J. Phys. Chem. 1900, 84, 3433-3438
of spherical and rodlike micelles and a small specificity of Br- for binding to the rods. Acknowledgment. We are grateful to Professor Bernard Brun for support and to Dr. HQlran Wennerstrom for valuable discussions. Financial support was obtained for the stay of G.J.T.T. in Lund from the Swedish Natural Science Research Council and for the stays of B.L. in Montpellier as well from the Centre National de la Recherche Scientifique.
References and Notes (1) (a) FacuU des Scknces, Montpellier; (b) Physlcal Chemistry 1, L m (c) Physlcal Chemilstry 2, Lund; (d) Unlkfver Research, Port Sunlight. (2) F. Reiss-tiusson and V. Lurrati, J. Phys. Chem., 86,3504 (1964). (3) G. Llndblom, B. Lindman, and L. Mandtrll, J. Colloid Interlace Sci., 42, 400 (1973). (4) U. Henriksson, L. &berg, J. C. Erlksson, and L. Westman, J. phys. Chem., Ell, 76 (1977). (5) J. Ulmius and H. Wennerstrom, J. Megn. Reson., 28, 309 (1977). (6) J. Uimlus, B. Lindinan, 0. Lindblom, and T. Drakenberg, J. Coibkj Interface Sci., 65, 88 (1978). (7) 6.Lindmn and B. Brun, J. CollOM Intcvface Sci., 42, 388 (1973). (8) N. Kamenka, B. Elrun, and 6.Llndman, Proc.-Int. Congr. Surf. Act. Subst., 7th, 7976, Sect. B, Part 11, p 1019.
3433
H. Wennerstrom and 8. Lindman, phys. Rep., 52, 1 (1979), and references therein. J. C. E r i k m and G. Gillberg, Acta Chem. S~end.,20,2019 (1986). R. M. Bain aind A. J. Hyde, Symp. faraday Soc., 5 , 145 (1971). H. Wennerstrom, 0. Llndblom, and B. Llndman, Chem. Scr., 8, 97 11974). b. Llndblom, 8.Llndman, and 0. J. T. TMdy, J . Am. Chem. Soc., 100, 2299 (1978). G. J. T. W ,G. Undbbm. and B. Undman, J. Chem. Soc., Faraihy Trans. 7, 74, 1290 (1978). H. Wennerstrbm, G. Lindblom, B. Lindman, and 0. J. T. Tlddy, J. Chem. SOC., faraday Trans. 7, 75, 663 (1979). N. Kamenka, H. Fabre, M. Chorro, and B. Lindman, J. Chhn. phys., 74, 510 (1977). D. H. Smith, J . Colloid Interlace Sci., 86, 70 (1979). N. A. Mazer, 0.8. Benedek, and M. C. Carey, J. phys. Chem., 80, 1075 (1976). D. E. Clarke fwd D. 0. Hall, Coibkj Polym. Scl., 252, 153 (1974). T. J. Price and D. 0. Hall, to be submitted. 0. Gunnarsson, B. Jonsson, and H. Wennerstrom, to be submitted. B. Llndman arid S. ForsBn, “Chlorine, Bromine and Iodine N.M.R.”, Springer-Verlsg, Heidelberg, 1976. H. Wennerstrdm, Chem. Phys. Lett., 18, 41 (1973). J. Ulmius and H. Wennerstrom, J. M g n . Reson., 23, 431 (1966). E. J. Staples and G. J. T. Tlddy, J. Chem. Soc., faraday Trans. 7, 74, 2530 (19.78). M. Almgren, J. E. Lofroth, and R. Rydholm, Chem. Phys. Left., 63, 265 (1979).
