T H E ELECTROLYSIS O F ACID SOLUTIOKS O F COPPER SULPHATE. 11. CONSTAKT CURREKTS BY J. T. BURT-GERRANS
The experimental work of Mr. L. V. Redmanl having shewn general agreement between certain predictions of the mathematical theory2 of changes of concentration at the electrode, and the behavior of acid solutions of copper sulphate on electrolysis, it remained to enquire whether the want of sharper agreement was due to inaccuracy in the fundamental assumption of the theory (viz: that the diffusion constant of copper is independent of its concentration in the electrolyte employed) or was due to insufficient approximation in the laboratory to the ideal experimental conditions postulated by the equations. The present paper gives an account of experiments on the electrolysis at 18.o”C of acid solutions of copper sulphate with constant current, which were undertaken to answer this question. I. THE ELECTROLYTIC CELL
Exclusion of air:-Mr. Redman himself had discovered one source of error in the apparatus used by him, viz: the action of air-saturated electrolyte on the copper electrodes. I therefore carried out all electrolyses in an atmosphere of carbon dioxide, after first freeing the electrolyte from air by evacuation. A large quantity of stock solution, containing 15.45 g. of copper per litre, was prepared by dissolving recrystallized (hydrated) copper sulphate in maximumconducting sulphuric acid (30.5% acid by weight, about 7.6 normal); this was diluted with the same acid to the desired concentration before each experiment, and freed from air by evacuation in a thick-walled glass bottle standing in the thermostat. Carbon dioxide was then bubbled in for two minutes, the solution evacuated again, treated with the gas for two minutes as before, evacuated once more, then left for at least two hours in the thermostat in a slow current of the gas, which was obtained from a cylinder, and was washed with water and passed through sulphuric acid on its way to the electrolyte. A few minutes before the electrolysis the electrolyte was transferred (by gravity, through rubber tubing) into the electrolytic cell (which had been standing ready for at least half an hour in the thermostat) and was protected again by the gas; two portions of IOO cc. each were removed at this stage for analysis, and two more after the electrolyses were completed, unless the four analyses agreed the experiment was rejected. The copper was determined electrolytically in a King’s electrolytic outfit3: the solutions were almost neutralized with ammonia, and sodium nitrate was added to secure a good deposit. L. V. Redman: J. Phys. Chem., 29, 1548 (1925). T. R. Rosebrugh and W. Lash Miller: J. Phys. Chem., 14, 816-884 (1910). Equations from this paper are indicated by “R & M”. Chem. and Met. Eng., 21, 2 5 (1919).
F,,
I
ends of t,he catho(lc t h i new tlie midille; while thr! cqii:rt,ions of t,hc “inatheirint,irnlthcory” :ir(?/ J & S P(in ~ t,hc :tssirmpt,iont,h:it. t,lic filni is of cqrr:rl thirkncss lhrougliont. I t,li?refore rc?construr:t,eiltlic ccll, :i,nd proviiled tlirtx! mthoiles on t,iie stime shaft, (Fig. i ), separat,ed frorn each otticr only by t,liiIi discs of itisiilating inaterial (“I~cilnianol”);the three cnlhoilcs wcre of t,hc snnic (Ii:lmct(w (4.60 ixi) tinil height (6.40 cm), and ciich w:is provided with its own rhrosltit, so that the same nnmlicr of amp< (mild he sent tliroiigh each, hut only the rent rid c:Lt~iodewas connected lo the osriliogral~h. Tlic: “current” rccordcd in the tables is that. through the central raI.hode, tind rcached it by a rnrrciiry cup 011 tlie t,op of the shaft; thc currents for t,he other two wcre led
398
J. T. BURT-GERRANS
in through brushes, The cathode shaft runs on a double-faced cone-bearing just above the cathodes and on a ball-bearing below the brushes. The Common anode, which also serves as cell, is a drawn copper cylinder 10.2 cm internal diameter and 2 I cni high, which screws into a flange on the casing of the lower bearing of the cathode shaft; it is provided with a delivery tube for filling the cell and with an overflow pipe to ensure that the electrolyte is always a t the same level. The whole is mounted on a lathe bed set vertically, so that it can be lowered into the bath, whose temperature is held within o . I O C by an electrically controlled thermostat. Stationary horizontal insulating plates were employed, as in Redman’s apparatus, one close to the top of the upper cathode and one close to the hot.L
3
Ur
FIG.2
tom of the lower cathode; with this arrangement the uniform electrolytic field was retained, but the plates were at such a distance from the central cathode that there seemed little danger of their affecting the thickness of its adherent film. 11. THE CIRCUITS
