A Chronopotentiometric Study of Gallium EDWARD D. MOORHEAD’ and
N. HOWELL FURMAN
Frick Chemicol loborotory, Princeton University, Princeton,
b Constant current studies a t the mercury pool electrode have yielded reversible cathodic-anodic chronopotentiograms for the gal\ium(mercury)gallium(I1I) couple in 7 to 10 formal potassium thiocyanate. However, POtential-time curves obtained for the cathodic-anodic processes in dilute potassium nitrate were ill-defined and variable in shape. Variation of the square root of the transition time ( ~ ~ with gallium concentration in 7.5F KSCN was linear. C vs. T ~ dafa ’ ~ a t current densities of 0.0464 and 0.231 ma. per sq. cm. were used to calculate a new diffusion coefficient for Ga(lll) in 7.5F KSCN which is 2.3 times larger than previously reported values.
A
with the dropping gallium and dropping mercury electrodes ( 4 ) has shown the normally gallium(mercury)-gallium irreversible (111) couple to exhibit a diffusion controlled, polarographically reversible three-electron oxidation-reduction in solutions 7.5F or higher in potassium thiocyanate (natural pH) containing Ga(II1) at concentrations less than 1.O mJ1. 7Kth the exception of fluoride, Ga(II1) is not known to complex strongly n-ith the halides or the pseudohalides (1). MacKevin and Moorhead (41, however, present polarographic evidence to suggest that the reversibility of the gallium reaction map result through the combined effects of Ga(II1)S C S complesing and adsorption of thiocyanate on the dropping electrode surface. The dependence of gallium electrode reversibility on thiocyanate present a t high concentrations is of considerable electrochemical significance, since the highly hydrolyzed Ga(II1) species represents a type of ion which does not readily lend itself to electrochemical reduction (j), Several aspects of the current-voltage work, especially the anomalously low limiting currents observed with the dropping mercury electrode (DA1.E.) in high thiocyanate concentrations and the unusually lon- value obtained for the Ga(II1) diffusion coefficient, prompted a more evtensive study of this unusual electrode reaction. AccordRECEKT STUDY
Present address, Chemistr Department, Harvard University, Caxntridge 38, Mass.
1
N. J.
ingly, voltammetry at constant current (2) (chronopotentiometry) was chosen as the means of investigation, because it presents alternative criteria for reversibility and is a n inherently accurate method for the determination of diffusion coefficients. Moreover, such a n examination would yield information, obtained a t relatively high current densities (C.D.), regarding the be~ havior ) of the gallium couple a t a flat, undisturbed mercury surface. EXPERIMENTAL
Constant-Current Supply and Electrolysis Cell. Constant current was provided b y a n instrument constructed after t h e design described b y Reilley, Adams and Furman, (6). Currents below 0.6 ma. were supplied by a coulometer, Type E-211 (Metrohm A.G., Herisau). All currents were calibrated just prior to electrolysis by measuring the I R drop across a precision resistance (General Radio Type 500-H) placed in series with the cell shunting resistor. The electrolysis cell Fyas specially constructed after a design by Delahay (2) and utilized a mercury pool-type electrode whose area (2.74 sq. em.) was determined from the transition time of a known concentration of cadmium chloride. The potential of the pool electrode was measured against a Leeds & S o r t h r u p industrial-type saturated calomel cell which was placed in a sidemounted Luggin probe. The probe electrode and cathode compartment were so constructed that the electric field normal to the mercury surface suffered a minimum of distortion. The anode compartment contained a platinum-disk electrode and was separated from the cathode compartment b y a finely-fritted glass disk. All measurements were made at 25,0° =t 0.1’ C. Solutions were purged of dissolved oxygen by outgassing for 20 to 30 minutes with dry nitrogen. Recorder. Potentials were led to a Leeds & N’orthrup Speedomax T y p e G recorder (20-mv. full scale, 1.0second full scan, chart speed of 8 inches per minute) via a pH meter (Leeds & Korthru T y p e 7664) n-hose internal recorder s t u n t was altered t o convert t h e recorder scale t o 2 volts. T h e input leads to the pH meter were also shunted with a high resistance (4.7 megohms) to minimize pickup on open circuit. The recorder was calibrated when necessary with a known voltage supplied by a student potentiometer. The measuring circuit was synchronized with the electrolysis circuit through a double pole-double thron. (D.P.D.T.)
