Table
Vanadium(1V) Taken, peq. 4124 2134 800 6 210 8
I.
Application of Background Corrections &total,
tl,
Sec. 3800 2100 1600 5500
&total. ‘2 J
‘1,
pF,
4826 2575 940 325
9 1
6
8
Sec. 4400 3800 2400 8900
mined experimentalIy. Indeed, in most macro scale work Q c and Q, , are negligibly small; then &:oh1
=
&om
[1+- ( k
+‘a)2 (bk - a ) ]
(17)
For an electrolysis in which an induced process occurs but a kinetic one does not, Equation 16 would become The correction mould then be a constant fraction of Q;,,,,,and independent of such experimental variables as electrode area and stirring rate. On the other hand, if a kinetic process occurs but an induced one does not, Equation 16 would become
Here k and a can be evaluated independently of coulometric measurements (the former by extrapolating log i to zero time, where the kinetic current is zero; and the latter by measuring the constant final electrolysis current, with the aid of a n obvious application of Equation 8, 11, and 12). I n this case, however, k
h, pF,
4851 2682 960 376
5 8
6
8
Error,
&total,
&corn
PFV
PFV
%
4061 2156
-1 5
4670 2479 900 243
4 1
6 2
783
211 5 Mean error
+lo
-2 2 +0 3 f l 2Yc
at least (and sometimes a as well, depending on the mechanism responsible for the kinetic current) depends on the experimental variables mentioned above, and much closer attention must be paid to these to ensure satisfactory results in replicate experiments. The validity of the general treatment may be assessed from the data given in Table I, which were secured in typical reductions of vanadium(1V) to vanadium(I1) in 2.7F hydrochloric acid at -0.85 volt us. S.C.E. The value of (bk2-ak)/(k a)* = 0.150 under the conditions of these experiments mis obtained from data like those of Figure 7 but secured at E, e = -0.85 volt. Although the mean error which would have been incurred by the use of Equation 2 was roughly +14%, results accurate and precise to j=1.2% were secured by the use of Equation 16. Although this accuracy and precision are by no means as good as those obtainable under ideal conditions, it is clear that the practical utility of coulometry a t controlled potential can be greatly extended by the proper correction of data secured under conditions which are far from ideal.
+
ilpproximately 100 ml. of a solution containing the specified amount of vanadium(1V) in 2.7 f 0.05F hydrochloric acid was electrolyzed with a mercury cathode of area 47.2 sq. cm. at -0.85 volt us. S.C.E. The values qf &’total were secured by reading a current integrator in series with the cell a t the specified times, and &:otal and pCor, were calculated. Under the conditions of these experiments both Q, and Qf,i r e r e negligibly small. LITERATURE CITED
(1) Bockris, J. O’ll., Azzam, A. hI., Trans. Faraday SOC.48, 145 (1952). (2) Delahay, P., “ S e w Instrumental
Methods in Electrochemistry,” Interscience, New York, 1954. (3) Kemula, W., Siekierski, S., Siekierska, K. E., Roczniki Chem. 29, 966 (1955). (4) Kortum. G.. Bockris. J. O’lI.%“Textbook of Electrochemistry,’’ pp. 360-3, Elsevier, Amsterdam, 1951. (5) Koutecky, J., Chem. l i s t y 47, 323 (1953). (6) Lingane, J. J., ”Electroanal>-tical Chemistry,” pp. 191-5, Interscience, Sew York, 1953. ( 7 ) Lingane, J. J., J . Aut, C h e m . Soc. 67, 18%(1945). (8) IIacNevin, IT. ?*I.,IIcIver, R. D., ANAL.C H E M .27, 1994 (195.5). (9) Meites, L., Zbid., 27, 416 (1955). (10) Zbid., p. 1116. (11) Moros, S., hleites, L., unpubhshed. (12) Page! J. A., Ph.D. thesis, Harvard Universitv. 1954. (13) Post, B.’, Hiskey, C. F.. J . A4vi.Chem. Soc. 72, 4203 (1950). (14) Siekierski, S., Siekierska. K. E., Rocznihi Chem. 30, 399 (1956). D., Raths, It-, E., ‘
Ch.em. Communs. 11, 216 (1939).
