of resin; however, the magnesium comes through in the effluent soon after the vanadium is eluted. LITERATURE CITED
(1) Ellis, Roscoe, Jr., Olson, R. V., ANAL. CHEnl. 22, 328-30 (1950). ( 2 ) Harvey, A. E., Kormarmy, J. M.,
Wyatt, G. M., Ibid., 25! 498-500 (1953). (3) Hastings, J., hfcclarity, T. A., Broderick, E. J., Zbid., 26, 379-81 (1954). (4) Huffman, E. H., Iddings, G. M., Lilly, R. C., J. Am. Chem. SOC.73, 4474-5 (1951).
(5) Karchmer, J. H., Proc. Am. Petrol. Inst., Sect. 111 29, b3: 72-8 (1949). (6) Kraus, K. A., Moore, G. E., J . Am. Chem. SOC.75, 1460 (1953). ( 7 ) Kraus, K. A., Nelson, F., Smith, C . W., J . Phys. Chem. 58, 11-17 (1954). (8) Kunin, Robert, “Ion Exchange Resins,” 2nd ed., Wiley, Neb.- York f1958). (9) Michaelis, C. I., Tarlano, N. S., Clune, J., Yolles, R. S., ANAL. CHEnf. 34, 1425-6 (1962). (10) Silverman, L., Hamley, D. W., Ibid., 28, 806-8 (1956).
(11) Snell, F. D., “Colorimetric hIet,hods of Analysis” Vol. IIA, p. 63, Van Nostrand, N. Y., 1959. (12) Walter, R. D., J . Inorg. Nucl. Chem. 6 , 58-62 (1958). (13) Woods, P. H., Cockerell, L. D., J . A m . Chem. Soc. 80, 1534-6 (1958).
RECEIVEDfor review March 19, 1962. Accepted October 8, 1962. Work done on contract with the Aeronautical Research Laboratory of the Air Force, Research Division, Wright-Patterson, Air Force Base, Ohio.
Alizarin Acid Black SN as a Metallochromic Indicator for Calcium Nature and Stability of Its Calcium Chelates GLENN ROSS,’ DAVID A. AIKENS? and CHARLES N. REILLEY Deparfmenf of Cbemisfry, Universify of North Carolina, Chapel Hill, N. C. ,The nature and stability of the calcium chelates of Alizarin Acid Black SN, an excellent and unusual metallochromic indicator for calcium, are established directly with the aid of calcium buffers. The reaction of the indicator with calcium is complex. Two major complexes exist: a red species, CazZz, stable above pH 11 and pCa 4, and a purple-blue species, CazZ, stable below pCa 4. These account for the dual color change observed with the indicator in chelometric titrations. Two other species, probably CaHZ and CaZ, exist under restricted conditions and could not b e characterized quantitatively. The behavior of the indicator with calcium is summarized in a pCa-pH diagram which predicts the color behavior of the indicator and allows selection of appropriate titration conditions.
A
Acid Black SN, AABSX, (2.1.21725, Mordant Black 25 ( I ) , 2-(l-azo-2-naphthol)-6- (1-azo-2- naphthol-6-sulfonic czcid)phenol-4-sulfonic acid, LAIZRIN
is a n interesting and unusual metallochromic indicator which gives two distinct color changes in the chelometric determination of calcium with (ethylene1766
ANALYTICAL CHEMISTRY
dinitri1o)tetraacetic acid. The dual color change was first observed by Belcher, Close, and West (2) in the titration of 0.01M calcium at p H 11.5 t o 12.5. They reported that the indicator changed from purple-blue to red about 90% through the titration and the equivalence point was marked by a remarkably sharp color change from red to clear blue. I n titrations of 0.1X calcium, however, the end poirit color change was reported to be from purple-blue to blue. On the basis of mole ratio studies, Close and West (5) suggested that the red complex formed at low calcium concentrations is CaZz, while the purple-blue complex formed a t high calcium concentrations is CaZ. AABSN is represented by Z throughout this discussion (with the charges omitted). Close and West present a striking example of the complicated behavior possible with metallochromic indicators. Obviously, the reaction of AABSN u-ith calcium is far more involved than that predicted by the often-cited analogy between metal complex formation and acid-base reactions. More intensive examination reveals an even more involved situation. To establish the optimal conditions for the use of this unusual indicator a detailed study has been made of the stability and nature of the calcium complexes of AABSN with the aid of calcium buffers. The calcium buffer proved to be a n estremely useful tool. It allowed direct study of the formation of the red complex, which is impossible by any other method. I n contrast to the conclusions of pre-