Rearrangement of circuits. Redman’s tuning-fork method of calibrating the time axis on the film, and of recording the rate of rotation of the cathode shaft, was retained; but the short-circuiting bar used to protect the cell while the current was being adjusted was found to leak a little, and was replaced by an automatic device which threw the cell completely out of circuit and replaced it by an equivalent resistance, except while the oscillograph shutter was oFen and the record was actually being made. Three exposures were needed for each film, one to record the line of zero voltage, one for the voltage-calibration line, and one for the voltage-time curve taken during the electrolysis. For each of these special electrical connections were required, which were made by amalgamated copper contacts mounted on wooden blocks and dipping in the cups of a &cup mercury switchboard. The actual electrolytic circuit was kept away from this board for fear of accidental leaks; therefore, before each exposure a number of well insulated knife-switches had to be opened or closed by hand, but for each operation the mercury switchboard kept a red light burning near each switch, and this was extinguished only when the switch was moved to the proper posi-
ELECTROLYSIS O F ACID COPPER SULPHATE SOLUTIONS
399
tion for the operation in hand. This arrangement milch facilitated the manipulation of what, in the end, became a very complicated piece of apparatus. Without going into details of the mercury switchboard, signal lights, safety devices, adjustable contacts geared to the oscillograph drum, etc., etc., the main electrical circuits will now be described in simplified form, then the results obtained, and finally the computations. T h e electrolysis circuit, (Fig. 2 ) . The three “cell-resistances” Ur, M r , and Lr were adjusted once for all to be equal to the resistance through the electrolytic cell and leads via the upper, middle, and lower cathode respectively. Except while the oscillograph shutter was open, contacts were maintained between Ur and the ‘(upper rheostat”, M r and the “middle rheostat”, and Lr and the “lower rheostat”; these three rheostats were adjusted until the same current flowed through each of the three “cell resistances”, by means of an ammeter, not shewn in the figure, which could be switched into series with each of the three rheostats in turn. This adjustment once made, the elecXQ
0
c
x
Sovolts
-
@L
0
FIQ.3
trolysis-current could be varied by means of the “main rheostat”, though before each electrolysis the equality of the three currents was checked; the source was a large I I O volt storage battery. When the oscillograph opened its shutter, the relays described below connected the upper cathode, instead of the upper cell-resistance, to the upper rheostat, and the same with the other two, thus sending the current through the cell; and oscillograph element S o . I recorded the potential-difference between the anode and the middle cathode, When the shutter closed, the former connections were automatically restored. To avoid induction, carbon lamp rheostats were used throughout, fine adjustment being effected by a slide wire rheostat in series with one of the lamps; the resistance of these lamps had a high temperature coefficient, but as the current flowed through them continuously this did not matter. The “cell resistances” were of manganin, wound non-inductively, and the leads to and from the cell, and from one connection to another, ran side by side in pairs, The ammeter used was a Weston Model 45 ( I j o divisions full scale) provided with suitable shunts; they were calibrated against a copper coulometer, and also by means of a potentiometer and standard ohm; for each electrolysiscurrent the appropriate shunt was used, so that the reading on the instrument was never less than IOO divisions of the scale, T h e voltage-calibration circuit. (Fig. 3 ) . The 3 2 c.p. carbon lamp L allowed about 0 . 3 2 amFeres to flow from the jo volt storage battery; thus with no resistance in the slide-wire rheostat R the voltmeter shewed about two volts; this was reduced to the desired value by means of R and recorded. When the
400
J. T. BURT-GERRANS
oscillograph shutter opened, contact was automatically made at X , and a line was photographed whose height corresponded to the recorded voltage, as the resistance of 280 ohms in series with the oscillograph element I prevented any drop in voltage when contact was made a t X. When the shutter closed again, the connection at X was automatically broken. To keep the second element of the oscillograph from drawing a horizontal line while the calibration-voltage line was being photographed, a circuit was arranged which sent sufficient current through that element to throw the light spot off the paper from the moment before the shutter opened until just after it closed again. The voltmeter was a Weston Model 45 with 500 ohms internal resistance, in a series with which was 4500 ohms; the combination was calibrated by the potentiometer, each division corresponded to 0.0206 volts.