Cuprlc Ion-Selective Electrode and Inorganic Cationic Complexes of Copper Rudolf Wagemann Depwfment of Fkheries and Oceans, Freshwater Instlfute, Winnipeg, Manitoba 1337’2N8 (Received: Mey 19, 7980)
The response of the solid-state, cupric ion-specific electrode toward some inorganic copper complexes was investigated by using E vs. pH titration curves. Different Nernlet slopes were obtained depending on the assumptions made concerning the identity of the species being sensed by the electrode. Correspondence between slopes based on different assumptions and the theoretical slope and experimental slopes was used as a criterion for determiningthe species being sensed by the electrode. In this way it is shown that the electrode very probably responds not only to C V + but also to CuOH’, CuZ(OH)?+, and CuHCOS+. At pH 8.3 and 9.0, cupric ion activities measured with this ellectrode would be determined too high by a fiilctor of 10 and 40, respectively, relative to the calculated cupric ion activities, if no allowance were made for this lack of specificity.
Introductioin In aqueous systems that are free from interfering ions the solid-state cupric ion electrode is generally considered to respond specifically to the cupric lion activity. Because in simple acidic aqueous systems (Le., distilled water solutions) the experimental slope of the Nernst equation for such an electrode has been found to be the same as the theoretical slope foir a doubly charged ion, this type of electrode has therefore been used with increasing confidence over a wide pH range for the measurement of the cupric ion activity or the “free” cupric ion concentration in such diverse areas as kinetic studies, toxicity studies, and the determination of stability constants of copper complexes. For solutions more complex than copper in distilled water, such as natural waters, for example, the slope of the Nernst equation may be quite different from the theoretical slope!, which has led to doubts about the specificity of the electrode.1$2 In an aqueous solution of copper (in equilibrium with the atmosphere) there are a number o€ inorganic complexes of copper that will be formed unavoidably to a greater or lesser extent depending on the pH of the solution: Cu2+, CuOH’, Cu2(0H)$+, Cu(OH)$, Cu(C03)$-, etc. If in addition some chelating agenb such as EDTA, humic acids, etc., are present, the corresponding chelates with copper will be formed, but these chelates are known not to be
sensed by the ion-selective electr~de”~ and are not of interest in this investigation. Of the inorganic complexes that may be present in “distilled water solutions” of copper, only Cu2+isl generally assumed to be sensed by the cupric ion-select,ive electrode, but this has never been demonstrated conclusively in basic solutions where such complexes occur. Certainly, nothing can be proved in this regard by calibrating the electrode in the usual way of successively increasing the total copper concentration under otherwise fixed conditions, since an increase in the concentration of total copper causes an increase in the concentration of the various species in direct proportion to the total increase. On the other hand, if one maintains the total copper concentration constant and changes the pH, the influence!of the copper species on the Nernstian slope is allowed to manifest itself. The purpose of this investigation was to determine the Nernstian slope i n three different ways and, from a comparison of these slopes with the theoretical slope, to deduce whether the solid-&ate, copper-selectiveelectrode responds only to cupric ion or also to other inorganic cationic complexes of copper. To this end the following scheme and rationale was employed: (1) to establish first of all whether the electrode behaved normally under the conditions of the experiment by determining the slope from purely experimental data and without assuming the identity of the 0 1980 American Chernical Society
