1232
Anal. Chem. 1983. 55. 1232-1236
not tissue specific although certain tissues such as the cephalothoracic region of the shrimp Palaemonetes pugio and rat lung were more likely to exhibit this phenomenon which could be caused by the presence of free ferrous chloride in the crude tissue extract. This premature color development cannot be accounted for in the control assay and thus the ascorbic acid contenit of these samples cannot be estimated by this method. Samples exhibiting premature color development were not inclluded in the data reported in Table 111. Zannoni et al. ( 4 ) suggested that ethanol can be used to solubilize a,a’-bipyritlyl to increase sensitivity with no effect on the complexing of Fez+. The results of the present study indicate that considerable variation is found between the two a,a’-bipyridyl methods. Dependipg on the species and the tissue, the ascorbic acid values obtained varied considerably between the two meithods and were rarely similar. It is apparent that the ascorbic acid values obtained for various tissues and lbiological fluids vary considerably depending on the method employed. The ascorbic acid values obtained by the LCEC method were generally lower than the values obtained by the other methods, as would be expected with a more specific technique. Because the ascorbic acid values obtained with the a,a‘-bipyridyl techniques for the majority of tissues examined were elevated, we recommend that these methods be used with considerable caution and be correlated with either the DNPH or preferably the LCEC
method for every different sample type analyzed before they are used routinely. Comparison of the results of studies which use different assay techniques should be made with caution in view of the considerable species, tissue, and assay-dependent variability inherent in ascorbic acid determinations.
ACKNOWLEDGMENT We thank Betty Lou Sinnott for typing the numerous revisions of this manuscript and Marcia Carr for her expert editorial assistance. Registry No. Ascorbic acid, 50-81-7. LITERATURE CITED Roe, Joseph H.; Kuether, Carl A. J. Biol. Ch8m. 1943, 147,
399-407. Sullivan, M. X.; Clarke, H. C. N. J. Assoc. Off. Agric. Ch8m. 1955,
38,514-518, Terada, Mamoru; Watanabe, Yoshinori; Kunitomo, Masaru; Hayashi, Eiichi Anal. Biochem. 1978,8 4 , 804-808. Zannoni, V.; Lynch, M.; Goldstein, S.; Sato, P. Biochem. Med. 1974,
II,41-48. Carr, Robert S.;Neff, Jerry M. Anal. Chem. 1980,52, 2428-2430. McGown, E. L.; Rusnak, M. G.; Lewis, C. M.; Tillatson, J. A. Anal. Biochem. 1982, 119, 55-61.
RECEIVED for review January 13, 1983. Accepted March 10, 1983. This investigation was supported, in part, by a grant (No. OCE-77-24551) from the National Science Foundation to Jerry M. Neff.
Equilibrium Constants for Cadmium Bromide Complexes by Coulometric Determination of Cadmium Iodate Solubility R. W. Ramette Department of Chemlstv, Carleton College, Northfield, Minnesota 55057
The theoretical bask for the use of a slightly soluble salt as a probe for studying metal-llgand complex equilibria Is reviewed. The solubility of recrystallized cadmlum Iodate was determined, uslng high accuracy controlled potentlal coulometry, In solutions of cadmlum perchlorate and In solutions of sodium bromide, (all at ionic strength 3.00 wlth sodlum perchlorate as Inert electrolyte. The assoclatlon constant fer the CdIO,’ specles ,and the solublllty product for cadmlum Iodate were determined at 25 O C and 35 O C . From the effects of bromide Ion on the solublllty the four successlve p values for cadmlum bvomlde complexes were determined and compared wlth the results of potentlometric measurements. Revised enthalpy changes for the complexation steps were calculated.
