59
0.728
0.353
0.704
4.00
0
0.01
0.05
0.10
0
0.01
0.05
0.10
0.15
0.097
0.0098
0.0030
0.025
4.52
3.11
2.02
4.34
4.74
5.47
7.07
8.25
9.02
1.07
0.388
0.760
6.58
Equilibrium*
pH
6.00
6.00
6.00
6.00
6.40
6.40
6.40
6.40
6.40
6.20
6.20
6.20
6.20
TCa
Tp
103mol L-1
103mol L-1
3.78
2.98
2.10
1.96
1.09
1.27
1.71
2.05
2.38
0.916
0.469
0.749
3.63
2.97
2.26
1.66
3.06
2.14
2.18
2.46
2.64
2.80
0.727
0.415
0.566
2.72
pH
5.48
5.69
5.94
5.85
5.95
5.96
5.98
5.97
5.95
6.56
6.72
6.29
5.72
*TCa and T denote the total concentration of calcium and phosphate.
tA, B, and t represent the type of crystal OCP used.
considerably larger than that reported for HAP[pKso =
58.33 at 25 C; 58.63 at 37C15 ], making OCP an even
more important potential precursor to HAP precipitation
with an increase in temperature.
Solubility isotherms for OCP at 370C are shown in
Fig. 2 at different values of calcium/phosphate molar ratio
(TCa/Tp) and ionic strength. It can be seen that the
solubility values are markedly dependent upon ionic
strength, emphasizing the importance of taking into account
activity corrections for the calculation of thermodynamic
precipitation driving forces. A convenient representation of
the solubility isotherms is shown in Fig. 3 for DCPD,16
OCP, and HAP.15 In this diagram, the curves for anhydrous
dicalcium phosphate (DCPA) and tricalcium phosphate
(TCP) have been omitted, since the precipitation of these
phases in aqueous solution at ambient temperatures has
never been convincingly demonstrated. The singular point
for OCP and DCPD (pH = 5.0 in Fig. 3) is considerably
lower than that (pH 6.4) calculated at 250C under the
same conditions of ionic strength and TCa/Tp ratio. It is
interesting to note that Madsen13 reported that OCP
became more soluble than did DCPD at a pH of 5.6 in the
absence of added electrolyte.
=
1.
2.
3.
4.
REFERENCES
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Jr.:
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