Titration of Microgram Amounts of Aminopolycarboxylic Acids with Manganese(l1) and lCata1yti.c End-Point Indication Horacio A. Mottola Department of Chemistry, Oklahoma State University, Stillwater, Okla. 74074
The term catalytic end-point indication is applied to cases in which the sought for constituent reacts fast and stoichiometrically with the titrant which is a catalyst for an otherwise slow reaction used as indicator. The use of the malachite green-periodate indicator reaction and of manganese(l1) as titrant allowed simple, sensitive, and reproducible determinations of microgram amounts of DCTA, DTPA, EDTA, and HEDTA in phosphate-acetate buffers of pH -3.50. Under certain ex pe rimenta I cond itions the manganese( I I)-I iga nd complex(es) exert a pronounced catalytic effect on the oxidation of the organic dye. These catalytic effects make impossible the titration of NTA and EGTA. At a pH of -5.50 (phosphate-acetate) only DCTA can be titrated, increasing the sensitivity. Most relative errors are in the order of 1-4%.
THE DETERMINATION of microgram quantities of anions of’ aminopolycarboxylic acids has become important recently in connection with their use in biology, medicine, and the food industry. The application of metal ion catalysis for the determination of microamounts of ethylenediamine-N,N,N’, ”-tetraacetic acid (EDTA) has been recently reported ( I ) . In the present study, the catalytic end-point indication approach (2, 3) is applied t o the microgram determination of some aminopolycarboxylic anions, and is compared with a more conventional and indirect method of analysis ( I ) . The possibility of using a catalytic approach to the indication of end points seems to originate in a report by Yatsimirskii and Fedorova who coined the term catalimetric titrations. An attempt to assess its impact on analytical applications and the different systems open to study, as well as some of its equilibrium and kinetic characteristics, has been published recently (3). In the catalytic indication of end point, the catalyst is used as titrant for a solution containing a species which reacts stoichiometrically and very fast with it, as well as a reaction mixture which is catalyzed by the titrant and whose rate is monitored to locate the end point of the titration. In addition to the sensitivity achieved, accuracy and reproducibility, and easy automation, the measurements involved are mostly relative. The absolute value of the variables chosen to monitor the indicator reaction does not need to be known accurately because only the measurement of the relative change of this parameter (absorbance, heat of reaction, cell potential, etc.) with time (volume of titrant) is required. The recording of the catalytic portion of the titration curve (the portion where the rate of the indicator reaction varies considerably with the titrant-time variable) provides a mean for indicating catalytic or promotion effects by metal complexes. Even though the quantitative evaluation of these aspects for the chemical system studied is not reported here, the basis for such evaluation is presented. (1) H. A. Mottola and H. Freiser, ANAL.CHEM., 39, 1294 (1967). (2) . , K. B. Yatsimirskii and T. J. Fedorova, Proc. Acad. Sci. USSR, 143, 143 (1962). (3) H. A. Mottola, Talanra, 16, 1267 (1969).
630
*
ANALYTICAL CHEMISTRY, VOL. 42, NO. 6, MAY 1970
EXPERIMENTAL
Apparatus. The control of p H was made with a Beckman Zeromatic p H meter and a glass-calomel electrode pair. The various parts of a n assembled laboratory titrator are shown in Figures 1 and 2. It consisted of a 0.2000-ml capacity, 0.5% accuracy, buret (R. Gilmont Instruments, Inc.) rpm motor and driven by a Hurst Model CA60CY 5W refilled by shifting to a motor of same characteristics but 8 rpm reversed speed. The titrant was delivered at a rate of 0.0067 ml/min. Mixing and circulation of the solutions from the reaction tube to the photometric flow-through cell, made of borosilicate glass, was accomplished by means of a variable speed Masterflex tubing pump with SRC Model 7020 speed controller, and No. 7014 pump head. Photometric measurements were performed with a Beckman D B spectrophotometer and a Sargent SRL recorder equipped with linear or logarithmic gears. The limited dynamic range of the logarithmic mechanical conversion was overcome by multiplying the signal by a factor of ten with a MP-1006A operational amplifier (McKee-Pedersen Instruments, D a n d l e , Calif.). Photometric scale expansion and/or base line selection was obtained using a MP-1004 “photo potentiometer” (McKee-Pedersen). A chart speed of 1 inch/min was used during this