RECEIVED for review July 14, 1958. Accepted October 6, 1958.
Therma I EIectroa na lysis HOWARD F. HOLMES and MICHEAL J. JONCICH Department of Chemistry, University of Tennessee, Knoxville, Tenn.
b A method of analysis, based on differential thermal measurements during electrolysis, has been developed. The difference of temperature between the anode and cathode, as well as between these electrodes and the solution, was measured. For a solution of cupric sulfate in the range of 0.02 to 0.20M, there is a definite relationship between these temperature differences and the concentration of the solution. Concentrations were determined to an accuracy of 1% by this method. 28
ANALYTICAL CHEMISTRY
W
direct current is passed through a n electrochemical cell, heat is evolved or absorbed a t the electrodes. This is also true for batteries. Studies of this type, first carried out by Bouty (1) and Jahn (6), demonstrated that these electrode heat effects exist and the magnitudes of the heat effects were determined, for both batteries and electrolytic cells. Lange (7) and Bruzs (2) also studied these effects. Bruzs measured the steadystate temperature difference between anode and cathode as a function of curHEN
rent density. Lange improved the conditions of temperature nieasurements and obtained precise values by the use of differential calorimetry and thermopiles. Richards (9) showed that overvoltage appears in a n electrolytic cell as a heat effect. With the exception of a fen- isolated experiments, work of this nature ceased until 1954, when the h-ational Bureau of Standards used these temperature effects to determine enthalpy changes for electrochemical reactions (10). These reactions were carried out in a
calorimeter and the enthalpy change was calculated from the difference of the energy input into the cell and the heat equivalent of the temperature rise of the calorimeter. Gritsan and Bulgakova (4) were the first to use electrode heat effects for analytical purposes. They measured the cathode temperature rise of cells of the type: metaljmetal sulfate solution/ metal, using copper, zinc, and cadmium. An empirical relationship was reported among temperature rise, current density, and concentration of the solution. Attempts to reproduce these results in this laboratory were unsuccessful. The results obtained indicate, holvever, that heat effects in electrocheniical systems could be used for analytical purposes. The true relationship between these quantities, therefore, v a s sought. MATERIALS
All chemicals used were reagent grade. Solutions were prepared by n-eighing the copper sulfate in the form of the pentahydrate. Potassium sulfate n a s added, when necessary, in the form of the anhydrous salt. All solutions containing gelatin were used Tithin 24 hours after preparation, to avoid bacterial action. APPARATUS
An apparatus mas designed which allow determination of electrode temperatures as well as the temperature of the solution. It n s necessary to measure small differences in temperature accurately and reproducibly, and n i t h a small temperature-sensing element. Fast response was desirable. Thermistors (matched pair, Victory Engineering Co., S o . 32A1) were chosen. They were baked for 2 weeks a t 160" C., then current of twice the amperage used in the folloiTing experiments was passed through the thermistors for 2 to 3 days. This treatment completelv stabilized the thermistors and prevented any drift. The resistance of these thermistors is approximately 2000 ohms a t 25" C. The thermistors were glass-enclosed ( 2 inches in length, 0.100 inch in diameter. with 0.012-inch Dumet leads). The copper electrodes were hollow rectangular parallelopipeds (3 X 1jls X :/le inch) with a metal thermistor well inside the electrodes for reproducible placing of the thermistor tubes. This arrangement also made it possible to move a thermistor from the electrode into the solution whenever it m s necessary to measure the difference of temperature of an electrode and the solution. The two thermistors were connected to opposite arms of a Kheatstone bridge circuit as shown in Figure 1. T n o separate bridge circuits n ere used, with each bridge containing a separate set of matched thermistors. One circuit (Ko. 1) was used to measure the temperature difference betxeen the n ould
