Chronopotentiometric and Electrode Potential Investigations in Molten Equimolar Sodium and Potassium Metaphosphates Clinton R. Wolfel and Roy D. Caton, Jr. Department of’Chemistry, The University of New Mexico, Albuquerque, N . M . 87106
Electrode potential investigations of V(V)/V(lV), U(VI)/ U(IV) and Cu(ll)/Cu(l) were conducted in equimolar NaP03-KP03at 700 OC and the values of the formal electrode potentials vs. the one molal AgP03 reference electrode were determined to be 0.394, 0.0976, and -0.121 volts, respectively. The number of electrons involved in the potential-determining electrochemical reactions were calculated from the Nernst slopes to be 1, 2, and 1 for V(V)/V(lV), U(VI)/U(IV), and Cu(ll)/Cu(l), respectively. Chronopotentiometric measurements in the same solutions that were used in the electrode potential studies indicated that the method can be used for analysis with a precision of better than 3%. The diffusion coefficients of V(V), U(VI), U(IV), Cu(ll), Cu(l), and Ag(l) were determined to be 1.69 x 1.26 x lo+, 0.318 x 0.460 x 7.00 x 10-6, and 1.09 x lo5 cm2sec-I, respectively. THEINCREASED INTEREST in the role of fused salts in modern technology has created a need for analytical procedures capable of direct application to the melts at high temperature. In many instances the analyses for the total concentrations of the species of interest will suffice; however, many times it is important to know the ratio of the oxidation states of the metal ion in the solution at high temperature. In order to obtain these values, it is necessary that one be able to perform in situ analyses for the various metal ions. An analysis of this type requires a knowledge of chemical reactions in the solvent of interest. In order to obtain information concerning chemical reactions in a solvent, it is necessary to establish in some form an electrochemical series. As in the case of the electrochemical series in water, one must select some reference point in order to compare the potentials of various redox couples. As a prerequisite then to the study of electrochemical reactions in the metaphosphate solvent, it was necessary to construct a stable and reproducible reference electrode. The AgPOa electrode used in this study is described in detail elsewhere ( I ) . The practical considerations concerning the fabrication of reference electrodes and their theoretical significance is discussed in a monograph by R.W. Laity (2). Potentiometric and chronopotentiometric measurements have been reviewed elsewhere (3). Diagnostic criteria for chronopotentiometry have been compiled by Reinmuth (4). EXPERIMENTAL
The Chronopotentiometric Circuit. The chronopotentiometric circuit used in this investigation is similar to those Present address, Research and Development Center, Westinghouse Electric Corporation,Pittsburgh, Pa. 15235. (1) R. D. Caton and C. R. Wolfe, ANAL.CHEM., 43,660 (1971). (2) R. W. Laity, “Electrodes in Fused Salt Systems,” Reference Electrodes, D. J. G. Ives, and G. J. Jam, Ed., Academic Press, New York, N. Y., 1961, pp 524-606. (3) C. H. Liu, K. E. Johnson, and H. A. Laitinen, “Electroanalytical Chemistry of Molten Salts,” Molten Salt Chemistry, M. Blander, Ed., Interscience, New York, N. Y., 1964, p 681. (4) W. H. Reinmuth, ANAL.CHEM., 32, 1514 (1960).
