water). The other cases are comprised in the preceding ones.
Table XVI. Analysis of T a p Water with t h e Proposed Method" HC 1/ ~o-~,M
V,/ml
0.00 0.30 0.60 0.90 1.30 2.30 2.60 2.90
(PH)~~
(Ccoz)fo/ IC O ~ ( a q h,.J cco3*-/ 10% io-3~ io-%
L I T E R A T U R E CITED
8.734 0.9474 0.0468 0.3905 8.576 0.9646 0.3344 0.1025 0.7809 8.284 0.9877 0.7207 0.1058 1.1711 7.936 1.0101 1.0953 0.1201 1.6911 7.586 1.0402 1.5987 0.1349 2.9905 7.254 1.0940 2.4983 3.3799 7.252 1.0944 2.5050 3.7691 7.252 2.517 X lW3M 0.047 x lW3M 0.106 x lW3M (calculated value at V, = 0.60 ml;Cco3z- = CHcl- [COz(aq)] + \
-
cHC03-
Total alkalinity = 2.576 x lV3M uReagent = 0.9983M HCI; ( P H ) = ~ 8.756; ( C C O ~=) 0.9446 ~
X
10-3M.
CO2(aq), HC03-, and C032- appears, but their relative amounts are not in accordance with the percentage values calculated a t = 0 (1.1,98.0, 0.9%, respectively) and a t = 0.1 (1.4, 97.4, 1.2%). A possible explanation is that the analyzed samples were not in equilibrium, because of the lower temperature and the higher Pco2 values in the pipe-line, and of the slowness of steps 3 and 4 in the following path:
co3'-
--+
1
H C O ~ - - - + H,CO,
-;+
2
CO,(aq)
-;-+
(1) S. Bruckenstein and I. M. Kolthoff in "Treatise on Analytical Chemistry", Part I, VoI. 1, I. M. Kolthoff, P. J. Elving, and E. B. Sandell, Ed., Interscience Publishers, New York, NY, 1959, pp 426-427. (2) T. B. Taylor in "Treatise on Analytical Chemistry", Part 111, Vol. 2, I. M. Kolthoff. P. J. Elvina. and F. H. Stross, Ed., lnterscience Publishers, New York, NY, 1971, p.-301. (3) "Handbook of Analytical Chemistry", L. Meites, Ed., McGraw-Hill. New York, NY, 1963. (4) H. B. Elkins and L. D. Pagnotto in "Treatise on Analytical Chemistry', Part Ill, Vol. 2, I. M. Kolthoff, P. J. Elving, and F. H. Stross. Ed.. Interscience Publishers, New York. NY, p 21. (5) J. P. Lodge, Jr.. E. R. Frank, and J. Ferguson, Anal. Chem.. 34, 702 (1962). (6) A. L. Underwood and L. H. Howe 111, Anal. Chem., 34, 692 (1962). (7) M. J. Fishman and D.E. Erdmann. Anal. Chem., 43, 356R (1971). (6)M. J. Fishman and D.E. Erdmann, Anal. Chem., 45,361R (1973). (9) P. E. Toren and B. J. Heinrich. Anal. Chem., 29, 185 (1957). (10) S. R. Gambino, Clin. Chem., 7, 236 (1961). (11) J. Severinghaus and A. F. Bradley, J. Appl. Phys., 13, 515 (1958). (12) G. G. Guilbault and F. R. Shu, Anal. Chem., 44, 2161 (1972). (13) J. W. Ross, J. H. Riseman, and J. A. Krueger, Pure Appl. Chem., 36, 473 (19731. (14) A. K. Covington. CRC Crit. Rev. Anal. Chem., 3 , 367 (1974). (15) D.Midgley and K. Torrance, Analyst(London),98, 217 (1973). (16) L. B. Macurdy in "Treatise on Analytical Chemistry", I. M. Kolthoff. P. J. Elving, and E. B. Sandell, Ed., lnterscience Publishers, New York. NY, Part I, Vol. 7, pp 4309-4313. (17) E. Scarano, M. Forina, and C. Calcagno, Anal. Chem., 45, 557 (1973). (18) T. S. Lee in "Treatise on Analytical Chemistry", Part I, Vol. 1, I. M. Kolthoff. P. J. Elving. and E. B. Sandell, Ed., lnterscience Publishers, New York, NY, 1959, p 234. (19) D P. Lucero and F. C. Haley, J. Gas Chromatogr., 6, 477 (1968). (20) "Handbook of Chemistry and Physics", 49th ed.. Chemical Rubber Company, Cleveland, Ohio, 1969, p B-189. (21) M. Forina and E. Scarano, h g . Chim. /tal., 7 , 77 (1971). (22) R. D.Caton, Jr., J. Chem. Educ., 50, A571 (1973). (23) R. D.Caton, Jr., J. Chem. Educ., 51, A7 (1974). (24) "Standard Methods for the Examination of Water and Waste Water", 1l t h ed., 1960, APHA, WPCF, pp 44-47.