I
Figure 1. Bridge circuits used to measure temperature differences during electrolysis
I
r
"
anode and cathode. By moving the thermistor from the anode into the solution, it was also possible to measure the difference in temperature of the cathode and the bulk of the solution. Circuit 2 was used to measure the temperature difference between the anode and the solution. RI and Rq were 2200-ohm. 1/2-watt radio resistances, while RB and Rd were decade resistance boxes (Heathkit, 0 to 99.999 ohms). -4fter thermal equilibrium had been attained, R2 and Rd were used to set the initial unbalance potential of the bridge circuits as close to zero as possible. This permitted a lower range on the K-3 potentiometer (Leeds B Sorthrup), thereby increasing the sensitivity of the circuits. As a source of bridge power, a regulated, low voltage supply described by Greenough, Killiams, and Taylor (3) \vas used. The output terminals of this power supply mere shunted with a 50-ohm (1-watt) resistance, so that the supply would put out enough current to give good voltage stability (i.1 mv.). The output voltage was set a t 1.000 volt and checked with the K-3 potentiometer, which 1%-asalso used to measure the unbalance potentials t o 0.001 mv. A Kin Tel RIodel 204% electronic galvanometer was ideally suited for use as a null detector. because of its high sensitivity (2 X 10-11 ampere per scale division), fast response, and stability. The unbalance potential of the upper bridge circuit in Figure 1 niay be represented by the following equation:
\%hereEa = unbalance potential 2'1 = resistance of thermistor 1 2'2 = resistance of thermistor 2 R1 = 2200 ohms Rf = 2300 ohms E , = supply voltage for bridge (1.ooo volt) From this equation and the negative temperature coefficient of resistance of the thermistors (approximately 4% per "C.) the bridge was calculated to have a sensitivity of approximately 10 mv. per "C. temperature difference betm-een the thermistors. As the unbalance potentials were measured to 0.001 mv., this corresponds to temperature differences of approximately
ELECTRODE
AREC
Figure 2.
Electrolysis cell
0.0001" C. The sensitivity and linearity of the bridge circuits were checked with t m Beckman thermometers. The sensitivity of bridge 1 was found to be 9.65 mv. per "C.; the sensitivity of bridge 2 was 9.28 mv. per "C. as accurately as could be measured by the Beckman thermometers. The change in bridge unbalance potential was linear with temperature difference over the range of temperature differences involved in these nieas~rements. To obtain reproducible results, the electrodes must be maintained a t a fixed position with respect to each other and a definite reproducible electrode area was necessary. K i t h this in mind, the electrolysis cell shown in Figure 2 was constructd from Lucite inch thick, to fit' snugly into 2 500-nil. Dewar flask. The esposed electrode area was 19.35 sy. cm. A11 measurenients were taken in the same 500-nil. cork-stoppered Dewar flask. A 32-volt batt,ery pack was used as a source of direct current for the electrolysis. I t was connected to the electrolysis cell through a 25-ohm potential divider and a 100-ohm variable resistance. This afforded manual control of the electrol? any selected value. The current IJ-as read from a 0-1000 ma. meter. This was sufficiently accurate to give reproducible results. I n some experinients. a constant temperature water bath set a t 30.0" =k 0.02" C. was used. All electrolysis times n-ere read from a stop n-atch. PROCEDURE
A solution volume of 200 ml. vas used in all measurements. ; i constant volume of solution is not necessary to VOL. 31, NO. 1, JANUARY 1959
29
a
> -10
f I
0
2
0
Figure 3.
