Table I. Values of the Ionization Constant of Water at Several Temperatures Temperature, "C
-log K,
0 25 50 60 75 100
14.944 13.997 13.262 13.017 12.691 12.258
KJX
ioL5)
1.1376 10.069 54.70 96.16 203.5 552.5
ion. A relatively strong base reagent is needed, and it should be chosen so that the electrode will be insensitive to the cations it produces (6). The reaction of base with water produces hydroxyl ions, which operate through the K , equilibrium to suppress hydrogen ion activity: aH+ =
KW -
(1)
aOH-
When hydroxyl ion activity is made large in value, hydrogen ion activity, of course, becomes small. The effect of temperature was measured on a 0.02M solution of diisopropylamine, a preferred base reagent for sodium ion measurement. From 0 to 60 "C, the pH change with temperature is nearly linear. In going from 25 to 60 "C, pH decreases about one pH unit, which corresponds to a tenfold increase in hydrogen ion activity. In going from 25 to 0 "C, pH increases by almost 0.7 pH unit. If suppression of hydrogen ion activity is only marginally adequate a t 25 "C, a rise in temperature will upset the situation. Instead of following sodium ion, the electrode will respond to the increase in hydrogen ion activity and give an erroneous upscale indication. The hydrogen ion activity of almost any base solution is strongly temperature dependent, giving a sharp rise in hydrogen ion activity as temperature rises (8). Equation 1 shows that hydrogen ion activity depends on the values of both hydroxyl ion activity and K,. Although temperature usually has some effect on the value of the ionization constant of the base, the hydroxyl ion activity of many base so-
lutions does not change drastically with temperature. The main cause of pH change is the change in value of K,. Values of K , at various temperatures are listed in Table I (9, IO). About a ninefold increase in value of K , occurs in going from 0 to 25 "C, and another ninefold increase takes place from 25 to 60 "C. The large observed change in pH of the diisopropylamine solution is thus largely attributable to change in K , value over the temperature range. It will be advisable to make low level sodium ion measurements at low rather than at high temperature. One should avoid heating the sample solution. Although use has not been made of the principle, it would appear desirable to cool the sample solution to the vicinity of 0 "C if one is striving to make the lowest possible concentration measurement of sodium ion. This way of suppressing hydrogen ion activity is achieved without corresponding increase in base cation concentration, which is an advantageous objective in its own right. Conversely, to maintain constant hydrogen ion activity, lowering of temperature offers a way of conserving on the use of base reagent, since less base will be required at lower temperature to hold the same hydrogen ion activity as that needed a t higher temperature. Another possible advantage of operating at low rather than high temperature is the probable lesser interference at low temperature from alkali metal ion leaching from the electrode (7). LITERATURE CITED (1)W. B. Gurney, Nect. World, March 23,1964,p 125. (2)D. Hawthorn and N. J. Ray, Analyst(London),93, 158 (1968). (3)H. M. Webber and A. L. Wilson, Analyst (London), 94,209 (1969). (4)E. L. Eckfeldt, W. E. Proctor, Jr., W. D. Howie, and W. A. Lower, Proc. 29th Inter. Water Conf., Engineers Society of Western Pennsylvania, Pittsburgh, November 19-21,1968,p 109. (5) A . A. Diggens, K. Parker, and H. M. Webber, Analyst(London),97, 198 (1972). (6)E. L. Eckfeldt and W. E. Proctor, Jr., Anal. Cbem., 43, 332 (1971). (7)E. L. Eckfeldt and W. E. Proctor, Jr., Anal. Cbem., 47,2307 (1975). (8)E. L. Eckfeldt, /SA Trans., 9, 45 (1970). (9)H. S. Harned and R. A. Robinson, Trans. Faraday SOC.,36, 973 (1940). (IO)R. A. Robinson and R . H. Stokes, "Electrolytic Solutions", 2nd ed., Academic Press, New York, N.Y.. 1959,p 544.
RECEIVEDfor review May 30, 1975. Accepted August 5 , 1975.
