2956
Anal. Chem. 1985, 57, 2956-2960
Ionic Strength Dependence of Formation Constants. Alkali Metal Complexes of Ethylenediaminetetraacetate, Nitrilotriacetate, Diphosphate, and Tripolyphosphate in Aqueous Solution Pier G. Daniele* Dipartimento di Chimica Analitica dell’llniversitci, via Giuria 5, 10125 Torino, Italy
Carmelo Rigano Dipartimento di Matematica dell’Universit6, viale A. Doria 6, 95125 Catania, Italy
Silvio Sammartano* Istituto di Chimica Analitica dell’universitci, via dei Verdi, 98100 Messina, Italy
The protonatlon constants of EDTA, NTA, dlphosphate (PP), and tripolyphosphate (TPP) were determlned at different temperatures (10 II5 45 “C) and lonlc strengths (0.02 5 Z I 1 mol dm-’). By experiments performed in varlous Ionic media, the formatlon constants of the complexes formed by the above ligands wlth alkali metal ions were obtained; polynuclear species were determined for EDTA, PP, and TPP, while only EDTA forms weak complexes with tetramethyl- and tetraethylammonium cations. Estlmates were deduced for AH O and AS O values from temperature dependence of stability constants. The overall analysis of present and previous data dealing wlth the determlnation of stability constants at different ionlc strengths allowed us to obtain a general equation, by which a formatlon constant determined at a fixed ionic strength can be calculated, with a good approximation, at another Ionic strength if Z I 1 mol dm-3: from error analysis we have also obtained an estlmation of the error connected to the use of such an equation.
Ethylenediaminetetraacetic acid (EDTA), nitrilotriacetic acid, diphosphoric acid (PP), and tripolyphosphoric acid (TPP) are compounds that form complexes with almost all metal ions. Recently two reviews have been published on the stability constants of EDTA (1) and NTA (2).Though the number of works on the determination of thermodynamic parameters for metal complex formation of the above ligands is very large (1-IO), some uncertainties are still present, particularly when dealing with alkali and alkaline-earth metals. This fact is mainly due to the uncertainties in numerical values for weak interactions that are very sensitive to the assumptions made in deriving them. In fact, by use of the constant ionic medium method in determining the stability constants, the ligand-background interactions make the log /3 values dependent on the cation of the background. For example, when using two different media, 1mol dm-3 Kf or 1mol dm-3 Na+, we observe a difference of about one log unit in the stability constants of EDTA complexes. The relevance of EDTA, NTA, PP, and TPP in industrial products, in analytical procedures, and in the speciation of biofluids explains our interest in studying the complex formation between these ligands and alkali metal cations, very often present in high concentration in natural multicomponent systems. Our investigation has been performed a t 10 It I 45 “C (25 I t I45 “C for PP and TPP) and 0.02 I I 5 1.0 0003-2700/85/0357-2956$01.50/0
mol dm-3, by means of pH-metric measurements, using a glass electrode. The wide range of ionic strength (at different temperatures) allows calculated stability constants to be applied to the solution of many analytical and speciation problems. The parameters which define the dependence on ionic strength were analyzed, as in previous papers (11-18), with the aim of obtaining further information with regards to their variation as a function of the charges involved in the reaction of complex formation. Moreover, the meaning of weak complex formation was analyzed in connection to speciation problems, as in our previous papers on alkali and alkaline-earth metal ion-low molecular weight ligand complexes in aqueous solution (19). Finally, the results here obtained were compared to our previous findings and a general equation was drawn for the dependence of formation constants on ionic strength. The general significance of this equation is strictly connected to the great number of experimental data available, to the different types of ions, with charges varying from one to five, involved in complex formation, and to the different binary and mixed-ligand or mixed-metal ternary species taken into account. This general equation gives the possibility of estimating a stability constant at a fixed ionic strength when its value is known a t another ionic strength (0.01 I S 1.0 mol dm-3) and therefore may give a significant contribution to solving many analytical and speciation problems.