used by other workers (5, 6). A Heath Model IP-32 400 VDC power supply was used in conjunction with load resistors to form the constant current source. Potentials were monitored with a Leeds & Northrup Model 7401 pH Meter. The output of the pH meter was displayed on a Sargent Model SR recorder with a chart speed of 30 in. per minute. The output resistance was an L & N decade resistance box set at a value that would allow the full voltage range of the pH meter to be displayed at full scale on the recorder. This arrangement gave a good approximation to the desired voltage range, but fine adjustments had to be made using a trimming resistor on a specially constructed range plug on the recorder. The range of load resistors used in this work was capable of providing currents from the microampere range up to 0.4 A; however, in this investigation it was necessary to employ only the 1 megohm, 0.1 megohm, and 10K resistors. The actual values of the currents were measured using a Rubicon Model 2745 potentiometer placed across a Cole Instrument precision resistor having a value of 100 ohms i 0.05%. A DPDT switch was used to select the proper polarity for the working electrode and was also used to reverse that polarity during the course of electrolysis in some specific experiments. A 3P3T switch provided a convenient switching arrangement. In the “operate” position, the output of the constant current source was applied to the working electrodes of the electrolysis cell. The onset of electrolysis was indicated on the recorder by a rapid change in potential. When the switch was in the “off” position, the circuit was open; in the “dummy cell” position, the output of the constant current source was applied across a 10-ohm resistor and the electrodes were shorted. In nearly all systems studied here, the potential of the working electrode returned to its original equilibrium potential almost instantaneously after shorting the electrodes. Since there was no easy method to stir the solutions between runs, this shorting of the electrodes provided a convenient means of reproducing diffusion conditions. The dummy cell resistor allowed the current to flow through the system at all times, thus keeping the resistors warm and eliminating significant changes in the current upon initiation of electrolysis. The value of the resistance for the dummy cell was chosen on the basis of conductance measurements made with an ac conductance bridge which showed the resistance of the melt to be approximately 10 ohms per cm as measured between two platinum wires. The fact that the electrolysis current was almost always slightly less than the dummy cell current, indicates that the effective dc resistance of the melt under conditions of electrolysis is greater than the resistance measured by ac conductance methods. A three-electrode system was always employed in these studies and the potential of the working electrode was monitored us. a reference which was not an integral part of the electrolysis circuit. The Solvent. The solvent system used in this study was an equimolar mixture of sodium and potassium metaphosphates. It was prepared by melting the appropriate amounts of reagent grade alkali dihydrogen phosphates in platinum (5) P. Delahay and C. C. Mattax, J. Amer. Chem. SOC.,76, 874
(1954).
(6) C. N. Reilley, G. W. Everett, and R. H. Johns, ANAL.CHEM., 27,483 (1955). ANALYTICAL CHEMISTRY, VOL. 43, NO. 6, MAY 1971
663
dishes and heating at 850 "C for at least three hours. No purification precautions were taken. Reference Electrode. Caton and Freund (7) first suggested that a silver metaphosphate reference electrode might be useful in the molten alkali metaphosphate solvents. This conclusion was based on the fact that of all the metal ions that they studied, silver was the only one that could be plated out of solution in the concentration ranges employed. The Ag/AgP03 reference electrode employed in this work has been characterized in detail elsewhere ( I ) . A 0.4m solution of AgP03was used in the reference electrodes employed in this work and all formal potentials were then corrected to the 1.Om reference. Working Electrodes. In the experimental arrangement used in this study, it was necessary that the indicating electrode for the emf studies also serve as a working electrode for the chronopotentiometric work. In the case of the electrode potential measurements, the geometry of the electrode is not critical so long as a relatively large area is exposed to the melt; however, in the case of the working electrode for chronopotentiometry, the physical shape of the electrode is important. Laitinen and Osteryoung (8) have compiled a table comparing the effects of electrode geometry on the product i%l'Z for various electrode geometries. These authors suggest the use of a vertical platinum plate approximately 0.5 cm X 0.5 cm welded to a platinum wire which should be sealed into glass of appropriate composition. The working electrode used in this study consisted of a platinum plate 0.008 in. thick and approximately 0.6 cm X 0.6 cm. The area of the electrode was measured directly with a micrometer and also by calibration using 0.025M thallous ion in one molar potassium nitrate. Thalmayer, Bruckenstein, and Gruen (9) used this method for calibrating their electrodes and found agreement to within 1 % of the directly measured value. Rouse (IO) has determined the diffusion coefficient of thallous ion in 1M K N 0 3 at 25 "C cmz sec-I. Comparisons of the measured to be 2.06 X values with the values determined by standardization with thallous ion for the working electrodes used in this study showed agreement to within 1%. The areas of all electrodes employed in this study were nominally 0.7 cm2. Counter Electrodes. Since all measurements in the emf studies and in the chronopotentiometric studies were made us. a Ag/AgP03 reference electrode, the nature of the counter electrode was relatively unimportant. In the vanadium and uranium systems, the counter electrode was the platinum crucible which was used to contain the melt. In the chronopotentiometric study of the silver system, the melt was contained in a quartz crucible and the counter electrode was a silver electrode identical to the one contained in the glass compartment of the reference. A platinum spiral was used as a counter electrode in the copper studies in which the melts were contained in a quartz crucible. Apparatus. The cell, furnace, and temperature control employed in this work are described elsewhere in this journal
(4.