The purpose of this research is to develop the theoretical basis and the experimlental techniques for an analytical probe, based on high accuracy solubility measurements, for improved equilibrium studies of weak metal-ligand complexes. The cadmium-bromide system was chosen because the results may be compared with previous studies that use potentiometry and polarography and are important for interpretation of calorimetric data. The development of a “totally chemical” probe is worthwhile for three reasons: One is the elimination of the electrochemical sourcles of error mentioned below. Although the new probe may have its own set of problems and uncer-
tainties, the fundamental approach is totally independent of electrode behavior. Secondly, the solubility approach may be the only useful technique for systems, such as complexes of the alkaline-earth metals, that do not respond to electrochemical probes. Finally, there is promise that high accuracy controlled potential coulometry will provide the excellent precision that is essential for the resolution of multistep complex systems. The determination of equilibrium constants ( p values) for the multistep formation of weak metal-ligand complexes is deceptively easy in principle. Given a set of solutions containing a known small concentration of the metal (e.g., 0.001 M) and varying concentrations of complexing ligand (e.g., 0.01-1.0 M), one only needs to determine the equilibrium concentrations of the uncomplexed metal ion in each of the solutions. Once the measurements have been made, the remaining task is an exercise in numerical analysis. An inherent problem in metal-ligand equilibrium studies is the variation of activity coefficients as the ionic medium is varied from a noncomplexing state (e.g., 3 M sodium perchlorate) to a state sufficient to form the highest complexes (e.g., 3 M sodium bromide). The medium effect cannot be estimated and it is commonly assumed that activity coefficients do not vary appreciably if the formal ionic strength is constant. One argument for working a t high ionic strength is that the complexing ligand concentration can be made large enough to effect appreciable formation of the highest complexes, while an even larger “swamping” concentration of inert
0003-2700/83/0355-1232$01.50/00 1983 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 55, NO. 8, JULY 1983
electrolyte preserves the character of the medium. For example, in the present work the medium ranges from 3 M sodium perchlorate to 2 M sodium perchlorate plus 1M sodium bromide. For determination of the free metal ion concentrations, only two analytical probes have been widely used in studies of weak complexes. The most common one is an indicator electrode specific for the metal, using potentiometric determination of galvanic cell voltage. Both pure metal and metal-amalgam electrodes have been used. The other technique is polarography, using the dropping mercury (or amalgam) electrode. In both cases it has been common practice to ignore the effects of varying liquid junction potentials formed between the reference electrode electrolyte and the solution containing the metal complex system. Even more serious is the typical assumption that the response of the electrode to changing metal ion concentrations follows the Nernstian ideal of 59.16/n mV/decade. One should at least do an electrode standardization with known metal ion concentrations in a noncomplexing medium. Even when standardization is attempted, it is usually impossible to extend the measurements to the very low values of metal ion concentration that exist in the complexing media. In addition, the polarographic approach requires assumptions about the relative diffusion coefficients of the successive complex species. Finally, the calculation of accurate p values requires electrochemical data of highest accuracy, with potential values having uncertainties of the order of 0.1 mV, a quality rarely obtained. Because of these problems some published equilibrium studies are very misleading. An overview of ways to use solubility data to study metal-ligand complex formation in solution has been published by Johansson ( I ) , who observed that the measurement of solubility was an early and still widely used method to show the existence of complexes in solution. He also pointed out the the versatility and accuracy of the method have not been fully appreciated, and that lack of familiarity with the underlying theory has often led to faulty experimental design and to misinterpretation of the data. A common and serious limitation has been the lack of high accuracy in the analytical determinations of solubility. Perhaps the only attempt to use solubility measurements, on a salt with a “foreign” anion, for determining multistep equilibrium constants was the work by King (2), who studied the effect of chloride ion on the solubility of cadmium ferricyanide. This research has made extensive use of computer program, which are mentioned in context. Further information about these programs, which are written in DEC VAX-11 BASIC, may be obtained from the author.
THEORY The Chemical Model. Although it is commonly assumed for simplicity that salt MA2 (e.g., cadmium iodate) is completely dissociated in solution, this is not likely. The classical solubility product by itself is insufficient for an accurate solubility model. It is realistic to assume a set of three simultaneous equilibria: M2++ A- = MA+ K L= [MA]/[M][Al (1)
MA+ + A- = MAz(aq)
K2 = [MA,I/[MAl[Al
MA2(s) = MAdaq)
KO= [MAzI/X
(2) (3)
where the brackets indicate molar concentrations of solution species and X is the mole fraction (assumed to be unity) of the solid phase. Ionic charges have been omitted from the equilibrium constant expressions for simplicity. Activity coefficients are defined as unity for the set of solutions at constant high ionic strength. The constant KOis also known as the intrinsic solubility of MA2.