COk)
+
Cases examined have been 8 (NaOH NaZCOs), 7 ( N a ~ C 0 3 )6, (Na2C03 NaHCOs), and an analytical case with characteristics of cases 6, 5 , 4 a t the same time (tap
+
RECEIVEDfor review September 30, 1974. Accepted February 5 , 1975. Work supported in part by a grant from the Consiglio Nazionale delle Ricerche, Rome, Italy.
General Computer Program for the Computation of Stability Constants from Absorbance Data D. J. Leggett and W. A. E. McBryde Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada
A new computer program, SQUAD, has been developed enabling the evaluation of the best set of stability constants from absorbance measurements. The method can be used to determine pKa's, metal Ion hydrolysis constants and study multicomponent equilibria. A rigorous testing procedure has been used to investigate the limitations of the method. SQUAD has been applied to the nickel ethylenediamine system to yield log plol = 7.36, log @,02 = 13.74, log @ l o 3 = 18.06.
The application of machine computation to the elucidation of solution equilibria has been reviewed up t o 1971 ( I , 2 ) . Since then, several authors have published programs which enable the calculation of stability constants from various types of data. These programs may be classified
into two groups, i.e., general and specific (usually with some approximations). Kankare (3) has developed a general approach, employing absorbance data, of the direct search type ( 4 ) designed for small core computers (16K bytes). This set of programs has a built-in safeguard against the calculation of negative molar absorbtivities during any stage of the calculation, a strategy also adopted by Nagano and Metzler ( 5 ) .Another general method, utilizing potentiometric data, by Sabatini and Gans (6, 7) employs the Davidon-Fletcher-Powell (8, 9) modification of the Gauss-Newton iterative method. These authors have commented on the unreliability of SCOGS ( 1 0 ) and we will discuss our experiences with this program later in this paper. Feldberg et al. ( 1 1 ) have used a simplified version of SillBn's twist matrix method ( 1 2 ) . ANALYTICAL CHEMISTRY, VOL. 47, NO. 7, JUNE 1975
1065
. MAINLINE
ECOEF etc.
Input 8 m i o r output step I
step 2
DIFF Builds up mlinear least squares eqns.
,
SEARCH Evaluates shifts
f o r p’s
I”’”’”]
1
Calculates U ,u,etc.
Solves linear
Coln. of
Caln. o f specks concen-
Figure 1. Simplified flow diagram illustrating the basic philosophy of SQUAD
However their program is very slow (20 minutes with a CDC6600). Kaden (13) has published a general program capable of processing either potentiometric or absorbance data by changing one or two subroutines. Within the second group of programs are those written with a specific spectrophotometric investigation in mind but which make approximations when setting up relevant equations. Programs of this type have been published by Siefker ( 1 4 ) , Kuban (15, 16) and Chattopadhyaya (17). Various simplifying techniques are made including neglecting minor species, using only absorbance data a t peak maxima etc. The use of a computer for these simple systems must be questioned since the time spent writing and debugging the program might be more profitably spent on a suitable graphical technique (18). This publication reports a new computer program, SQUAD (Stability Quotients from Absorbance Data) derived from SCOGS. The program is written in FORTRAN IV. I t is capable of calculating simultaneously, or individually, overall stability constants (of the concentration type) for any species formed in systems containing up to two metals and two ligands, provided that the degree of complex formation is pH-dependent. The method is therefore capable of yielding, from appropriate absorbance data, acid association constants (and hence pK,’s), metal-ion hydrolysis constants, stability constants of simple complexes (ML, ML2, etc.) and stability constants of polynuclear complexes (M2L3, M z L ~ HM3Ld(OH)2, , etc.). In addition, it may also be used to study mixed complexes containing two metals and/or two ligands and complexes of these various types.