EXPERIMENTAL SECTION Materials. Ethylenediaminetetraacetic and nitrilotriacetic acids (puriss. Fluka) were used without further purification; their purity, checked by alkalimetric titrations, was always >99.5%. Tetrasodium pyrophosphate (diphosphate) decahydrate was Anal& BDH. Pentasodium tripolyphosphate (technical Janssen Chimica product) was purified by crystallization from ethanolwater and Na6P,010.6H20was obtained, according to the method of Quimby (20). The purity of P P and TPP was checked by alkalimetric titrations after adding dilute nitric acid in slight excess to the complete protonation of the salt. Lithium, sodium, and potassium nitrates were purissimum Fluka products. Tetraethylammonium bromide (Carlo Erba RS “per polarografia”) was used without further purification while tetramethylammonium bromide, tetraethylammonium iodide, and tetrapropylammonium bromide (Fluka) were twice recrystallized from ethanol-water, after washing with ethyl acetate. Nitric acid and potassium hydroxide standard solutions were prepared by diluting concentrated ampules (Merck or Fluka). Twice-distilled water and grade A glassware were employed. Potentiometric Equipment. All the measurements were carried out with a Model E600 Metrohm potentiometer equipped 0 1985 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 57, NO. 14, DECEMBER 1985
2957
Table I. Conditional Protonation Constants of EDTA in Different Backgrounds" Li+ I
t
log P'Oll
0.02
10 25 37 45
9.39 9.20 9.04 8.95 8.93 8.75 8.61 8.52 8.72 8.54 8.41 8.33 8.27 8.12 8.01 7.95 7.99 7.88 7.80 7.75 7.79 7.70 7.64 7.60
0.06
10
25 37 45 0.10
10
25 37 45 0.30
10
25 37 45 0.60
10
25 37 45 1.00
10
25 37 45
log
P o 1 2
15.89 15.55 15.27 15.09 15.27 14.92 14.63 14.44 14.98 14.62 14.33 14.14 14.37 14.00 13.70 13.50 14.00 13.62 13.31 13.11 13.68 13.31 13.00 12.80
log Poll
K+
NaC 1% Po12
10.27 10.11 9.98 9.90 9.86 9.70 9.57 9.49 9.66 9.50 9.38 9.30 9.23 9.08 8.96 8.89 8.97 8.83 8.73 8.67 8.80 8.68 8.60 8.55
Pr4N+
log Poll
log Po12
Me4Nf 1% Po11
Et4N' bp'O11
log Po11
log Po12
10.74 10.57 10.43 10.33 10.50 10.31 10.16 10.05 10.37 10.18 10.02 9.91 10.11 9.89 9.71 9.59 9.93 9.69 9.51 9.39 9.76 9.52 9.34 9.21
17.27 16.96 16.71 16.54 16.89 16.56 16.29 16.11 16.71 16.37 16.09 15.90 16.39 16.01 15.70 15.50 16.26 15.85 15.53 15.32 16.14 15.75 15.43 15.22
10.81 10.65 10.52 10.43 10.62 10.45 10.31 10.22 10.53 10.35 10.21 10.12 10.40 10.21 10.05 9.94 10.37 10.16 10.00 9.89 10.31 10.11 9.96 9.86
10.81 10.65 10.53 10.44 10.63 10.46 10.33 10.24 10.55 10.37 10.23 10.14 10.44 10.25 10.09 9.98 10.44 10.24 10.07 9.96 10.43 10.23 10.08 9.97
10.82 (5)b 10.66 ( 5 ) 10.53 (4) 10.45 (5) 10.64 (3) 10.47 (3) 10.34 (3) 10.25 (4) 10.56 (3) 10.39 (3) 10.25 (3) 10.16 (3) 10.48 (2) 10.28 (2) 10.13 (3) 10.02 (3) 10.53 (3) 10.32 (2) 10.15 (3) 10.04 (3) 10.57 (4) 10.37 (5) 10.22 (5) 10.11 (6)
17.34 (7) 17.05 (7) 16.81 (6) 16.65 (7) 17.03 (6) 16.72 (5) 16.47 (6) 16.31 (6) 16.90 (4) 16.58 (4) 16.32 (5) 16.15 (4) 16.76 (4) 16.40 (3) 16.12 (3) 15.92 (4) 16.86 ( 5 ) 16.48 (3) 16.17 (4) 15.97 (4) 16.95 (6) 16.59 (5) 16.31 (7) 16.12 (7)
16.79 16.49 16.25 16.09 16.24 15.94 15.69 15.53 15.99 15.68 15.43 15.26 15.49 15.16 14.90 14.72 15.25 14.91 14.65 14.47 15.09 14.76 14.50 14.33
" The indexes refer to reaction 1. 39 in parentheses. with glass and saturated calomel electrodes supplied by the same firm. The calibration of the electrode couple, in -log CH = pH units (cH is the proton free concentration), was achieved by titrating nitric acid (4-8 mmol dm-3) with standard carbonate-free potassium hydroxide. The experimental conditions of the calibration solution (temperature, ionic strength, and background salt) were the same as those of the solution under study. The titrating solution (KOH 1.000 mol dm-9 was delivered by a microsyringe (5000 div/cm3). The reliability of the calibration in the alkaline range was checked by calculatingpK, values (21). The titration vessel, containing25 or 50 cm3of the solution under study, was thermostated by a Model D1-G Haake thermocryostat. Magnetic stirring was employed. A steam of purified nitrogen flowed through all of the solutions in order to exclude COz and 02.