Reagents. AgP03 was prepared according to the procedure described elsewhere in this journal ( I ) . Cuprous oxide was prepared by precipitation from basic solution. Cuprous chloride (95 purity) was dissolved in HC1 under COz and a few strips of copper metal were added. This solution was boiled for about 45 minutes before adding sodium hydroxide. The precipitate was filtered and washed
(7) R. D. Caton and H. Freund, Anal. Chem., 35,2103-07 (1963). (8) H. A. Laitinen and R. A. Osteryoung, "Electrochemistry in Molten Salts," Fused Salts, B. R. Sundheim, Ed., McGraw-Hill, New York, N. Y ., 1964,p 255. (9) C. E. Thalmayer, S. Bruckenstein, and D. M. Gruen, J. Inorg. Nucl. Chem., 26, 347 (1964). (10) T. 0. Rouse, Ph.D. Thesis, University of Minnesota, Minneapolis, Minn., 1960. 664
ANALYTICAL CHEMISTRY, VOL. 43, NO. 6, MAY 1971
with water and acetone and placed in a vacuum desiccator for several hours at 30 "C. All other chemicals used in this work were of reagent grade quality. Transition Time Measurement. Several methods for the determination of transition times have been reported in the literature (5, 9). The transition times reported in this work have been measured in the following manner: (a) time zero has been taken as the point at which the trace on the recorder left the rest potential, and (b) the end of the transition time was taken as the point at which a line drawn tangent to the steeply rising portion of the potential-time curve left the wave. In all of the experiments, a visible change in potential occurred at the onset of electrolysis. In general, current densities were varied to yield transition times between five and ten seconds. Density Measurements. An Archimedian method for measuring density using two gold bobs was employed in this investigation. This method and various other methods of density measurements in fused salts and the inherent problems involved have been discussed in a monograph by J. L. White (11). The densities of all the solutions used in this study were measured but even the most concentrated solutions differed from the solvent by less than 1 %. The density of the 1:1 solvent at 700 "C was determined to be 2.231 g/ml. Preparation of Test Solutions. Solutions of V(V) were prepared by dissolving NH4V03in the equimolar NaP03K P 0 3 in a muffle furnace at 850 "C. Equilibrium compositions in air contained appreciable amounts of V(1V). The solutions were enriched in V(IV), when necessary, by bubbling SO2 through the melt. After a minimum of three hours heating at 850 "C, the melts were poured onto a stainless steel slab contained in a lucite box which was lined with dry ice. The resulting glasses were crushed and ground to a powder in an agate mortar. These solutions were then stored in glass stoppered bottles until needed. Stock solutions of U(V1) were prepared by dissolving uranyl nitrate in the equimolar solvent at 850 "C in air. The dissolution of the compound in the melt was accompanied by the evolution of dense brown fumes indicating the immediate decomposition of the nitrate. Stock solutions of U(1V) were prepared by dissolving UOz in the melt under an argon atmosphere. These glasses were then used to prepare solutions of varying composition which were poured, ground, and stored as described above. Stock solutions of Cu(I1) in equimolar solvent were prepared by adding CuO to the appropriate amounts of alkali dihydrogen phosphates and fusing in air at 850 "C for a minimum of three hours. Stock solutions of Cu(1) were prepared by dissolving CUZOin the equimolar solvent at 850 "C in an argon atmosphere. These solutions were then used to prepare test melts of varying composition which were poured, ground, and stored as described above. Analyses of the Glasses. All of the metals employed in these investigations, with the exception of silver, were present in mixed oxidation states. This necessitated the analysis for each of the oxidation states in a given melt. At the conclusion of each experiment, the top of the furnace was dismantled and the melt removed from the furnace and poured on a stainless steel slab contained in a lucite box which was lined with dry ice. It was unavoidable however, that the melt be exposed to the air during the period when the crucible was being transferred from the furnace to the box. It was hoped that by employing this manner of solidifying the sample, there would be a minimum amount of exposure (1 1) J. L. White, "Liquid Densitometry," Physicochemical Measurements at High Temperatures, J. O'M. Bockris, J. L. White, and J. D. Mackenzie, Ed., Academic Press, New York, N. Y.,
1959,pp 193-207.