li
Primary 6OVolts and Rssfetonce)
FIG.4
u
The oscillograph was the Siemens-Halske two-element instrument used by Redman; a current of 4 milamperes through the element gave a deflection of 4 j millimeters on the photographic paper; on most of the oscillograms the deflections ran from 15 to 30 mm. The tuning-fork circuit. (Fig. 4). A constant current of about one ampere from a storage battery passed through the primary of a small induction coil, the secondary winding of which ( 7 ohms) was in series with the second element (11) of the oscillograph; the latter was short-circuited for a moment during each revolution of the cathodes, by means of a brass contact attached to the cathode shaft, When the tuning fork was struck (hammer and solenoid) its vibrations induced a sinusoidal current in the secondary of the coil; the resulting wavy line on the photographic paper served to calibrate the time axis, and its interruptions recorded the speed of rotation of the cathodes. To get a nice curve, free from the evanescent distortions which follow the hammer blow, the fork had to be struck about one second before the shutter opened; this was attended to by a contact wheel geared to the oscillograph drum which rotated once for every four revolutions of the drum. Relay circuits. (Fig. 5 ) . A system of three 20-ohm telegraph relays was used to make the contacts indicated in Fig. 5 ; the primary of each of them was connected to a dry cell through a resistance so adjusted that the current from the dry cell was insufficient to pull the armature of the relay up to the
ELECTROLYSIS O F ACID COPPER SULPHATE SOLUTIONS
40 1
magnet, but was sufficient to hold it there (against the pull of the relay spring) if a surge of current from some other source had once brought it close; these dry-cell circuits are omitted in the figure. In the normal state of the relays, with their tongues held away from their magnets by the springs (as in Fig. 5 ) , contact was made in the secondary circuit of Relay I1 but not in either of the others. When the oscillograph shutter opened, a surge of current from the “opening magnet” of the oscillograph (special connections to which were made for this purpose) excited the magnet of Relay I, which thereupon closed the circuit through the secondary of Relay I1 to the “electrolysis-magnet” ; this circuit remained closed (because of the dry cell on the primary of Relay I) until the “closing-magnet” of the oscillograph was excited and closed the shutter. A surge of current from
this “closing-magnet” passed through the primary of Relay I11 and thus closed the circuit through the secondary of that relay, activated the magnet of Relay I1 and broke the electrolysis-magnet circuit. To set the relays ready for use again, it is only necessary to break the dry cell circuits for a moment; the tongues are thereupon pulled away from the magnets, and remain away when the dry cell circuits are completed again. The “cell-resistance magnet” is supplied with current sufficient to attract its armature and hold it firmly against the contact P ; the electrolysis-current then passes via armature and P to the cell-resistance (Fig, 2 ) . When the “electrolysis-magnet” is excited, however, it not only makes the contact a t &, which sends the current through the cathode, but being much stronger than the “cell resistance magnet” jt pulls back the armature of the latter and breaks the circuit through P ; as, for a moment, the cell-resistance is in parallel with the cell, the contact at P breaks without a spark. There is a “cell-resistance magnet”and an "electrolysis-magnet" for each of the three cathodes; the three electrolysis-magnets are connected in series, and operated from the same relays. In order that the moment at which electrolysis begins might be recorded accurately, a reactance coil was inserted in the circuit leading from the relays to the electrolysis-magnets; this delays the action of these magnets a little, so that the time-voltage curve begins with a short horizontal portion on the zerovoltage line, and rises perpendicularly when the current passes through the cell.
402
J. T. BURT-GERRANS 111. MANIPULATIONS TO SECURE A TIME-VOLTAGE CURVE
While the electrolyte .was being freed from air, photographic paper was placed on the oscillograph drum, switches were closed to supply current to the oscillograph magnets and motor, fork-hammer, signals, relays, voltage circuit, etc. ; the “calibration-voltage” block was put on the mercury switchboard, circuits corrected until the red lights went out, the arc lamp adjusted, voltage set and read, and the switch thrown which permits the oscillograph to open its shutter and record the calibration-vol tage line, The oscillograph handles were reset, the current to the calibration-voltage circuit broken, and the zerovoltage line secured. The electrolyte was then transferred to the cell, the cathode-shaft motor set going, and its speed read on an electric speed-counter and adjusted by means of a rheostat in series with the armature of the motor. The cell thermometer was read, and the temperature of the electrolyte recorded. The “D. C. electrolysis” block was then put on the mercury switchboard, red lights put out, “relay jack” closed (to complete the dry-cell circuits), and a t a signal from the oscillograph the “fork jack” closed, which made it possible for the machine to operate the tuning-fork hammer; immediately after the blow, the “operating jack” was closed, and after waiting a second for the fork to assume steady vibrations, the oscillograph opened its shutter, sent the current through the cell, and photographed the time-voltage curve and the timecalibration curve simultaneously; it then closed its shutter, and the relays stopped the electrolysis. After two or a t most three electrolyses the electrolyte was removed, taking samples for analysis, and the cathodes cleaned. This precaution was necessary because during part of the time of each electrolysis hydrogen was being liberated together with the copper, and the powdery deposit formed under these conditions must obviously affect the thickness of the diffusion film. Under conditions of current, concentration, temperature, and speed of rotation such that comparatively little of this deposit was formed, five time-voltage curves (recorded one under the other on the same photographic paper) which were obtained from five successive electrolyses made without cleaning the cathodes, proved to be almost identical; but under less favorable conditions, there was a distinct difference between the first and the last curve; and in the final determinations, those recorded below, the cathodes were cleaned after every tmo electrolyses. Fig. 6 shews one of the time-voltage curves obtained as just described.l A B is the zero-voltage line, CD is the voltage-calibration line, EF is the timevoltage curve. Each revolution of the cathodes required 19.; “waves” of 1/128 second, Le. the shaft revolved once in 0 . 1 5 2 seconds. The point marked with an arrow, where the curve shews a point of inflexion, was taken to indicate the moment a t which the concentration of copper at the cathode The actual oscillograms were all
21
cm long and 9 cm wide.