1233
The familiar “solubility product constant” K,, is a combination of the above MA&) = M2++ 2AKsp [Ml[A12= KO/KI& (4) When the solution also contains CLmol/L of ligand L which can form complexes with the metal ion, there is an overall equilibrium formation constant for each species in the sequence M + j L = MLj Pj = [MLj]/[M][L]’ (5) where j may range from 0 (no complexing and Po is defined as 1)to a typical maximum of 4. Alternatively the system may be described in terms of equilibrium constants for the individual steps
Kj = WLjI / iMLj-11 [LI Two material balance expressions are sufficient to complete the algebraic model. One deals with the total concentration of metal in solution, i.e., the solubility S = [MA,] + [MA] + [MI + [ML] + [ML,] +
[MLd + [MLI (6)
which may also be expressed in terms of the anion A
S ([A] + [MA] + 2[MA2])/2 (7) and the other deals with the total concentration of the complexing ligand
CL = [L] + [ML] + 2[ML2] + 3[ML,]
+ 4[ML4]
(8) If ligand L forms proton complexes under the conditiQns of the experiment, it is necessary to consider the acid dissociation constants, but in the present work with bromide ion this is unnecessary. Interpretation of Experimental Solubility Data. Assuming that none of the above equilibrium constants is already known from previous work, it is necessary to carry out two solubility experiments. One is a study of the solubility of MA2 in a series of solutions containing varying concentrations of the metal ion, typically provided by using the metal perchlorate salt. This experiment determines the values for K,, and K1 and, if possible, KB The second experiment is a study of the solubility of MA2 in solutions having varying concentrations of ligand L and enables determination of the /3 values. Determination of Ksp,K1,and K,. With excess metal ion (C mol/L) present, the solubility of MA2 is half the total concentration of anion A S = ([A] + [MA] 2[MA,])/2 (9) By using 1-4 we derive 2s = 2K,3 + K1K,p1/2[M]1/2 + K,,1/2/[M]1/2 (10)
+
Given a set of S, C data, an iterative computer program begins with the first approximation that in each of the solutions [MI = C 5’. A least-squares fit of the form
KSPKlFIT
+ +
+
2s = a l ~ [ M ] l / ~C / [ M ] ~ / ~ (11) gives tentative values for KO= a / 2 , for K,, = c2 and for K1 = b / c . These values are used to calculate provisional values for the concentrations of MA2 and MA, so that more accurate values for [MI = C + S - [MA] - [MA,] may be used in the second approximation. The process is continued until the values of the equilibrium constants converge to constancy. If KOis quite small it may not be possible to determine it by this algorithm. Then it is necessary to assume KOto be negligible and to omit it from eq 10. Determination of3!, Values. From eq 5 and 6 it follows that the corrected solubility of MA2 in the presence of ligand L is S - [MA] - [MA,] = CM = [Ml(1 + Pi[Ll + Pz[L12+ ...) (12)
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ANALYTICAL CHEMISTRY, VOL. 55, NO. 8, JULY 1983
where CM is the total metal concentration exclusive of the complexes with anion A. The parenthetical expression i s the formation function Fo CM/[M] = Fo = (1 + pl[L]
+ p2[L]2 + ...)
(13)
First, to convert the observed solubility values to the corresponding C, values we recognize that eq 9 is also valid so that
S - KO = [A] /2
+ K1Ksp/2[A]
(14)
If KOis neglected (or known), this is a quadratic equation that may be solved for this equilibrium [A], using the observed S value and the previously determined values for K1 and Ksp. Once [A] is known, then [MI = Ks,/[A12 and [MA] = [MI. [A]Kl, so that the vallue for C M and hence Fo may be calculated. A computer program FMSOmAT carries out the iterative solution. At this point the problem is no longer related to the fact that a solubility approach has been used. The formation function Fo is at the heart of all metal-ligand equilibrium studies, whether the data come from spectrophotometry, electrode potentiometry, polarography, or solubility. Given a set of Fo values corresponding to varying values of initial ligand concentrations, CL,an iterative computer program FORMSOLVE may be used to find the best set of p values to describe the data. As a first approximation, [L] = CL, and a least-squares fit of the form
(Fo - l)/[L]I = u
+ b[L] + c[L]' + d[LI3
(15)
gives provisional values for p1 = a, pZ= b, etc. These values are used with eq 8 to find how much ligand is tied up in the several complexes, SO that a refined set of values may be obtained for [L]. The process is continued until the J/' values converge to constancy. This iteration is essential to obtain the equilibrium concentrations of ligand L, even if C L is much larger than CM. Because the Fo values may range over several orders of magnitude, it is important to carry out the least-squares fits with all points weighted equally. This is equivalent to requiring that the sum of the squares of the relative deviations is minimized, rather than the usual use of absolute deviations. Otherwise large errors in the inferred /3 values may result.