toggle switch, and the recorder drive motor was always started a few seconds ahead of time to ensure constant chart speed during measurement, Reagents. Stock gallium nitrate solutions were prepared from Johnson, M a t t h e y Go., Ltd., “spectroscopically pure” grade Ga(N03)3.8H20 and were standardized gravimetrically b y precipitation with 8-quinolinol. Gallium (and indium) stock solutions were also prepared from the spectroscopically pure metals b y dissolving in hot, concentrated nitric acid. All other chemicals were of analytical reagent grade and were standardized when necessary according to accepted procedures. Reversibility, Cadmium and Indium. Several preliminary potential-time experiments were performed with cadmium and indium to characterize exactly the behavior of processes whose reversibility is well known. Indium(II1) in dilute solutions of potassium thiocyanate and cadmium in both chloride and nitrate supporting electrolytes were chosen because they are known to yield polarographically reversible currentvoltage wares in the isoelectric region of mercury and thus do not require surface-active agents to suppress maxima. Cadmium chloride in 0.1X KCl yielded a well defined potential-time waye whose E114 was in the potential region expected from polarographic half-vave potentials. Experiments with and without the use of Desicote (Beckman Instruments, Inc.) to stabilize the electrode area showed that transition times could be measured with satisfactory reproducibility (within 1%) in the absence of this surface-active agent, provided special caution was taken to protect the electrode from ambient vibrations and to prevent inordinate wetting of the mercury-glass interface with the test solution. Indeed, it was found in later work that potassium thiocyanate a t high concentrations (7 to 10F) gradually displaced Desicote from the malls of the electrolysis vessel. Solutions of indium nitrate in dilute potassium thiocyanate, which were slightly acidified to suppress hydrolysis, yielded sharply defined, reversible cathodic E-T curves. The anodic wares, obtained by reversing the current polarity a t the transition time, were also reversible in shape and evhibited transition times which n ere one third the value observed for the cathodic waves. Incremental increase of the current density a t a fixed concentration of indium yielded a series of reversible cathodic waves with the espected transition times and invariant E1,4.A typical anodic-cathodic wave for 0.85 VOL. 32, NO. 1 1 , OCTOBER 1960
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Figure 1.
Cathodic and anodic potential-time waves
0.85 mM In(NO& in 0.1 F KSCN (C.D. = 0.268 ma./cm.*) 1.0 mM Ga(NOJ3 in 0.1F KNOl (C.D. = 0.232 ma./cm.z) 2.5 mM Ga(NO& in 7 . S KSCN (C.D. = 0.231 ma./cm.2)
A.
B. C.
0
m M In(NOs)a in 0.1M KSCN (current density = 0.268 ma. per sq. cm.) is shown in Figure 1, curve A . The slope, dt/dE, is small both before and after the cathodic stabilization of the potential. Unlike the current-voltage wave, the chronopotentiogram does not show the usual minimum a t about -1.4 volts us. the S.C.E. which has been observed (3) for the reduction of indium in chloride solutions a t the D.M.E. RESULTS AND DISCUSSION
Gallium in Potassium Nitrate. Figure 1, curve B , shows a typical cathodic-anodic chronopotentiogram obtained with 1 x 10-3X Ga(NO& in 0.1X KSOa (natural p H = 3.2) a t a current density of 0.232 ma. per sq. em. The "quarter wave" potentials occurred a t approximately - 1.02 and -0.72 volt us. S.C.E. for the cathodic and anodic waves, respectively. The difference of 0.30 volt between the forward and reverse processes is in gQod agreement with the polarographic value of 0.29 volt obtained with the dropping gallium amalgam electrode (4). Prolonged electrolysis of this solution gave no evidence of a transition time corresponding to the reduction of hydrogen ion derived from hydrolysis of Ga(III), even though a wave for this process is invariably observed on the currentvoltage curve for gallium under these conditions (4). Reference to Figure 1, curve B, reveals further that the cathodic and anodic transition times are not in the 3 to 1 ratio expected from theory (.2) for the ideal case of reduction followed b y reoxidation from the amalgam. It is suggested that oxide film formation in the oxidation process limits further reaction; this would result in a potential sweep t o more positive values a t times less than the theoretically expected transition time. 1508
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ANALYTICAL CHEMISTRY
2.0
1.0