PROGRAM DETAILS Figure 1 shows a simplified flow diagram describing the basic philosophy of the program. We do not intend to present here the mathematical theory behind each subroutine but rather to indicate its use in the program. The MAINLINE program reads in supplied data: stoichiometric coefficients and stability constants of all expected species together with several integers related to positioning concentrations, constants, and relevant molar absorptivities within arrays. The output consists of the values of the refining constants after each cycle, and after convergence has been achieved, the final calculated molar absorptivities, stability constants, and concentrations of all species for each solution. A printer plot is also given enabling a 1066
rapid visual evaluation to be made of the fit between each experimental and theoretical spectrum. The latter is based on constants derived from the final iterative cycle. Punched cards are also produced containing the molar absorptivities of all species for each wavelength and concentrations of all species for each solution. These are used in a second program, SQUADPLOT, that produces diagrams of the individual species spectra and the ‘goodness of fit’, using a Calcomp digital incremental plotter (19). All nonlinear least squares methods are based on the minimisation of the function, U , where
ANALYTICAL CHEMISTRY, VOL. 47, NO. 7 , JUNE 1975
where N is the number of data points. The derivation of a suitable value of wn is left to the individual user. In all examples cited in this publication w j = 1.0. The minimization of U is controlled within subroutine REFINE. The completion of one iteration involves three major steps, as indicated in Figure 1. The first step, performed by DIFF, is complete once the nonlinear least squares equations have been completely developed. This process is achieved, together with the calcu(Fcalcd - F & s d ) j and u in subroutine RESID. lation of The theoretical absorbance, F & d , is obtained from Beer’s law as follows. The current set of stability constants, together with the chemical composition of each solution and the stoichiometric coefficients of each species are passed to the subroutines CCSCC and COGSNR. CCSCC is a “bookkeeping” routine for COGSNR. This latter routine, as in SCOGS (IO),evaluates from the input data the concentration of the j t h species in the i t h solution, Cij, by the Newton-Raphson method. Control returns to ECOEF and the molar absorptivities for the j t h species and the h t h wavelength, € j k , are calculated. The subroutine package LLSQAR (obtained from IMSL, Houston, T X ) performs this evaluation and, finally, the theoretical absorbance is obtained for the ith solution and h t h wavelength. Control now returns to RESID and hence to DIFF, once all values of U have been obtained for the current set of stability constants. The second step involves the solution of the least squares equations. This is performed in SEARCH and when complete yields shifts by which the sought constants must be changed to lower the value of U. Finally, in step three, a check is made to ensure that the updated stability constants provide a better description of the data than the previous set. Provided this is true, this iterative cycle is completed. If the shifts applied to the sought constants are all less than 0.001, refinement is terminated and control returned to the mainline. Further details concerning the method of implementation and modus operandi of the program is given in a manual and program listing available, upon request, from the author (D. J. L.).
u,
PROGRAM TESTING T o test the performance of this program absorbances were calculated for systems of hypothetical complex species for which values of the formation constants and molar absorptivities a t various wavelengths were assumed. The formation of both metal-ligand and proton-ligand complexes was provided for, and in some cases the protonation or deprotonation of metal-ligand complexes was assumed as a variant on simple complex formation. The following sets of species were considered as possibly forming together:
Table I . Stability Constants Generated by SQUAD from Synthetic Data Log 3101 b System
Subseta
a101
A
1
10 .oooo 0.0001 9.9987 0.0025 10.0016 0.0052 9.9963 0.0075 9.9996 0.01 06 10.0143 0.0127
2 3 4
5 6
B
1
2 3 4 5
6 C
1
2 3 4 5 6
D
1
2 3 4 5
6
Log 0 1 0 2 b
Log 4 1 1 1 b
‘102
ulll
Log 31-116 U
1-11
Log 6 2 0 2 6
10.0000 0.0001 9.9976 0.0056 10.0050 0.0115 10.0281 0.0175 9.9989 0.0235 9.9900 0.0288