study. Reagents. Malachite green (K & K Laboratories) was used without further purification. The solution, containing around 15 mg/100 ml of double distilled water, was discarded after three or four days of preparation. All solutions were prepared with double distilled water. The possible metal content of samples of aminopolycarboxylic acids was reduced by precipitation of the free acid from basic solutions by adding HC104, or washing the solid acid with a 50% ethanol-50 3N HC1 and finally with double distilled water. All other chemicals were of reagent grade. Procedure. Samples containing at least 1.5 pg/ml of aminopolycarboxylic acid (ranging between fractions of a ml to 6 ml) are added to the titration tube. One milliliter of malachite green solution, and 1 ml of a 1% sodium periodate solution, are then added. The total volume is finally adjusted to 10 ml with phosphate-acetate buffer (35 grams of NaH2P04and 15 ml of glacial acetic acid are diluted to 500 ml with double distilled water and the pH adjusted to -3.50 with 1.OM NaOH). The buret tip is introduced into the titration tube, the circulation pump is started and adjusted to a pumping rate of around 25 ml/min. After allowing mixing (less than 20 seconds is required to pump through the cell and back to the titration tube), the buret and recorder are simultaneously started. The titration curve is recorded, the end point located as described later and the content of aminopolycarboxylic acid calculated by reference to a working curve. The absorptiometric measurement is made at 620 nm. RESULTS AND DISCUSSION
The complexometric titration of aminopolycarboxylic acids would be more favorably performed at a rather high pH where a large concentration of complexing anion is present. High pH values, however, would decrease selectivity and increase the possibility of competing hydroxo-complexes or precipitation of hydrated oxides in the vicinity of the end point. Man-
\/Recorder
Gilmont Microburet 0.2 ml
FLOW CELL I
-
H B
m
m
c
-4 L
I
,OK
D
Figure 2. Schematic circuit-block diagram of titration assembly
Figure 1. Titration cell, micro-buret, and flow cell
ganese (11), being rather selective to aminopolycarboxylic acids and forming protonated complexes capable of operating at relatively low pH, suggests itself as a useful titrant. The most sensitive of chemical methods available for the determination of traces of manganese in solution involves its catalytic effect on the oxidation of leucobases of triphenylaryl dyes to the cationic dye or the oxidation of the dye itself to colorless products ( 4 , 5 ) . These reactions have been used to determine submicrogram amounts of manganese (5) and microgram amounts of EDTA by kinetic methods ( I ) . The malachite green-periodate reaction was, therefore, chosen as indicator reaction. The manganese determination is generally performed at a pH of 3.4-3.7 provided by a phosphate-acetate buffer (5). No reason for the use of this specific buffer seems to be reported in the literature. Titrations in different solution backgrounds and in absence of phosphate or acetate ions, however, demonstrated that the phosphate-acetate buffer offers a medium to obtain better developed titration curves and sharper end point indication with inherent good accuracy and reproducibility. Both buffer components seem to promote the catalytic effect of manganese(I1). These titrations were performed in the pH range of 3 to 6. No attempt was made to titrate at higher pH’s because the observed overall first-order rate constants for the catalyzed and uncatalyzed oxidation of malachite green by periodate at pH 9.2 (borate buffer) are 0.0182 min-l and 0.0156 min-’, respectively (6). The probable species of manganese involved in these titrations may range from Mn(I1) to Mn(VI1) (1). Considering the use of a noncomplexing (other than hydroxyl ion) aqueous medium of variable pH, and assuming that the Mn(1V) concentration builds up to the concentration of total manganese added-e.g., 5 X 10-6M, precipitation of Mn(0H)A should occur at pH > 1.6 (7). It might be mentioned that this concentration is orders of magnitude higher in the solution boundary established in the vicinity of the buret tip. Manganese (11), on the other hand, should not start precipitating as hy(4) K. B. Yatsimirskii, “Kinetic Methods of Analysis,” Pergamon Press, Oxford, 1966, pp 114-115. (5) A. A. Fernandez, C. Sobel, and S. L. Jacobs, ANAL.CHEM., 35, 1721 (1963). re(6) . . Gerald L. Ellis. Oklahoma State University. _ . unmblished . sults, 1969. (7) G. Charlot, “Theorie et methode nouvelles d’analyse qualitative,” 3rd ed., Casa Mason et Cie., Paris 1954.