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The Journal of Physical Chemistry, Vol. 84, No. 25, 1980
Wagemann
species being sensed by the electrode; (2) to determine the slope from calculated activities of only the cupric ion (by solving the equilibrium equations) and measured potentials and to compare this with the theoretical and purely experimental slopes; (3) to determine the slope from the sum of the calculated activities of all cupric cations (Cu2+, CuOH', Cuz(OH)2', CuHC03+) present in the simple solutions studied and the measured potentials. If a normally responding electrode yielded a Nerstian slope by this approach but not when cupric ion alone was considered (i.e., by approach 21, this would be taken to indicate that the electrode sensed not only cupric ion but also other cupric cations. Experimental Section A copper solution (1000 mg/L) was prepared by dissolving metallic copper (99.9% Cu analyzed, J. T. Baker Chemical Co.) in high-purity nitric acid. Working solutions (100 mL) of 500-, 300-, 150-, 60-, and 30-pg/L Cu were prepared by dilution of stock solution. Water, doublydistilled from quartz, was used throughout. The highest and lowest concentrations were chosen to avoid precipitation of cupric hydroxide or formation of a hydroxide colloid on the one hand, and nonlinearity of response (E vs. log) on the other. All working solutions were made 0.1 M in ionic strength with KNOB(Analytical Reagent, BDH Chemicals Ltd.), acidified to pH 1-1.5 with high-purity nitric acid (redistilled from Teflon), and then titrated stepwise (using Eppendorf pipettes, 50-200 pL) with 2 and 0.05 N sodium hydroxide (Reagent Grade, J. T. Baker Chemical Co.). After each addition, 2-3 min6were allowed to elapse before reading the voltage and pH. Throughout the titration (23 i 1 OC) a relatively large area of solution was in contact with the atmosphere, and the solution was stirred with a Teflon-coated magnetic stirrer. Each concentration set of solutions was titrated four times, each time with a different combination of measuring elements. Otherwise, the conditions were the same for all titrations. Concentrations were corrected for volume of titrant added, and ionic strength was corrected for addition of acid. The following measuring elements were used: two different Orion solid-state, ion-specific (Cuzf) electrodes, Model 94-29A, Serial No. GO1 and DQ1; two different meters, an Orion Model 801 and a Weston and Stack Model 650; two different Orion Ag-AgC1 reference electrodes with the respective filling solutions recommended by the manufacturer, a single-junction electrode Model 90-01 (junction solution, 90-00-01) and a double-junction electrode Model 90-02 (inner solution, 90-00-02, outer solution 90-00-01). The pH was measured, at the same time as the voltage, with an Orion pH meter, Model 401, using a standard combination glass electrode (Model 13-639-90, Fisher Scientific Co.). Before each titration the pH electrode was checked against standard buffer solutions (Fisher certified), and the sensing surface of the ion-selective electrode was polished with fine alumina paper before each titration run, but not during titration. The modified Davies equation' was used to calculate activity coefficients. A Fortran-based computer program (a finite difference Levenberg-Marquardt algorithm for minimization of the sum of squares)8was used for fitting functions to data. Results and Discussion The usual method of determining the slope ( b ) of the Nernst equation (eq 1)is to maintain the pH constant and E = u + b log AcU (1)
to vary the total copper concentration (CUT). The inde-
y ' o -.-
500
eo
"I5O0 0-•
\ I
2
3
4
5
6
7
8
9
IO
PH
Flgure 1. The response (mV) of the Orion solid-state, ion-selective (Cu2+)electrode as a function of pH (dots), at concentrations of 500, 150, and 30 bglL of total copper in a solution of 0.1 M KNOBin distilled water. The solld line represents the best fit of the function A s$m to measured potentials and pH.