17.7999 0.0001 17.7978 0.0056 17.8136 0.0115 17.8305 0.0178 17.7931 0.0236 17.8133 0.029
14.1000 0.0001 14.0959 0.0035 14.1055 0.0071 14.1169 0.0111 14.0937 0.0147 14.0705 0.0182
9.9999 0.0001 9.9971 0.0057 10.0033 0.0119 10.0340 0.0179 9.9976 0.0240 9.9789 0.0295
17.7997 0.0001 17.8063 0.0070 17.8133 0.0146 17.8512 0.0222 17.7539 0.0296 17.7906 0.0358
14.1000 0.0001 14.0952 0.0036 14.1 046 0.0074 14.1190 0.0114 14.0942 0.0149 14.0643 0.0184
9.9999 0.0001 9.9901 0.0061 10.0160 0.0118 9.9926 0.0200 9.9828 0.0264 10.0154 0.0319
17.8000 0.0001 17.7937 0.0051 17.7990 0.0106 17.8050 0.0166 17.7738 0.0220 17.8653 0.0266
of cycles
0.0283
3
1.384
3
2.915
3
4.230
3
5.937
3
7.191
3
0.0288
3
1.404
4
2.887
4
4.459
4
5.963
4
7.310
4
0.0299
7
1.405
7
2.923
8
4.439
8
5.892
8
7.331
8
0.0280
5
1.379
5
2.848
5
4.459
6
5.937
6
7.093
6
202
1.9999 0.0001 1.9985 0.0027 1.9998 0.0056 2.0060 0.0081 2.0092 0.0114 2.0056 0.0138
2.0022 0.0013 1.9608 0.0802 1.9370 0.1460 2.0204 0.1913 2.1174 0.1421 1.7512 0.2395 24.0003 0.0002 24.0083 0.0101 23.9653 0.0217 24.0183 0.0325 23.991 1 0.0430 24.0825 0.0511
NO.
‘ D A TAC 103
“ Subset numbers refer t o standard error of synthetic d a t a . 1 = Exact d a t a (to 4 decimal places), 2 = *0.00138; 3 = *0.00293; 4 = *0.00436: 5 = rt0.00587; 6 = *0.00741. Initial guesses for program are log 3101 = 9.1. log 3102 = 18.6, log 3111 = 15.5, log 31-11 = 1.3. log 3 2 0 2 = 22.5. Values used to generate the synthetic d a t a were 10.0, 17.8, 14.1, 2.0.and 24.0, respectively. u11.4.r~ is the standard deviation of the calculated spectra with respect to the observed spectra.
A B
C D
1
+ MOHL ML + ML2 + MHL HL H2L ML + MLz + MOHL + MHL + M + MOH ML
+
ML
+ MLz + M2Lz
+
+
Twenty-three values of molar absorptivities for each complex were fixed over a range of wavelengths, and twelve solutions containing the several species within each set dis-
tributed over a range of p H values, and hence a variety of relative concentrations of the species were assumed t o be available. The twelve solutions in a set were taken as having various CM:CL ratios, and p H values ranging from 2 to 9. Thus for each solution, 23 absorbance values were calculated. Onto each absorbance value could then be superimposed a random error; first no error was tried, and then this was increased in six stages of increasing error up to 10.0074 unit of absorbance. The error was generated by the multiANALYTICAL CHEMISTRY, VOL. 47, NO. 7, JUNE 1975
1067
0
o
c
0
P -
0 ;
c
0
s C
c C
5
K ?
E 8 Lr, m
5
X
0
9
C
1150.0
WRVELENGTH ;NM)
475.0
500.0
525.0
550.0
575.0
WfiVELENSTH ;NMl
Figure 2. Calculated (points) and supplied (solid line) molar absorptivities for system B
Figure 3. Calculated (points) and supplied (solid line) for molar absorptivities for system D, “DATA = 0.007og
(0) Calculated values for ML, (A)Calculated values for ML2, (+) Calculated values for MHL
(0) Calculated values for ML, (A)Calculated values for ML2. (+) Calculated
plicative-congruential method. The error of set B was investigated up to f0.0273 unit. The testing of the program followed the sequence of normal investigation of metal-ligand interactions, viz.-(a) Evaluation of pK, values for the ligand and 6 values for all species. (b) Evaluation of hydrolysis constants for the metal ion and any corresponding t values. (c) Evaluation, with the aid of results from (a) and (b), of stability constants and molar absorptivities of the metal-ligand complexes assumed in the sets A to D. (d) Testing, specifically with set B, whether other groups of species were capable of describing the observed properties of the solution. The stability constants for the assumed complex species which were generated by the program are given in Table I, and these may be compared with the initially assumed values. Subsequently, the program was applied to data accumulated with the real system nickel-ethylenediamine. Twelve solutions were prepared encompassing the CM:CL ratio from 1:2.5 to 1:4 and the pH range 6.0 to 7.8. The absorbance of eight of these, measured with a Cary Model 16 spectrophotometer were digitized between 500.0 and 660.0 nm a t 5.0-nm intervals and then processed by SQUAD. After refinement was complete, the calculated stability constants and absorptivities were used to predict the spectra of the remaining four solutions, the values calculated in this way being compared with the observed data. An IBM 360/75 computer was used for all calculations performed in this study.
