312
Anal. Chem. 1981, 53, 312-316
parameter which is an increasing function of kD/Cu1f2. If we take the propionate esters as an example of a series of polar compounds and assume that the dipole moment is 1.80 D, we can calculate the relative snesitivity per gram (relative to toluene) for this series. The theoretical curve, B, is shown in Figure 3 as well. The calculated sensitivity for a polar compound is higher than the calculated sensitivity for a nonpolar compound of the same molecular weight at relatively low molecular weights, but the difference in sensitivities decreases with increasing molecular weight. The sensitivities per gram for a series of propionate esters appear to decrease as the molecular weight increases, but additional data on higher molecular weight compounds are necessary. There are few data on chemical ionization sensitivities with which we can make comparisons. The propionate esters were examined several years ago in some of the early chemical ionization studies (18). It was suggested then, based on total sample ion currents, that the molar sensitivities for the esters (methyl through heptyl) were essentially the same: no significant variation with structure or with molecular weight. Our data indicate a small increase in molar sensitivity over this range: about a 40% increase in molar sensitivity between methyl propionate and hexyl propionate, although the spread about the average is *E%. There is no disagreement between these two observations. Essentially identical observations have been made by using CzH5+ (also present in CHI) as the reactant ion. Because the proton and hydride transfer reactions of CzH5+ with organic compounds are all vigorously exothermic, there is little structural specificity in the rate constants and selectivities for this ion ether. Quantitation by either CH5+or CzH5+with average values of experimentally determined sensitivities for each compound gives results which agree within 3-8% (relative) of the syn-
thetic results for several mixtures of different compound types. At present, we cannot determine simultaneously components differing by more than about a factor of 10 in concentration with reasonable accuracy.
ACKNOWLEDGMENT The authors are grateful to Robert Kobelski for the synthesis of some of the propionate esters.
LITERATURE CITED Hatch, F.; Munson, B. Anal. Chem. 1977, 49, 169-174. Hatch, F.; Munson, B. Anal. Chem. 1977, 49, 731-733 Subba Rao, S. C.; Fenselau, C. Anal. Chem. 1978, 50, 511-515. Hatch, F.; Munson, B. J. Phys. Chem. 1978, 62, 2362-2369. Andersen, J. S.; Munson, B. Int. J. Mass Spectrom. Ion Phys. 1980, 34, 141-146. Poiley, C. W. Ph.D. Dissertation, Unlverslty of Delaware, Newark, DE 1980. Field, F. H.; Munson, M. S. B. J . Am. Chem. SOC. 1985, 87, 3289-3294. Hartman, C. H. Anal. Chem. 1971, 43, 113A. Su, T.; Bowers, M. T. Int. J . Mass. Spectrom. Ion Phys. 1975, 17, 211-212. Barker, R. A.; Ridge, D. P. J. Chem. Phys. 1976, 64, 4411-4416. Su, T.; Bowers, M. T. Int. J . Mass Spectrom. Ion Phys. 1973, 12, 347-356. Denbigh, K. G. Trans. Faraday SOC. 1940, 36, 936-948. Moelwyn-Hughes, E. A. ”Physical Chemlstry”; Pergamon Press: New York, 1957; pp 371-375. McClellan, A. L. “Tables of Experlmental Dipole Moments”; W. H. Freeman: San Francisco, CA, 1963. Smyth, C. P. “Dlelectrlc Behavlor and Structure”; McGraw-Hill: New York, 1955. Smith, J. W. “Electric Dipole Moments”; Butterworths: London, 1955. Lias, S. G.; Eyier, J. R.; Ausloos, P. Int. J. Mass Spectrom. Ion Phys. 1978, 19, 219-239. Munson, M. S. B.; Field, F. H. J. Am. Chem. SOC. 1966, 66, 4337-4345.
R E Cfor~review September 29,1980. Accepted November 21, 1980. Taken in part from Ph.D. Thesis of C. W. Polley, Jr.