-
pendent variable (CU,) is then related linearly to the activity of any mononuclear copper complex, and therefore such a functional relationship between the independent variable and the activity can have no influence on the magnitude of the slope. This means that any of the mononuclear copper complexes (or total copper), regardless of whether the electrode actually senses that particular species (as long as it senses some copper species), could be used as the independent variable to determine the slope (electrode calibration) without any effect on the slope. The slope can also be determined for copper from an E vs. pH titration curve at constant total copper concentration (CUT)with a solid-state ion-selective (Cuz+)electrode if the activity (Acu) or the concentration of the species being sensed by the electrode can be calculated as a function of pH. Ordinarily this requires an a priori knowledge or assumption concerning the species being sensed by the electrode. Such an assumption and the explicit calculation of activity itself can be avoided if a suitable function can be fitted to the E vs. pH data. Any function which can represent sufficiently well the experimental data in the pH range studied and whose constants can be easily related to those of the Nernst equation can be used. A function that was found suitable is eq 2, where
E = A - BekPH
(2)
the constants A, B, and k were determined by minimization of the sum of squares. This approach provided a method of determining the slope from a titration curve without resort to assumptions concerning the identity of species being sensed by the electrode. It was then only necessary to assume the validity at low pH (1-2.5) of eq 3, where y is the activity coefficient of the cupric ion (0.41). (Cud7 = ACU (3) The slope of the Nernst equation was then given by eq 4, b = (A - BekpH- a)/lOg [(CUT)r] (4) where a was obtained independently of the titration data by calibrating the electrode at a constant pH (2.5) in the usual way by successively increasing the total copper concentration and extrapolating the calibration graph to unit activity. In Figure 1, a representative set of titration data with eq 2 fitted to the data is shown. The error of fit ranged from 3 to 5 mV, which translates into an error
The Journel of Physical Chemistty, Vol. 84, No. 25, 1980 3435
Cupric Ion-Selective Electrode
TABLE I: Nernst Slope ( b )for Copper Obtained from Measurements of Electrode Potential as a Function of pH with an Orion Solid-state, Ion-Selective ( Cuz+) Electrode at Various Total Dissolved Coppix - Concentrations (CUT)" 1 2 3 measuring elements CUT, Pg/L b, mV b, mV b, mV WS, sngl jnct, GO1
av WS, sngl jnct, DQ1
500 300 150 60 30 500 300 150 60 30
av Orion, dbl jnct, DQ1
av WS, dbl jnct, GO1
av
500 300 150 60 30 500 300 150 60 30
-
27.25 27.13 26.86 27.84 25.82 26.98 i: 0.74 27.01 27.07 26.00 26.58 28.10 26.95 t 0.77
30.00 29.67 29.48 30.08 30.29 29.90 k 0.33 29.10 29.41 29.60 30.23 31.84 30.04 t 1.01
16.13 15.4 1 12.72 13.019 13.00 14.07 t 1.58 17.30 14.44 13.57 13.95 14.51 14.76 t 1.47
32.25 29.94 24.73 26.94 24.99 27.77 2 3.26 32.03 28.82 27.85 28.19 27.08 28.79 i: 1.91
16.59 15.91 13.30 13.15 15.38 14.87 k 1.35 15.83 13.15 12.85 '15.20 115.20 14.46 f 1.35
31.68 28.43 25.22 25.45 27.62 27.68 i: 2.63 29.09 28.58 23.76 26.25 27.46 27.03 f 2.12
An Orion or Weston and Stack (WS) meter, a single-junction (sngl jnct) or double-junction (dbl jnct) Ag/AgCl reference electrode, and two Orion ion-selective electrodes (Serial no. DQ1 and GO1) were used. Column 1: based entirely on experimental data. Column 2: based on calculated activities of Cu2+and measured potentials. Column 3: based on calculated sum of all cationic inorganic complexes of copper and measured potentials. The given errors are one standard deviation from the average.