EXPERIMENTAL SECTION The preparation of' recrystallized cadmium iodate and its saturated solutions, the techniques for sampling, and the equipment and procedure for coulometric analysis have been described (3). Program COULANAL was used to process the coulometric data and to calculate the solubilities. All solutions were prepared and analyzed on a mass basis to eliminate volumetric glassware errors. Later conversion of data to a molarity basis required the determination of solution densities by weighing of precise volumes delivered by a standardized and siliconized pipet. Reagent grade cadmium perchlorate, sodium perchlorate, and sodium bromide were dissolved in water redistilled from alkaline permanganate. All solutions used for the solubility equilibrationsi had an equilibrium ionic strength of 3.00. Experience showed that the equilibrationscould not be rushed. It takes several repeated charges with fresh solution before the solid phases settle down to constant behavior, i.e., reproducibility to within 1 ppt. After satisfactory results were obtained at 25 "C, the equilibrations were repeated in a 35 "C bath. RESU1,TS AND DISCUSSION The solubility of cadmium iodate was determined in five solutions of cadmium. perchlorate (C mol/L, I = 3) and the average results from four independent equilibrations are summarized in Table I. The standard deviation of the S values from the calculated values is about 2 ppt and is due to variations in the heterogeneous equilibrium system itself rather than in the coulometric determination procedure. The latter is reproducible
Table I. Solubility (mmol/L) of Cadmium Iodate in Cadmium Perchlorate (C mol/L) at 35 "C
at 25 "C C, mol/L 0.010 836
0.021 816 0.032 373 0.043 448 0.054 196 KSPU
K,
Sobsd
Scald
Sobsd
Scalcd
1.020 1.022 0.7675 0.7657 0.6534 0.6550 0.5830 0.5845 0.5406 0.5405 4.55 (0.03) X lo-' 3.36 (0.08)
0.9352 0.9363 0.7010 0.6992 0.5958 0.5961 0.5304 0.5324 0.4929 0.4919 3.81 (0.03) X lo-' 3.25 (0.08)
cal/ (mol K )
AS,
reaction 4 reaction 1
AG, cal/mol
AH,
t 10120 (9)
t 3230 (190)
-698 (20)
cal/mol
t 6 0 0 (620)
-23.1 (0.6) r 4 . 4 (2.1)
Uncertainties for Ksp and K , were calculated by simulation with GENKSPKl and KSPKlFIT, assuming 2 ppt standard deviation in S. Table 11. Solubility (mol/L) of Cadmium Iodate in Sodium Solutions at 25 "C
0.020 46 0.018 70 0.002 810 0.030 27 0.027 86 0.003 076 0.044 62 0.041 29 0.003 459 0.066 33 0.061 58 0.003 973 0.098 91 0.091 80 0.004 760 0.148 64 0.137 23 0.005 976 0.223 87 0.204 52 0.007 946 0.333 57 0.300 54 0.011 25 0.488 20 0.433 33 0.016 50 0.731 38 0.638 32 0.025 77 1.100 8 0.943 42 0.041 84 13 values (std dev):a 61.3 (0.6), 378 7987 (150)
2.293 0.002 808 0.003 081 3.017 0.003 453 4.302 6.534 0.003 983 0.004 757 11.263 22.33 0.005 967 0.007 958 52.58 0.01124 149.3 0.016 49 471.1 1795.8 0.025 83 0.041 78 7689.7 (18), 1110 (110),
Uncertainties in 13 values were stimated by simulation of the solubility experiments by using GENSOLDAT, FIXSOLDAT, and FORMSOLVE, assuming 2 ppt standard deviation in S.