Effects of Bromide on Silver Chloride Electrodes J. R. Sandifer Research Laboratories, Eastman Kodak Company, Rochester, New York 14650
Responses of silver chloride membrane electrodes and of siiver/sllver chloride electrodes of the second klnd to solutlons of chloride conlalnlng traces of bromide were investigated. Potentlometry, neutron activation, X-ray diffractlon, and scanning electron mlcroscopy were used to show that silver chloride crystals are converted to mixed crystals of AgClflr, In their entirety and not Just their surfaces, as was previously assumed, when they are contacted by solutions whlch contaln both chiorlde and bromlde Ions. The compositions of the mixed crystals obey, approximately, a simple ion-exchange equiilbrlum equatlon in whlch the Ion-exchange constant equals the ratio of solublllty product constants of AgCl and AgBr.
Theoretically, the potential of a silver/silver chloride electrode which is exposed to a solution containing both chloride and bromide ions should obey eq 1. E is the potential
E = EoAg/AgC1 - 59 log (%-
+ KPotC1-/Br-aBr-)
(1)
of the electrode in millivolts, E” is the reduction potential of 0003-2700/81/0353-0312$01 .OO/O
the Ag/AgCl couple, a c l - and asi are activities of chloride and bromide ions, respectively, and KPotC1-/B,- is the selectivity coefficient of this electrode. Buck (1)derived eq 1 (for iodide interference instead of bromide) subject to the assumption that a heterogeneous, ion-exchange equilibrium is established between the ions in the solution and a mixed crystal of AgClxly which is confined to the AgCl/solution interface because of the immobility of halide ions within the bulk of the crystal (2). The theoretical value of the selectivity coefficient turns out to be the ratio of the solubility product constants of silver chloride and silver iodide (1). In the present situation the analysis remains the same except the interfering halide is bromide. Buck’s derivation pertains particularly to solid-state membrane electrodes. These consist of crystals of AgCl attached to the ends of tubes which are f i e d with a solution containing chloride. A suitable reference electrode is then inserted into this solution to complete construction. Electrodes of the second kind differ from this construction in that a layer of insoluble salt is deposited directly onto the surface of the metal. In this case, AgCl is deposited onto Ago. If the silver is completely covered with AgC1, such electrodes should behave analogously to solid-state membrane electrodes, differing 0 1981 American Chemlcai Soclety
ANALYTICAL CHEMISTRY, VOL. 53, NO. 2, FEBRUARY 1981
only in the nature of the contact on one side of the crystal. On this basis, Buck’s theory can be extended to include electrodes of the second kind (3). If the layer of silver chloride is porous, silver ions will be sensed directly by exposed silver. The activity of silver ions will be fixed by the activities of chloride and bromide, however, and by the solubility product constants of their silver compounds. Formation of mixed crystalline phases a t the surfaces could again be postulated, and the final result would be mathematically identical with the other two cases. Potentiometric titrations of mixed halide solutions with silver nitrate have long been interpreted in terms of ion-exchange equilibria involving mixed-crystal formation ( 4 , 5 ) . Buck’s derivation seems to be a reasonable extension of previous work in this regard. The assumption that immobility of halide ions maintains the proposed mixed-crystal phase at the surface seems to have been generally accepted also (6). However, it is not consistent with the observations of Kelly and Mason (7), who used X-ray photoelectron spectroscopy in conjunction with ion etching to show that microcrystals of silver chloride are converted throughout, not merely their surfaces, to mixed-halide crystals by bromide ions. Furthermore, Klasens and Goosen (8) concluded from their work with solid-state silver chloride electrodes that iodide ions will react with the crystal “until either the AgCl of the membrane or the iodide of the solution becomes exhausted.” On this basis, sensitivity to the interfering halide may be a function of the total