Table I. Results of Electrode Potential Studies Nernst Equation at 800 "C
System Theoretical ( n
a
=
1)
E = E"'
E"' in Va
+ 0.193 log ox Red ox
Theoretical (n = 2)
E = E"' +0.096610g Red
V(V)/V(W
E
=
U(VI)/U(IV)
E
=
CU(II)jCU(I)
E
=
...
0.489(&0.006)+0.197(~0.010)10g-V(V)
+o .394
VW)
+
0.192(j=0.002) 0.0962(+0.0050) log U(VU UUV) -0.0259(&0.0011) +0.194(=kO.O03)10g-Cu(1I)
+0.0976
~
-0.121
cm
These values are corrected to the one molal AgPO8 reference electrode.
to the air, and therefore freeze the oxidation states which were present at 700 "C in the glass. Vanadium glasses containing both the +4 and $5 oxidation states were dissolved in oxygen-free water under an atmosphere of COn and titrated potentiometrically with standard Fe(I1) to obtain the V(V) and then with standard KMn04 to obtain the sum of V(V) and V(IV), the V(1V) being obtained by difference. The analysis for total vanadium in the glasses was accurate to within 2 %. The uranium melts were analyzed for the +6 and +4 oxidation states by dissolving the sample in 0.5M H2S04 under a C 0 2 atmosphere and titrating potentiometrically first with 0.1N Ti(1II) solution to obtain U(V1) and then with KMnO4 to obtain total uranium as U(IV). The U(IV) present in the initial sample was then obtained by difference. These analyses are estimated to be accurate to within 2 % for total uranium. Melts containing Cu(I1) and Cu(1) were analyzed by titrating the Cu(1) with standard Ce(IV) in a solution 0.50M in H2S04and 0.50M in HC1. Total copper was determined by electrodeposition, Cu(I1) being obtained by difference. ELECTRODE POTENTIAL STUDIES
The potential span between the limiting electrode reactions of the equimolar NaP03-KP03 solvent was determined to be 0.95 V. The 0.4m A g W 3 reference electrode had a potential which was 0.369 V from the cathodic limiting process for the melt and 0.582 V from the anodic limiting process. These data were obtained by controlled potential voltammetry at a stationary platinum electrode using the 0.4m AgP03 electrode as the reference. After correction for the "asymmetry potential," the potential for the one molal reference electrode was determined to be 0.095 V us. the glass enclosed 0.4 molal electrode. Thus, the position of the one molal reference electrode, which was arbitrarily assigned the value of zero volts at 700 "C, was located 0.464 V from the cathodic limiting process. The values of potentials presented in the tables and figures that follow will be the actual measured values, i.e., cs. the 0.4 molal reference, unless stated otherwise. A plot was made of potential US. the log of the ratio of molalities for every system that was studied. The least squares equations of the lines and the corrected formal potentials are given in Table I. The theoretical Nernst slope at 700 "C for a one-electron reaction is 0.193 and 0.0966 for a two-electron reaction. Vanadium. The voltammetric studies conducted by Caton and Freund (7) in solutions of V20, in LiP03-KP03 eutectic at 730 "C indicated that there were three oxidation states of vanadium which were stable in this melt, namely V(III), V(IV), and VW). Since V203 is only sparingly soluble in equimolar NaP03-KP03, only the V(V)jV(W) couple was studied in this investigation. The determination of the proper
ratio of the oxidation states present in the melt was complicated by the tendency of the ratios of the oxidation states to change during the course of an experiment. This was evident from the fact that analyses performed on the glasses before and after an experiment differed and because the potential of the indicator electrode gradually changed during the course of the experiment. The proper value of the ratio was estimated using either the initial or the final analyses depending upon whether stable potential readings were obtained near the beginning or the end of an experiment. The large standard deviations in the least squares line in Table I are undoubtedly due to difficulty in determining the proper oxidation state ratio. Copper. The observed potentials of these solutions did not appear to change significantly during the course of an experiment, but the melts seemed particularly susceptible to air oxidation during the brief period of exposure to the atmosphere. This is not surprising in view of the formal electrode potential for this couple which is given in Table I. Uranium. Like the vanadium solutions, the ratio of U(V1) of U(IV) would often change during the course of an experiment. In this case, however, the proper ratio was not estimated from the analyses of the glasses obtained upon cooling to room