in the slope ( b ) of 6-9%. As expected, the electrode response (voltage) is clearly quite constant with changing pH in the acidic pH region up to pH 6-6,5.At higher pH, the response declines with increasing p l l as a result of a decrease in the activity of copper cation complexes. In view of the existence of a well-defined plateau in the acid pH region of the E vs. pH curve (Figure 11, the assumption of direct proportionality between total copper concentration and activity at low pH (eq 3) appears to be justified. The slopes in column 1 of Table I were calculated from eq 4. They are therefore derived entirely from experimental data without resort to assumptions concerning the identity of tho species being sensed by the electrode. To obtain a measure of reproducibility for different measuring elements and to guard against artifacts entering into the determination of slopes, we repeated the titrations by using different ion-selective electrodes, different voltage meters, and a single- and double-junction Ag/AgCl reference electrode (Table I). Depending on whether a single- or double-junction reference electrode was used, the experimental slopes (column 1,Table I) are on the average 26.96 f 0.71 and 29.97 f 0.76 mV, respectively. At the 99% confidence level this difference is significant (F-test). The smaller slope obtaineld with the single-junction reference electrode may have lbeen caused by a greater change in junction potential during titration with this electrode than with the double-junction reference electrode. The interchange of other measuring elements produced no significant difference in slope. If one allows for a 1 "C temperature fluctuation about the experimental temperature of 23 "C, the theoretical slope for a doubly charged ion is 29.29 f 0.08 mV at this temperature. The standard deviation (f0.08) was calculated from five different slopes (0.5 "C temperature intervals) within the specified temperature range. No sigrificant difference exists at the 99% confidence level (F test) between this theoretical slope and those slopes in colunnn 1, which were obtained with a
TABLE II: Reactions Considered in the Calculation of Inorganic Copper Complexes in a Distilled Water-Copper Solution (0.1 M in KNO,) in Equilibrium with Atmospheric Carbon Dioxide
K ( 2 5 "C) 3.47 x CO,(g) 2 H,O H,CO, H2C0, .-r Hi. + HC0,4.43 x 10-7 HC0,- H t + C0,Z4.69 X lo-'' cu2++ (20;- cuc0,o 5.37 x lo6 cuz++ 2co;- 6; cu(cO,),21.02 x 1O'O CU'+ t H+ t C O l - CuHCO,' 2.0 x 10'2 Cuz+ t H,O=CuOH+ t H+ 4.57 x lo-* Cu2++ 2H,Q + Cu(OH),O + 2H+ 2.09 x 10-14 Cu2++ 3H2(3+Cu(OH),- t 3" 1.58 x 20-27 Cu2++ 4H,O Cu(OH),2- + 4H+ 1.26 x 10-40 2Cu" + 2 H 2 0 Cu,(OH),2+ t 2H+ 2.69 X lo-''
*:
*
*
*
**;
ref 9 9 10 9 10 11 9 9 12 12 9
double-junction reference electrode. The sensing electrode was therefore considered to behave normally over the pH range studied# Slopes were then calculated from measured E values, based on the assumption that the electrode sensed only the cupric ion, by fitting the function E = a + b log Acu to measured E values and calculated activities of the cupric ion (by simultaneous solution of the equilibrium equations, in Table 11). The slopes obtained in this way (column 2, Table I) ranged on the average from 14.07 to 14.87 mV; they are obviously quite different from the slopes in coluinn 1 (Table I) or the theoretical slope, so that with this assumption the Nernst equation is not well obeyed. A Foirtran-based, iterative computer program was used to calculate activities as a function of pH. The set of chemical equations and stability constants that entered into these cislculations are shown in Table 11. The slopes in column 3 (Table I) were obtained in much the same way as those in column 2, except that the calculated activity used in conjunction with each measured potential was the sum of all the cation activities of copper, namely, Cu2++ CuOH+ + C U ~ ( O H )+~ CuHC03+. ~+ The
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The Journal of Physlcal Chemistry, Vol. 84, No. 25, 1980
IS
0.E
0.E
0.7
e
0.6
!f! > 2 a
c
a5 0.4
0.3
0.2
0.I
6.5
7.0
75
8.0
85
9.0
PH Flgure 2. The change with pH in the ratio of the cupric ion actlvity to the sum of all the activities of inorganlc cation complexes of copper CU~(OH),~+ CUHsensed by electrode: Cu2+/(Cu2+ CuOH+ C03+).