to within about 3 parts in 10000 when replicate homogeneous samples are used. The value of KO, the intrinsic solubility, is too small to be determined with these data, and KOand K2 remain unknown. There are no comparative literature data on cadmium iodate a t this ionic strength. The solubility of cadmium iodate was determined in sodium bromide solutions ranging from 0.02 to 1.1M initial bromide concentration. The concentrations of sodium perchlorate needed to provide I = 3 were chosen on the basis of earlier experiments and anticipated the contribution of the dissolved cadmium iodate to the equilibrium ionic strength. When cadmium iodate dissolves there is a slight increase in solution volume, which was calculated by assuming the molar volume of the dissolved salt to be the same as that of the solid. For the sodium bromide solutions the data are given in Tables I1 and 111. @ values were calculated by using program FORMSOLVE. The calculated solubility values were found by using the Ksp,K1, and p values with the program GENSOLDAT. The standard deviation in the solubility values is about 2 ppt, which corresponds to about 4 ppt in the calculated Fo values. Equivalent precision in potentiometric measurements would require a standard deviation of only 0.05 mV. As with the Ksp,K1 study, the errors are related to the behavior of the heterogeneous system rather than to the errors of the coulometric determination. The deviations do not show a trend
ANALYTICAL CHEMISTRY, VOL. 55, NO. 8, JULY 1983
1235
Table 111. Solubility (mol/L) of Cadmium Iodate in Bromide Solutions at 35 “C CNaBn mol/L
[Br-le@l, mol/L 0.018 58 0.027 67 0.041 00 0.061 13 0.091 06 0.135 99 0.202 4 1 0.297 07 0.427 87 0.629 58 0.929 37
0.020 39 0.030 1 8 0.044 48 0.066 13 0.098 6 1 0.148 1 9 0.223 19 0.332 55 0.486 69 0.729 1 1.097 3
p values (std dev): 8611 (150) ~~~
Scaled
Sobsd
0.002 964 0.003 236 0.003 637 0.004 180 0.005 004 0.006 302 0.008 406 0.011 934 0.017 57 0.027 43 0.044 59
Fo
0.002 0.003 0.003 0.004 0.005 0.006 0.008
960 244 631 187 003 289 417 0.011929 0.017 55 0.027 52 0.044 50
2.2 50 2.936 4.179 6.363 10.95 21.92 52.10 149.3 476.3 1815 7793
59.5 (0.6), 366 (18), 1183 (110),
LOG [Ll Flgure 1. Distributlon (fraction) of CdBr,(*-” as a function of bromide concentration. The points are the experimental values of 17,the average ligand number. The smooth curve through the points was calculated by using the 6 values determined in the present work. Plotted by program BETAPLOT.
~~~
Table IV. p Values for Cadmium Bromide Complexes at I = 3, t = 25 “C 0,
0,
04
PB
Eriksson, as published Eriksson, recalculated Leden, as published Leden, recalculated
58 54
275 372
1600 1215
5400 6229
57 54.7 (1.0)
220 369 (30)
2100 1429 (150)
5000 7943 (180)
61.3 (0.6) 61.3 (0.6)
378 (20) 6.2 (0.3)
1110 (110) 2.9 (0.3)
7987 presentwork (150) 7.2 present work, (0.7) individual step values
a Uncertainties in Leden’s recalculated values were estimated by simulation of Leden’s experiment by using GENPOTDAT, FIXPOTDAT, and FORMSOLVE, assuming 0.1 mV standard deviation in potential values.
