THE DISSOCIATION OF CALCIUM AND MAGNESIUM PHOSPHATES · of phosphoric acid and of calcium and magnesium chloride were greater than in the first series and there were a number of experi-

THE DISSOCIATION OF CALCIUM AND MAGNESIUM PHOSPHATES

BY ISIDOR GREENWALD, JULES REDISH, AND

ANDRE C. KIBRICK

(From th,e Department of Chemistry, New York University College of Medicine, New York)

(Received for publication, May 6, 1940)

There is an increasing body of evidence (l-7) tending to show that the salts of divalent cations with organic acids are only incompletely dissociated in aqueous solution. This apparent incomplete dissociation seems also to be true of calcium sulfate (2).

The present paper is concerned with the possibility of such apparent incomplete dissociation of calcium phosphate and of magnesium phosphate. The existence of a soluble complex of calcium, carbonate, and phosphate was postulated by Benjamin and Hess (8) but the unsatisfactory character of their evidence was pointed out by Greenberg and Larson (9). In spite of the reply by Benjamin (lo), we believe that the observations of Greenberg and Larson, which have been repeated in this labora- tory (II), make it impossible to consider the experiments of Benjamin and Hess as valid evidence of the existence, in solution, of the postulated complex.

From the equation, pH = pK + log (base/acid), it is evident that the addition, to a mixture of an acid and its conjugated base, of the halide of any cation capable of forming a complex with the anion must decrease the pH of the mixture. The effect is that of a lowering of the apparent value of pK and was, in fact, so regarded by Simms (12) and by Shima (13).

The effect is readily measurable and the values obtained may be used for calculation of the degree of association of the ions. We, therefore, determined the pH of various mixtures of phosphoric acid and sodium hydroxide, in the presence of CaC12, or of MgC12, and compared the values with those obtained in

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66 Dissociation of Ca and Mg Phosphates

similar mixtures containing NaCl or KC1 of the same ionic strength.

EXPERIMENTAL

Calcium, magnesium, sodium, and potassium chloride solutions were prepared from good grades of commercial salts. The con-

TABLE I

Titration of 1.868 rnM i!lJ’Od in Presence of 11.60 rnM NaCl or of 3.869 m&f MgCl?

p = 0.0015.

i NaOH added

mill

1.20 1.60 1.80 2.00 2.26 2.40 2.60 2.80 3.00 3.20 3.40 3.60 3.80

N&l

I- PH

3.32 3.78 4.59 6.01 6.34 6.61 6.82 7.00 7.15 7.40 7.64 7.99 9.30

PK2 I&PO4

7.10 7.09 7.11 7.00 6.96 7.13 6.98

Average Kz = 8.80 X 10d8 Average K = 3.93 X 1OF pK2 = 7.06 pK = 2.41$

- * Excluded from the average.

PH

3.32 3.79 4.50 5.75 6.10 6.38 6.59 6.80 6.98 7.15 7.42 7.78 8.75T

MgClz

01

0.026 0.089 0.131 0.185 0.220 0.278 0.354 0.400 0.541

iv&O,

2.17* 2.42 2.38 2.40 2.36 2.40 2.49 2.40 2.67*

t At this pH, the calculated amount of NaOH to be added in NaCl solution is 3.66 ml. or 1.96 equivalents per mole of acid. LY is indeterminate. The formula (B/S. - R)/2 - R gives a = 0, but a change of pH to 8.72 makes (Y = 1.

$ This number is the negative logarithm of the average value of K. This procedure has been followed in all the tables.

centrations of the first two were determined from the chloride content; the sodium and potassium chlorides were weighed as such. Phosphoric acid was prepared from syrupy phosphoric acid and was standardized by precipitation and weighing as MgNHdP04.6HzO.


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Greenwald, Redish, and Kibrick 67

A series of volumetric flasks, each containing the same amount of phosphoric acid, salt, and water, was prepared for each titration. 0.1 N NaOH was then added. After the contents had been diluted to the mark and mixed, the pH was determined with the Coleman glass electrode at room temperature, with a saturated solution of KC1 for the liquid junction. In a number of instances, the pH of the mixtures containing Ca or Mg chloride was determined at intervals for 2 hours. No change was observed.

