THE ANORMLOUS EFFECT OF MAGNESIUM CHLORIDE UPON T H E DISSOCIATION OF WEAK ACIDS ISIDOR GREENWALD Department of Chemistry, New York University Medical College, New York, New York Received May 9, 1938
In two papers published in this Journal Simms (4) called attention to the anomalous effect of the magnesium ion upon the dissociation of weak acids. Since the author of this paper has, in the course of other work (2), come to the conclusion that the calcium salts of organic acids, and of sulfuric and phosphoric wids as well, are only partly dissociated, it seemed possible that the anomalous effects obtained by Simms might similarly be due to incomplete dissociation of the magnesium salts. The discussion in this paper will be limited to four of the acids with which Simms observed the greatest effects, viz, oxalic, malonic, aspartic, and aminoacetic acids.’ From the equation pH = pK
+ log anion acid --
It is evident that the addition of Mg++, or of any other cation capable of forming a complex with the anion, must decrease the pH of the solution. To bring the solution back to its original pH will require a certain amount of base. .4t this pH the acid not bound as complex will, of course, be distributed as free acid, as monanion and as dianion, in exactly the same proportions as in a solution containing the same amount of total acid but no Mg++or other cation capable of forming a complex with either of the anions. At any given pH, let b’ = corrected equivalents of base per mole of acid in the absence of Mgw, and B’ = corrected equivalents of base per mole of total acid in the presence of Mg”. If we assume that the reaction in the case of dibasic acids is Mg++
+ A--
= MgA
then
B’
=
b’(1 - MgA)
+ 2MgA
1 The case of citric acid will be considered by Cannan and Abels in another communication. 379
380
ISIDOR GREENWALD
from which
B’ - b’ MgA= 2 - b‘ The data of Simms for pH, B‘, and b’ were plotted on large-scale coordinate paper. There were thus obtained, for each acid, two pairs of curves, one for solutions of 2/; 0.20 and the other for solutions of di 0.28. From each of these, three points were taken, representing the two extreme observed points at which direct comparisons were poasible and one intermediate one. The treatment of one pair of figures for oxalic acid will be given in detail, I n a solution containing a total of 9.53 millimoles of oxalate and 25 millimoles of magnesium chloride at pH = 2.885, b’ = 1.102 and B’ = 1.510. From equation 1, B’ - b‘ [MgOx] = -9.53 = 4.33 millimoles 2 - b’ The removal of this much Mg++ and of the same amount of oxalic acid (in its three forms) lowered 2/;from 0.292 to 0.266. At this ionic strength, I
b1
+ 2K1& + [H+]&+R1K2
H+Ki = [H+]*
Using values for K 1and Ka given by Simms (4, 5), b: = 1.078
We now obtained MgOx = 4.46 millimoles, from which the remaining oxalic acid 5.07 millimoles and Mg++ = 20.54 millimoles. & was now 0.265. The concentration of O r - was then calculated to be 0.460, and the value of K to be E
The other values for oxalic acid given in the table weie calculated in a similar manner. With malonic acid the calculation was somewhat simpler because, at the pH of the observations, no appreciable quantity of free malonic acid could be present. In the cme of aspartic acid, it was assumed that the complex formed WM OOCCHNHn /
I
It was assumed that, at pH 8.64 to 9.06, there were no NH3+ groups.
381
DIBBOCIATION OF WEAK ACIDS
With glycine two formulations appeared equally probable. The complex might be (MgOOCCHzNH2)+or Mg(OOCCH2NH2)2. As in the case of aspartic acid, it was assumed that, at pH 9, there were no NH3+ groups. If each Mg binds one mole of glycine,
whereas if two moles of glycine are bound MgGlycz =
1 B’ - b’ - 2 1-b’
TABLE 1 Values joor the dissociation constants* of magnesium oxalate, magnesium malonate, magnesium aspartate, and magnesium aminoacetate, calculated f r o m the data of Simms YAQNEBIUY O X U A T E
MAQNEBlUY MALONATE YAQNEBIUY ABPARTATI
YAQNEBIUY AMIIfOACETA~
dM IKXlW K X l W x 1D PH 4 PH 6 K x( 1l) D p= 6 c(3) (2) (1) __ - -- - ---2.885 0.26 2.12 5.022 0.27 8.69 8.661 0.28 6.35 8.930 0.28 0.111 31.5 3.182 0.26 2.23 5.260 0.27 8.66 8.847 0.28 5.96 9.065 0.28 0.088 21.9 8.979 0.27 5.26 9.248 0.28 0.091 19.5 3.585 0.25 2.31 _ . -
-
“8;”
~
2.925 0.19 1.86 5.100 0.20 6.72 8.643 0.20 4.73 9.020 0.20 0.082 20.4 3.479 0.18 1.96 5.436 0.20 7.32 8.884 0.20 4.49 9.128 0.20 0.046 11.2 3.949 0.18 2.05 5.538 0.20 7.60 9.064 0.20 3.98 9.316 0.201 0.059 10.3
* These constants are stoichiometric, not thermodynamic.
As may be seen from the table, the latter hypothesis gives a more constant value for K . This is contrary to what has been assumed by Davies (1) for the calcium salt, but it does not appear from his paper that the alternative hypothesis had been considered. The stoichiometric constants for the dissociation of calcium malonate and oxalate derived in this paper from the data of Simms are much greater respectively, than the absolute constants, 16 X lo-‘ and 3.7 X derived by Money and Davies (3) from conductivity data. From the table it will be seen that the,palues of K decrease as the ionic strength is diminished, but, from t h e data available, extrapolation to zero ionic strength is not possible. I n all probability such values, if obtained, would be closer to those of Money and Davies than are those presented in the table.
382
IBIDOR GREENWALD SUMMARY
The anomalous effect of magnesium ions upon the dissociation of weak acids is shown to be consistent with the assumption of the formation of slightly dissociated complexes. REFERENCES (1) DAVIES,C. W.: J. Chem. SOC.1938, 277. (2) GREENWALD, I.: J. Biol. Chem. 124, 437 (1938). (3) MONEY,R. W.,AND DAVIES,C. W.: Trana. Faraday SOC.28, 609 (1932). (4) SIMMS, H.S.: J. Phys. Chem. 33, 1121, 1495 (1928). (5) SIMMS, H.S.: J. Gen. Physiol. 12, 241 (1928).