Procedure. The titrations were performed on 25-50 cm3 of solution containing variable amounts (0.02-1.0 mol dmm3)of M+ (M+ = Li+, Na+, K+, Me4N+,Et4N+,Pr4N+)and 1-4 mmol dm-3 of ligand (when studying EDTA at pH Na+ = K+. For PP the third protonation step was considered also and its equilibrium constant has the same value in all ionic media studied. As one would expect, a strong dependence on temperature was found for the first two protonation steps of EDTA and for the first protonation step of NTA. In the other cases the variation of log POqrwith temperature is not relevant. On the basis of the above observations and by assuming that (i) the differences on log @'&, values in different backgrounds are due to complex formation between ligands and alkali metal (or tetraalkylammonium) cations; (ii) the dependence on ionic strength of activity coefficients, and hence of stability constants, is only a function of the type of complex formed; (iii) the dependence on temperature can be described by a Taylor expansion, we calculated by the computer program E S ~ W C (Appendix) the formation constants for all the species present in the various systems, their dependence on temperature and their dependence on ionic strength, according to the equation (11-17)
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ANALYTICAL CHEMISTRY, VOL. 57, NO. 14, DECEMBER 1985
Table 11. Protonation Constants, Mt-EDTA, -NTA, -PP, and -TPP Complex Formation Constants at t = 25 OC and I = 0.1 mol dm-3, and Parameters for the Dependence on Ionic Strength at t = 25 OC (eq 2) Protonation Constants ligand
log Poiin
1% Poiz
log Poi3
log Poia
EDTA NTA PP TPP
10.39 (3)* 9.84 (2) 8.77 (3) 8.44 (3)
16.58 (4) 12.40 (4) 14.95 (5) 14.30 (5)
19.26 (5) 14.23 (5) 16.89 (8)
21.22 (9)
2
Formation Constants ligand metal ion EDTA
log Pllo
log Pill
other constants
Li+ Na+ K+ Me4Nt Et4N+ Lit Na+ K+ Na'
2.90 (3) 10.85 (5) log Pzlo = 3.05 (9) 1.84 ( 5 ) 9.94 (10) 0.80 (10) -0.1 (2) -0.4 (2) NTA 2.56 (3) 9.62 (15) 1.35 (5) 9.88 (9) 0.79 (8) 9.86 (10) PP 1.33 (11) 9.86 (7) log = 15.4 (2);" log Pzlo = 2.67 (7); log Pzli = 9.75 (8) K+ 1.51 (9) 9.81 (7) log P I 1 2 = 15.5 (2)"; log &lo = 2.14 (9); log P Z l l = 9.47 (10) TPP Na+ 1.43 (11) 9.81 (5) log P z l o = 3.16 (5) K+ 1.55 (9) 9.76 (4) log &lo = 2.81 (3) Parameters for the Dependence on Ionic Strengthd ligand
z*
P*
C
-D
EDTA
8 14 18 20 6 10
1 2
3 4
0.96 1.68 2.2 2.4
12
3
PP
8 14 18
1 2
1.84 3.27 4.3 4.9 1.09 1.69 2.4 1.76 3.13
TPP
10
NTA
18
1 2
3
4.1
1 2
2.37 4.30
0.46
0.77 0.92 0.85 1.48 1.9 1.14 2.06
OIndexes of stability constants refer to reaction 1. '3s in parentheses. " t = 35 O C . d Since for each ligand Cpsrand DPqrvalues depend only on z* and p* values, we reported mean values. The variability of the parameters in the various complexes is very low, ranging from fO.O1 to f0.05. where I and I' are the actual and reference ionic strength, respectively, and z* = pn2 qz2 r - (pn - qz + r)2 for reaction 1. In Table I1 are collected the values of protonation and formation constants at t = 25 "C and I = 0.1 mol dm-3 together with Cpqrand Dpqrparameters obtained at t = 25 "C. Complete data are available as supplementary material (Tables IV-S to VII-S). The errors (3s)associated with the stability constant values seem to be reasonable, in particular for the species whose existence is certain, such as [M(EDTA)I3-, [M(NTA)I2-, [M(PP)I3-, [M(TPP)I4-,and [M2(TPP)]3-with M being alkali metal ion. As concerns the other species a criterion might be proposed: if 3s 5 Ppqr 5 49, species doubtful, if 4s 5 Ppqr 5 5s, species uncertain; if Bpqr > 5s, species certain. On this basis some of the complexes here reported must be considered uncertain. EDTA forms [M(EDTA)I3-species with Li+, Na+, K+, and Me4Nf or Et4N+ as well. We were able to confirm a homobinuclear complex of the type [Li,(EDTA)]", already reported by Both et al. (24),who found a similar species with Na+ also, but our value for the stability constant of the reaction Li+ +
+
+
6
pH
10
Fi ure 1. Distribution of the species as a, vs. pH, for the system Li f-EDTA: 1, [H,(EDTA)]; 2, [H,(EDTA)]-; 3, [H2(EDTA)I2-;4, [H(EDTA)],-; 5, [LiH(EDTA)]'-;6, [LI(EDTA)13-;7, [Li,(EDTA)]'-. C,, = 0.25; CEorA= 0.001 mol dm-3.