ELECTROLYSIS O F ACID COPPER SULPHATE SOLUTIONS
403
reached zero; this is 84.5 “waves”, or 0.660 seconds, after the point a t which electrolysis began; in Table I1 this determination would be recorded as 9 = 0.660. I V . LIMITING-CURRENT DETERMINATIOLUS
When the “limiting-current block” was put on the mercury switchboard, it made contacts to the “push-button” as shewn in Fig. j ; when this button was pressed, it completed the secondary circuit of Relay I and, therefore, sent the electrolysis current through the cell; when the pressure was removed, the current flowed through the cell-resistances again. The block also arranged to have the potential difference between the anode and the middle cathode shewn on the calibration voltmeter. The current was first adjusted to an amperage somewhat lower than that of the estimated limiting-current, this current was recorded; the button was
then pressed, and the potential difference read and recorded. These operations were repeated with successively greater currents, and the observed voltages plotted against the currents; the point a t which the curve shewed a sudden increase in steepness gave an approximate value of the limiting-current under the known conditions of concentration, temperature, and rate of rotation of the cathodes. This preliminary determination, however, involved repeated electrolyses, each lasting several seconds, so that the cathodes became covered with a deposit which affected the thickness of the diffusion film; to obtain the definitive value of the limiting-current, therefore, the cathodes were cleaned and a few voltage determinations made with currents closely below and above the provisionally determined value of the limiting current; to cut down the duration of each electrolysis, a lens was held over the voltmeter near the expected reading, and the button was pressed just long enough for the reading to be taken. Thus the final value for the limiting-current was obtained before the cathode surfaces were spoilt; immediately after the last voltage reading a switch was closed which caused the oscillograph to record the speed of rotation of the cathodes, the cell thermometer was read, and a portion of the electrolyte was removed for analysis. Results of the Limiting-current Determinations Fig. 7 shews that, within the limits of experimental error, the limiting current is connected with the concentration of the electrolyte and the rate of rotation of the cathode by the relation
404
J. T. BURT-GERRANS
(Lim.current) X (sec. per rev.) 0.'' = 0.0790 X (9. C u per L.) (1) which is the equation to the curve drawn on the figure; the lowest concentration used in these experiments was 0.46 grams of copper per litre and the highest was 4.0 grams. The form of this relation is that used by Brunner', the exponent 0.77 signifies that doubling the peripheral speed of the cathode increases the limiting current to 1.71 times its original value; the theory accounts for this by assuming that the adherent film has been reduced to 1.0/1.71 = 0.59 of its original thickness, Forty unpublished determinations by Redman (I 8"C, 1.0to 6.0 g Cu per L) are in good agreement with the exponent 0.55; that is, with Redman's apparatus, doubling the speed of rotation reduced the thickness to two-thirds. The peripherical velocities and the form and dimensions of the cathode in Redman's experiments were almost exactly the same as in mine; - Between 3 a n d34 gg Cvcv per Ittm per litre
P -Leas tho" I 4 cu per htre D - B e t w e e n Iond e g cu per lotre
Zand
iBetween
cu per Intrc)
(Limiting CurrentI/(g 042
056
040
O X
O M
036
030
OEB
026
0 22
0 IL
0.14
0 16
0 18
0 to
Seconds p e r Revolution
FIG.7
but in his, the stationary plates were close to the ends of t6e rotating electrode, while in my three-cathode cell they were 6.5 cm distant from the middle cathode (for which the limiting currents were obtained). To test the effect of the position of these stationary plates, two thin circular plates of Redmanol were cut to fit across the cell and perforated in the centres so that they would just slip over the cathodes, These plates were attached by three rods of the same material (at their outer edges, near the anode) to the upper and to the lower stationary plate respectively, so that the central cathode revolved in a cell of its own with stationary plates close to its upper and lower ends. With this arrangement the limiting current was greater (Le,, the film was thinner) than when the plates were at a distance from the central cathode, and the effect of changing the speed of the cathodes was less. The four experiments of Table I fit the equation (Lim.current) X (sec. per rev.) = 0.206 X (g.p.L.) (2)
TABLE I 1.950 g copper per litre, 18'C. 8ec. per rev.
obs.
Limiting current (amp.) calc. by Eq. ( I ) calc. by Eq.