TABLE II

Titration of I.&91 rnM Hap04 in Presence of MgC12

?nM 1.60 1.80 2.00 2.20 2.40 2.60 2.80

7.737 EIM MgClz, ,I = 0.026 15.47111~ MgClz, p = 0.049

PH

5.68 6.12 6.39 6.61 6.82 7.11 7.49

a PK PH 0 PK

0.027 1.88* 0.097 2.06 0.149 2.05 0.216 2.06 0.329 2.21 0.383 2.18 0.474 2.22

Kz of H3POa in NaCl = 1.06 X 10-7 1.49 x 10-y

7.47 x 10-a pK = 2.13

* Excluded from the average.

5.40 0.032 1.77* 5.89 0.107 1.88 6.19 0.167 1.85 6.38 0.259 1.95 6.60 0.364 2.01 6.88 0.435 1.99

--

1.74 x 10-e

1.93

In another series of experiments, the hydrogen electrode, at 25’, was employed. In these, the variations in the proportions of phosphoric acid and of calcium and magnesium chloride were greater than in the first series and there were a number of experiments in which mixtures of potassium chloride and calcium chloride or magnesium chloride were used. The titration intervals were greater than in the first series. Mixtures in which a pre- cipitate formed either immediately or within 24 hours were discarded.

The composition of the mixtures and the values for pH obtained are given in Tables I to VI. The ionic strengths are calculated


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TABLE III

Titration of 0.747 mat HsPOa in Presence of CaCb

1.515 InId CaClr, /.1=0.006

3.788 Imd tack p = 0.013

7.576 nxv Cd%, p = 0.024

NaOH

__- InM

0.80 0.88 0.90 0.96 1.01 1.05 1.06 1.12 1.14 1.15 1.17 1.24

PH OI PK PH a PK PH a PK -I.

6.35 0.048 2.37

6.64 0.059 2.24

6.90 0.066 2.11

5.80 0.032 2.21 6.22 0.057 2.04

6.49 0.086 2.06

6.71 0.133 2.12

6.22 0.094 2.04 6.39 0.125 2.03 6.50 0.172 2.11

6.66 0.188 2.16 6.76 0.244 2.12

6.91 0.180 2.15 7.14

7.31

0.076 2.04 6.81 0.328 2.27

0.165 2.37 7.11 0.252 I 2.24 I-

Kz of H,POa in iYd.21 = 7.53 x 10-S

Average K = [Ca++l [HPO4=1 [CaHP04] =

6.24 X 1W pK = 2.20

9.00 x 10-S 8.69 X lO-8

7.40 x 10-z 7.66 X 1OF 2.13 2.12

TABLE IV

Titration of 1.488 mM H3P04 in Presence of MgClz

13.3 mix M&h, P = 0.043 8.33 ned MgCit, J, = 0.027

PH OL PK

6.226 0.137 2.12 6.558 0.261 2.22 6.945 0.399 2.26

PH cl PK

~ -I---- ----- n&M

1.879 2.192 2.506

6.136 0.141 I 1.95 6.459 0.727 2.05 6.814 0.563 2.15

K2 of H,POI in KC1 = 1.02 X lo-’ 1 1.20 x 10-1

9.10 X 10-s

2.06

Average K = !!++I [HPoa-’ [MHPOII

= 6.37 X 1O-3

pK = 2.20


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without correction for the complex formed. The effect of this upon the ionic strength and the dissociation of phosphoric acid was negligible. The values for the dissociation constant of phosphoric acid given in Tables I to VI were calculated in the usual manner from the data obtained in solutions containing NaCl or KCI. It will be noted that the values of Kz are not quite the same, at identical ionic strength, in Tables II and III. However, the values used were, in each case, obtained with the electrometer standardized on the same occasion for mixtures containing NaCl as for those containing CaClz or MgCl,. If an error in standardi-

NaOH

nm

0.940 1.086 1.253

..- I

TABLE V

Titration of O.Y& rnM HsPOa in Presence of CaClq

8.33 m&l cac12, p = 0.027 13.3 nm CaCl*, p = 0.043

PK PH a PK

2.08 6.193 0.125 1.84 3.84

K, of H3P04 in KC1 = 1.02 X lo+ 1.20 X lo-’

IM++l WOPI = 6 47 x 1o-3 ’ AverageK = [MHPOI, .

pK = 2.19

zation was responsible for a displacement of the titration curve in NaCl solution, there should have been a parallel, and equal, displacement in CaC!& or MgCI2 solution.

Results

No difference in pH between mixtures containing CaClz or MgC12, and those containing NaCl was observed until after the addition of more than 1 equivalent of alkali per mole of phosphoric acid. Because precipitates appeared in many of the more alkaline mixtures, the complete range of dissociation of the second proton of phosphoric acid could be followed in only one experiment, that with the lowest concentrations of phosphoric acid and of magnesium (Table I). Inspection of the figures shows that the titration in the presence of MgC12 became nearly the same as in NaCI, as the pH approached 9.0.