when plotted vs. the bromide concentration. To provide an estimate of uncertainty for the p values, program GENSOLDAT was used to simulate ten runs of the experiment, with the specification that the standard deviation for the solubility determinations is 2 ppt. Random errors were imposed by a subroutine that provides a Gaussian distribution. The simulated data were treated by the same calculation procedures as used for the actual data, using FIXSOLDAT and FORMSOLVE, and the resulting p values were examined to find the standard deviations. Analogous procedures were followed to estimate the uncertainties of Ksp,K1, and the enthalpy values. The standard deviations of calculated quantities are shown in parentheses in the tables. Figure 1 is the conventional type of distribution diagram and includes a plot of the experimental ii values along with the smooth curve for ii calculated from the @ values: ii = (C, - [Ll)/cM*
The potentiometric study of cadmium halide complexes by Leden (4)stands as a benchmark of excellent experimental work of its type. His published results for the four values are included in Table IV, and it is obvious that they do not agree well with the present results obtained by solubility. Fortunately, Leden’s paper includes a full summary of raw data and it is worthwhile to review the calculations. The program FMpoTDAT was designed to transform potentiometric data to the format suitable for program FORMSOLVE. First, Leden determined the response of a cadmium amalgam electrode in cadmium perchlorate solutions ranging in concentration from 0.001 to 0.1 M and concluded that dE/d log C was essentially constant, with a slope of 29.55 mV/ decade, close to the Nernstian ideal of 29.58. A least-squares examination of the data shows that the slope was not quite constant, but followed the equation 29.75 + 0.154 log C. There is no guarantee that this drift in slope continues at the same rate through the entire data set, but there is merit in seeing what effect such a drift has on the calculated p values. Secondly, Leden did not consider the effect of liquid junction potentials on the data. A recent paper by Hefter (5) discusses the estimation of the junction potential between two solutions of the type used in Leden’s work (3 M NaC104/x M NaBr, 3 - x M NaC104). The Henderson equation yields a value of 0.75 mV/(mol/L) of sodium bromide in the complexing solution. Finally, Leden did not have access to iterative computer programs that can do a more reliable data analysis than is possible by graphical techniques. Table IV includes the recalculated p values taking these factors into account, using Leden’s data set a t 0.00333 M cadmium. The internal precision of the data is excellent, with a standard deviation in calculated potentials of about 0.1 mV, which corresponds to a relative standard deviation of 8 ppt in the calculated Fo values. The agreement of the recalculated p values with those obtained in the present work is encouraging, except for the
Table V. Quantities (cal/mol), Calculated for Overall Stages of Cadmium Bromide Complexationa 2
1
4
-976
-1541
+ 183
+487
-984
-1749
+412
t 163
-978 (13)
-1317 (60)
+ 1306 (160)
+ 12 (50)
-2438 (12)
-3516 (56)
-4154 (118)
-5323 (22)
4.90 (0.06) a
3
7.4 (0.3)
18.3 (0.7)
17.9 (0.2)
enthalpy change as published by Gerding, with Leden’s published 4 values recalculated by CALSOLVE,with Leden’s published 0 values enthalpy change, Gerding’s data with P values from present work Gibbs free energy change, from 0 values of present work entropy change, cal/(mol K)
Uncertainties in enthalpy changes were estimated by simulation of Gerding’s experiment, using GENCALDAT and assuming 0.02 cal standard deviation in observed heat effects.
CALSOLVE,
Anal. Chem. 1983, 55, 1236-1240
1236
unexplained difference in PI, which is the value that should be the most reliable of the set. Clearly, the corrections for junction potential and slope drift are in the direction to make the /3 values much more nearly in accord with the solubility results of the present work. The conclusion is that the solubility method is a valid alternative to the electrochemical methods. The polarographic study at I = 3 by Eriksson (6) is lower in precision than Leden's work but is included in Table IV for comparison. Rocalculation of Eriksson's results, taking account of liquid junction potential but not of possible drift in slope, yields results in fairly good agreement with the other sets, but with an internal precision of about 0.3 mV. It is interesting that the step formation of the fourth complex is more favorable than for the third complex. Perhaps there is a thermodynamic factor related to the formation of a symmetrical species. A similar effect has long been noted for the formation of the second silver-ammonia complex (Kl = 2000, Kz = 8000). Thermodynamic Calculations. A calorimetric study of the cadmium bromide system at I = 3 has been published by Gerding (7), who relied on Leden's values to calculate the enthalpies for the fiour stages of complexation. Program CALSOLVEwas written to check the calculations. CALSOLVE has been checked for reliability both with exact data generated by program GENCALDAT, and with other published calorimetric data. Table V shows considerable discrepancies based on calculations alone, especially for mH,. The recalculations were carried out by using Gerding's data with 0.049 M cadmium, since that seemed to be the most reliable data set. The internal precision is about 0.02 cal. When the p values obtained in the present work are used in conjunction with Gerding's calorimetric data, the resulting
enthalpy changes are significantly different for the third and fourth stages. The solubility results for p values at 25 and 35 "C are not adequate for estimating enthalpy changes, because the effect of temperature is rather small. However, the temperature effects are in the right direction, though larger than expected for the fourth stage. To determine reliable enthalpy changes from the effect of temperature on p values, it would be necessary to carry out the solubility measurements over a wider range of temperatures. This work shows that equilibria constants for the formation of weak metal-ligand complexes may be determined by accurate measurements of the effect of ligands on the solubility of slightly soluble metal iodates. Cadmium, copper, silver, thallium, lead, calcium, barium, and lanthanum are candidates for future work, which should include further refinements in the reproducibility of the heterogeneous equilibrium system.