0.825
0.599 643
131
860 911
0,823 861
73 7
924
117
967
803
968
0.172
156
Z. physik. Chem., 47, 56 (1904).
(2)
405
ELECTROLYSIS OF ACID COPPER SULPHATE SOLUTIONS
In view of these results, it is obviously illegitimate to assume that there is a diffusion film of uniform thickness over the whole surface of a rotating electrode, unless the latter is kept well away from the stationary ends of the electrolytic cell. A . COMPUTATIONS O F k AND 1 FROM THE LIMITING-CURRENTS AND T H E TIME-VOLTAGE CURVES.
From the assumptions (i) that the diffusion constant k is independent of the concentration of copper in the electrolyte, (ii) that the diffusion film is of uniform thickness 1 cm, (iii) that in these strongly acid solutions there is no electrolytic migration of the copper, and (iv) that the jump in voltage used to determine the limiting-current occurs when the concentration of copper a t the cathode is brought to zero, there follows that the limiting current1 (-I’ amperes), the concentration2of copper in the body of the electrolyte ( x o ) , and the area of the cathode ( A sq. cm.), are connected by the equation I’ = 96500 A zo k/Z = 96500 X 92.5 X (9. p . L ) X k/(31800 X 1) (3) whence k/Z = 0.003562 X I‘/(g. p. L.) (4) Expressing the limiting-current in terms of concentration and speed of rotation (Eq I) this gives k / l = 0.000281 5/(sec. per rev.) 0.77 (5) The quantity 29 (the interval in seconds between the beginning of electrolysis and the first liberation of hydrogen) which is determined experimentally by means of the time-voltage curve as explained above, is related to the electrolysis current ( - I amp.) by the equation -96500 A k x o
=
I 1 (1 - 8/n2 2e-m2a6/m2[R & M 161
(6) a
where m is written as an abbreviation for Wn+
I,
a for n2k/412and 2 for 2 . n=r
The two equations (4) and (6) thus furnish two independent relations between k , 1, 1’, and 8,so that from a time-voltage curve and the value of I’ for the same experimental conditions (which may be found from Eq. I), both k and 1 may be computed. If the electrolysis-current be twice the limiting-current, or greater, k can be computed from the time-voltage curve alone, for in that case Eq. (6) may be replaced by I ’ / I = 0 . 7 1 8 3 5 d a [R & M 2za3] (7) whence k = 1.616 X 10-~Pb/(g. p . L.)2 (8) But if the electrolysis-current be less than twice the limiting-current, Eq. (6) becomes The convention adopted in the “mathematical theory” and followed here, is that a current is reckoned positive if it increases the concentration-at-the-electrode of the substance whose diffusion-constant is represented by k. At the cathode in solutions of copper sulphate, the current decreases the concentration of copper; the “limiting-current” as defined above thus corresponds to - I’ of the equations, and the electrolysis current to - I . The number of equivalents of copper in one cubic centimetre of the solution taken for electrolysis is represented by z,; the number of grams of copper in a litre of the same solution by (9. p . L ) ;thus (8. p . L ) = 31800 z,. Since, when z = 0, (z-z,)/Cl = I‘/I; see R. & M., Eq. 24.
406
J. T. BUHT-GERRANS
I ' / I = I - 8e-aG/r2e-a8 [R & M 171 (9) and both time-voltage curve and limiting-current determination are needed. The actual computations are most conveniently carried out by means of a table giving log (I'/z,) for different rates of revolution of the cathode, and a second table giving log at for different values of log I ' / I . VI. RESULTS O F THE COMPUTATIONS I. When the electrolysis-current is twice the limiting-current or greater, the theory predicts that the time needed to bring the concentration of copper a t the electrode to zero will be independent of the rate of rotation of the cathode. This follows a t once from equation (7) by substituting for I' its value from equation (4) and for a its value, r2k/4Z2; the expression for 9 so
I
I
I
I
I
FIG.8 obtained, viz 9 = factor X (9. p . L.)2X k / P , does not contain 1 and is therefore independent of the rate of rotation of the electrode (see Eq. 5 ) . Figure 8 gives the time-voltage curves for three electrolyses carried out one immediately after the other, with the same electrolyte (9. p . L. = 1.910) and the same current ( - I = 1.180); the cathode speeds were o.z80,0.184, and 0.110 seconds per revolution respectively1. From these data, the values of I ' / I , viz 0.341, 0.471, and 0.700, were computed. The values of 9 read from the oscillogram are 0.644, 0.648 and 0.700 seconds respectively-the first two equal, within the limits of error of the experiments, and the third greater, as predicted. 2. Table I1 gives the experimental data for 42 time-voltage curves, and the value of k computed from each; the determinations are arranged in order of increasing I ' / I in the table, and the values of k are plotted against copperconcentration in Fig. 9. In neither case is there positive evidence of a trend in the values of k , although the graph hints a t a decrease with increasing concentrations; all the determinations lie around k = 4.0 X 10-6. Rejecting the three extreme values (one below and two above the mean), the remaining thirty-nine give k = (4.00 zt 0.07) X 10-0; thus the dispersion, or "probable error" is one and three-quarters percent of the mean value, 19 of the determinations shew less. An error of one percent in the copper-determination or in the electrolysiscurrent would introduce an error of two percent in k ; an error of one percent The interruptions on the third tuning fork curve, which are quite distinct on the original oscillogram, have their positions indicated by pen marks in this reproduction.