DISCUSSION Systems A, B, and D all produced the correct stability constants to within two u. Figure 2 shows the calculated molar absorptivities for System B (points) together with those used to calculate the synthetic data. The figure depicts the calculated 6’s as derived from subset 6, the least precise, of this system. With System C, some difficulty was encountered in obtaining the correct value for log p1-11. This is attributed to the low contribution of this complex to the total absorbance. In fact, the complex is chemically insignificant in eight of the solutions and only in one does it contribute to more than 10% of the absorbance. The discrepancy between calculated and actual molar 1068
ANALYTICAL CHEMISTRY, VOL. 47, NO. 7, JUNE 1975
values for M2L2 c
s0
.
U
?
Flgure 4. As Figure 3 but UDATA
= 0.00446
absorptivities for System D (Figure 3) is due to a slightly different cause. In this system, competition between the metal and protons for the ligand is high in all but four solutions. Metal-ligand interactions occur significantly only in alkaline solutions where ML2 is the predominant species; hence there is little contribution to the observed spectra from ML and MzLz. This problem is hidden by the apparently good agreement shown in Table I for the derived constants of this system. However, if the molar absorptivities from subset 4 are plotted, the agreement is substantially improved (Figure 4). The conclusions to be drawn from these observations are applicable not only to this program but to all such least squares investigations. (1) As the number of unknowns to be found increases, the likelihood of finding the correct answer decreases. (2) Successful differentiation of “unique” results is improved with increasing accuracy of the data. (3) Within the limitations of available computer time and core, the more data supplied, the greater the confidence of the resulting solution. If it is envisaged that 400 absorbance
5 0
-
B
I
500.0
520.0
540.0
560.0
580.0
600.0
620.C
640.0
660.0
dFIVELENGTH :NMI
Figure 5. Comparison between predicted spectra (solid line) and ac-
Figure 6. Molar absorptivities of the nickel-ethylenediamine com-
tual spectra (points) for the nickel-ethylenediamine system
plexes. Curve 1, Ni(en); Curve 2, Ni(enk; Curve 3, Ni(en)s
(0) pH = 7.525, Ct = 0.050M,
CDATA = 0.00033; (A)pH = 6.464, C, = = 0.00167: (+) pH = 7.458, 9 = 0.075M, CDATA = 0.00021; f& = 0.020M. T = 25 O C . I = 0.50MKN03
0.050M,
UDATA
values will be used, 20 solutions and 20 wavelengths are to be preferred rather than 10 solutions and 40 wavelengths. T h e former experimental technique gives, for each wavelength, 20 absorbances values from which N unknown molar absorptivities are to be calculated, i.e., a total of 20N unknowns. The latter case increases the total number of unknown 6's to 40N but decreases the number of absorbance values available to evaluate these parameters. (4) I t may be necessary to subdivide the data into regions where only some of the complexes predominate. For instance, in system C, data below p H 6, can be investigated for ML, ML2, and MHL only. Once satisfactory values for these stability constants have been obtained, they are held constant and the data above pH 6 are processed, M ( 0 H ) L being the only complex to be found. On the other hand, for System D, there is no point in attempting to process data from solutions where less than 10%of the metal is bound to the ligand. While these comments may seem trivial, it has become apparent from the literature that the computer is being increasingly used with decreasing regard, unfortunately, for the chemical significance of answers thus obtained. When Systems C and D were processed in the more discriminating manner suggested, the values for stability constants and molar absorptivities were appreciable closer to the original values. The results from the first two testing procedures merely confirmed the ability of the program to evaluate ligand pK,'s and metal hydrolysis reactions. Each system was well-behaved and none of the aforementioned difficulties arose. SQUAD was also tested to investigate the possibility of force-fitting the wrong model. All of the models tried on the data for System B, subset 5 (i.e., ML, ML2 or ML, ML2, M(OH)L, or ML, M(OH)L, MHL) failed to refine. In the latter two examples, the constant for the nonexistent complex was altered in such a way as to make that species chemically (and arithmetically) insignificant. The error applied to the data for System B was increased to f0.0273 yielding the following values, log plol = 10.151 (f0.104), log pi02 = 17.825 (&0.113), log pill = 14.219 (f0.069). At this level of data imprecision some doubt may