ACKNOWLEDGMENT The author is grateful to the New Brunswick Laboratory for the loan of the coulometry equipment. Registry No. Cd(IO&, 7790-81-0. LITERATURE CITED ( 1 ) Johansson, L. Coord. Chem. Rev. 1988, 3, 293-318. (2) King, E. J. J . Am. Chem. Soc. 1949, 71, 319. (3) Ramette, R. W. Anal. Cbem. 1981, 53, 2244-2246. (4) Leden, I. 2.Phys. Chem., Abt. A 1941, 188, 160-181. (5) Hefter, G. T. Anal. Chem. 1982, 5 4 , 2518-2524. (6) Eriksson, L. Acta Cbem. Scand. 1953, 7 , 1146-1154. (7) Gerding. P. Acta Cbem. Scand. 1988, 2 0 , 79-94.
RECEIVED for review January 12,1983. Accepted March 14, 1983. This research was supported by a Northwest Area Foundation Grant from Research Corporation.
Quantitative and Qualitative Information from Single Coulostatic Decay Curves John J. Relss' and Tlmothy A. Nleman" School of Chemical Sciences, University of Illlnois, 1209 West California Street, Urbana, Illlnois 6 180 1
Information contalned In the shape of slngle coulostatlc decay curves Is analyzed to yleld both concentratlons and E l l , values for electroactlve specles. For reductlons of Pb( I I ) and Cd( I I ) at a mercury electrode a plot of E vs. t 'I' Is h e a r In potentlal regions where a reaction Is dlffuslon llmlted and curved at potentlals riear an E,,, value. A plot of AE/At'/' resembles a normal voltammogram. Scans of several hundred mllllvolts are obtalned In 20-25 ms. The detectlon llmlt for Pb( I I ) Is 3.6 pM. For a reactlon whlch Is not dlffuslon llmlted (the oxldatloin of ferrocyanlde at a carbon paste electrode In thls case!) a plot of log E V.I log t , rather than E vs. t 1 I 2 , Is used to [Dbtalnconcentratlons and E,,, values. The detectlon llmlt for ferrocyanlde Is 69 pM.
The coulostatic or charge-step method was developed in 1962 by Dalahay (1-9) and by Reinmuth (4).Since that time 'Present address: IBM Instruments Inc., Orchard Park, P.O. Box 332, Danbury, CT 06810.
there has been considerable work on the theory of the method and on application to study of the kinetics of electrode reactions, but there has been relatively limited application for analysis. Previous analytical work has generally used coulostatics for quantitation and has largely used the coulostatic method to imitate more conventional electroanalytical techniques like polarography (5,6),differential pulse polarography (7), chronocoulometry (8), chronopotentiometry (9), anodic stripping voltammetry (6,9),coulometry (IO), and amperometry (11). A recent review covers theory and applications of coulostatic pulse techniques (12). Conventional electroanalytical techniques are limited in the scan rates attainable by the influence of charging current. At high scan rates in linear sweep voltammetry or high pulse repetition rates (with resulting narrow pulse widths) in differential pulse voltammetry, the increase in the ratio of charging to faradaic current greatly erodes sensitivity. A way of avoiding this problem is to use a technique which is independent of charging current, such as coulostatic analysis. By imitating a linear scan with a series of coulostatic pulses,
0003-2700/83/0355-1236$01.50/00 1983 American Chemical Society