+
+
+
difference between values (average) in column 3 and column 1 (Table I) is not significant at the 99% confidence level (Ftest) for any of the four sets of data. A small trend can be discerned in the data of column 2 (Table I) with changing total copper concentration, but this does not affect the interpretation of results in view of the rather large difference between these data and those in column 1or column 3. As was expected, the slopes in column 1 and column 3 show no such dependence on total copper concentration. It appears that the slopes in column 2 (Table I) are as small as they are because the calculated activities did not in this case correspond to the actual activities producing the potentials. If, on the other hand, this discrepancy had been caused by an actual physical or chemical process in the system, then the experimental data itself would have had to reflect this, and the slopes obtained from the experimental data (column 1,Table I) should not agree as they do with the theoretical slope for a divalent cation. The combined activities of the cation complexes used to obtain this slopes in column 3 (Table I) do apparently correspond to the actual activities producing the measured potential much more closely than the cupric ion activity alone, since there is agreement between slopes in column 3 and column 1,and the theoretical slope, but disagreement between slopes in columns 2 and 1. These results tend to indicate that the electrode responds not only to
Wagemann
the cupric ion but also to all other inorganic cation complexes of copper present in this simple system. This conclusion rests ultimately on the validity of the stability constants that entered into the calculation of activities and on the completeness of the set of equilibria used to define the system (Table 11). For a simple aqueous system such as was investigated here the given set of equilibrium equations (Table 11) is believed to define all significant complexes and major ions, and only rather large errors (order of magnitude) in the equilibrium constants could invalidate the conclusion. It would appear that a true measure of cupic ion activity is not obtained with the cupric ion-selective electrode in solutions of pH I 7 which includes most natural waters. At pH I 6, in a distilled water solution such as is generally used for standardizing the electrode, no significant error in the measurement of the cupric ion activity with this electrode would be incurred since the activity of inorganic copper species other than the cupric ion is negligibly small below pH 6. At pH I 7 the cupric ion activity begins to differ substantially from the total cupric cation activity which is apparently sensed by the electrode, and this difference increases with increasing pH (Figure 2). At pH 7.3 the cupric ion activity is one-half of the total cationic activity of copper, and at pH 8.3 it is only one-tenth of the combined activity (Figure 2). If one assumed that the electrode responds only to Cu2+,the cupric ion activity would be determined 10 times too high (relative to the calculated cupric ion activity) at pH 8.3,20times too high at pH 8.6 (Figure 21, and a factor of 40 too high at pH 9. This kind of error, if unaccounted for, may be of considerable consequence in the determination of stability constants of copper, for example, and generally whenever free cupric ion concentrations are measured with such an electrode in basic solution.
Acknowledgment. I thank Mrs. Monika Dajie for performing the titrations, Mr. Dave Abrams and Miss Dona Janke for executing the computer calculations, Miss Marlis Ziprick for typing the manuscript, and Mr. Lauri Taite for drawing the figures. I am grateful to Dr. Jan Barica for valuable discussions leading to this investigation. References and Notes (1) J. Barica, J . Fish. Res. Board Can., 35, 141 (1978). (2) R. Jasinski, I. Trachtenberg, and D. Andrychuk, Anal. Chem., 46, 364 (1974). (3) G. J. Moody and J. D. R. Thomas in “Ion-Selective Electrodes In Analytical Chemistry”, H. Frlesen, Ed., Plenum Press, New York, 1978, p 339. (4) W. T. Bresnahan, C. L. Grant, and J. H. Weber, Anal. Chem., 50, 1675 (1978). (5) C. J. M. Heijne and W. E. van der Linden, Anal. Chlm. Acta, 96, 13 (1978). (6) W. J. Blaedel and D. E. Dinwiddie, Anal. Chem., 46, 873 (1974). (7) L. Meites, “Handbook of Analytlcal Chemistry”, McGraw-Hill, New York, 1963, pp 1-8. (8) Computer Subroutine Libraries In Mathematics and Statistics (Subroutine ZXSSQ), Internatlonal Mathematlcal and Statlstlcal Libraries Inc., Houston, TX, pp 1-7. (9) L. G. Slll6n and A. E. Martell, Spec. Pub/.-Chem. SOC.,No. 26, 865 (1971). (10) L. 0. Slllbn and A. E. Martell, Spec. Pub/.-Chem. SOC.,No. 17, 754 (1964). (11) C. W. Chllds, Roc.-Conf. GreatLakes Res., 14, 198-210 (1971). (12) P. W. Schindler, Adv. Chem. Ser., NO. 67, 196 (1967).