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N / 2 XZ 8 ti -

!- -

,

.- , t

- i

li - i <

j- . : L

-

7 3 KY 3 ?i

-T-

-


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DISCUSSION

The absence of any effect of CaClz or of MgClz upon the titration of the first proton of phosphoric acid indicates that there was, in these experiments, no appreciable formation of complexes of Ca++, or of Mg++, with HzPOh-.

Because of the format,ion of precipitates, we were rarely able to continue our observations beyond pH 7.0, and, in only one case, beyond pH 8.0. Only above this pH does the concentration of POIE become significant. Therefore, our results yield no informa- tion on the tendency of this ion to associate.*

The effects observed must, therefore, be ascribed to association of Ca++, or of Mg++, with HPOh. The most probable product is MHPO,. Accordingly, the data obtained have been treated upon this assumption.

The method of calculation resembles that employed by Cannan and Kibrick (2) in the study of complex formation with dibasic acids.

The postulated complex MHP04 might, dissociate! into M and HIV4 The constant for this would be

[M++] [HP04 = KMHPOa = --MHPO,]

] (1)

However, it might also dissociate into H and MPOJ, for which we may write

I( 4

= IH+lN’O,-1 ..~ [MHPOJ

(2)

If S, = concentration of total phosphate and cy = the fraction present as complex,

DfPO,lEI+l &,, = [MPO,-] + ----rc-~ -- -.- 4

from which

(3)

1 If the formation of undissociated Ma(POJz were appreciable in these csperiments, the value of the dissociation constant, K = [M++]3 [P04’12/ [M8(P04)2], would be of the order of 10-17.


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If B’ = total base (titration + II+), then, at our range of pH,

B’ = (1 - a)S, lH+P 2[H+]Kz a&. Kn -----.

[H+]Z + H’Kz + [H+]z + H+E + 2as, + ---~--.-

IH+l + K

= (1 - cu)S,.IZ + CYSa~V

and

B’/S, - R

in which

R = [H+l + 2Kz lH+l + Kz

and v = 3Ka + 2[H+1

[H+I + 6

From Equations 2 and 3

lH+l&‘, MHPo4 = [H+] + K,

When the appropriate values are substituted in Equation 1,

[total M - a&I [E;T~; .(I - a)&

RMHPOa = 2 >

lH+l(~So lH+l + &

1-a Kz a IH+l + Kz

.‘G+ [total M - cd’,]

(4)

(5)

(6)

(7)

(8)

It at first appeared reasonable to believe that Kd would be of the order of low2 or 10p4. However, substitution of such values in Equation 8 failed to give constant or reasonable values for K MHpoa. On the other hand, the assumption that KJ was much lower than [Hf], 10dg or less, gave reasonable and consistent values for KMHpoa. As Kd is made smaller with respect to [II+], the value of V approaches and becomes equal to 2. Accordingly, all subsequent calculations were based upon the assumption that V = 2 and that

B’/S, - R oL=

2-R (9)


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and

KMHPO~ = l--a a.[~:lle~ [total M - C&J (10)

2

In these calculations, [H+] was taken as equal to a[H+]. In the value for B’, [H+] was of significance in only a few instances, so the effect on B’ of substituting [H+] by a[H+] was negligible.

As is apparent from the results presented in Tables I to VI, the assumptions outlined above lead to fairly constant values for the dissociation of the supposed complex. A few of the recorded values diverge considerably, but inspection shows that these were obtained from measurements made under conditions at which (Y (the fraction of phosphate bound) was small. Such low values of a! are encountered at low concentrations of MC12 or at low pH. Under these conditions, the difference between the amounts of alkali required by the mixtures containing MC12 and those containing NaCl or KC1 is very small. A similar unreliability is to be expected at the upper range of pH, as the Gtration curves again approach each other. In our experiments, this occurred only once (Table I). It will be noted that pK calculated for pH 7.78 was 2.67, instead of the 2.36 to 2.49 obtained for pH 6.10 to 7.42. At pH 8.75, LY became indeterminate.

Table VI shows that concordant values of pK are to be obtained at p = 0.2, regardless of whether all, or only 10 per cent, of this is furnished by MCI,.

After the experimental work reported in this paper had been completed, it was discovered that Bjerrum and Dahm (14) had obtained a similar, and more marked, effect of AlCls upon the apparent dissociation of phosphoric acid. Their results indicated the formation of several types of complex, including Al(HzPO&.