vious workers, the formula of the red complex is established as CazZz (rather than CaZz) while that of the purpleblue complex is CazZ (rather than CaZ). The behavior of the indicator is summarized by a pCa-pH diagram estabIished from the formation constants of the metal-indicator species. The conflict between the conclusions of this study and those of Close and West underscores the difficulty in interpreting such a n involved system from a partial study. Even the present study failed t o define completely all the complexes of calcium with AABSN. In addition to CazZz and CazZ, at least one and possibly two other complexes exist under restricted conditions but were not characterized quantitatively in spite of considerable effort. EXPERIMENTAL
Purification of AABSN. llizarin Acid Black SN, suitable for uie as a metallochromic indicator, was obtained as the trisodium salt from Lamont Laboratories, 5002 K e d Mockingbird Lane, Dallas, Tes. The indicator is about 3570 pure, the major impurities being sodium salts used to salt out the indicator in manufacture. The indicator was purified for stability constant studies by two precipitations from aqueous solution by addition of HCl. The precipitated indicator was dried a t 80” C. under vacuum and stored in a 1 Present address, Chemstrand Research Center, Durham, N. C. 2 Present address, Department of Chemistry, Rensselaer Polytechnic Institute, Troy, N. Y.
desiccator. The indicator purity was found to be 88% (by photometric titration with standard calcium a t pH 12.8) and 89% (by photometric titration with standard copper at p H Q), assuming 1t o 1 metal-indicator stoichiometry. From 4 to 5% of the purified indicator was contaminated with metal ions transferable to EDTA, as judged from the increase in absorbance a t 630 mp when a 1 x lO-bM solution of AABSN a t pH 10 was made 0.01M in EDTA. Dumas nitrogen analyses gave 93% purity corresponding t o the sum of free plus complexed indicator. The remaining impurity is undoubtedly water which is held tenaciously by sulfonates or noncomplexing salts. Ignition of a 500-mg. sample of the indicator gave approximately 2.8 mg. of ash. The apparent paradox of the recovery of only 0.6% ash and the contamination of 4 to 5% of the indicator by metals is resolved when it is realized that the atomic weight of a typical contaminante.g., iron, 56-is about one tenth that of AABSN, 594. No structural changes were induced in AABSN by the reprecipitation. The visible absorption spectrum of the reprecipitated indicator a t pH 10 was identical to t h a t of the commercial material in the presence of EDTA, the absorptivity of the purified material on a meight basis being approximately triple that of the commercial material. Reagents. Unless noted, analytical reagent grade chemicals were used. Demineralized water was used in the preparation of all solutions.
Hydroxyethylethylenediaminetriacetic acid, HEDTA, was obtained from Lamont Laboratories. Calcium solutions were standardized against EDTA, which had been compared to copper metal. For preparation of calcium buffers, HEDTA a a s compared to standard calcium a t pH 10, using Eriochrome R a t the indicator. The end point was taken as the disappearance of the last trace of red. Stock solutions of 0.0208M HEDTA, 0.0484M HEDTA, O.O208:1f Ca-HEDTA, and 0.0484M Ca-HEDTA were then prepared and used in all buffer experiments, General Procedures. All measurements below p H 1 3 were performed in solutions of ionic strength 0.1, maintained by addition of the appropriate amount of NaN03. Absorbance d a t a were obtained with a Cary Xodel 14 recording spectrophotometer in a n air-conditioned room maintained a t 25 O + 1O C. A properly calibrated Leeds & Northrup Model 7664 pH meter with a 1199-30 S T D Leeds I%Northrup glass electrode was used for p H determinations, which were reproducible to h0.02 pH unit. Solution pH was adjusted by the addition of small amounts of NaOH or HNOa. Experimental solutions were prepared and diluted to about 90 ml., and the p H was adjusted to the approximate value. The solution was transferred to a 100ml. volumetric flask and diluted to the mark. The p H was measured, the absorption spectrum secured from 700 to 450 mp, and the pH rechecked. Tristimulus color coordinates were