[Li(EDTA)J3-= [Li2(EDTA)I2-is significantly lower. Complexes of the type [M(EDTA)HI2-are formed in the presence of Li+ or Na+. NTA forms [M(NTA)I2-and [M(NTA)H]- species with Li+, Na', and K+. No evidence was found for the formation of binuclear or [R4N(NTA)I2-complexes. Pyrophosphate forms both homobinuclear and protonated complexes with Na+ and K+. It is noteworthy that these binuclear species are very stable if compared to mononuclear PP complexes and to [Li2(EDTA)I2-.The strong stabilization of binuclear species is evident from the evaluation of the parameter A log Kzlo= log pzl0- 2 log pll0, which at t = 25 "C and I = 0.25 mol dm-3 assumes the values of +0.05 and -0.85 for Na+ and K', respectively, while its statistical value should be highly negative ( [Na2(PP)]2and [Kz(TPP)l3-> [K2(PP)J2-. As an example, the formation of various species, as a function of pH, in the system Li+-EDTA is shown by the distribution diagram of Figure 1;the relevance of Li-EDTA complexes is noticeable. Temperature Dependence of Formation Constants. The values of AH"and AS", obtained by the dependence on temperature of formation constants (Table III), can be considered satisfactory for protonation and complex formation with Li+ and Na+ of EDTA and NTA. It is to be noted that the agreement between ours and literature data (1,2) is good if allowance is made for the difference between AH" and AHo' (AH"' is the value obtained when neglecting the formation of weak alkali metal complexes (25)). Moreover, our values for the formation of Li+ and Na+ complexes with EDTA show the same behavior as that found by calorimetric measurements ( I ) : this independent check confirms the correctness of the present approach in determining the thermodynamic parameters for weak complex formation. For the other species the values reported must be considered only as rough estimates. Ionic Strength Dependence of Formation Constants. In Table I1 Cpqrand Dpqrvalues (eq 2) are collected for each system here studied, at t = 25 O C (complete data are available as supplementary material, Table VIII-S). They are strongly dependent on the stoichiometry of the reaction and quite independent of metal ion and ligand involved. As previously proposed (11-17), Cpqrand Dpqrvalues can be expressed in a general manner Cpqr= p*co z*c1 (3)
+
Dpqr= z*d
+ +
(4)
where p* = p q r - 1. By taking into account at the same time all the CPqtand Dpqrvalues for EDTA, NTA, PP, and
ANALYTICAL CHEMISTRY, VOL. 57, NO. 14, DECEMBER 1985
2959
Table 111. Values of the Thermodynamic Parameters at I = 0.25 mol dm-3 M+
PVb
mow
-AGopqr
AS"pqr
M+
PVb
011 012 013 014 110 210 111 110 111 110
Lit Na' K+
58.73 (11) 93.67 (17) 109.0 (4) 120 (1) 15.98 (17) 16.5 (5) 61.0 (3) 9.97 (17) 55.8 (6) 4.0 (6)
NTA (25
H+
011 012 013
Lit Na+ K+
110 111 110 111 110 111
55.63 (11) 69.9 (3) 80.2 (4) 14.1 (2) 54.1 (8) 7.2 (2) 55.6 (5) 4.0 (5) 55.5 ( 7 )
-22 (1) -40 (2) -35 (3) -34 (3) 2 (1) 3 (2) -2 (2) -3.2 (9) 0 (3) 5 (3)
123 (3) 180 ( 7 ) 248 (11) 288 (13) 60 (4) 65 (7) 198 ( 7 ) 23 (3) 187 (11) 30 (10)
-13 (1) -17 (2) -16 (2) 8 (2) 15 (8) 8 (2) -14 (6) 17 (6) -3 ( 7 )
143 (3)
H+
011 012 013
Na'
110 111 112 210 211 110 111 112 210 211
K+
OC)
AGO and AHo in kJ mol-'. AS" in J des? mol-l.