temperature. Instead, calibration curves were constructed for both the U(IV) and U(V1) species using chronopotentiometric methods. By preparing several solutions which contained only U(IV), a calibration curve was established and used to analyze for U(IV) in the solutions containing both oxidation states. A similar curve was constructed for U(VI), and thus the ratio of the oxidation states was obtained by means of an in situ analysis. The rather large standard deviation of the Nernst slope in Table I is not surprising in view of the fact that the experimental errors from two prior analyses are inherent in the selection of the ratio of the oxidation states present, Le., the analyses of the stock U(V1) and U(IV) solutions by volumetric methods and the determination of the appropriate ratios by chronopotentiometric methods. CHRONOPOTENTIOMETRY
The basic equation for chronopotentiometry is ~Fp112D1/2C0 T112
=
(1)
2i"
where 7 is the transition time, n is the number of electrons involved in the electrochemical reaction, F is the Faraday constant, a is 3.1416, D is the diffusion coefficient of the reacting substance, Co is the concentration of the reacting substance, ANALYTICAL CHEMISTRY, VOL. 43, NO. 6, MAY 1971
0
665
This is a completely general expression for a reversible, diffusion controlled process. When the initial concentration of R = 0, the left-hand term of the denominator vanishes and the ratio of the square roots of the diffusion coefficients can be factored out, thus giving
Table 11. ChronopotentiometricData C in ior1/2 f in mA Metal ion moles/cc x lo* sec 112/cm2 Cu(I1) 1.01 5.32 i 0.03 1.97 11.1 i 0.1 3.32 18.7 i 0 . 2 CU(1) 0.822 21.9 =t0 . 1 33.8 f 0 . 1 1.37 1.63 40.4 f 0 . 1 1.79 43.5 i 0.3 1.94 47.0 f 0 . 2 &(I) 1.46 39.3 i 0.2 1.86 50.5 f 0 . 5 2.14 58.5 f 0 . 1 V(V) 0.677 8.48 f 0.15 1.31 15.9 i 0 . 1 1.37 15.9 f 0 . 1 2.45 28.2 i 0.2 U(VI) 0.432 1.79 i 0.02 0.830 4.37 f 0.02 1.90 11.0 f 0 . 1 2.12 12.1 f 0 . 1 2.19 12.5 + 0 . 1 UW) 0.325 1.24 i 0.01 0.376 1.40 f 0.01 0.403 1.48 f 0.01 0.466 1.68 f 0.03 0.568 1.98 f 0.03
(5)
This equation is well known and has been developed by other authors (13, 14); however, Equation 4 is of particular interest in this study since both oxidation states may be present in appreciable amounts in the original solution. When t = 0.257 the loe term of Eauation 5 vanishes and RT' & RT DE1/2 the potential is equal to E' - In - Inn F f~ n F D o l i z or Eliras the expression is commonly known in chronopotentiometry. In many solvents, it is possible to ignore differences between fo and f E and between Do and DR and thereby be able to approximate the standard electrode potential for an electroactive couple by measuring Since Do and D R may differ substantially in the metaphosphate solvent this kind of approximation is not valid in 1 : 1 NaP03-KP03. From Equation 1 it is evident that a plot of io r1I2us. C yields a straight line whose slope is llznF 1r~12D"Z. All of these terms are known except the square root of the diffusion is equal to 8.552 X lo4 coefficient. The quantity '/2nF r1I2 for a one-electron process; hence, one can calculate the diffusion coefficient if a direct proportionality can be demonstrated between io 7 1 ' 2 and the concentration in moles per cubic centimeter, C. Table 11 lists all of the metal ions studied and each data point used to obtain the straight line plots from which the diffusion coefficients were calculated. Table I11 contains a summary of the results of the chronopotentiometric studies. The diffusion coefficients that were determined from the slopes of the straight lines obtained from plotting i o 7 1 1 2 us. C were used in the analyses of the chronopotentiograms. These analyses all resulted in straight line plots when the potential at any point on the curve was plotted us. the appropriate log function (see below). The corrected intercepts of these lines should correspond to the formal electrode potentials determined in the previous section if the values for the diffusion coefficients are correct and the equations are applicable. The only theoretical difference between the two potentials is that the formal potentials determined Y
+
+
and io is the current density (12). If one considers a reversible diffusion controlled reduction at constant current, the concentrations of the reactants at the electrode surface at any time t are given by (13)
and (3)
If these expressions are substituted into the Nernst equation and the resultant expression simplified, one obtains
(12) H. J. S. Sand, Phil. Mug., 1, 45 (1901). (13) L. B. Anderson and D. J. Macero, ANAL.CHEM.,37, 322 (1965).