be cast on the values of the refined stability constants. The final test of SQUAD was performed on data obtained for the nickel-ethylenediamine system. The stability constants determined in 0.50M potassium nitrate were in satisfactory agreement with published values (20). log p i 0 1 = 7.364 f 0.015 log p i 0 3 = 13.739 f 0.023 (pK2 = 6.375) log pi03 = 18.061 f 0.043 (pK3 = 4.322) UDATA = 0.00056 (Measured in 0.50M potassium nitrate; 25 "c.) Removal of any one of the eight solutions and reprocessing the remaining data caused the above constants to be changed only within the original u's, thus confirming the validity of these values. These constants, together with the molar absorptivities of the three species were used to predict the spectra of four additional solutions. Figure 5 shows the comparison between three of the four computed spectra (solid line) and the actual spectra (points) for this prediction. Figure 6 shows the molar absorptivities of the three complexes. The prediction of spectra is a particularly valuable method of testing the correctness of both the model and the values of the refined stability constants, I t avoids the possibility that the answers supplied by the program describe only the data rather than the chemical system. The minimization procedure has been based on that used by Sayce ( 1 0 ) .SCOGS has been used extensively in this laboratory for five years and, in the authors' experiences, has performed reliably. However, some qualifications of this statement must be made. The authors agree with the general observations of Sabatini (6) and Gans ( 7 ) concerning SCOGS, viz, ". . . the program still appears to require good initial parameter estimates", but believe that this state of affairs is more to be recommended than condemned. The use of graphical techniques, although sometimes cumbersome, demands personal intervention between the raw data and the final results (211. I t seems preferable that the role of the computer be one of confirming conclusions rather than its use to the exclusion of these methods. In 1962, SillBn (22) cautioned against too much reliance on the computer, and these remarks are still relevant. Obviously, there are some instances where prior graphical treatment of the data or analogy with literature values is impossible. In this situation, the user of any powerful proANALYTICAL CHEMISTRY, VOL. 47, NO. 7, JUNE 1975
* 1069
gram should be careful not to add species to a particular model merely in an attempt to improve the statistical fit of the data. If all prior treatment techniques are inapplicable, it is possible systematically to examine the error surface with a variety of models. In this approach, the sum of squares of the residuals (SSR) is calculated for each constant over a predetermined range of values. The initial guesses would then be those constants giving the lowest SSR. This approach (although unnecessary) was used for the nickel-ethylenediamine data. It was effective in locating a suitable set of P's but was very slow and is obviously inefficient. This program has also been applied to analysis of spectrophotometric data obtained for the reaction of picoline2-aldehyde thiosemicarbazone with iron(II), cobalt, mercury(II), and silver. The results of these investigations will be published shortly.
LITERATURE CITED (1) C. W. Childs, P. S. Hailman, and D.D.Perrin, Talanta, 16, 1119 (1969). (2) F. J. C. Rossotti, H. S. Rossot!i, and R. J. Whewell, J. lnorg. Nucl. Chem., 33, 2051, (1971).
(3) J. J. Kankare, Anal. Chem., 42, 1322 (1970). (4) J. P. Chandler, "Minimum of a Function of Several Variables", Program 66.1, Quantum Chemistry Program Exchange, Indiana University, Bloomington, IN, 1966. (5) K. Nagano and D. E. Metzler, J. Am. Chem. Soc., 89, 2891 (1967). (6) A. Sabatini, A. Vacca, and P.Gans. Talanta, 21, 53 (1974). (7) P. Gans and A. Vacca, Talanta, 21, 45 (1974). (8)W. C. Davidon, U S .At. Energy Comm. Rept., ANL-5990 (1959). (9) R . Fletcher and M. J. D. Powell, Computer J., 6, 163 (1963). (10) I. G. Sayce, Talanta, 15, 1397 (1968). (11) S. Feldberg. P. Klotz, and L. Newman, lnorg. Chem., 11, 2860 (1972). (12) L. G. Silbn, Acta. Chem. Scand., 18, 1085 (1964). (13) T. Kaden and A. Zuberbuhler, Talanta, 18, 61 (1971). (14) J. R. Siefker, Anal. Chim. Acta, 52, 545 (1970). (15) V. Kuban and J. Havel, Scripta Fac. Sci. Univ. &no, Chemia 2, 1, 87 ( 197 1). (16) V. Kuban, Scripta f a c . Sci. Univ. Brno, Chemia 2,2, 81 (1972). (17) M. C. Chattopadhyaya and R. S. Singh, Anal. Chim. Acta., 70, 49 (1974). (18) F. J. C. Rossotti and H. Rossotti, "The Determination of Stability Constants", McGraw-Hill. New York, 1964. (19) D.Leggett, J. Chem. Educ., 51, 502 (1974). (20) L. G. Sillen and A. E. Martell, Ed. "Stability Constants of Metal-ion Complexes'', Chemical Society, London, 1964. (21) H. S. Rossotti, Talanta, 21, 809 (1974). (22) L. G. Sillen, Acta Chem. Scand., 16, 159 (1962).