215 (8) 74 ( 7 ) 232 (27) 51 ( 7 ) 140 (23) 70 (23) 176 (24)
- (2.0 x 10-3)(t - 25) X 10-3)(t - 25)
d = -0.110
+ (1.63 X 10-3)(t - 25)
(6)
The values of eq 6 are in good agreement with our previous findings (11-17). This result encourages the use of eq 2 with parameters of eq 6. In order to evaluate the error arising from the use of such an equation, we calculate the errors on log Opqr by the expression
sy2 = $(log P / Z * ) = Ycl2Scl2 Yd2sd2
+ Yc1,2scl,2f Yd!2sdt2 + ydscld + ycl ycl'sclcll + 2 y c l yd'sc,d' + 2YdYcl'Sdclt + 2YdYd'Sdd' + 2Ycl'Y&sc1td' (7) +
yc,
159 (11) 266 (14) 320 (16) 20 (14) 165 (14)
-2 (3) -5 (4) 0 (5) -1 (4) -6 (4)
(5) (6) (4) (5) (4) (5) (6) (5) (6) (5)
-3 -2 -18 -9
38 (14)
(4) (5)
177 (17)
(7)
-33 (24) 154 (17)
(5)
129 (19) 298 (36)
27 (6) 36 (10)
(7)
H+ Nat
KC
011 012 110 111 210 110 111 210
48.98 (12) 83.1 (2) 7.2 (5) 56.5 (3) 16.9 (3) 8.2 (5) 56.2 (3) 15.1 (3)
133 (7) 253 (11) -35 (17) 151 (15) -7 (15) -3 (17) 156 (15) 17 (15)
-8 (2) -5 (3) -18 (5) -10 (4) -19 (4) -9 (5) -8 (4) -10 (4)
The indexes refer to reaction 1.
calculated a t the experimental values of I and considering a linear temperature dependence for co, cl, and d. The parameters calculated by a linear least squares procedure are (the mean values co = 0.2 and cb = 8co/dt = -2.0 X taken from previous results (15),were kept constant in the calculations. This introduces negligible errors when dealing with species with z* # 0)
- (1.32
(2) (3)
TPP (35 " C )
Table IV. Errors on (log p/z*) (ea 7) at t = 25 "C for the Systems Reported in This PaperD 103 x s(l0g P / Z * )
Z
c1 = 0.198
51.1 87.1 98.5 7.3 57.0 89.7 14.7 56.4 7.7 56.6 89.8 12.6 55.9
177 ( 7 )
TPP complexes, we were able to calculate the parameters of eq 3 and 4 and their temperature coefficients, from the function
co = 0.20
AS",,,
PP (35 O C )
EDTA (25 " C )
H+
mow
-AGO,,,
where cl' and d' are temperature coefficients of c1 and d, respectively, Y, = aY/ax and S,b are covariance terms deduced from the covariance matrix (26) (very often in drawing variance propagation the covariance terms are neglected: this can lead to unrealistic values for s,,). In Table IV some numerical values of s(1og ,8/z*) a t t = 25 O C (at the other temperatures they are not very different) are reported; for example, if we have the formation constant of [M(EDTA)I3(whose stoichiometric parameters are z* = 8 and p* = 1) a t zero ionic strength and we must calculate the constant a t I = 0.5 mol dm-3, the error, a t 25 O C , using the eq 2 is s(log p) = 8 X 1.3 X = 0.01.