(14) P. Delahay and T. Berzins, J. Amer. Cheni. Soc., 75, 2486 (1953).
Table 111. Results of ChronopotentiometricStudies Nature of wave n-value 7 !Ira Slopeb i u Cathodic 1 0 111 i 3 58.0 f 1 . 0 Cu(I1) Cathodic 1 'i s CU(I) Anodic 1 . . .c 226 f 4 Cathodic 1 ... U(VU 2 'la €0.820 . 8 Cathodic WV) 2 'la 30.5 + 0 . 2 Anodic Cathodic Ag(U 1 1 282 f 2 a T ' is the transition time for the reverse process. * This is the slope of the line obtained when i o r 1 ' 2was plotted us. C in A cm sec1i2mole-'. There were no solutions containing only Cu(1) investigated in this study. Ion V(V)
666
0
ANALYTICAL CHEMISTRY, VOL. 43, NO. 6, MAY 1971
D7OO'C
f
(cm2sec-1) (lo6) 1.69 f 0.08 0.460 f 0.02 7.00 + 0.24 0.126 L'O.OO3 0.0318 =k 0.0003 10.9 & 0 . 2
VI
Figure 1. Cathodic chronopotentiogram of 0.179M Cu(I1) in a solution containing 2.3 times as much Cu (11) as Cu(1) at a current density of 8.92 mA cm-2
0 >
-0,085-
g
L
-0.255
from the electrode potential measurements have a term involving the ratio of the respective activity coefficients for concentrations expressed in molalities, whereas the term includes activity coefficients for concentrations expressed in moles/cc in the chronopotentiometric studies. Current Reversal. When a substance is reduced, 7 for the chronopotentiogram is given by Equation 1. If the polarity of the working electrode is suddenly reversed at or before the transition time, then the transition time for the re-oxidation process is equal to one third the transition time for the reduction for reversible electrochemical reactions (15, p 195). This latter statement is true if both species are soluble in the solvent or if the reduction product is soluble in the electrode. If the forward reaction is the reversible deposition of a solid then the transition time for the anodization of the deposit is equal to the forward transition time ( 4 ) . The experimental determinations of the ratio r'/r are given in Table I11 where T' is the transition time for the reverse process. The Solvent. Chronopotentiograms of a sample of the solvent which had been heated at 850 "Cfor five days showed a small shoulder near the cathodic end of the melt. The product of current density times the square root of the transition time for this wave was 0.075. Wave analysis of this shoulder was impossible due to the distortion created by the limiting process of the melt. The initial potential of the working electrode in this study was very nearly the same as (1 5 ) Paul Delahay. "New Instrumental Methods in Electrochemistry, Interscience, New York, N. Y . , 1954.