ELECTROLYSIS O F ACID COPPER SULPHATE SOLUTIONS
407
TABLE I1 ( 9 . P. 1.)
2.556 I .910 I . 600 0.460 3 ' 795
Sec. p . r
-I
I'/I
0.146
2.667 I . 180 1 ' 583 0.416 3,077
0.334 0.341 0.367 0.395 0.420
0.280
0.138 0.141 0 . I50
a6
ep
106k
0.216
0.227
0.225
0.261 0.302 0.342
0.644 0.261 0.316 0.383
3.98 3.98 4 . I3 4.18 4.07
0.420 0.424 0.428 0.433 0.433
0.342 0.349 0.355 0.363 0.363
0.323 0.316 0.348 0.336 0.356
3.68 3.97 3.80 4.04 3.79
I . 200
0.
I . 600
0 . I33
3.875 3.440 3.875
0 . I44
0 . I44
.032 .410 3.185 2.968 3.137
3.875 3.795 3.795 2.244 I . 910
0.141 0.149 0.141 0.223 0.184
3 ' 198 2.983 2.983 0.204 I . 180
0.433 0.436 0.455 0.468 0.471
0.363 0.368 0.401 0.424 0.430
0.348 0.398 0.391 0.844 0,648
8.83 3.97 3.90 3.92 4.00
0.472 0.472 0.501
0.432 0.432 0.486
0.350 0.445 0.481 0.453 0.480
4. I O 4.07 4.04 4.00 4.05
0.571 0.547 0.523
0.
I39
I33
I I
I . 200
0 . I21
1.020
2.556 0.460 3.924 3.440
0.142 0 . I39 0.131 0.131
1.930 0.356 2.900 2.488
0.512
0.507
0.523
0.530
I . 566
0.141 0 . I39 0 . I33 0.138 0.140
1.061 I .061 2 ' 730 I .061 0.975
0.528 0.536 0.537 0.538 0.538
0.541
I
.085
0.551
1.012
3.440
0.133 0 . I34 0.133
I . 200
0. I 2 1
2.400
0.
I5 1
2.185 0.804 1.462
0.569 0.589 0.599 0.599
0.
I47
1.592 1.925 1.543 0.796 1.990
0.610 0.612 0.645 0.649 0.654
1.578 3.924 1 .,572 I .460 I . 600
1.550
2.802 3.332 2 ' 753 I .460 3 * 440
0 . I43
0.139 0 . I43
0.131
0.560 0.562 0.562
0.555 0.578
4.22 4.00 4.08 4.08 4 . I5
0.591 0.632 0.681 0.704 0.704
0.522 0.584 0.630 0.562 0.789
3.86 4.00 4.04 4.04 3.99
0.732 0.737 0.826 0.837
0.773
3.96 3.98 4.21 3.96 3.81
0.558
0.851
0.750 0.851 0.848 0.725
J.
408
T.
BURT-GERRANS
TABLE I1 (continuedj (9. P. 1.)
See. p . r.
-I
I'/I
a79
79
2,050
0.134
I . 708
0.127
0.137
0.671 0.695 0.699
.910 1.378
0.110
0.901 0.977 0.991 0.994 1.028
0.852 0.832
2.802
1.136 0.952 1.465 1.180 0.726
0.990 0.700 0.963
4.07 4.00 3.80 4 . I3 4. I O
I . 708
0.125
2.244
0.921 1.204
0,727
0.111
1.088 1.405
0.922 0.977
4.08 4.01
I
0.133
0.700 0.710
0.801
g.Cu.p.
i06k
L.
FIG.g
in reading 8 would cause an error of one percent in k ; an error of one percent in the rate of rotation of the cathode might cause an error of 1.2 percent in k . A few determinations made a t varying temperatures shew that an error of o . I O C in the temperature of the electrolyte (which affects 1 as well as k ) would cause an error of 0.6% in k . Thus it seems justified to adopt the value k = 4.0 X IO-^ as the diffusion constant of copper in 7.6 normal sulphuric acid at I~OC, for concentrations from 0.5 to 4.0 grams per litre; and to conclude that the predictions of the mathematical theory for electrolysis with constant currents are borne out by the experiments within the limits of experimental error, 3, To test the theory under unfavorable experimental conditions, two electrolyses were carried out with very slow rotation of the cathode, five with the cathode stationary, and four in a rectangular glass cell with flat copper electrodes 6.5 cm X 7.5 cm, which fitted closely to the sides of the cell and were 2 . 0 cm apart; Eq. (8) was used to calculate k . The results are given in Table 111;they agree with the others as well as could be expected, when the probability of accidental motion of the liquid is taken into consideration, VII. EFFECT O F VARIATION OF
1 ALONG
THE CATHODE
The very noticeable increase of the limiting-current brought about by placing stationary plates close to the two ends of the middle cathode (pg.404)~ must be due to their action in retarding the circular motion of the electrolyte, which would increase the friction at the surface of the revolving cathode, and, therefore, decrease the thickness of the adherent liquid film; it follows that when the plates are close to the ends of the cathode, the film must be thinner at its ends than at its middle.