0 0.2 0.4 0.6 0.8
1.0
Z'=
0.1
0.6 (0.5) 0.4 (0.3) 0.7 (0.6) 0.8 (0.6) 0.8 (0.6) 1.4 (1.1)
I ' = 0.3
Z ' = 0.5
1'= 0.7
Z'= 0.9
1.2 (1.0) 0.2 (0.2)
1.3 (1.1) 0.4 (0.3)
(1.0)
0.1 0.4 0.9 1.7
(0.1)
0.1 (0.1)
(0.3)
0.2 (0.1) 0.8 (0.6) 1.6 (1.3)
1.2 0.6 0.5 0.3 0.3 1.2
1.1(0.8) 1.1 (0.9) 1.2 (1.0) 1.0 (0.8) 0.4 (0.3) 0.5 (0.4)
(0.7) (1.4)
(0.5) (0.4) (0.2) (0.3)
(1.0)
"In parentheses the errors on the same function, relative to all the systems reported here and in the ref 11-19.
Finally we verified the consistency of the above results with all the data previously reported for the dependence on ionic strength of formation constants (11-19), by performing the calculations with an expression similar to that of eq 7, in which the variability of co was considered also. The values of the parameters found for the dependence on I , relative to all the systems of ref 11-19 and of this paper, are co = 0.213
d c o / 8 t = -1.10 X
c1 = 0.203
&,/at = -1.18
d = -0.104
X
(8)
a d / & = 1.41 X
The errors arising from the use of eq 2 and 8 in calculating log are very similar to those calculated for the systems studied in this work and are reported as s(1og p/z*) in Table IV (values in parentheses). When dealing with species with z* = 0, the errors can be simply calculated by the expression S ( h g 0)= O.Olp*)I - I'I + O.OOlp*JI - I ' ) ( t- 25)
CONCLUSIONS When eq 2 and 8 are used in deriving the value of log Ppqr a t a fixed ionic strength (0.01 5 I 5 1 mol dm-3) from that determined a t another ionic strength, the errors on log Pppr are low enough to allow a wide practical application of these equations. Another important consequence of the above generalization is that activity coefficients as well do not depend, with a good
2960
ANALYTICAL CHEMISTRY, VOL. 57, NO. 14, DECEMBER 1985
approximation, on the type of ion involved but only on its charge; although there is no doubt on the specificity of activity coefficients (for ions with the same charge), when the dependence of stability constants on ionic strength in the range 0.01 I I I 1mol dm-3 is investigated, this effect is considerably reduced if alkali metal weak complexes (or ion pairs) are taken into account.
APPENDIX Weak complexes, such as alkali metal complexes, are often neglected and a strong dependence of protonation constants on the concentration of background is generally ascribed to activity factors. A rigorous treatment of acid-base equilibria, however, must also take into account weak interactions between the ligand under study and the cation of background. If we assume that activity coefficients are not individual (i.e., they depend only on ionic strength and on their charge) for I < 1mol dm-3 (see also ref 11-17 and 19 and Discussion of this paper), the differences between the protonation constants determined in the presence and in the absence of complexing cations can be used to calculate formation constants (19,23). The mass balance equations, for a system containing one metal and one ligand, can be written, if the stoichiometric coefficient of the ligand is always 1
or, by neglecting the formation of weak complexes
CH
=
CH
+ CL'Cr@O1rCHr
(1-5)
where primes indicate conditional quantities and Ciand ci, represent analytical and free concentrations, respectively. By equating 1-3 and 1-5 and substituting CL and cL' from 1-2 and 1-4, we obtain CrPplrCdCHr
p =
1+
(1-6) CPplrChlPCHr
(1-7) These two parameters (which indicate the mean proton displacement of the ligand) should assume the same value for a given value of cH and cM and, therefore, the minimization of the function
u = C(p - p'I2 allows the obtainment of Pplr values, using the nonlinear least
squares method, as in the program ESBWC (23). Registry No. EDTA, 60-00-4;NTA, 139-13-9;PP, 2466-09-3; TPP, 10380-08-2. Supplementary Material Available: Protonation constants, complex formation constants, and parameters for the dependence of ionic strength (8 pages) will appear following these pages in the microfilm edition of this volume of the journal. Photocopies of the supplementary material from this paper or microfiche (105 X 148 mm, 24X reduction, negatives) may be obtained from Microforms Office, American Chemical Society, 1155 16th Street, NW, Washington, DC 20036. Orders must state whether for photocopy or microfiche and give complete title of article, names of authors, journal issue date, and page numbers. Prepayment, check or money order for $13.50 for photocopy ($15.50 foreign) or $6.00 for microfiche ($7.00 foreign), is required and prices are subject to change.
LITERATURE CITED (1) Anderegg, G. "Critical Survey of Stability Constants of EDTA
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RECEIVED for review March 25, 1985. Resubmitted July 17, 1985. Accepted July 17, 1985.