Ion-Selective Electrode Determination of Complex Formation Constants in Sub-Micromolar Silver Nitrate Solution Arthur L. Cummings and Keith P. Anderson Department of Chemistry, Brigham Young University, Provo, Utah 84602
The Nernstian response of silver ion sensitive membrane or electrodes in solutions containing between 10-l and molar silver ion has been well established (1-5). Furthermore, the Nernstian electrode response has been shown to extend to levels of free silver ion below molar (2, 6 ) in solutions wherein most of the silver present is bound by strong complexing agents ("buffered" solutions). In unbuffered solutions, deviations from Nernstian response have or been reported when silver ion is less than molar (3, 5 ) . This paper reports the observation of deviations from Nernstian electrode response in solutions in which most of the silver is strongly complexed, but the total formal concentration of silver is less than molar. A method is presented by which a correction for the non2310
Nernstian response can be determined as a function of formal silver concentration. The method is applied to the potentiometric determination of stability constants of bromoargentate complexes. EXPERIMENTAL Reagent grade sodium bromide and silver nitrate were dried at 110 "C prior to the preparation of solutions. Doubly distilled or distilled-deionized water having a specific conductance of less than 1.5 X mho/cm a t 25 O C was used. Apparatus. Solutions were prepared and dispensed using a Mettler P1200 or a Mettler P160 top-loading, constant-load balance. Polyethylene gravimetric burets (7) were used to dispense the solutions. Potential differences between an Orion Sulfide Ion Activity Electrode, Model 94-16A, and an Orion Double-Junction
ANALYTICAL CHEMISTRY, VOL. 47, NO. 13, NOVEMBER 1975
Reference Electrode, Model 92-02-00, were measured with an Orion “Ionalyzer”, Model 801, digital voltmeter. A 10% KN03 solution was used in the outer chamber of the reference electrode. The temperature of the reaction solution was maintained at 25.00 f 0.01 “ C by immersion of the reaction vessel in a circulating water bath. The contents of the reaction vessel were stirred at a constant rate using a magnetic stirrer and Teflon-coated stirring bar. Procedure. Electrode calibration data and complex formation data were obtained by similar titration procedures. The advantages of calibration of the electrode by “titration” are enumerated by Mueller, West, and Mueller (2). Starting with approximately 130 grams of water in the reaction vessel, increments of silver nitrate or sodium bromide solutions were added. Following each addition of titrant, potential measurements were taken only after the potential had remained the same (fO.l mV) for at least one minute. The formal concentration of silver nitrate ranged from loe4 to lo-’ molal in the electrode calibration experiments, and from in the complex formation experiments. Values of the therto modynamic activities of the ionic species were calculated from molalities using the extended Debye-Hueckel equation to calculate values of the activity coefficients.
RESULTS AND DISCUSSION The electrode calibration data were fit to the equation
E = E’
Table I. Stability Constants Complexes
of Silver Bromide
A . Uncorrected Data
Log
Expt.
I I1 I11 IV V VI
C
A
-6.78 -6.20 -6.81 -6.22 -6.78 -7.61
~ Log, 8 1 ~
5.43 5.41 5.39 4.57
LO9 ~ 8 2~
6.55 7.37 6.88 7.49 6.89 5.99
LO3 ~ 83~
7.79 7.98 7.97 7.12
~cNaBr1 0 3 b
0.59-43.9 42 3-116.7 0.55-42.7 42.7-1 39.6 0.48-79.4 0 -93-77.3
B . Corrected Data Rel. std devc
I I1 I11 IV V VI
Av .