calculated from absorption spectra by use of the analog computer described by Reilley and Smith (1%'). Absorbances a t ten equally spaced wavelengths from 520 to 700 mp were substituted in order into the ten computer inputs originally designated 415 to 685 mp. Color concentration was calculated by the usual method. Indicator Acid Dissociation Constants. Solutions containing 2.0 x lo-5M AABSN and 0.01M EDTA were prepared a t 1 pH intervals from pH 4 t o 14 and the spectra recorded. I n acid-base transition regions, additional spectra were obtained a t approximately 0.3 pH increment. Calcium Buffer Studies of Ca&. For the determination of the number of moles of AABSN per mole of compleu, three Ca buffer solutions were prepared, each 1.04 X l O - 3 M in CaHEDTA and 1.04 X 10-331 in HEDTA and 9.8 X 10-6M, 1.96 X l O - 5 M , and 3.92 x 10-5111 in AABSN, respectively. After adjustment to pH 13.00 f 0.02, the visible absorption spectra were obtained. For each measurement, two additional solutions containing the same concentration of AABSN were prepared, the first containing a 10% excess of Ca over the amount required to react with the indicator, and the second 0.01~14 HEDTA; the spectrum of each was recorded. ildditional measurements were made a t pH 12.00 with 9.8 x 10-6M AABSN, 2.42 X 10-zM CaHEDTA. and 9.68 X 10-2X HEDTA: a t pH 12.50 with 1.04 X 10-2M CaHEDTA. 1.04 X 10-3M HEDTA, and both 8.45 X 10-631 and 1.69 X l O - 5 M A4BSN: and at pH 13.5 with 2.08 x lO-3dl Ca-HEDTA, 8.32 X lO-3M HEDTA, and 9.65 X 10-6M AABSN. To determine the number of moles of calcium per mole of complex, a series of 11 calcium buffers a t pH 13.00 f 0.02 was prepared. Each was from 1.04 x l O - 3 J f to 1.25 X 10-2M in HEDTA and from 1.04 X 1O-sM to 6.24 X lO-3ill in Ca-HEDTA, giving a series of solutions a t approximately equally spaced pCa intervals from pCa 7.2 to 9.0. Each solution contained 1.96 x 10-6M AABSN. Two additional solutions 1.96 X 10-jM in AABSN were made up, the first containing a 10% excess of Ca and the second 0.01M HEDTA. The visible spectra of all 13 solutions were recorded. Reaction of Ca2Z2 with Calcium. The reaction of Ca2Z2 with calcium was followed spectrophotometrically a t p H 11.50, 12.00, and 12.50 by adding successively larger amounts of standard calcium to a series of solutions containing 1.69 X 10-6.1.1 AABSY. After pH adjustment to the nominal value =t0.02, the visible absorption spectra were obtained. At least six solutions in each case contained insufficient calcium to react with all the AABSN and one contained a 10% excess of calcium. Twelve to 20 additional solutions containing increasingly larger excess of calcium were prepared until the absorption spectra became independent of the calcium concentration (at approximately 0.02M calcium).
Formation of CaHZ. T o solutions 1.50 X 10-6M in AABSN at p H 9.20 and 10.00 were added increasing known amounts of standard calcium until the absorption spectra were not affected b y additional calcium. At least ten calcium concentrations were prepared at each pH. DISCUSSION
Stoichiometry and Stability of Complexes. Although the stoichiometry and stability of CazZ2can be evaluated by spectrophotometric measurements of the extent of dissociation of the complex, the unusual nature of the complex requires a different approach from t h a t usually employed in studies of metallochromic indicators. The effective formation constant of a complex, hl,Lb, where M represents a metal ion and L a ligand, is given by
where [ X l fequals total concentration of metal ion and [LIrequals total concentration of free indicator, regardless of protonation. Conversion of Equation 1to logarithmic form gives lbli
which, a t constant [MI, and pH, rearranges to
where all the constant quantities are collected in K ' . The value (b-1) is given by the slope of a n experimental plot of Equation 3. The ratio
is related directly to the absorbance of the mixture, A M , and the absorbances of the same concentration of the ligand in its free form, AL, and its cornplexed form, AM& by
At first glance it appears that an independent determination of b is impossible, since b appears in Equation 4. However, the determination of b requires only that quantities proportional to R and to [Lit be used in A L - AM Equation 3. Thus, A ,~- AiMoLb can be substituted for R and b(dJbf - . ~ , M ~ L J for [LIf. The substitutions shift the numerical value of the coordinates and do not affect the slope. Once the value of b is established, a can be determined by similar experiments in which the total concentration of indicator (free plus complexed) VOL. 34, NO. 13, DECEMBER 1962
1767
and the pH are maintained constant and [MI is varied. Equation 2 then takes the form $05
z 4 04
so that the value of a is given by the slope of a plot of Equation 5. The prior determination of b is necessary because the quantity determined spectrophotometrically is [MaLb] [LI f
not
[Md$ [LI! If the extent of dissociation were evaluated from measurement of
vr 0
s 03 02 01 0.0
10 .