ELECTROLYSIS O F ACID COPPER SULPHATE SOLUTIONS
409
TABLE I11 No. 371 37 2 382 3 54 3 63 3 60 361 366 365 364 3 63
g. p . 1.
See. p e r rev.
1.938 1.938 I . 868 I .868 I . 868 I .868 I . 868 1.838 1.838 1.838 I . 838
0.582 0.781
stationary
-I 1.379 I . 408 1.073
11
I . I10 11 11 11
flat cell 11 11 11
1 ' I97 1.404 I . 486 I .023 I .038 1 . I95 1.337
106k
19
0.516 0.488 0.688 0.656 0.590 0.477 0.406 0.219 0.219 0 . I49 0.125
4.22
.
4. I 7 3.67 3 75 3.92 4'36 4. I 5 3.92 4.04 3.64 3.83
The theory of elect'rolysis when the thickness of the film is different at different points of the electrode was not dealt with in the paper on "mathematical theory", and it cannot be treated quantitatively unless the distribution of the different thicknesses along the electrode is known. It would seem that some theory of this distribution should be found in treat,ises on hydrodynamics, but I have not been able to find one; and in what follows have restricted myself to a rough qualitative treatment of the problem. Consider the surface of the vertical cathode to be divided int'o a number of infinitesimal horizontal strips, each passing completely around the cat,hode, and each of t'he area AI; since the strips are parallel to the plates, the film will have the same thickness opposite every part of the same strip, its thickness will be leastJfor the end strips, will increase towards the middle, and will be the same for pairs of strips situated symmetrically wit,h respect t.o the middle of the cathode. The suffix is used to indicate the middle strip, and one of the end strips; thus, 11> 1 2 . At any moment during electrolysis the whole surface of the cathode mus be at the sa,me electrical potenDia1; t'he i.r drop from anode to cathode is the sacmefor each strip; and if it be assumed that the rest of the potential difference (viz : concentration-voltage and overvolt'age) depends merely on the concentration of copper in the electrolyte at the surface of the cathode, it follows that at any moment during electrolysis the concentration must be the same opposite every strip. This hypo+,hesisis in accordance with experimental results obtained by Mr. A. R. Gordon, a preliminary account of which has already been published1. From the beginning of the electrolysis unOil a d = 0.5 (at which moment at for every other strip2will be less t,han 0 . 5 ) ~the rate of fall of concentration a t the cathode is independent of 1 and is proportional to t.he current density (R & M 2 2 ) ; hence in order to maintain the same concentration opposite every strip, the current density must have the value - I / A at every point on the W. Lash Miller: Franklin Institute, Centenary Puhlications, September, (1924). 2at = ?rZkt/412
410
J. T. BURT-GERRANS
cathode until az.t = 0.5; and if the concentration of copper falls t o zero before that moment, it is obvious that the variation in l along the cathode can have no effect on the value of 6. From then on, however, the current-density a t the end strips must be appreciably greater than that at any other strip (including the middle strip) where the film is thicker than a t the end strip; but as the electrolysis-current is maintained a t constant intensity, this means that from a2.t = 0.5 on, the current-density a t the middle strip must fall, and that at the end strips increase. Equations have been developed for following the concentration changes a t the cathode when the current-density changes with the time according to any given law, but as the distribution of 1 is not known, they cannot be made use of. Two propositions, however, can be established : (i) There must be some constant current-density, - B1/A1amperes per cm.2, less than-I/A (the actual current density a t the middle strip when t = 0 ) but greater than the actual current density a t the middle strip when t = 6 , which, if maintained a t the middle strip from t = o to t = 6 , would just bring the concentration a t the strip to zero a t the moment t = 8. Thus
Bi A/IA1< 1.0 (10) The limiting-currents for each strip, viz: -Il, -I2, etc., are related to (ii) - I f J the limiting-current for the cathode as a whole, by the equations:
I : . &/AI = I : , lJAr
=
. , . = I f , L/A; whence I f / I i = l , A / L , A,
(11)
This follows from Eq. ( 6 ) , since by definition the limiting currents make z = o a t the electrode, when t = I n this equation, L i s the fictitious film thickness introduced by making the false assumption that the film is of uniform thickness throughout. By means of equations ( I O ) and ( I I), a lower limit to the value of 11/L may be obtained from the data of Table IV, as follows:-Each value of k given in this Table was computed by looking up the value of at that corresponds to the fraction I f / I and multiplying it by 4L2/a26;the true value of k would be found by looking up the value of at that corresponds to the fraction 1’1/B1 and multiplying it by 4P1/.rr28. Near at = 0.8 (an average value for Table IV) the ratio of these two values of at is close to the 2 . 2 power of the ratio of the two fractions; hence
.
k (table)
k (true) =
I f * B1 I -Il’
(-)z:(t)z
=
(
B1. A
)‘:“(t)’= (-).