coverage of silver chloride on the electrode (in the case of electrodes of the second kind) as well as to the volume and composition of the sample. Rhodes and Buck (9) have recently reported potentiometric data, collected with anodized silver/silver chloride electrodes, which show that not only the surface but also the interior of the electrode is metathesized to silver bromide when contacted by dilute bromide/chloride solutions. Their study was similar to some unpublished Kodak Research Laboratories experiments, with which they were familiar, in pursuit of a chloride-selective electrode for clinical analysis (10). Some of the results of that research are presented here and serve to extend and clarify conclusions drawn by Rhodes and Buck (9). EXPERIMENTAL SECTION Preparation of Ag/AgCl Electrodes of the Second Kind. Silver/silverchloride electrodes of the second kind were prepared by anodizing silver wires in a saturated sodium chloride solution by use of a Beckman Model PK-1A platinizing kit or an operational amplifier (Analog Devices 425) circuit employing a constant current loop. Different coverages were obtained by varying the current density or the period of anodization. Other wires were converted chemically in a chlorochromate bath containing 15.4 g of KCl/L, 10.1 g of K2CrzO7/L,and 25 mL of 6 N HCl/L. Time of exposure to this solution was varied in order to obtain different coverages. Thin-film electrodes, prepared by vapor deposition of silver onto plastic support followed by partial chemical conversion to silver chloride in the chlorochromate bath (11),were also investigated. These were industrial preparations and, as such, were highly reproducible. They were continuous sheets several inches wide. Electrodes were cathodically stripped after use in order to estimate their halide coverages. Potentiometric Measurements. Potentiometric measurements were made by using the junctionless cell (chloride ion selective electrode/sample/Beckman 39047 general purpose cationic glass electrode) and an Orion Model 801 millivoltmeter. Time response curves were recorded with a Fisher Recordall Series 5000 recorder. All potentials were stable to within 0.5 mV for at least 1 min before measurement. Solutions were stirred. Radiotracer Measurements. The radiotracer was used to follow the attack of bromide on thin-film silver/silver chloride electrodes by monitoring the appearance of bromide on their surfaces. Neutron Activation. Coverages by bromide and chloride were also determined in some instances by CFX neutron activation
313
(12). The coated portions of anodized wires were placed in polyethylene capsules containing a KCN solution sufficiently concentrated to dissolve the silver halide. The chloride and bromide concentrations were then determined relative to a standard solution. Preparation of AgCl Membrane Electrodes. Silver chloride membrane electrodes were prepared by pressure sealing sheet crystals between aqueous solutions in a concentration cell. Apiezon grease was used to prevent leakage. One side of the cell was f i e d with 0.1 M NaCl and referenced with an anodized wire electrode prepared as described above. The other side of the cell served as the sample compartment. Potentiometric measurements were then made as described. Sheet crystals between 200 and 250 Ccm thick were formed by sandwiching molten silver chloride between plates of Vycor. The plates were separated, no more than 1 day before the crystals were tested, by soaking them for several hours in chlorine water. X-ray Diffraction. X-ray diffraction was used to determine the orientations of the sheet crystals and also to verify the formation of mixed crystals after exposure to bromide. The X-rays penetrate to a depth of 10-50 km. It was therefore possible to determine the orientation of the silver chloride substrate beneath the mixed crystals, as well as the orientations of the mixed crystals themselves. Scanning Electron Microscopy. Scanning electron microscopy was used to characterize the surface of the sheet crystals both before and after exposure to bromide. The crystals were carbon coated. A 25-kV accelerating voltage was used at 0’ of tilt. Stereoscopic photographs were taken at angles of 0’ and 10’.