Co,
ml.
2.0
3.0
Photometric titration of 2 X 1 O+M AABSN with calcium at pH 12.5 1.98 X 1O + mmole AABSN
Figure 1.
Volume -1 00 mi. 1.05 X 1O%4 calcium X = 620 mp
[M=Lb]
[Jfl the determination of a would necessarily precede that of b. The stoichiometry of the complex with respect to hydrogen ion is determined from the pH dependence of K e f f after the protonation of L and the hydrolysis of M are taken into account. Substitution of the concentration of unprotonated L for [Lit and of the concentration of free metal ion for yields the absolute stability constant. Metal BufIers. Metal buffers are extremely useful for direct determination of both the stoichiometry and the stability of metal complexes. The technique is of general applicability and should be useful in a wide variety of complex formation studies. By controlling the metal ion concentration a t a desired low level, a metal buffer permits the study of complexes of great stability. The buffer method effectively complements methods of stability constant determination based on acid-induced dissociation of the complex in the presence of a large excess of metal ion. Metal buffers allow the direct study of complexes which cannot be examined by the acid-dissociation method. A case in point is the present study. The species CapZ2is stable only above pH 11 in the presence of calcium concentrations lower than 10-4Af. A decrease in p H or increase in the calcium concentrations leads to the formation of CazZ which, in turn, dissociates stepwise to give the free indicator, the intermediate species being spectrally similar to CaPZ. The dissociation of CanZl above pH 11 is straightforward, however, and readily measured by maintaining known calcium concentrations a t the to 10-9X level through the use of a metal buffer. The extremely low metal concentration is in equilibrium with much higher concentration of a metal chelonate and of 1768
ANALYTICAL CHEMISTRY
free chelon. It is controlled solely by the concentration of these two species and the effective stability constant of the metal chelonate. Hence, a metal buffer system controls pM in the same manner as an acid-base buffer system regulates pH. Above the pH corresponding to complete deprotonation of the chelon, the effective chelonate stability and the free metal concentration are pH independent and unaffected by competitive side reactions such as hydrolysis or complex formation with the ionic medium. Reilley has given a detailed discussion of metal b d e r s (10). The basic requirements are that the metal buffer be well poised and not interfere with the measurement of the equilibrium under study. I n the present case, this simpIy means that the buffer system must not absorb visible light. Consideration of the stability constants of calcium chelonates led to the selection of HEDTA as the metal buffer system in this study. Above pH 10.7 the effective stability constant of the calcium chelonate is pH independent and the calcium concentration is well buffered from pCa 7 to 9. RESULTS
AABSN Acid Dissociation Constants. The stepwise acid dissociation of AABSW involves the loss of five protons, the two most acidic of which are associated with the sulfonate groups. These groups play no part in the complex formation and The pK8 and dissociate a t p H -1. pK4 values, corresponding to loss of the first and second phenolic protons, were determined from the pH dependence of the absorbance of the indicator a t 630 mp. Log plots of the acid-base ratio of the indicator us. pH indicate successive one-proton reactions. The value of pKs is 5.79 and the slope of the log plot is 0.95, while the value
of p& is 12.80 with a log plot slope of 0.92. The third phenolic proton is lost above p H 14 and the dissociation constant could not be determined. The only disadvantage is that complex equilibria must be written in terms of HZ rather than Z as is customary. CazZ2. The formula of the red calcium-AABSN complex is established as Ca2Zzand the stability constant determined by two types of calcium buffer experiments. The stoichiometry is confirmed by photometric titration of AABSN with calcium, which indicates a n equimolar Ca:AABSN ratio. A Ca:AABSN mole ratio of 1 to 2 can be ruled out immediately, as this would require a nearly 200% pure indicator, which is