MILLIMUS G ~(111) Figure 2. Concentration vs. square root of transition time (seconds 'I2) C.D.,ma./cm.2: A. 0.0464 B. 0.231
Gallium in Potassium Thiocyanate. Preliminary residual (blank) potential-time curves, which were obtained for the stock (10F) and diluted stock (7 t o 8 F ) potassium thiocyanate solutions a t a current density of 0,011 m a . per sq. em. shoiyed two small cathodic waves occurring a t -0.7 and -1.2 volts us. S.C.E. Consecutive constant current electrolyses of the same solution drastically reduced the height (transition time) of these waves. Identical behavior was observed also in the presence of gallium, but the height of the gallium wave was not appreciably altered on repeated electrolyses. Current-voltage curves of the stock solution of potassium thiocyanate which were obtained with the dropping mercury electrode (Leeds & Korthrup Electro-Chemograph) showed no evidence of the presence of reducible species. The residual E-T waves a t high thiocyanate concentrations were most probably caused by substances adsorbed on the surface of the quiet mercury pool. These adsorption waves caused no noticeable interference a t current densities higher than 0.0464 ma. per sq. em. Figure 1, curve C, shows the typical behavior of 2.5 X 10-3Jf Ga(No3)3 in 7.5F KSCN (natural p H ) a t 25.0" C. a t a current density of 0.231 ma. per sq. cm. The E1,4for both the cathodic and anodic wave was -0.900 =t0.005 volt us. S.C.E. in agreement with the polarographic value of -0.900 =t0.003 volt us. S.C.E., I n addition, the
cathodic transition tinic. r , was very nearly three times the anodic transition t,ime, T', in complete agreement with theory (2), which predict's this relationship for equal current densities. The slope of the wave folloning thc cathodic potential holdup is much greater than zero, This contrasts sharply x i t h the behavior of indium (Figure 1. curve A ) and with the polarographic behavior of gallium in 7 . 3 KSCS ( 4 ) . This excessive slope niergrs gradually with the hydrogen wave and may in fact represent the cominenceinent of hydrogen ion reduction. since it is known (4, 7 ) that gallium amalgam pools are unstable in this respect. Measurement of the true transition time for the cathodic wave proved somen-hat difficult because of the large, almost linear slope of that part of the curve follorr-ing the potential holdup. However, an ordinary extrapolation of the kind used to measure polarographic diffusion currents yielded very reproducible t'ransition times which agreed well with the 7 = 3 r' relationship for the well defined anodic wave. When introduced into the equation for the chronopotentiometric wave of a reversible process ( 2 ) . these transit'ion times resulted in a linear plot of E o b s 2's. log (,1'2-t1'*) ' t 1 i 2 n-hich had nearly the theoretical slope for a three-electron reduction process. Concentration us. ~ 1 ' 2 . N a c S e v i n and Xoorhead ( 4 ) have shown that the corrected polarographic diffusion cure rent at the D.M.E. varies linearly [abov-
0.3mV Ga(III)] with the conccntration of gallium in 7.5F KSCK’. A plot of their data, however, does not pass through the origin but is displaced, instead, along the concentration axis. This behavior is regarded as highly unusual. It was therefore of considerable interest to determine if the chronopotentiometric transition time behaved in a corresponding manner. Two series of potential-time experiments were performed a t 0.0464 and 0.231 ma. per sq. cm. The results are shown plotted in Figure 2, curves A and B, respectively. Each point represents a n average value for T ~ of a t least three runs on as many portions of solution. The solutions were aged 5 hours to ensure equilibrium before making the potential-time measurcments. The C 4 2 relationship is linear at both current densities, and Figure 2 shows that an extrapolation of these lines intercepts the concentration axis a t 0.21mM Ga(II1) compared with 0.23mM reported for the current-voltage data ( 4 ) . The observed T ~ a’ t ~ 0.5mN Ga(II1) is 0.55 to 0.59 of the expected value had the esperimental data actually passed through the origin with the same slope. This is in good agreement ( 4 ) with the polarographic data (0.52), and i t suggests that the factors responsible for this behavior are independent of electrode geometry. LlacTevin and Moorhead have suggested ( 4 ) t h a t the low diffusion current observed for the Ga(II1) in high concentrations of thiocyanate may result through the combined effects of increased solution viscosity, a distribution of gallium over several complex species not all of which are reduced, and adsorption of thiocyanate on the electrode surface. Furthermore, if the