RESULTS AND DISCUSSION Ag/AgCl Electrodes of t h e Second Kind. Potentiometry a n d Radiotracer. Responses of Ag/AgCl electrodes of the second kind to small increments of bromide added to 50, 100, or 200 mM sodium chloride solutions were investigated. Bromide was added at 1-min intervals so that its concentration ranged from 0.04 mM, after the first addition, to a final value of -10 mM. In all cases, measured potentials indicated substantially less sensitivity to bromide than predicted by Buck’s theory (1). Potentials of heavily coated AgIAgC1 electrodes varied linearly with the logarithm of added bromide up to about 1 mM with slopes of less than 10 mV/decade. Fairly abrupt changes in potential occurred above certain concentrations of bromide, depending upon the level of chloride and the coverage of AgC1. These changes occurred at concentrations of bromide near the product KPot~rlBr-[Br-] when the coverage of AgCl was very small, but at much higher concentrations when the coverage was great. They did not occur immediately but rather required several minutes, as shown in Figure 1. Each c w e in the figure represents a fresh piece of thin-film electrode (area -0.7 cm2, coverage -1 pequiv) and a different concentration of sodium bromide injected into 25 mL of 100 mM sodium chloride solution. Although not as reproducible, similar results were obtained with anodized and chemically converted wires. These results are similar to those reported by Rhodes and Buck (9) at lower concentrations. However, they reported an initial overshoot in the potential which they described as a relaxing diffusion potential. Such overshoots do not appear in Figure 1but were observed in some cases, depending upon method of electrode preparation. They seemed to be most apparent when the silver chloride did not adhere strongly to the silver. Known areas of the thin-film electrode were bathed in solutions containing 100 mM NaCl plus 0.4, 1.0, and 2.0 mM NaBr tagged with (8zBr)-for known periods of time. They were then washed in distilled water and analyzed to determine the course of reaction between bromide and silver chloride. These radiotracer data, shown in Figure 2, indicate that bromide reacts continuously with silver chloride even though the potentials vary in discrete steps during the reaction (Figure 1). Each data point in Figure 2 represents a separate ex-
ANALYTICAL CHEMISTRY, VOL. 53, NO. 2, FEBRUARY 1981
314
.,,,I
c
A
12oc
-loot
4
2.0 mM
100
a
- 40
-20t ol
0
I
2
4
1
6
1
8
I
IO
1
I2
I
I4
I
I6
I
18
1 J
20
Time, minutes
Flgure 1. PotentiaVtime responses of industrially prepared (chlorochromate-converted) Ag/AgCI electrodes after addition of different concentrations of NaBr to 100 mM NaCl solutions. Concentrations of NaBr added are shown above each curve.
Flgure 3. Responses of Ag/AgCI electrodes. Each point represents a different electrode which has soaked in 100 mM NaCllx mM NaBr solution for 5 days: 0, formal concentration of NaBr; +, concentration after 5 days. Curve is calculated from eq 1, with activity coefficient and reference potential incorporated into EOA,,ASI. Sign reversed in accordance with experimental conditions.
4007
I
7Z'omM
Time, minutes
Flgure 2. Dependence of bromide coverage of industrially prepared Ag/AgCI electrode on time of exposure to different solutions. Bromide concentrations shown beside each curve. Chloride concentration was 100 mM in all cases.
periment involving a different piece of the same thin-film electrode. Notice that the degree of conversion appears to be far greater than that expected for mere surface reaction. Neutron Activation. Six Ag/AgCl electrodes were prepared by anodization and placed in 25-mL solutions of 100 mM NaCl to which various concentrations of NaBr had been added. After 5 days the potential of the cell (Ag/AgCl/solution/Beckman 39047 general purpose cationic glass electrode) was determined for each wire in its respective solution. The wires were then analyzed by neutron activation to determine the AgCl and AgBr coverages. Results for these wires as well as four others similarly treated but without performance of the potentiometric experiment are shown in Figures 3 and 4. Concentrations of bromide in the solutions were recalculated from their initial values and from the AgBr coverages. Figure 3 shows a graph of the measured potentials vs. the logarithm of the initial bromide concentration (open circles) and the recalculated concentrations (crosses) after equilibration. Notice that a reasonably good fit of the data can be obtained with eq 1. The value of KpotcI-/Brused to calculate the curve shown in the figure is fairly close to the theoretical value (380 compared to 420), suggesting the correctness of the ion-exchange hypothesis involving the bulk of the silver halide layer. Mole fractions of bromide (XBr)on the wires were also calculated from the neutron activation data and are plotted
O
0
Y
1
-
I
I
2
3
4
[Si-], mM
Figure 4. Mole fraction bromide, to whlch Ag/AgCI electrodes of Figure 3 were converted after 5 days, plotted against calculated solutlon
concentrations of sodium bromide. Curve calculated from ion-ex= 420. change model using KPota-,Brvs. equilibrium bromide concentrations in Figure 4. Error bars were estimated assuming that the uncertainty in XBr is dXBr/aWcl times the uncertainty in the weight of chloride (WCJ plus dXBr/dW& times the uncertainty in the weight of bromide ( WBr). The error bars were limited at the extremes by knowledge that 0 IXBr I1. Also shown in the figure is a theoretical curve based on the ion-exchange equilibrium assumed by Buck.