4 TIME
6 IN M I N U T E S
obtain reproducible results for determinations of temperature differences between the two electrodes, as long as the entire electrode area is covered. When the temperature of the solution is involved in the measurements, a constant volume of solution must be used. For measurements of the temperature differences b e h e e n the electrodes and the solution, or between the cathode and the anode when room temperature varies more than 2" to 3" C., the solution must be brought to bath temperature before the start of electrolysis. For these measurements the solutions were thermostated in the water bath before being pipetted into the Dewar flask (also contained in the water bath). Before insertion into the solution, the cathode was cleaned by rubbing with emery cloth, then dipping into concentrated potassium cyanide solution for 15 seconds. Only the cyanide dip was necessary for cleaning the anode. These procedures were necessary to obtain reproducible results. After the solution was pipetted into the Dewar flask, the clean and dry electrode, cell, and thermistor assembly was inserted into the flask and the electrode and thermistor leads were connected. The thermistor bridge power supply was turned on at this point. The entire
0.12
0.08
assembly was allowed to stand 15 minutes after inserting the cell assembly and before starting the electrolysis. This period is necessary for two reasons. Thermal equilibrium must be attained in the solution; attainment of thermal equilibrium was indicated by a constant unbalance potential of the bridge. Polarization characteristics of the electrode change with time and become constant after 10 minutes (8). The electrolysis current was then turned on and the current manually adjusted to the selected value (usually 300 ma.). The current was manually controlled a t this value for the entire electrolysis period, which was 10 minutes in all cases. Readings of the unbalance potential of the bridge circuit were taken every 30 seconds for the first 2 minutes and a t 2-minute intervals for the remainder of the electrolysis period. The difference between these potentials and the steady unbalance potential before the start of electrolysis gives the temperature difference in millivolts. This value can be divided by the bridge sensitivity to obtain the temperature difference in degrees centigrade. Because the authors were interested primarily in temperature differences, the temperatures were recorded in millivolts.
0.20
0.16
MOLESILITER
Figure 4. Ten-minute values of Tccupric sulfate concentration
as a function of time of electrolysis
Tc-TA
0.04
CONC. OF CuSO, IN
IO
8
TA
as a function of
RESULTS
The results are expressed in terms of three temperature variables, Tc, T A , and Ts, where Tc is the temperature of the cathode, TAis the temperature of the anode, and TS is the temperature of the solution. Some typical plots of Tc - TA us. time of electrolysis a t a current of 300 ma. are shown in Figure 3. This is the type of curve expected in all cases, with the steady-state temperature of the anode higher than the steady-state temperature of the cathode. The specific shape of the curve, however, will vary n-ith the current, and, as can be noted from Figure 3, the concentration of the solution being electrolyzed. After about 2 minutes of electrolysis, the curves of Tc - TA for the solutions of lower concentration approach a negative value of Tc - T A a t a faster rate than the more concentrated solutions. The curve for 0.20M cupric sulfate is completely smooth and no maximum is observed, as with 0.04, 0.08, and 0.12M cupric sulfate. I n general, with concentrations above 0.12M the curves tended to become smooth and exhibit little variation
Tc- Ts Ti.- Ts
>' f
5 4 F $ 2
Tc- To
K
E
0
$ 0
w
+ 0
0.04 CONC.
OF
0.08 CuSO,
0.12 0.16 IN M O L E S I L I T E R
0.20
Figure 5. One-minute values of Tc- TA as a function of cupric sulfate concentration
30
0
ANALYTICAL CHEMISTRY
-20 0
I
I
I
I
2 4 6 TIME IN M I N U T E S
8
IO
I
1
Figure 6. Tc-Ts electrolysis
and TA-Ts as a function of time of
150 MA. L
250 MA.
0
w -5 J
7
350 MA. 0
4
2 TIME
IN
6 MINUTES
Figure 7. Effect of current on Tc-T.4 trolysis curves
,
with concentration. With concentrations below 0.12M, the curves always exhibited a portion with positive slope and wide variation with concentration. I n Figure 4 the value of Tc - TA a t the end of 10 minutes of electrolysis is plotted against the molar concentration of cupric sulfate. All values were obtained a t a constant current of 300 ma. The maximum in this curve at approximately 0.10M cupric sulfate corresponds to the point above which a portion of the copper plated on the cathode is darker in appearance than the base metal. From 0.16 to 0.20111, the horizontal portion of the curve, the copper plated over the entire cathode mas dark, indicating a high degree of subdivision of the deposit. Up to a concentration of 0.1OLV, no plating was evident, as the copper was deposited in the form of a finely divided metal powder. The values of Tc - T A at the end of 1 minute of electrolysis a t a current of 300 ma. are shown as a function of concentration in Figure 5. The effect is opposite to that observed for the 10-minute values. The slope in this case is opposite in sign. The I-minute values of T c - TA were not as reproducible as the IO-minute values and are probably more closely associated with polarization effects. The Tc - T Sand TA- TS curves are shown in Figure 6, where T S is the temperature of the solution. These curves TA mere obtained to check the Tc values obtained previously. The difference between the two curves TC- T s and T A - T s should reproduce the experimentally obtained Tc - TA curve. Within experimental error this was true in all cases. The check, therefore, is exceedingly good, particularly in view of the fact that two different bridge circuits were used. I n no case was a negative value of TA - Ts or T C - T S observed after 1 minute of electrolysis (see Discussion). Figure 7 illustrates the effect of cur-
-
8
I -7 0 0
100 200 CURRENT I N M A .