absurd. A photometric titration of 2 X 10-6X AABSN with calcium a t pH 13 is shown in Figure 1. Noteworthy is the almost total absence of rounding near the end point, a reflection of the unusually high stability of the complex. Because of this remarkable stability and the large change in absorptivity on chelation, AABSN is extremely promising as a unique photometric titrant for the determination of calcium at the 10-6 to 10-651 levels. The red complex is remarkably stable with respect to not only dissociation but also further reaction with calcium. Virtually no change in color occurs even when a tenfold excess of calcium is added. Because the high stability of the red complex resulted in virtually linear photometric titration segments, the stability constant could not be estimated. Furthermore, the photometric titration merely indicates the combining ratio of calcium and AABSN but does not distinguish betn-een, for example, a 1 to I and a 2 to 2 complex, the formation of which was actually observed with AABSN. The presence of two molecules of -4ABSN in the red complex was established from calcium buffer experiments in which the total concentration of AABSN was varied at pH 13.0 and pCa 8.0 (Table I). Substitution into Equation 3 and plotting give an excellent straight line, the slope of which is 1.06, corresponding to a b value of 2.06. Thus there are 2 moles of AABSN per mole of complex. iilthough determination of b and the demonstration that a equals b in the photometric titration of the indicator Kith calcium define the stoichiometry of the. complex, the direct determination of a, the number of moles of calcium per mole of complex, was dictated by the unusual nature of the complex. This is accomplished readily by a second type of buffer experiment, in which the pH and indicator concentration are held constant and the calcium concentration is varied. The absorbance a t 600 mp of
Table I. Determination of Stoichiometry of Red Chelate with Respect to AABSN
Total A L - AM A M- A I M ~ L ~ [AABSN], M 9.80 x l o + 0.079 0.131 1.96 X 0.293 0.257 0.327 0.205 3.92 x p H 13.00 Z!Z 0.02. Absorbance at 600 mp. a 2-cm. cell. * 1-em. cell.
L I -I 0.0
I
I
I
I
I
I
I
-7.0
-8.0
-9.0
I
-6.0
LOG (Ca)
1.96 X 10-aiM AABSN as a function of pCa is shown in Figure 2, where a smooth curve has been drawn through the points which show appreciable scatter. The values corresponding t o the smooth curve rather than the individual evperirnental points were used in plotting Equation 5. The plot corresponds to the assumption that b = 2 is linear and the value of a found from the slope is 1.85, indicating 2 moles of calcium per mole of complex and confirming the stoichiometry as Ca2Z2. -% decrease in slope at pCa -9 may indicate the formation of species containing only 1 mole of calcium at these lon calcium concentrations. Attempts to analyze the data in Figure 2 on the basis of a 1 to 1 complex give a sigmoidal curve rather than a straight line, showing the error of this assumption. The determination of a is not strictly independent of the determination of b, because the value of b appears in Equation 5. However, the equal values of a and b obtained in the buffer experiments and the equality of a and b deduced from the photometric titration demonstrate the correctness of the 2:2 stoichiometry. Complete deprotonation of ABBSS in the complex CazZ2is indicated by the p H independence of the absolute stability constant calculated on this basis (Table 11). From these data, the value of Kabs corresponding to the formation of Ca2Z2from HZ 2Ca
+ 2HZ
-+
CanZr
+ 2H+
(6)
was takcn as 3.2 X 10-5. The p H independence of Kaba gives an indirect check on the values of a and b. because the free calcium concentration varies from 2.5 X lO-’M at p H 12 t o 1.0 x 10-8M a t p H 13 and the fraction of AABSIY in the form HZ, as used in the formulation of Reaction 6, varies from 0.14 to 0.70 over this p H interval. An error in either a or b would be apparent as a drastic shift in Ksbs with pH. The value of Keff at p H 13.5 is of only qualitative significance, as several unevaluable opposing factors influence the results. An unknown
Figure 2. Absorbance a t 600 mp of 1.96 function of calcium concentration
X 1 O-5M AABSN as a
pH 13.00 2-cm. cell