Br-
+ AgCl
KP"c r p r
C1-
+ AgBr
(2)
(3) MBr and
Mcl are the ionic weights of bromide and chloride, respectively. Notice that eq 3 fits the data well at the extremes but there is significant deviation within the 0.2-0.6 mM bromide range. The discrepancy is not necessarily a t odds with the ion-exchange model, since one could reformulate the data in terms of solid-state activities rather than mole fractions if the activity coefficients were known. This formulation would be more in line with theory. However, the excess bromide might also be due to adsorption. Since the potentials obey the ion-exchange model, it follows that the effect of adsorption would be fairly small.
ANALYTICAL CHEMISTRY. VOL. 53. NO. 2. FEBRUARY 1981 315
Table 1. Heterogeneous Rate Constants for Bromide Attack on Silver Chloride sample preparation mea” volb concnE 1 2
i 3
sheetcrystal sheet crystal chlorochromate conversjOn
6.7
3.4 2.9 1.0 1.9
3.3
30 25 25 20 20 20
0.2
0.2 0.2 0.1 0.1
0.1
kd
..
0.22 0.63 0.23 0.46 0.51 0.52
A
.
B
Mauoscopic area in em’. In em’. In mM NaBr. In cmlmin. Samples 3 and 4 are industrial preparations.
a
AgCl Membrane Electrodes. Potentiometry and Extent of Conversion. Three AgCl membrane electrodes were prepared from different pieces of the same sheet crystal. These electrcdes and an Orion Model 94-17A chlorideselective electrode were used in a bromide sensitivity study analogous to that described earlier with Ag/AgCI electrodes. Potentials were monitored after stepwise additions of sodium bromide to SO, 100. or 200 mM sodium chloride solutions. Results were similar to those obtained with the Ag/AgCl electrodes-far less sensitivity to bromide than predicted by eq 1. The abrupt change in potential mentioned previously occurred in this study only in the case of SO mM sodium chloride background. In that case the potential changed by -16 mV a t 10 mM added sodium bromide but was still almost 80 mV less negative than that predicted by eq 1. Little difference was noticed between the Orion Model 94-17A electrode and a sheet crwtal electrode investigated under identical conditions. A disk with diameter 2.1 cm was punched out of a crystal and supported in 30 mL of 0.2 mM NaBr such that both sides were bathed by the rapidly stirred solution. The rate of disappearance of bromide was then monitored with the cell Ag/AgBr/NaBr solution/Beckman 39047 general purpose cationic glass electrode. A linear change in potential prevailed for a t least 49 min with dAE/dt = -1.14 mV/min. Since the change in potential should follow eq 4, it follows that [Br-Io,., = 0.02 mM. A
total of 5.3 pmol of bromide must have been consumed from the solution. This amounts to a coverage of lo00 A by AgBr, given a density of 6.47 (13),and is far more than a few monolayers. The fact that dAE/dt is constant has important kinetic consequences. Since
AE = A E O ‘ where
+ 59 log [Br-]
(5)
AE”’is the formal cell potential, it follows that
- 59 d In Wr-1 dt 2.3 dt If first-order kinetics is obeyed
(6)
d In [Br-j/dt = -kA/V
(7)
dAE
where k is a heterogeneousrate constant, A is the microscopic surface area of the crystal, and Vis the volume of the solution. Substitution of eq I into eq 6 results in eq 8. The experi-
dm = --59kA/V -
(8)
dt 2.3 mental parameters (including the macroscopic surface area) yield k = 0.22 cm/min. Similar experiments were run with
D
C
npve 5.
Scanning eleCbOn photomlcrcgraphs of dmerenl pleces of ths same sheet uvstal a h diiferem periods of exposue to soluiknm of NaCIINaBr: (A) exposed fw 1 day 10 100 mM NaCl contalnlng IY) NaBr (100OOX): (B) exposed fa 10 min: (C) exposed for 4 h (D) exposed for 16 h 10 100 mM NaCII10 mM NaBr (lOOOX).