droxide until a pH of 9-10 (8), and manganese(II1) at a pH greater than 4 (8). The concentration conditions are favorable for precipitation of either Mn(II1) or Mn(1V) in the neighborhood of the buret tip. In fact, a black-brownish film was observed in some titrations performed in absence of phosphate or acetate. The appearance of this film was paralleled by a slower rate of the catalyzed reaction and would point to the formation of MnOn aq., because Mn(II1) oxide is rather unstable and dismutates to Mn(I1) and MnOz aq. Phosphate and acetate ions are known to form compounds with Mn(II1) and in the analytical methods involving periodate as prior oxidant, phosphoric acid is recommended to prevent formation of manganese dioxide (9). Phosphate and acetate, evidently, both play a role in the stabilization of Mn(III), and possibly Mn(IV), in the titrations reported here, yielding by complexation more active species (from a redox viewpoint) and at the same time preventing the formation of manganese dioxide. Effect of Some Variables on the Analytical Procedure. The periodate concentration was kept constant through this study at a level at which the reaction rate is independent of it (1). The pumping rate was varied between 12 and 75 ml/min without significant effect on the precision of the end point location. At low speeds, however, the end point is slightly retarded and at high speeds bubbles may be formed and introduce some noise in the recorded signal. A pumping rate of 25 ml/min is recommended. The level of concentration of malachite green solutions was maintained around lO-5M. Initial absorbance readings from 0.80 to 0.50 did not show significant effect on the precision of the end point location. Titration Curves with Catalytic End Point Indication. Analytical conditions are adjusted, during the course of these titrations, such that one of the reagents (the one whose concentration is not monitored) is kept at a rather large concentration to affect pseudo zero-order dependence on this species. Temperature and other variables that affect the rate, except the concentrations of catalyst and monitored species, are kept constant during the course of the titration. Under these conditions, and as it is generally the case, the monitored signal is proportional to the concentration of the monitored species. In the particular case of this study, absorbance was used as monitored variable and the following (8) L. G. Sillen and A. E. Martell, Eds., “Stability Constants of
Metal Ion Complexes,” The Chemical Society, London, 1964. (9) H. A. Laitinen, “Chemical Analysis,” McGraw-Hill,New York, N. Y.,1960, p 345. ANALYTICAL CHEMISTRY, VOL. 42, NO. 6, MAY 1970
631
la
e
b
\ \
\
I
\\
10.1A
io., A
\\
h-
Figure 3. Titration curves
h-
+
Indicator reaction: MG+ IO,-; Mn(II), 1 X l o M 3 M as titrant. Phosphate-acetate buffer, pH = 3.45. A : 1.07 X 10-5MEDTA, B: 3.21 X 10-5MEDTA (origin offset for comparison. For an explanation of points a, b, c, d, and e see text)
Figure 5. Titration curves for EDTA according to procedure Phosphate-acetate buffer, pH = 5.40. A : 0.54 X 10-6M EDTA, B: 1.07 X 10" MEDTA, C: 3.21 X 10-5MEDTA. Blank at pl I = 3.45 included for comparison
with q and m as proportionality constants and CMm= total analytical concentration of titrant species. When the only catalytically active species is the free hydrated metal ion, the following can be derived:
_ dA _ -- A dh
'
q(k1
+ k2ao
'
m
. h)
(4)
with k l and k2as constants related to the uncatalyzed and catalyzed reactions, respectively, and (YO = ratio of free hydrated manganese(I1) ion concentration to the analytical concentration of metal. In case of catalysis, promotion, or inhibition by the species formed during titration, Equation 4 should include terms of the form i k i a i .m h, such as:
-
_ dA _ -- A . q [kl + m . h(knao f Zktatll dt 1.00
3.00
CFmAxlflM
7-00
9.00
Figure 4. Working curve for EDTA according to procedure and conditions in Figure 3
expression applies during the titration:
- dA -= dt
Eb-
d[MG+] dt
with MG+ = malachite green cation. If h = distance along the abscissa of the titration curve--e.g., in mm, see Figure 3 for reference-it is possible to write the following relationships : dh = q * dt (2) and chin = m . h (3) 632
ANALYTICAL CHEMISTRY, VOL. 42, NO. 6, MAY 1970
(5)
A computational analysis of the curves experimentally obtained as well as computer simulation and curve fitting analysis is under consideration at the present time. A different mathematical model may describe different portions of the titration curves. An examination of Figure 3 suggests the following qualitative description: th'e distance a-b in the blank is related to achieving an effective catalyst concentration to modify the rate of the uncatalyzed reaction in an amount compatible with the sensitivity of the detection device. It can be related to an induction period and is a function of such variables as titrant concentration and rate of addition of titrant. From b to c the rate of the indicator reaction is dramatically affected by the increasing amount of catalyst. After c and up to d, it seems that the catalyst concentration has become large enough to give a maximum rate independent, or practically so, of catalyst concentration. Beyond d the rate decreases with increasing catalyst, probably due to the effects of decreasing reactant (malachite green) concentration.