fraction of AABSN is converted from HZ to Z a t p H 13.5, tending t o decrease the value of K based on the assumption of HZ as the only form of AABSX’. The sodium ion error, for which the p H is corrected, is about 0.13 p H unit. Finally, the increase in ionic strength from 0.1 t o 0.3M undoubtedly depresses the formation of CazZz. The data show considerable scatter because of the extreme sensitivity of both the extent of reaction and estimation of the extent of reaction t o pH. At p H 12.0, for example, an error of 0.05 p H is reflected as a discrepancy of 0.2 pK unit. Further, the concentrations of free AABSN and of CazZ2 are estimated by comparison of spectra obtained from three solutions and the square of the concentration of AABSY enters the computation of K . At p H 13.0, the p H dependence of the reaction is lower, but the proximity of the H2Z/HZ transition increases the error in estimating the concentration of AABSN. A two-dimensional representation of Ca2Z2is given in Figure 3. The extreme stability of the chelate, evident in the linearity of photometric titrations of AABSN with calcium, reflects the efficient use of the ligand sites. Each calcium ion is coordinated strongly to two oxygens, somewhat more weakly to a second pair of oxygen atoms shared
13.00 13.50
r 2 O 3 -
Figure 3. Ca2Zz
Proposed structure of
Absolute Siability Constant of Ca2Zz as Function of pH 2Ca 2HZ --+ CasZ:. 2Hf [AABSN], AI [Ca-HEDTA],M [HEDTB], [Ca], 31 total -.log K 2.42 x 1 0 - 2 9 . 6 8 x 10-4 2 . 5 x 10-7 9.80 x 1 0 - 6 4.3,4.1 1.04 X 1.04 X 1.0 X 8 . 4 5 X 10” 4.4 1.04 X lo-* 1.04 X 10-8 1 . 0 X lo-’ 1 . 6 9 X 10-5 4.6, 4.5 1.04 x 10-8 1.04 x 10-* 1 . 0 x 10-8 1.69 x 10-5 4.5, 4.6 2.08 X 8.32 X 2 . 5 X 10-9 9 . 6 5 X 105,2
Table [I.
pH 12.00 12.50
with the other calcium, and may be bonded to the azo group. Each molecule of AABSS is bound to both calcium ions, giving a rigid structure and locking the calcium ions securely in place. Of course, the actual geometry of the complex can be defined onlv by x-ray studies. In a kinetic sense, the extreme stability of the complex is attributed to the difficulty of stepwise dissociation caused by the rigid structure. Effectively, the degree of chelation is much higher than is common with a terdentate ligand. Ca2Z. T h e formula of the purpleblue complex stable in excess calcium
+
+
pH adjusted ~ k 0 . 0 2
VOL. 34, NO. 13, DECEMBER 1 9 6 2
1769
was established as CazZ from the extent of reaction between CazZz and excess calcium. The consistency of the resultant equilibrium constant confirms the formula CazZ. The extent of reaction was deduced from the tristimulus color coordinates derived from the absorption spectra of mixtures of Ca2Z2and excess calcium. The tristimulus presentation was chosen in preference to absorbance measurements a t one wavelength because the presence of three species can be detected by the former treatment. To define the color coordinates of CazZz more precisely, points corresponding to the formation of this species from the free indicator were obtained and the coordinates of CazZz located by intersection of the two lines corresponding to its conversion to Cat2 and free indicator, respectively. The tristimulus color coordinates plot, z J us. yJ, of the reaction a t pH 12.50 is shown in Figure 4, each point corresponding to a different calcium concentration. The linearity of segments AB and BC indicates that only two absorbing species are detectable a t any calcium concentration up to 0.04111. Both XJ and yJ and, therefore, the distance along any linear segment of the diagram, are directly proportional to the distribution of absorbing species in the same manner as absorbancies; hence, the reaction is analyzed as described for the formation of CaZZz. Because the concentration of free calcium a t points between B and C is readily determined, the stoichiometry and equilibrium constant of the reaction are accessible. Assuming the reaction CalZn
+ 2Ca
+
2CaiZ
(7)
the values of the effective equilibrium constant a t points D, E, and F are
Table 111. Equilibrium Constant for Formation of CazZ from CazZz PH Kerf Kaba 11.5 2.0 X lo2 2 . 1 X lo2 12.0 1 . 7 X lo2 1 . 8 X loa 12.5 1 . 5 X 10' 1 . 9 X lo*
Table IV. Acid Dissociation and Calcium Complex Formation Constants of AABSN log K HsZ + HzZ H+ -5.79 HzZ + HZ H+ -12.80 HZ + Z Hf