-
a sewnd crystal and with chlorochromate-convertedthin-fh electrodes, and the results are shown in Table I. The rate of reaction is not profoundly different whether the bromide is attacking a sheet crystal or a chlorochromate-converted surface. Data collected with the thin-film electrodes substantiate the correctness of the approach, since different m, volumes, and concentrations yield the enme rate conatants to within 15%-a reasonable expectation. If k were limited by ion-exchange kinetics, then the use of macrosmpic, rather than microscopic, surface areaa should have resulted in much larger calculated k values for the porous (chlorochromateconverted) electrodes than for the sheet-crystal electrodes. This is to be expected because the microscopic areas of porous electrodes are much larger than their macroscopic areas. Since the calculated values are very nearly the same in the two canes, it follows that k is not limited by ion-exchange kinetics. Diffusion of bromide to the silver chloride “macroscopic surface” is therefore likely to be the rate-limiting step. X-ray Diffraction. Characterization of several sheet crystals by X-ray diffraction revealed the following observations. First, within that portion of the crystal area exposed to radiation (-0.7 em2), there were never more than three orientations. Second, after exposure to bromide, mixed crystals of AgCI,Br, were clearly indicated. Third, the mixed crystals had the m e orientations as the silver chloride substrate if the time of exposure was about 0.5 h or less. Longer exposures resulted in a random distribution of orientations. Scanning Electron Microscopy. A sheet crystal was cut into four pieces, three of which were then exposed to a stirred solution containing 100 mM NaCl and 10 mM NaBr for different periods of time. The fourth was exposed to a 100 mM NaCl solution which contained no bromide and served as a control. Scanning electron photomicrographs were then taken of various portions of their surfaces, and some of these are shown in Figure 5. The photograph shown in the upper left portion of the figure is that of the control under lOo00X magnification. It reveals a featureless surface even under 10 times the magnification used for the other photographs in this figure. After 10 min the surface has the appearance shown in the upper right portion of the figure. Clearly the bromide has had a highly disruptive effect upon the AgCI. Notice that
316
ANALYTICAL CHEMISTRY, VOL. 53, NO. 2, FEBRUARY 1981
there are two distinct regions of disruption. The nature of the surface inhomogeneity was not explored but it was a generally observed phenomenon. The surface of the crystal acquires a spongy appearance after 4 h (lower left photpgraph) but acquires a harder, more angular appearance after 16 h (lower right photograph). Stereoscopic photomicrographs of the crystal exposed for 4 h were taken a t lOOOX,3000X,and lOOOOx magnification and reveal hollow domes which cover pores -3 pm in diameter. The domes are very thin and appear to have formed as bubbles which have broken open from the inside. These photographs explain how the bromide can exchange so deeply into the crystals and why solid-state electrodes should behave like electrodes of the second kind regarding bromide interference.
CONCLUSIONS On the basis of the observations of this study, the following mechanism may be hypothesized. When a silver chloride electrode contacts a solution containing chloride and bromide, its surface quickly converts to a composition intermediate between pure AgCl and the final, equilibrium composition. The potential of the electrode remains stable so long as this surface composition does not change. However, bromide continuously moves into the bulk of the crystal. This does not imply solid-state diffusion but rather movement into an open, porous structure formed by disruptive bromide attack, as indicated by the photomicrographs. When the bulk approaches the same composition as the surface, the surface begins to incorporate additional bromide until a new intermediate composition is achieved. The potential varies during this transition but again stabilizes when the surface has reached the new composition. The potential remains stable as the bulk of the layer is brought up to the corresponding level of bromide. The process repeats itself until the equilibrium composition (given by the ion-exchange equations) is reached. This model accounts for the shapes of the potential/time curves shown in Figure l (and ref 9)and also for the conversion data shown in Figures 2 and 4. Dependence of rate of equilibration upon coverage is readily understood because thicker coatings will require longer