-
I C 2
5ri.-q
that for the anodic limiting process for the melt and, hence, no anodic waves could be observed. Copper, The solutions studied in this system ranged in concentration from 0.08M to 0.20M for Cu(1) and from 0.1 M to 0.33M for Cu(I1). Although no particular study was undertaken to determine the concentration at which copper metal would just begin to plate out, it was observed that at concentrations of total copper above 0.2M some copper was deposited on the electrode under the conditions of electrolysis employed for the chronopotentiograms. The chronopotentiograms were useless for analysis whenever Cu(1) was present in significant amounts since the reduction wave for Cu(1) to copper metal seriously distorted the prior wave and caused a premature halt in the reduction wave for Cu(I1). Figure 1 shows the reduction wave for Cu(I1) in a solution containing 2.3 times as much Cu(I1) as Cu(1). This figure illustrates the difficulty involved in obtaining meaningful transition time measurements for Cu(I1) in a solution of this type. A chronopotentiogram of the same solution at a higher current density is shown in Figure 2. The wave for the deposition of copper is now clearly evident. It should be noted that no attempt was made to calculate the n-value for the second wave but it was assumed to be the reduction of Cu(1) to copper metal. This seems reasonable since the n-value for the first wave will be shown below to be equal to one. In addition, at the current densities employed, there are no other electroactive species in the solution which could cause even the slightest distortion, much less a wave the size of the one in Figure 2 . Added proof for the deposition of
h
-0 1
1-2
s c . 4
Time
ANALYTICAL CHEMISTRY, VOL. 43, NO. 6, MAY 1971
667
the metal is that the electrode gave a positive flame test for copper after it was cleaned and dried following an experiment. Figure 3 shows a chronopotentiogram of O.197M Cu(I1) in the absence of Cu(1). A plot of In ( ~ 1 1-~ t1/2)/(Do1'z/ D R 1 ~ z ) t lus. ' z E for this wave gave a straight line with a slope of 0.192 and an intercept of -0.0137 V. The slope is in excellent agreement with the theoretical value of 0.193 at 700 OC and the intercept was -0.109 V when corrected to the one molal AgP03 reference electrode. The formal electrode potential calculated from the electrode potential study was -0.121 v. A typical chronopotentiogram of Cu(1) is given in Figure 4. Fortunately this wave is well defined even in the presence of large quantities of Cu(I1). Silver. A typical chronopotentiogram of a 0.186M solution of AgP03 is shown in Figure 5. A plot of In ( r 1 I 2- t112) us. E gave a straight line with a slope of 0.184 indicating a one-electron reduction. The transition time for the anodic wave obtained upon current reversal was equal to the forward transition time. This behavior indicates that the reduction of silver results in a solid deposit rather than alloy formation with the platinum, The close proximity of the solvent decomposition process creates a slight distortion of the shape of the reduction wave for silver.
668
ANALYTICAL CHEMISTRY, VOL. 43, NO. 6 , MAY 1971
Vanadium. The reduction wave obtained for V(V) is unique compared to the waves obtained in other systems in that it begins at a potential very close to the anodic limiting process for the melt and ends very near the cathodic limiting process (see Figure 6). The initial potential is determined by the ratio of the concentrations of the oxidation states since pure V(V) melts could not be prepared due to the fact that V(V) reacts with the melt until appreciable amounts of V(1V) are formed. Although Caton and Freund (7) reported a reduction wave with a half wave potential of -0.46 V us. the anodic limiting process for the melt, corresponding to the reduction of V(1V) to V(II1) in their voltammetric studies in LiP03-NaP03 eutectic at 730 "C, only one wave was observed in this work. The product i O T 1 / zfor this wave was directly proportional t o the concentration of V(V). Laitinen and Rhodes (16) also observed that while voltammetric studies on Vz06 performed in LiC1-KC1 at 450 "C gave two reduction waves, chronopotentiometry of the same solutions yielded only one wave at the more positive potential. Attempts to analyze the potential-time curve shown in Figure 6 were inconclusive since plots of both In ( ~ - ~ t 1 I 21 ) / - ~ (16) H. A. Laitinen and D. R. Rhodes, J. Elecfrochem. SOC.,109, 413 (1962).