5.83 5.82 5.79 5.75 5.80
7.06 7.44 7.41 7.56 7.38 7.40 7.38
7.93 8.13 8.45 8.40 8.23
0.10 0.003 0.12 0.01 0.09 0.09
C , Literature Values
+ S log a A g +
by the method of least squares to obtain the electrode slope, S, and the intercept, E’. In this equation E represents the measured potential and a A g + represents the thermodynamic activity of silver ion. The electrode was calibrated over the above noted range of silver ion concentrations before and/or after each of the complexation titrations reported here. In each case, the plot of potential against log a A g + was linear over the entire range and had a slope of 58.3 f 0.1 mV/log a A g + unit. The theoretical Nerstian value of the slope a t 25 O C is 59.16 mV. The lack of agreement between the theoretical and measured slopes could be due to a nonideality in the electrode system or a functional dependence of the intercept E’ on the silver ion activity. The intercept includes the liquid junction potential which is expected t o be a function of solution ionic strength (8). No inert electrolyte was added to any of the solutions: the ionic strength varied with titrant concentration. Calculation of the intercept, E’, by Equation 1 for all calibration data showed that when a value of 59.16 mV was used for S, E’ decreased about 0.8 mV per decade increase in ionic strength. When 58.3 mV was used for the value of S , E‘ was constant within f 0 . 5 mV over a three-decade change in ionic strength. Because slopes of approximately 58 mV have been determined experimentally in this laboratory for other ion-selective electrodes in constant ionic strength media, it was concluded that the experimentally determined value of S was the correct value rather than the theoretical value. Implicit in this conclusion is the assumption that the liquid junction potential a t the reference electrode varied insignificantly over the two- to three-decade range of ionic strengths realized in this study. I t is notable that in Experiment VI1 where variance in E’ was most apparent, the ionic strength was virtually constant. Values of the overall formation constants for the formation of aqueous silver bromide, dibromoargentate anion, and tribromoargentate anion were calculated by Equation 2, using a relative deviation least squares curve-fitting procedure described by Anderson and Snow (9) and modified according to Kohman’s suggestion (10).In Equation 2, is the activity coefficient of the subscript species, and a denotes the thermodynamic activity of the subscript species.
8.72 Ref ( 17) 4.38 7.34 8.00 Ref (11) 8.53 Ref ( 1 6 ) 6.09 6.54 8.64 Ref (15) “Logarithm of silver formality at the beginning of the experiment. * Range of bromide ion activities. Relative standard deviation of the data.
Equation 2 is valid if no species are formed which contain more than one silver ion (11,12). (3)
(4) Equation 3 can be used to calculate the value of F, from electrode measurements if the electrode response consistently obeys Equation 1. If either of these conditions is violated, the apparent values of the stability constants will show a dependence on the formal concentration of silver. Table IA shows the results of six experiments in which the formal concentration of silver was unchanged (except slightly by dilution) and sodium bromide solution was added incrementally to produce the concentration range indicated. A correspondence between the values of the constants obtained and the formal concentration of silver is apparent. I t is highly unlikely that polynuclear species are formed under the conditions of these experiments (11, 13, 1 4 ) ; thus the electrode response must have deviated from the behavior predicted by Equation 1 to varying degrees in each experiment. The results of an experiment (Experiment VII) in which silver nitrate solution was incrementally added to a solution containing sodium bromide are graphically represented in Figure 1. The lower curve is the result of processing the data in the same way (Le., using Equations 1 and 3) as were the data of Experiments I-VI (Table IA). The downward concavity of the lower curve is indicative of departure from Nernstian electrode response ( 1 1 ) . The data of experiments I-VI concordently showed that the value of Fo varied as the square of the bromide ion activity over the small range of bromide ion activities present in Experiment VII. This fact enabled the calculation of “correct” F , values for each of the data points, assuming one of the data points to be correct, or in other words, assuming that in the region of that data point the electrode was responding in the Nern-
ANALYTICAL CHEMISTRY, VOL. 47, NO. 13, NOVEMBER 1975
2311
I
3
/-
uA
$1
x
c"
Figure 1. Fo vs AAg+: (0) from uncorrected data; (0)from corrected data. Silver nitrate formalities ranged from 4 X lo-' to 2 X to 6.5 X molal and aBr-decreased from 7.7 X stian manner. The upper curve in Figure 1 resulted. The coincidence of the two curves over a short range (rather than a t only one point) supports the validity of the treatment. It is apparent from comparison of the two curves that the magnitude of the departure of the electrode response from that predicted by Equation 1 decreases with increasing concentration of silver nitrate until it becomes zero. The magnitude D of the electrode error was found to be described by the empirical relationship
D
= 578 + 204 (log CAg(tota1))
+ 18.0 (log CAg(total))*
(5)
for values of log CAg(tota1) more negative than -5.9. The results of a recalculation of the data of Experiments I-VI are shown in Table IB. This table also includes literature values for comparison. The correction D was calculated by Equation 5; Fo was calculated by Equation 6.