times to reach equilibrium. Dependence upon solution bromide concentration is readily understood, since higher concentrations will accelerate the rate of reaction. This interpretation is similar to that of Rhodes and Buck (9) except for their report of a negative overshoot in the potential/time curves, which was explained as a collapsing diffusion potential. They assumed that bromide diffuses into the silver chloride crystal, resulting in concentration profiles of chloride and bromide within the crystal itself. These profiles would then generate a diffusion potential which would decay to zero within a few minutes. Batra and Slifkin (14) were cited for evidence of bromide diffusion into silver chloride. They report a diffusion coefficient of 1.28 X cmz/s at 304.8 “C. If their data are extrapolated to room temperature, a diffusion coefficient of cm2/s is predicted. A bromide ion could not possibly diffuse even 0.01 8,within a few minutes if the diffusion coefficient is that small. Such overshoots were observed in the present study in some cases with anodized and chlorochromate-converted wires but seldom with thin-film (chlorochromate-converted) electrodes. Furthermore, transients within the first minute after exposure
-
to a new solution composition can occur even in the absence of bromide. Concentration gradients in the depletion layer of the solution or the disrupted region of mixed-crystal formation (not the crystal itself) might conceivably produce a diffusion potential. It seems equally likely, however, that the potential overshoots are simply due to the rate of equilibration with the solution, coupled with electrode charging. If the composition of the bulk of the crystal must be brought to equilibrium with the solution, then theories such as Buck’s (1)will be of limited value in many cases. He assumed that the electrodes are at thermodynamic equilibrium when potentials are measured. Since equilibrium will hardly ever be achieved, especially for membrane electrodes, theories such as that of Hulanicki and Lewenstam (15)are more practical in these situations. They show that selectivity coefficients can be calculated from ratios of aqueous diffusion coefficients rather than solubility product constants and therefore recognize the dynamic nature of the response mechanism. Theirs is a “diffusion control” theory in which the response of a silver chloride based electrode to bromide depends upon the ability of the bromide, relative to chloride, to approach the surface of the crystal for subsequent reaction. The heterogeneous rate constants reported in Table I might indicate diffusion control At the smallest microscopic surface area considered (a sheet crystal), the rate of reaction is comparable to that of a porous surface (chlorochromate-converted sheet of silver) which should have a very much larger microscopic surface area. The rate of reaction at the surface may be so fast that the overall rate is controlled by diffusion, consistent with theory (15).However, Hulanicki and Lewenstam did not take crystal composition into account. Therefore, according to the results of the present study, their theory can be valid only until the crystal becomes enriched with bromide. For porous electrodes of the second kind, this enrichment can occur very quickly.
ACKNOWLEDGMENT The author gratefully acknowledges the contributions made by J. Gerard (neutron activation), R. Miller (radiotracer), L. Spaulding (X-ray), D. Black and R. Rice (SEM), and most especially V. Saunders, who supplied the sheet crystals. A special thanks also to L. Spaulding who single-handedly interpreted the X-ray data.
LITERATURE CITED Buck, R. P. Anal. Chem. 1966, 40, 1432. Koch, E.; Wagner, C. Phys. Chem. B 1937, 38, 295. Buck, R. P.; Shepard, V. R., Jr. Anal. Chem. 1974, 46, 2097. Bowers, R. C.; Hsu, L.; Goldman, J. A. Anal. Chem. 1961, 33, 190. Yutzy, H. C.; Kolthoff, I. M. J. Am. Chem. SOC. 1937, 59, 916. Koryta, J. ”Ion Selective Electrodes”, Cambrldge Monographs in Physical Chemistry, Cambrldge University Press: New York, 1975; Chapter 2. Kelly, T. M.; Mason, M. G. J. Appl. Phys. 1976, 4 7 , 4721. Klasens, H. A,; Goosen, J. Anal. Chlm. Acta 1977, 88, 41. Rhodes, R. K.; Buck, R. P. Anal. Chim. Acta 1960, 113, 55. Curme, H. 0. et al. Clln. Chem. (Winston-Salem, N.C.) 1979, 25, Abstract 262 1115. Res. Dlscl. 1979, 787, 626. Gerard, J. T.; Pietruszewski, J. L. Anal. Chem. 1978, 50, 900. “Handbook of Chernlstw and Phvslcs”. 48th ed.: The Chemical Rubber Co.: Cleveland, OH, 1967; p 6220. Batra, A. P.; Slifkin, L. J. Phys. Chem. Sollds 1969, 30, 1315. Hulanlckl, A.; Lewenstam, A. Talanta 1977, 24, 171.
RECEIVED for review June 16, 1980. Accepted October 24, 1980.