Time
Figure 5. Chronopotentiogram for reduction of Ag(1)
0.39
\
\
1
\
\
\
-0.31
\
~~
Time
Time
Figure 6. Chronopotentiogram for reduction of V(V)
Figure 7. Chronopotentiogram for reduction of U(V1)
(rl/*) and In (rl'*- t 1 l 2 )us. Ewere hyperbolic. Theminimum slopes of the curves corresponded to an n-value of approximately 0.67 while the maximum slopes indicated an n-value of 0.2. Chronopotentiometric curves which behave in this manner have been discussed by Anderson and Macero (13). The quantitative treatment of these quasi-reversible curves is quite tedious, and no attempt will be made here to further elucidate the nature of the electrode phenomena involved. It is interesting to note however, that upon current reversal, the potential rises abruptly until the wave starts to round off near the potential for the solvent decomposition. It is difficult to say if any V(1V) is being oxidized during this current reversal since the formal electrode potential of the couple is so near the
potential for the anodic decomposition process. There is certainly no indication that V(1V) is being oxidized prior to the anodic end of the melt, and since no reduction wave was obtained for this ion it is quite likely that V(1V) is not electroactive in this solvent at the current densities employed. Uranium. A chronopotentiogram of 0.212M U(V1) in the equimolar solvent is shown in Figure 7. A plot of In (r1iZ- f 1 / 2 ) / [ b r 1 / 2( D , 1 ~ 2 / D R 1t1l2] / * ) US. E for the reduction of U(VI), where b = CR/Co= 0.579, gave a straight line whose slope was 0.118 compared to 0.097 for a two-electron reduction and 0.193 for a one-electron reduction. When the intercept was corrected to the one molal reference electrode, a value of 0.0932 was obtained which is in very good
+
ANALYTICAL CHEMISTRY, VOL. 43, NO. 6, MAY 1971
669
1
Time
Figure 8. Chronopotentiogram for oxidation of U(1V) agreement with the value 0.0976 V obtained by electrode potential measurements. A typical chronopotentiogram for the oxidation of U(1V) is shown in Figure 8. A plot of In (r1l2- t1/2)/(DR1’2/Do2) tl’* us. E for a solution containing only U(IV) gave a straight line with a slope of 0.102 indicating a two-electron oxidation and an intercept which when corrected to the one molal reference gave a value of 0.1 18 V. CONCLUSIONS
The electrode potential studies demonstrated the utility of the reference electrode in the solvent and established an electrochemical series for the metal ions studied. This should be of value in future studies with regard to predicting reaction products and the stabilities of solutions containing more than one metal ion. The chronopotentiometric investigations showed the technique to be analytically useful for the determination of V(V), Ag (I), U(VI), U(IV), Cu(I), and Cu(I1) in the absence of CU(1). In some cases, it was possible to estimate the formal electrode potentials of the redox couple under investigation from the intercept of the plot of potential us. the appropriate log term for the potential-time curves. The agreement with the formal potentials determined by electrode potential measurements was reasonably good, considering that the electrochemical reaction must be highly reversible in order for the intercept of the log plot to equal the formal electrode potential (13). In addition, the shape of the wave may be distorted by one of the solvent decomposition processes which would cause an error in the value of the intercept. The agreement between the formal potentials measured by electrode potential measurements and by the chronopotentiometric method provides supporting evidence that the values determined for the diffusion coefficients are valid. Ag (1) has a diffusion coefficient that is of the same order of magnitude as those reported in LiC1-KC1 eutectic at 450 “C (9). The others are one or two orders of magnitude less. Since the equimolar NaP03-KP03 is considerably more vis-
670
ANALYTICAL CHEMISTRY, VOL. 43, NO. 6, MAY 1971
cous than the LiCI-KC1 eutectic, one might expect lower values for the diffusion coefficients. If viscosity were the only factor involved, one would expect all of the diffusion coefficients to be affected equally; since they are not, there must be another contributing factor. The relatively high concentrations employed in this work might possibly yield different values than would be obtained in more dilute solutions (8, p 262); however, since the concentration ranges studied were approximately the same for all of the metal ions, one could expect the effect of concentration to be approximately the same for all of the ions. Since metaphosphates are known for their ability to complex metal ions, it seems likely that the unusually large differences in the diffusion coefficients can be explained on the basis of the degree of complexation, i.e., the size of the solvated electroactive entity. The speed of diffusion should be inversely proportional to the size of the diffusing entity. On this basis one must postulate that Ag(1) has a smaller solvation sphere than Cu(1) since Ag(1) would have the smaller diffusion coefficient considering only the sizes of the bare ions. The high charge to ionic radius ratios of the multivalent ions undoubtedly causes them to have larger solvation spheres than monovalent ions having approximately the same ionic radii. This reasoning would account for the very small diffusion coefficients that have been observed for these ions. The solvent is known to be a very good complexing agent, and the complexes formed are most likely considerably larger than those formed in other fused salts. In view of this it is not unreasonable to expect the differences in the magnitudes of the various diffusion coefficients to be larger than those observed in other molten salt systems. RECEIVED for review August 18, 1970. Accepted January 18, 1971. Portions of this paper were presented at the Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, Cleveland, Ohio, March 7, 1969. This investigation was supported by Contract No. 53-2290 from Sandia Corporation, Albuquerque, N. M., and was performed under the auspices of the United States Atomic Energy Commission.