I
I
\
I
h -
h -
Figure 7. Titration curyes for DCTA and NTA according to procedure and conditions in Figure 5 A: 1.01 x 1 0 - 5 ~DCTA, B: 3.03 x 1 0 - 5 ~DCTA (PH = 3.49, C: Blank, pH = 5.50. The origin of curves A and B has been offset to permit comparison of the curves. D: 1.02 x 1 0 - 5 NTA, ~ E: 2.04 x 1 0 - 5 ~NTA, F: 3.06 x 1 0 - 5 ~ NTA
Figure 6. Titration curves for NTA and EGTA ac. cording to procedure and conditions in Figure 3 A : 1.09 x 1 0 - 5 ~EGTA, B: 2.18 x 1 0 - 5 ~EGTA, c: 1.02 X 10"MNTA, D : 2.04 X MNTA
When a complexing agent is present the induction period is enlarged in a length proportional to the amount of ligand present. The empirical end points obtained by extrapolation of the two linear segments of a titration curve, when plotted against amount (concentration) of ligand, yield working curves allowing the determination of the complexing agent (see Figure 4). Other means of locating an end point (3), even though less arbitrary, are more involved. Determination of Aminopolycarboxylic Acids. Figures 3, 5, 6, and 7 show typical titration curves for different acids and at different pH's. Figure 4 shows a typical working curve for microgram amounts of EDTA. Figure 8 shows results obtained in the vicinity of the limit of detection at the 10-SM level for EDTA, 1,Zdiaminocyclohexane-tetraacetic acid (DCTA), diethylenetriamine-pentaacetic acid (DTPA), and 2-hydroxyethylenediaminetriacetic acid (HEDTA). The sensitivity is comparable for the four ligands and the slight displacement of the curves follows the trend in the stability constant values for the 1 :1 complexes with Mn(l1). DCTA is the only compound of the six included in this study which can be titrated at a pH of 5.50. The determination at this pH, as expected, is 3.5 times more sensitive than at pH 3.40. EDTA, DCTA, DTPA, and HEDTA can be titrated at pH-3.50. The shape of the titration curve for DCTA at pH 5.50 seems to indicate a slight catalytic effect exerted by the Mn-DCTA complex(es). Nitrilotriacetic acid (NTA) and ethyleneglycol bis(2-aminoethylether) tetraacetic acid (EGTA) are not amenable to complexometric titration with the catalytic end-point indication reported here. Both ligands, when present, increase considerably the catalytic effect of manganese (Figures 6 and 7). DTPA and HEDTA can be titrated at pH = 3.40 but they also increase the catalytic effect of Mn(I1) at a pH of 5.50. In the titration of EDTA at pH 3.40, as the concentration of ligand increases, a slight increase in AAjAh ratio in the portion
e .
180-
X
A
160 -
0
140 -
4
120 -
I
X
A 0
Figure 8. Working curves for low concentrations of EDTA, DTPA, DCTA, and HEDTA Phosphate-acetate buffer, pH = 3.45. 0 EDTA, 0 DTPA, A DCTA, X HEDTA
c-d of the curve, and a more pronounced increase of this ratio from d o n , was observed. This may be due to the catalytic or prprpoting effect of the Mn-EDTA complex(es) observed at higher pH values. This can be seen in Figure 5 where a blank at pH 3.45 is also included for comparison with the blank at ANALYTICAL CHEMISTRY, VOL. 42, NO. 6, MAY 1970
633
Table I. Precision of Microgram Titrations of Aminopolycarboxylic Acids by Catalytic End-Point Indication Indicator reaction: malachite green periodate, titrant: Mn(I1) 1.00 X 10+M, phosphate-acetate buffer of pH = 3.45
+
Compound Blank EDTA
Concentration, M
na
... 0.54 x 10-6 1.07 x 10-6 2.14 x 10-6 3.21 x 0.50 x 1.01 x 10-6 2.02 x 10-5
DCTA
11 10 8 8
7 9 8 7 6 8 8 6 8 6 7
3.03 X le6 x 10-6 2.00 x 10-6 3.00 X 1.02 x 10-6 2.04 x 10-6 3.06 x 10-6 1.oo
DTPA HEDTA
h (mm)b 44.1 57.0 74.1 131.9 190.1 59.5 81.O 135.2 163.8 75.1 129.1 188.1 73.1 129.1 188.2
Shc
10.8 fl.1 11.7 f2.0 f2.3 11.0 f2.0 f1.8 12.1 11.8 f1.3 3~2.7 5z2.1 11.9 13.2
VLd
... 4.4 3.4 2.0 1.5 4.0 4.1 1.9 1.4 3.9 2.8 1.9 4.4 2.0 2.2
n = number of samples.