reducible Ga(II1) is hydrolyzed in the unbuffered medium, i t is likely that hydroxyl ions released in the reduction process combine, to some extent, with the gallium diffusing toward the electrode surface. Measurement of Diffusion Coefficient. Voltammetry a t constant current is recognized a s an accurate method for measuring the diffusion voefficient of aqueous ions ( d , 6 ) . From the equation (B),
/
(where 7 1 / 2is the square root of the ~ transition time, and all other terms have their usual electrochemical significance) it can be seen that a plot of 7 l I 2 us. C, should be linear with slope equal t o kD1lz, where k is a collection of known constants. Thus the diffusion coefficient, D, may be obtained graphically. =Iccordingly, the data obtained at 0.0464 and 0.231 ma. per sq. cm. (Figure 2) in 7.5F KSCN yielded 1.85 X and 2.04 X IO+ sq. cm. per sec. for the constant, respectively. The value, 2.0 X sq. cm. per sec. a t 25.0 0.1’ C., is reported. This value is 2.3 times larger than the polarographic value calculated from the diffusion current and 0.65 times the yalue calculated for the constant from the C vs. i d slope (4). The reported value is, of course, relative to the diffusion coefficient of cadmium(II), since this ion \Tas used to determine the electrode area. Hcrausc of the simpler diffusion vonditions underlying the chronopotentiomrtric method, the value, 2.0 X sq. cm. per see., is believed to be the more accurate constant. I t was concluded on the basis of the prcwding observations that the Ga(Hg)-
*
Ga(II1) couple in 7 to 108’ KSCN exhibits chronopotentiometric reversibility. However, a t progressively higher current densities (greater than 0.231 ma. per sq. cm.) the slope, dt/dE, of the cathodic potential holdup decreased, and the rising portion of the wave became distorted. This behavior resulted in a less accurately measured cathodic transition time. The anodic wave a t the higher currept densities was, however, very well shaped, and i t is suggested that measurement of r’ in this current region may be substituted for the ill-defined cathodic transition time in precise analytical applications of this method. ACKNOWLEDGMENT
The support of this investigation by a grant of research funds from Carter Products, Inc., is gratefully acknowledged. LITERATURF CITED
(1) Bjerrum,
J., Schwarzenbach, G., Sillen, L. G., “Stability Constants Part 11, Inorganic Ligands,” The Chemical Society, London, 1958. (2) Delahny, P., T e w Instrumental Methods in Electrochemistry,” Chap. VIII, Interscience, Yew York, 1954. (3) Lingane, J. J., J. Am. Chem. SOC.61, 2099 (1939); Kolthoff, I. M., Lingane, J. J., “Polarography,” Vol. 2, p. 519, Interscience, New York, 1952. (4) MacKevin, W. M., Moorhead, E. D., IZnd., 81,6382 (1959); E. D. Moorhead, Ph.D. dissertation, Ohio State, 1959. (5) Moeller, T., “Inorganic Chemistry,” p. 734, Wiley, S e w York, 1952. (6) Reilleo, C. N., Adams, R. N., Furman, N. H., ANAL.CHEY.24,1044 (1952). (7) Stelling, O., 2. Elektrochem. 41, 799 , . , . e \
(lY6J).
(8) Von Stackelberg, >I., Pilgram, hI., Toome, V., Zbid., 57,342 (1953).
RECEIVED for review April 20, 1960. ilccepted July 14, 1960.
Three-Dimensional Representation of Voltammetric Processes WILLIAM H. REINMUTH Department o f Chemisfry, Columbia University, New York,
b A three-dimensional surface is proposed which shows the relationships among various time-dependent voltammetric techniques using microelectrodes. This surface is analogous to one given by Reilley, Cooke, and Furman for the description of timeindependent current-potential-concentration relationships. Intersections of the surface with appropriately oriented planes represent conventional polarography, chronopotentiometry, polarog-
N. Y.
raphy a t a stationary electrode, and constant-potential voltammetry. N e w techniques suggested by the model are discussed.
T
model of Reilley, Cooke, and Furman (8) has proved valuable in representing clearly the relationships among various time-independent electrometric techniques. This success leads naturally to the question of n-hether time-depenHE THREE-DIIIIENSIONAL
dent voltammetric processes can be similarly portrayed. It is obvious that no unique current-potential-time surface can be drawn for a given system. The current-potential relationship at a given time in that system is dependent on its previous history. Fevertheless, it is possible t o draw a representative surface which shows clearly the relationships aniong various techniques and predicts qualitatively the results t o he expected with each. Proper adjustVOL. 32, NO. 1 1 , OCTOBER 1960
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