c1CYCLIC CHELONO, DIFPU- c2SOLVE GENERATED EQUA- 903 FORMAT (5HRR =, F10.5, SION CONTROLL, PLANE TION BEGIN AT 96 READ 8HFRACT =, F10.5) ELECTRODE, READ IN K IN NOSIG FOR ACCURACY GO TO 920 NOSIG RR FRACT, TWO 96 IF(M- 1)300,100,102 300 PRINT905 SOLUBLE ElPECIES 100 Z=Y 905 FORRSAT (2X,5HEItROR) READ 900,K,NOSlG, RR, M=M+l 920 STOP FRACT 102 IF (Z) 98,200,99 EXD DIMENSION X (100),T (1 00) , 98 IF (Y) 71,200,73 END R(100) 99 IF (Y) 73,200,71 C GENERATION OF EQUA- 71 T(N) = T(N) + 10.0 **(-LA) LITERATURE CITED TIONS GO TO 10 (1) Alden, J. R., Chambers, J. Q., Adams, DO200N = 1,K 73 T(N) = T(K) - 10.0 **(-LA) R. N., J. Electroanal. Chem. 5, 152 T(N) = 0.0 LA=LA+I (1963). M=l 199 IF (NOSIG - LA) 300,200,71 (2) Bard, A. J., ANAL. CHEM. 33, 11 (1961). LA = 0 200 CONTIXUE (3) Churchill, R. V., “Operational Mathe- 10 DO 80 I = 1,N c3EQUATION SOLVED PRINT matics,” p. 39, McGraw-Hill, New York, SUM = 0.0 ANSWER 1958. DO 60 J = I,N DO201 J = 1,K,2 (4) Galus, Z., Lee, H. Y., Adams, R. N., = 201 R(J) = T(J)/T(J 1) J. Electroanal. Chem. 5, 17 (1963). 60 SUM SUM -- T(J) + (5) Murra,y, R. W., Reilley, C. N., Ibid., X(1) = SQRTF(SUM) PRINT 903, RR, FRACT 3, 182 (1962). 80 CONTIXUE PRINT 901 (6) Piette, L. H., Ludwig, P., Adams, Y = X(1) - 1.13 PRINT 902, [S,T(K),R(N), R. K., ANAL.CHEM. 34, 916 (1962). (7) Reinmuth, W. H., Ibid., 34, 1446 IF (1 - pu’) 81,96,300 K = 1.K1 (1962). 81 SIGN = 1.0 500 CONTIkUE (8) Testa, A. C., Reinmuth, W. H., Ibid., DO 95 L = 2,N 900 FORMAT (2110, 2F10.5) 33, 1324 (1961). = FORMAT [4(3X, lHN, 6X, SIGN -SIGN 901 RECEIVEDfor review March 27, 1963. 95 Y = Y + SIGN * RR *X(L) - 4II TAU, 5X, 5HRATIO)//] Accepted May 8, 1963. Work supported SIGN - SIaK * FRACT 902 FORMAT [4(1X, 113,2F10.6)/] by the Robert A. Welch Foundation. High Speed Controlled Potential Coulometry ALLEN J. BARD Department of Chemisfry, The University of Texas, Austin, Texas b An electrolysis cell for rapid con- reference to calibration curves, etc.-the and depends upon such experimental trolled potential coulometric determi- long electrolysis times usually required conditions as electrode shape, cell nations, employing a large electrode sometimes discourage potential users of geometry, and turbulence of flow. It is area-to-solution volume ratio and using this technique. The aim of this study probably better to write simply ultrasonic and nitrogen stirring, was was to consider the factors governing the designed. This cell allowed deter- speed of an electrolysis, and to design a minations to be performed with total cell capable of performing a controlled where m is a mass transfer constant. electrolysis times of less than 100 potential coulometric analysis in a short There is frequently no direct propor- seconds. The apparcitus was tested time. tionality between p and A; the dimen- by determining silver (I) and iodide by For a single electrode reaction carried sions of the electrode, rather than the electrodeposition of silver and silver out at potentials at which the rate of the area, are more important (3). Com- iodide, respectively. From 2.5 to reaction is limited by the rate of mass pletion of electrolysis is generally taken 25 pmoles of each was determined transfer of the electroactive species to at the time when the current has de- with an average error of 2 to 0.270. the electrode, the current decays ac- cayed to 0.1% of its initial value, that is The application of t7is cell to the cording to the equation (7) study of mechanisms of electrode t = 6.9/p (4) reactions was also considered. it = ;&-P’ (1) To decrease the electrolysis time, p must where it is the current at time t, 6 is the be made as large as possible. In this initial current, and p is a function of the study an electrolysis cell was designed ONTROLLED potential coulometry electrode dimensions, solution volume, with a large electrode area-to-solution C has been useful both as an ana- cell geometry, and rate of mass transfer. volume ratio, which employed ultra- lytical technique and for the investiga- For a simple Nernst diffusion layer sonic and nitrogen stirring. With this tion of mechanisms of electrode re- model of convection, p is given by the cell 811 “effective p” of about 0.1 actions. The time required to perform expression second-’ was obtained, so that elec- a controlled potential determination is trolysis times were only slightly longer p = DA/6V (2) usually hetween 20 miniites and 2 hours, than one minute. dqiriidiiig upou tlir c.qxrirnonta1 ap- wlitve z) is the diffusion coeflicient of I l:Lr:i t I IS f?mjIloyed. hltl~ough