*h
= length (mean) along the abscissa used to locate end point. = standard deviation of h. d VL = relative standard deviation based on ligand concentration. Sh
t c
I-/ 0'
I
I
I
0.8
1.0
1.2
I cEDTAx'05
Figure 9. Sensitivity comparisons at the 10-6M concentrationlevel
-e-
Catalytic end point (MG +
+ IO4-), S = 12 X +
106 M -1 mm -ACatalytic end point (Ascorbic acid S = 5.5 X loeM-l mm
-m-
Indirect first order plot; (MG'
3 X 106M-lmm
0 2 ) ,
+ IO4'-),S
=
S = Amm/A Concn
p H = 5.40. Contrary to early observations ( I ) the rate of the uncatalyzed reaction is smaller at pH 5.40 than a t 3.45. The induction period, however, is smaller a t the higher p H ; this would account for a n observed faster rate using the low concentration of catalyst reported in ( I ) . The possibility of simultaneous determination of two or more of these compounds based on the different catalytic effect of the complexes with manganese is being considered at present. 634
Table I summarizes the reproducibility of data for the determination of the various aminopolycarboxylic acids amenable to titration according to procedure. Titrations using different chart settings have shown that a slight increase in sensitivity is obtained by using the 1.00 absorbance/lO inch chart setting. No significant increase in sensitivity is gained by using the 10% transmittance or 0.10 span; the time required for titration, however, is decreased enough to deserve analytical consideration but only by sacrificing the recording of the complete titration curve. Sensitivity Comparison at a Given Concentration Level. Comparison of different analytical methods for the determination of a given common species is many times difficult due to the different characteristics inherent in each method. In an attempt to evaluate the analytical approach reported in reference ( I ) , for instance, some redefinitions of measurements and practical handling of the data were necessary. The comparison must be made around a concentration value accessible to both methods and approximately equally close t o a concentration boundary condition. For this purpose the value of 1 X 10-6MEDTA was chosen. As a second condition the simplest measurement step for each case was adopted, and as third condition comparable length of time for analysis were chosen. In the case of the indirect method ( I ) , the following applies:
ANALYTICAL CHEMISTRY, VOL. 42, NO. 6, MAY 1970
where K* is the overall pseudo-first order constant, A1 and AS absorbance readings a t time tl and tp, respectively. First order plots of log A us. time in one cycle semi-log paper is the simplest way of obtaining a graphical presentation of the variation of K* with catalyst concentration. The data from first order plots obtained by the indirect procedure were translated to a calibration curve in which the dependence of reaction rate with EDTA concentration was measured in a form and units comparable to those used in the preparation of calibration curves obtained by titrations with end point indication. Three points were then used for comparison to locate the sensitivity of the method at the lO-SM level, defined as S(10-s)= (41nm/4C)(~~-~), Figure 9 shows the plots obtained
for comparison. These sensitivity values, in agreement with a precise definition of sensitivity in trace analysis (IO), are 12 X 108 mm.M-' and 3 X loe mm.M-' for the titration with catalytic end-point indication [malachite green-periodate ionmanganese(I1) system] and for the indirect kinetic method, and for volumes of 10 and 15 ml, respectively. If a similar treatment is performed with titrations of EDTA with Cu(I1) as catalytic titrant and 1-ascorbic acid-Oz indicator is equal to 5.5 X lo6mm.M-'. This reaction (11, I2), S(lo-~) is half the sensitivity of the malachite green-periodate-Mn(I1) system. It should be mentioned that even though the titra(10) J. E. Barney 11, Tufuntu,14,1363 (1967). 40, (11) H. A . Mottola, M. S. Haro, and H. Freiser, ANAL. CHEM., 1263 (1968). (12) H. A. Mottola, K. Muller, and H. Freiser, unpublished results, 1967.
tion with Cu(I1) can be performed at a pH between 6 and 7, the catalyst must be used at rather high concentrations to get well developed curves. This works against the low limit of detection expected by using a rather high pH. ACKNOWLEDGMENT
The author gratefully acknowledges the assistance of Steven E. Henley in some of the experimental work.