At this time, there appeared a paper by Shima (13) in which he reported the effect of KCl, NaCl, MgC12, and MgS04 upon the pH of half neutralized 12.5 mM phosphoric acid, as determined by the quinhydrone electrode. By calculation from his data, we obtained the figures shown in the last column of Table VII. The first three figures are rather unreliable, because they are based on differences in pH of only 0.037, 0.055, and 0.075, respectively. Thereafter, the figures are quite in agreement with ours and show the same increasing dissociation with increasing ionic strength.


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The equation pK = 2.50 - 2.15 di gives fair agreement with the observed values, whether obtained by Shima with the quinhydrone electrode or by us with glass and hydrogen electrodes.

Physiological SigniJicance-The value of the dissociation constant for CaHPOa indicates that in plasma, at pH 7.35 and p =

TABLE VII

P

0.006 0.013 0.015 0.026 0.027 0.030 0.032 0.034 0.040 0.041 0.043 0.044 0.049 0.055 0.063 0.100 0.175 0.200 0.325

Relation of pK = ---Log @I++1 [HPO4=1

,MHPOI, to Ionic Strength

CaHPOa

GhSS electrode

2.20 2.13

2.12

Hydrogen electrode

2.19 2.20

1.84 2.06

1.93

1.50 1.65

Glass electrode

2.41 2.13

MgHPO4

Hydrogen electrode

buinhydrom electrode

1.84* 1.57* 1.85* 1.94

2.01

1.97 1.95 1.77 1.62

1.29

Cak;ged

pK = 2.50 - 2.15 4;

2.24 2.15 2.15 2.13 2.11 2.10 2.07

2.05 2.05 2.02 2.00 1.96 1.82 1.60 1.54 1.28

* Inaccurate, because of small differences in pH; see the text (p. 74).

0.152, containing 1 mM phosphate and 1.25 InM Ca not combined with protein, approximately 0.055 mM CaHP04 is present.

SUMMARY

Phosphoric acid was titrated electrometrically in the presence of KCl, NaC1, MgCL, and CaC12. No differences were observed up to the addition of 1 equivalent of NaOH. Thereafter, the


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mixtures containing MgClz or CaC&. were more acid than the corresponding mixtures containing NaCl or KCl. The results can be formulated as being due to the formation of slightly dissociated MgHP04 and CaHP04. The value for the negative logarithm of the dissociation constant of MgHP04 is approximately 2.50 - 2.&/i. CaHP04 shows a slightly greater tendency to dissociate.

BIBLIOGRAPHY

1. Greenwald, I., J. Biol. Chem., 134, 437 (1938); J. Physic. Chem., 43’ 379 (1939).

2. Cannan, R. K., and Kibrick, A., J. Am. Chem. Sot., 60, 2314 (1938). 3. Money, R. W., and Davies, C. W., Tr. Faraday Sot., 28, 609 (1932). 4. MacDougall, F. H., and Larson, W. D., J. Physic. Chem., 41,417 (1937). 5. Kilde, G., Z. anorg. U. allg. Chem., 229, 321 (1936). 6. Davies, C. W., J. Chem. Sot., 277 (1938). 7. Topp, N. E., and Davies, C. W., J. Chem. Sot., 87 (1940). 8. Benjamin, H. R., and Hess, A. F., J. Biol. Chem., 100, 27 (1933). Ben-

jamin, H. R., J. Biol. Chem., 100, 57 (1933). 9. Greenberg, D. M., and Larson, C. E., J. BioZ. Chem., 109, 105 (1935).

10. Benjamin, H. R., J. BioZ. Chem., 109, 123 (1935). 11. Greenwald, I., and Rubin, S. H., Proc. Am. Sot. BioZ. Chem., J. BioZ.

Chem., 114, p. XIV (1936). 12. Simms, H. S., J. Physic. Chem., 32, 1121, 1495 (1928). 13. Shima, K., J. Biochem., Japan, 29, 121 (1939). 14. Bjerrum, N., and Dahm, C. R., Z. physik. Chem., Bodeustein Fest-

band, 627 (1931).


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KibrickIsidor Greenwald, Jules Redish and Andre C.

MAGNESIUM PHOSPHATESTHE DISSOCIATION OF CALCIUM AND

1940, 135:65-76.J. Biol. Chem.

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THE DISSOCIATION OF CALCIUM AND MAGNESIUM PHOSPHATES · of phosphoric acid and of calcium and magnesium chloride were greater than in the first series and there were a number of experi-