RECEIVEDfor review November 12, 1974. Accepted February 3,1975.
Behavior of a Micro Flowthrough Copper Ion-Selective Electrode System in the Millimolar to Submicromolar Concentration Range W. J. Blaedel and D. E. Dinwiddie Department of Chemistry, University of Wisconsin, Madison, WI 53706
The behavior of a copper ion-selective electrode in a flowing system is investigated in the range 10-3-10-9M of copper Ion. Steady state potentials are independent of electrode pretreatment, and are Nernstian down to 10-8M, but below steady-state potentials are attained only after long periods of flowing solution contact with the electrode. Electrode and flowthrough cell construction is described.
I t has been shown that a t submicromolar concentrations, a copper ion-selective electrode can change the copper concentration of the solution in which it is immersed ( I , 2 ) . Therefore, for the measurement of low copper ion concentrations, a micro flowthrough electrode would seem to possess a marked advantage over the conventional batch technique. Some studies have been made of the behavior of the copper ion-selective electrode in flowing solutions. Thompson and Rechnitz ( 3 ) have described a fast flow system containing a fluoride ion-selective electrode with rapid response and Nernstian behavior down to about 10-7M. They have also designed and studied the behavior of heavy metal ion-selective electrodes in flowing systems (4).For the copper ion-selective electrode, they found Nerstian response down to 10-6M copper ion, with equilibrium potentials being achieved rapidly for freshly polished electrodes. Rechnitz and coworkers have also described the advantages of making potentiometric measurements with ion-selective electrodes in a differential mode, so that the junction potentials are compensated for, and so that external reference electrodes are not needed (5, 6). Llenado and Rechnitz (7) 1070
ANALYTICAL CHEMISTRY, VOL. 47, NO. 7, JUNE 1975
have devised a continuous system for glucose analysis, using a flowthrough iodide ion-selective electrode, based on the glucose oxidase reaction. Alexander and Rechnitz have described an automated method of protein determination with a flowthrough silver ion-selective electrode (8). Flowing systems designed for the implementation of standard addition techniques have been described in the literature (9, 1 0 ) . I t has recently been reported that the injection of copper and silver ions from the electrode into the solution must be recognized a t copper ion levels of 1 ppb (around 10-8M) ( 2 ) . This paper describes the construction of a gravity-fed micro flowthrough electrode system fabricated from commercially manufactured Ag2S-CuS pellets. The behavior of the system over a wide range of copper ion concentration is described.
EXPERIMENTAL F a b r i c a t i o n of the M i c r o C o p p e r I o n - S e l e c t i v e E l e c t r o d e s . Figure 1is a schematic of t h e electrode, which consists of an Ag2SCuS chip epoxied into the end of a threaded acrylic rod. As received, t h e Ag2S-CuS pellets were 716 inch in diameter a n d 3/32 inch thick (Orion Research, Cambridge, MA). T h e pellet came pressed onto a disk of silver metal, which was pried away. T h e pellet was c u t into quarters with a jewelers saw, and then each quarter was cut into thirds, giving 12 chips per original pellet. T h e electrode body was a n acrylic rod, 2 inches long and 0.25 inch in diameter, center bored t o accept t h e silver electrical contact wire, and with a cavity drilled into one end t o accept t h e AgzSCuS chip. T h e silver wire was cemented t o t h e back side of t h e chip with conducting gold-filled epoxy (Epo-Tek H 80, Epoxy Technology Inc., Watertown, MA). T h e silver wire, once inserted