300
400
10
vs. time of elec-
Figure 8. Ten-minute values of Tc-TA of electrolysis current
rent variation on the shapes and magnitudes of the TC - T A values. These curves were obtained using the same concentration of cupric sulfate (0.08M) for all the experiments. This set of curves shows a striking resemblance to the family shown in Figure 3, in which the current was held constant and the copper concentration was varied. It appears that decreasing the current has the same effect on the shape and magnitude of the Tc - TA curves as does increasing the concentration. I n Figure 8 the IO-minute values of Tc T A for the electrolysis of 0.08M cupric sulfate are plotted as a function of the electrolysis current. This curve shows the great need for maintaining a constant electrolysis current, if this method is to be used for the accurate determination of concentration. Figure 9 shows the effect of the addition of potassium sulfate on the Tc TA, T C - T s , and T a Ts curves. From a comparison of Figure 9 and Figure 6, it can be seen that the major effect of the potassium sulfate is a reduction of the heat evolved a t the anode. This gives rise to a more positive Tc T A curve, while the TC - Ts curve remains relatively unchanged, I n Figure 10, results are shown for the cupric sulfate solutions to which 40 mg. per liter of gelatin has been added. I n contrast to the effect of potassium sulfate, addition of gelatin increases the evolution of heat a t the anode. This results in a slightly more negative TC - T A curve than in the case of pure cupric sulfate solutions. Repeats of runs on 0.08df cupric sulfate solutions over several weeks showed the average deviation of the 10-minute values of TC - TA to be h0.025 mv. This corresponds to an uncertainty of j=O.O005X on the curve shown in Figure 4 . This was the curve used to obtain and check the concentrations of cupric sulfate solutions which were prepared by weight from cupric sulfate pentahydrate.
-
as a function
DISCUSSION
The basic concepts of irreversible thermodynamics can be used to derive a general equation for the energy balance in an electrolytic cell. The treatment based on the work of Van Rysselberghe (11) leads to the equation: -EIt = AH - TAS RI't t ?It in which E = applied potential t = time of electrolysis AH = enthalpy change for the total reaction T = absolute temperature A S = entropy change for the total reaction R = ohmic resistance of the cell 7 = polarization of all types
+
This equation may also be derived from the first and second laws of classical thermodynamics, if an isothcrmal system is assumed, but the irreversible treatment gives a more complete picture of the system. I n this equation the sensible heat effect is made up of the three terms: -TAS R12t VIt. For a reversible cell (ideal) the only heat effect is -TAS. It is the variation of these three terms with concentration which causes the heat effect during electrolysis to vary with the concentration of the electrolytic solution. As can be noted from the curves involving Tc - /'A, the anodic process is more exothermic. This is true in every case and results from a difference in sign of the entropy change a t the anode as compared to the entropy change a t the cathode. The positive portion of plot of Tc TA as a function of time is caused by concentration polarization a t the cathode. This is indicated by three experimental observations. First, there is a short time lag before the temperature of the cathode rises above that of the anode. I n most cases, especially with the less concentrated solutions, this time lag was of such short duration
+
+
VOL. 3 1 , NO. 1, JANUARY 1959
31
-21 0
I
I
I
4 6 TIME I N M I N U T E S
8
I
2
Figure 9. Effect of potassium sulfate on and TA- Ts 0.02M in K2S04 at 300 ma.