Fo =
YA
+CA (total) D !. E ' ) / S
Table IB shows that the corrected results of Experiments I-VI are in considerably better agreement than are the uncorrected results (Table IA). They also compare favorably with values reported in the literature. The uncertainty in the correction is ,estimated to be less than 2 mV, which would propagate a relative uncertainty of 0.08 in Fo. The relative standard deviation in Fo calculated from the scatter of the data in Experiment I-VI is 0.12 or less in each case. The failure of the ion-selective electrode measurements to follow Equation 1 at low total silver concentrations might be attributed to any one or a combination of three causes: 1) Electrode disfunction, or failure to respond to changes in silver ion activity in any reproducible manner. 2) Variation of S (slope) with total silver concentration. 3) Variation in E' (intercept) with total silver concentration. Several experimental runs indicated that electrode response, though non-Nernstian, was indeed reproducible. In the absence of polynuclear complexes the ratio of bound ligand to total silver, R, is a function only of bromide ion concentration. Equation 7 , which is similar to the Bodlaender equation (11, 12, 18, 19), defines fi mathematically.
A ( E / S - log Y f C A g ( t o t a 1 ) ) = (7) A log C B ~ The symbol A signifies a small change. The log Y*CAg(total) 2312
term corrects for small (in most cases negligible) differences in silver formality between data points. Had the value of S varied with silver formality (and thus varied to an unknown degree from the value used in the calculations), the value of fi evaluated at any given bromide ion concentration would have varied depending on the silver formality. Although the silver formalities of Experiments I-VI ranged from to molal, no such variation in R was observed. The non-Nernstian electrode behavior is therefore due only to changes in E' with total silver formality. This was the assumption made in this study. This method of data treatment makes it possible to use electrode data obtained in an otherwise excluded concentration range. It has been shown to apply very well to a specific system. The method as presented is, however, entirely empirical. A theoretical treatment of the response of silver compound membrane electrodes by Morf, Kahr, and Simon (20) has been published recently. I t is informative to review the results of this research in the terminology of Morf et al. as an illustration of the response of a silver sulfide electrode to a silver-complexing ligand. Equations 8 and 9 describe the response when dibromoargentate anion is the predominant complex according to Morf treatment (see Equation 35 in Ref. 20).
E = Exo 4-
s log a - 2s log (a a ~
Since K = ~ z ( L A ~ , sand ) ~ /E,~' = E'
~ - )
(8)
+ ?&log L A g z s
E = E' 4- s log a - s log 0 2 - 2s log a ~ ~ -(9) L denotes the thermodynamic solubility product and a is the defect activity, which is used to describe the deviations in activities between the membrane-solution boundary and the bulk sample solution. Equations 8 and 9 were derived assuming the absence of silver ion and silver complexes in the bulk sample solution and do not apply directly to the results of our research. A similar equation can be derived using the Morf, Kahr, and Simon approach but including other species present. Equation 10 describes the cell potential in a solution containing both silver(1) and bromide ions and in which the predominant silver-containing species is dibromoargentate anion. The occurrence of the silver bromide solubility equilibrium at the electrode surface is also assumed.