ContIolled the electroactive species, d is the elec- EXPERIMENTAL potential coulometric analysis has the trode area, V is the total solution vol- Apparatus. Kith a suitable po- advantage of being an rabsolute method ume, and 6 is the thickness of the diffu- tentiostat and coulometer, the design -Le., allowing the direct determination sion layer. The actual dependence of p of the electrolysis cell usually governs of the quantity of a substance without upon these variables is very complex, the electrolysis time. After experi- VOL 35, NO. 9, AUGUST 1963 1125 other contact of the transducer was pecially in the early stages of elec- connected by means of a small metal trolysis, that electromechanical po- piece, 3, leading around the Teflon tentiostats and coulometers cannot be gasket and connecting to the brass wall used. In this investigation an electronic of the piece. This, in turn, connected potentiostat, based on one commercially to the outside (ground) terminal of the available from Brinkmann Instruments, BNC connector. An inlet, 1, was used Great Neck, L. I., N. Y.,as a Wenking to direct a stream of compressed air or Potentiostat, with an output of other coolant against the transducer about 25 volts at 250 ma. and a to cool it. The glass cell was held response time in the order of micro- against the transducer by the upper seconds, was employed. The coulometer threaded brass piece, which screwed was based on a voltage-to-frequency onto the second brass piece and pressed converter and a digital counter (2). the lip of the cell down against the trans- A block diagram of the apparatus is ducer gasket. shown in Figure 3. A Sargent Model Another Teflon gasket between the SR recorder, measuring the voltage drop upper part of the cell lip and the upper over a standard resistor, Kas used to machined brass piece relieved the strain obtain current-time curves. Since the on the glass lip. This rather complex recorder could not follow the rapid mounting arrangement assured that current changes during the first few the transducer and cell would be seconds of electrolysis, the ball-and- rigidly held in place and could be disk integrator which is connected to easily disassembled for cleaning or for this recorder is not suitable for determin- making cell or transducer modifications. ing the total number of coulombs in- il simpler cell and transducer mounting volved in the electrolysis. A Model could probably be designed. 35 ultrasonic generator (McKenna Lab- The cell cover, which contained a tube oratories, Santa Monica, Calif.) , op- bil- closed at the bottom with a fine porosity erating at 1 Mc. per second at Figure l. Schematic diagram of elec- sintered glass disk, 9, for the auxiliary power levels up to 35 watts, was used electrode, 10, fitted to the cell body with a one-inch barium titanate trans- trolysis cell by means of a standard taper joint. ducer in these experiments. Additional standard taper joint con- Procedure. The electrolyses mere nections in the cell cover permitted performed by adding about 7 ml. of menting with several types of cells, the introduction of a reference elec- supporting electrolyte solution to the we found the one shown schematically trode, 7, nitrogen, 8, and sample cell, deaerating, and prc-electrolyzing in Figure 1 to be most useful. Details aliquots. With this arrangement, and the solution at the control potential of the cell construction are shown in because a stirrer did not have to be Figure 2 and are described below. positioned, the cell could be assembled The solution volume was about 7.5 very rapidly. I mi. when the cell was filled to slightly The requirements for the potentiostat above the bottom of the auxiliary and coulometer are somewhat more electrode chamber. A platinum gauze stringent for high speed electrolg& electrode, 6, wound in a tight spiral than for the usual slower methods. so as to fill the sample solution com- The current changes so rapidly, es- pletely, was used as a working electrode. With this electrode design, the usual types of stirring by rotating the working electrode or by employing a propeller or magnetic stirrer could not be used. Ultrasonic stirring eliminated the need for moving parts within the cell, and by making the base of the cell a barium titanate transducer driven by an ultra- sonic generator, effective stirring could be accomplished. A rapid flow of nitrogen through the solution also 6 aided in increasing the mass transfer rate. The base of the cell consisted of three 10 pieces of machined brass.