that it could not be measured nith the equipment used. This corresponds to the time necessary to deplete the copper ions in the vicinity of the cathode. When the copper ions are depleted by the plating reaction] a concentration gradient will be set up, resulting in a concentration polarization effect, and a heat effect due to this concentration polarization. The second bit of experimental evidence for the above statement is obtained by observing the effect of concentration on the shape of the T c - T A curve. The portion of the curve at which Tc - T Ais positive is decreased by increasing the concentration] and finally no positive values of T c - T A are observed a t the highest concentrations (Figure 3). This is in line with the fact that concentration polarization will not be observed in concentrated solutions. The third effect observed, which is consistent with the above reasoning] deals with experimental results obtained by holding the concentration constant and decreasing the current (see Figure 6). I n this case, the concentration polarization effect will not be present if the current is sufficiently low to allow time for the copper ions to migrate to the cathode. These last two observations are consistent with other experimental information dealing with Concentration polarization. The chief effect of potassium sulfate is to alter the heat effect at the anode. Two explanations h a r e been devised to explain the effect of inert electrolytes such as potassium sulfate. One is that the potassium sulfate decreases the anodic polarization of copper in a cupric sulfate solution. This would
32
ANALYTICAL CHEMISTRY
I IO
-61 0
I
I
2 TIME
I
6
4 IN
I
8
L
IO
MINUTES
Figure 1 0. Effect of gelatin on Tc - Tal lc- ls,and T,
have to be tested by experiment. The other explanation lies in the theory of irreversible thermodynamics as applied to thermocells (6). This involves ionic heats of transfer and transport numbers of the current-carrying species. It is probable that both effects are to be considered. The effect of gelatin on the timetemperature curves as shown in Figure 10 is much smaller than that of potassium sulfate. The effect on the TA T s curve is opposite to that observed with potassium sulfate. These results interpreted in terms of polarization are consistent with the results of Parsons and Winkler (8) on the cathodic polarization of copper in the presence of gelatin. I n using thermal electroanalysis for the determination of concentration of cupric sulfate solutions (or possibly for other solutions) the horizontal portion in the calibration curve (Figure 4) is to be avoided. This can easily be done by operating at a higher current density with the more concentrated solutions. Preliminary studies have indicated that, to avoid the interference of inert substances such as potassium sulfate, a technique similar to the radiation buffer technique used in flame spectrophotometry could be used -that is, enough of the interfering substance could be added to obtain a constant effect on the values of T C- T A . This method of analysis could lend itself well to instrumentation, in that the unbalance signal of the bridge is easily amplified or recorded for either automatic or control operations. I n the case of such applications as process control, the method would have to be
- Ts
modified for continuous operation. The magnitude of the temperature differences] but not the shape of the curves, will be changed if the equipment is changed-that is, there will be a difference in the values of Tc - T A if the electrodes, bridge circuits, thermistors] or geometry of the cell are changed. Another possible application of this type of measurement would be to study the effect of addition agents on polarization in plating solutions. This could be based on curves such as those shown in Figures 9 and 10. This method of polarization study would be fast and simple in comparison to the conventional method of using probes and measuring electromotive force, if only relative effects and not absolute values were desired. LITERATURE CITED
(1) Bouty, M.E., J . phys. 9, 306 (1880). (2) Bruzs, B., Z . physik. Chem. (Leipzig) 145A, 243 (1929). (3) Greenough, 31. L., Williams, W. E., Taylor, J. K., Rev. Sci. Instr. 22, 484 (\1- 9.51 _-- \
(4) Gri(san, D. N., Bulgakova, A. M., Zhur. Fiz. Khim. 29, 345 (1955). (5) ~, Hasse. R . , Trans. Faradau Sol:. 49, 724 (1953). ' (6) H.. Jahn, H., Z . vhvsik. physik. Chem. (Leiv(Leip\ , dahn. zig) 118, 8 , 416 (l896)." (1895). ( 7 ) Lange, E., Hesse, T., Z . Elektrochsm. 39, 374 (1933). (8) Parsons, B. J., Winkler, C. A., A,, Can. J . Chem. 32, 581 (1954). (9) Trans. Faradau SOC.9, ~, Richards. J. W., 140 (i913j. (10) Sherfev, J. S., Brenner, A., Xational Bureau 'of Standards, Washington, D. C., private communication. (11) Van Rysselberghe, P., J. Phys. Chem. 57, 275 (1953). RECEIVEDfor review May 10, 1958. Accepted October 9, 1958.
a