E = E'
- S lOg/32 - 2s 1ogaBr- + s log ( P l L A g B r + aAg(tota1))
(10)
The data of Experiment VI1 were used to confirm the applicability of Equation 10. Values for 01 were obtained by iteration. The iteration quickly converged to give log /31 = 5.65 or log 02 = 7.81 in reasonable agreement with the values listed in Tables IB and IC. If one initiates the iteration procedure using estimated values of @1 and @2 as 1 X lo5 and 5 X lo4,the same final values are calculated. The average of the several reported values (11, 15, 19, 21-27) for the thermodynamic solubility product, 10-12.28, was used in these calculations. The data of Experiments I-VI, where R = 2 (Equation 7 ) also fit Equation 10. When iz = 1, one must use Equation 11?
E = E'
- s log 6 1 - s log
s 1% ( @ l L A g B r + aAg(tota1))
(11)
The semiempirical Equation 10 can readily be applied to systems involving ligands other than the bromide ion. I t gives a direct relationship between total silver concentration (activity) and observed cell potential providing a means for the direct determination of low concentrations of
ANALYTICAL CHEMISTRY, VOL. 47, NO. 13, NOVEMBER 1975
silver, and there is no necessity for an externally stated limiting minimum total silver concentration.
LITERATURE CITED (1) T. M. Hseu and G. A. Rechnitz, Anal. Chem., 40, 1054 (1966). (2) D. C. Muelier, P. W. West, and R. H. Mueller, Anal. Chem., 41, 2038 (1969). (3) R. A. Durst, Ed., "Ion Selective Electrodes", Net. Bur. Stand. (U.S.), Spec. Pub/. 314, Washington, D.C., 1969, pp 402-3. (4) J. Ruzicka and C. G. Lamm, Anal. Chim. Acta, 54, 1 (1972). (5)P. L. Bailey and E. Pungor, Anal. Chim. Acta, 64, 423 (1973). (6) J. W. Ross, Jr., in Ref. 3, p 77. (7) E. A. Butler and E. H. Swift, J. Chem. Educ., 49, 425 (1972). (8) A. K. Covington in Ref. 3, pp 127-36. (9) K. P. Anderson and R. L. Snow, J. Chem. €doc., 44, 756 (1967). (10) T. P. Kohman, J. Chem. Educ., 47, 657 (1970). (11) E. Berne and I. Leden, Z. Naturforsch. Ea, 719 (1953). (12) L. Johansson, Coord. Chem. Rev., 3, 293 (1968). (13) K. H. Lieser, Z. Anorg. A/@. Chem., 292, 97 (1957).
(14) V. B. Vouk, J. Kratohvil, and B. Tezak, Arkiv. Kemi, 25, 219 (1953). (15) K. P. Anderson, E. A. Butler, and E. M. Wooliey, J. Phys. Chem., 77, 2564 (1973). (16) K. S.Lyalikov and V. N. Piskunova, Zh. Flz. Khim., 28, 127, 595 (1954). (17) H. Chateau and J. Pouradler, Science lnd. Phot., 23, 225 (1952). (16) G. Bodlaender, "Festschrift fuer R. Dedeklnd", Braunschweig, 1901. (19) G. Bodlaender and R. Fittig, 2.Pbys. Chem., 39, 597 (1902). (20) W. E. Morf, G. Kahr, and W. Simon, Anal. Chem., 46, 1538 (1974). (21) P. S.Smith and E. M. Wooliey, private communication. (22) J. A. Gledhiii and G. M. Malan, Trans. Faraday SOC., 50, 126 (1954); ibid., 49, 166 (1953). (23) A. L. Cummlngs, Dissertatlon, Brigham Young University, Provo, Utah, 1974. (24) B. B. Owen and S.R. Brinkley, Jr., J. Am. Chem. Soc., 60, 2233 (1938). (25) K. Hass and K. Jeliinek, Z.fhys. Chem., A, 162, 153 (1933). (26) A. E. Hill, J. Am. Chem. SOC.,39, 66 (1908). (27) L. G. Sillen, "Soiublllties of Silver Halogenides", Report July 1953 to the
Analytical section, I.U.P.A.C.
RECEIVEDfor review December 2, 1974. Accepted August 8,1975.