RECEIVED for review December 22, 1969. Accepted February 24, 1970. Paper presented at the 17th Anachem Conference, Detroit, Mich., September 1969. This work was supported by the Oklahoma State University Research Foundation and the National Science Foundation (Grant GP13472).
Calorimetric Determination of EquiIibrium Constants for Very Stable Metal-Ligand Complexes Delbert J. Eatough'
Shell Development Company, Emeryuille, Cal$ It has been previously demonstrated that titration calorimetry can be used to obtain reliable equilibrium constants for complex metal-ligand systems if the K values for the stepwise addition of the Ii ands are less than approximately lo4. A procedure or the calori. metric determination of Kvalues for very stable metalligand systems i s given in this work. Log K, AH", and A S O values have been calorimetrically determined for the interaction of Hgz+ion with 2-aminoethanol and of Cu2+and Zn* ions with 1,lO-phenanthroline in aqueous solutions at 25 O C . For these systems the equilibrium constants for the formation of the various species vary from 106 to lolo. The calorimetric results are in good agreement with previously reported values determined by potentiometric techniques and demonstrate that titration calorimetry can be used to quantitatively determine the thermodynamics of interaction for any metal-ligand system if the proper choice of titrant can be found.
P
less than about lo4. Equilibrium constants for several complex systems where the various K values are less than l o 4 have been reported (2, 4), and excellent agreement is found between the calorimetrically determined values and values determined by more conventional techniques such as potentiometry or spectrophotometry. However, no calorimetrically determined equilibrium constants have been reported for any metal-ligand system where K is greater than lo4. Equilibrium constants greater than lo4 could be reliably determined if a competitive equilibrium of the type,
is found such that KR values for the stepwise removal of the ligand, L, from MLn by N are in the region I KR I lo4. If the equilibrium constant for the reaction N+L=NL,
CALORIMETRIC determination of equilibrium constants requires that significant concentrations of both reactants and products be in equilibrium during the titration of one reactant with another (1-3). If the equilibrium constant for the interaction is large enough that the products are stoichiometrically formed as the reactants are mixed, then the thermometric titration curve will be linear and independent of the magnitude of the equilibrium constant for the interaction. This restriction limits these systems which can be studied by titration of a metal species with a ligand to those for which the K values for stepwise addition of the ligand to the metal are Present address, Center for Thermochemical Studies, Brigham Young University, Provo, Utah 84601 (1) J. J. Christensen,R. M. Izatt, L. D. Hansen, and J. A. Partridge, J . Phys. Chem., 70,2003 (1966). (2) R. M. Izatt, D. Eatough, R. L. Snow, and J. J. Christensen, ibid.,72, 1208 (1968). (3) J. J. Christensen, D. P. Wrathall, and R. M. Izatt, ANAL. CHEM., 40, 175 (1968).
KN
is independently known, then the K values for the formation of the ML, species from M and L could be obtained by this method. The application of this technique to the determination of p K values in the region 4-9 for a single protonation step has been demonstrated (3). If the principle can be reliably applied to the study of complex systems, then the possible systems for which equilibrium constants may be determined calorimetrically is greatly increased. Using titration calorimetry techniques we have determined stepwise equilibrium constants, enthalpy and entropy change values for the interaction of Hg2+ion with 2-aminoethanol, A , to form HgA2+and HgA22+ and of Cu2+and Zn2+ ions with 1,lO-phenanthroline, P, to form MPZf, MPz2f, and MPZ2+. The competing ion, N, in all cases is the hydrogen ion. These systems were chosen for the study for the following reasons: (1) Accurate p K values valid at 25 "C and zero ionic strength, (4) D. J. Eatough, Ph.D. Thesis, Brigham Young University, Provo, Utah, 1967. ANALYTICAL CHEMISTRY, VOL. 42. NO. 6, MAY 1970
635