Alternating Current Polarographic Evidence for the Reversible Reduction of Trivalent Gallium from Acidified 1.O-Molar Sodium Thiocyanate at 60 OC Edward D. Moorhead and Gustaf A. Forsberg Department of Chemical Engineering, University of Kentucky, Lexington, Ky. 40506
Clinical research ( 1 - 5 ) has established that neoplastic sarcomas and certain categories of carcinoma (lung, breast, colon, etc.) (6) exhibit a pronounced tendency to sequester serum gallium citrate and other gallium salts. The metal's therapeutic effectiveness in regressing or arresting malignant growth-either as absorbed nonradiogallium ( 6 ) or as (principally) the 67 isotope used for in situ radiotherapy (2)-has prompted exploration of new benchtop analytical procedures ( 7 ) for the measurement of trace Ga which might speed up tissue assay efforts and aid in the eventual identification of the responsible biochemical mechanism. Were it not for the classically severe kinetic complications which are associated with the aqueous gallium electrode reaction (GER) (8-12), the electroanalysis of Ga(II1) a t trace and ultratrace concentration levels could be readily accomplished using a variety of acidified supporting electrolyte media. As described (10-14) in several earlier studies, the chemical composition of the electrolyte can play a catalytic role in moderating the actual charge transfer rate. For example, it has been found (IO) that a kinetically fast (Le., Nernstian) gallium electrode process is attainable a t the dropping mercury electrode (DME) if the supporting electrolyte is adjusted to satisfy two criteria simultaneously: 1) the presence of an inert salt at a very high ionic strength ( J ) ;and 2) the incorporation of >0.1 M SCN(12) or NB- ( 1 3 ) (halides are also marginally effective a t extremely high J values of 1 1 3 M ( I d ) ] .A supporting electrolyte comprised of acidified NaSCN/G.OM NaC104 was successfully employed in three recent investigations in which trace levels of gallium, including gallium in ashed tissue, were measured by ac phase-selective anodic stripping (PSAS) procedures (15-177, and Demerie et al. employed essentially the same media as the basis for their pulse polarographic analysis of gallium in samples of gallium arsenide semiconductors (18). However, binary electrolytes of the above types-which to our knowledge are the only ones known so far to produce room temperature
GER reversibility-can pose a variety of practical analytical difficulties ( 1 9 ) , due to the densely concentrated salts required, problems that could be substantially alleviated by discovery of milder electrolyte conditions. We wish to report in this note evidence that the degree of kinetic reversibility of the gallium electrode process exhibits a pronounced reciprocal dependence on ionic strength and temperature. Results obtained from single sweep alternating current phase-selective polarograms (PSP) show that a simple 30-OC increment in reaction temperature removes the historical necessity for densely concentrated inert salts and enables one to obtain a Nernstian voltammetric current readout from acidified NaSCN alone a t the 1.0-molar level (J = l),and an analytically useful peak in 0.1M NaSCN.
EXPERIMENTAL Apparatus and Reagents. The apparatus and reagents used to obtain the phase-selective polarographic results reported here have recently been described in detail elsewhere (16) and will not be reiterated. The mercury capillary electrode used was supplied by Princeton Applied Research. The capillary was driven by a Princeton Applied Research Model 174A drop knocker which was adjusted for a 2.0-sec drop time. Reaction temperatures between 20 and 70 O C were obtained using a Forma-Temp Model 2095 thermostated water bath which supplied a glass-jacketed Metrohm EA-876-20 electrolysis cell. Supply and return lines to the cell jacket were enclosed in foam insulation to lessen heat loss, but the .cell structure itself was not SO protected. Nonetheless, cell temperature was controllable to f l . O "C at 70 "C. Elevated solution temperatures combined with argon deaeration of the cell resulted in some evaporative loss of the test solution over prolonged periods of time, and therefore it is recommended that repeated runs on the same solution under such conditions should probably be avoided.
RESULTS AND DISCUSSION The rather extreme electrolyte concentrations required to effect reversible pseudohalide catalyzed voltammetric behavior present a t least two obstacles that are significant
ANALYTICAL CHEMISTRY, VOL. 47, NO. 13, NOVEMBER 1975
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