B1 * A * ZI I ’A 1* L
I
*
A1
2.2
ll
0.2
(L)
so that, by Eq. ( I O ) , (ll/L)O.Z must be at least equal to the ratio of the values of k. While the results of Table IV differ rather widely, due to the difficulty of fitting the plates in exactly the same positions after each electrolysis, yet every experiment with rotating cathode gives a higher value of k than the three with cathode stationary; the average with rotating cathode is 4.14 X IO-^, with
ELECTROLYSIS OF ACID COPP.ER SCLPHATE SOLUTIONS
41 1
stationary' cathode 3.83 X 10-6, and the quotient 1.08. Using this quotient for want of a better, (and remembering that R,A/IA, is less than unity) Eq. (12) gives 1.47as the minimum value of h / L ;as L (calculated by Eqs. 2 and 4) runs from 2.3 X 10-3 to 2.7 X IO-^, this would make the film at the middle of the cathode a little thicker than in the experiments of Table 11; and as it seems unlikely that the friction of the plates could actually increase 1 a t any point of the rotating electrode, it may be concluded that the thickness of the film a t the centre of the cathode is the same whether the plates are close to its ends, or are separated by the lengths of the upper and lower electrodes.
TABLE IV No. 88 89 87 90 81 79 86 92 80 91 85 82 83 84
Sec. per rev.
-I
0.126
1.508
0.I 2 1
I .522
0.129
1.393 1.379 1.173
0.I 2 1
0.172
0.148 0.131
0.124 0.164 0.123
0.126 stationary 11
2)
1.173 1.223
1.237
1.095 1.166 1.137 0.981 1.138 I . 202
I'/I
ab
0.623 0.627 0.666 0.692 0.703 0.749 0.756 0.764 0.769 0.813 0.826
0.766 0.776 0.887 0.967 I .004
.....
..... ..... .....
..... .....
6
I. 1 7 2
0.414 0.445 0.j16 0.547 0.724 0.801
I . 201
0.711
1.234 1.256 1.464 1.538
0.648 0.989 0.844 0.883 0.922 0.703 0.625
10%
3.92 4.30 4.I 3 4.24 4.04 4.33' 4.16 3.86 4.18 4.26 4.I 7 3.78 3.88 3.84
Thus, although the experiments of Table IV are obviously not accurate enough for individual computation, they serve to shew that the disturbing influence of the stationary plates does not extend far along the cathode, and that when the plates are removed to the ends of the cell, as in the experiments of Table 11, the film may be regarded as of uniform thickness throughout. VIII. E F F E C T O F AN UNSYMMETRICAL ELECTROLYTIC FIELD
The first and second experiments of Table V were made exactly as those of Table 11;in the third and fourth no current was sent through the upper and lower electrodes. Owing to the low i.r drop through the electrolyte, and to the high polarization from the very first moment of electrolysis, one would expect the current to distribute itself fairly uniformly over the cathode, in spite of the fact that the anode was three times as high. The results bear out this conclusion, and shew that the provision of additional cathodes is not so imThis value is lower than the average of the more reliable determinations of Table 11; but it seems better to compare values which were obtained during the same series of determinations and which, therefore, may be assumed to be affected with the same constant experimental errors. Substitution of the value k = 4.0 X 1 0 - 6 does not alter the final conclusion.
412
J . T. BURT-GERRANS
portant as it is to keep the working cathode away from the ends of the cell. A further experiment, in which current was sent through all three cathodes, but the upper cathode (instead of the middle cathode) was connected to the oscillograph, gave k = 4.38 X IO-^; while a duplicate in which the middle cathode was connected gave 4.18 X IO-^, shewing again that it is more necessary to keep the hydrostatic field uniform than the electric.
TABLE V No.
71 72
73 74
Sec. per rev.
-I
2.552
0.133
1.236
7,
7,
,, ,,
7)
1,
t,
g. p . 1.
,,
,,
I !/I
a79
0.772
1.269
),
,7
77
1,
7)
),
19
10%
1.164 1.195
4.04 4.01 4.12
1.191
4.10
1.172
Summary The paFer c‘escrihes apparatus and circuits for recording the potential difference over an electrolytic cell during the first second or so of anelectrolysis, and for calibrating the oscillographic record with respect to the time and to voltage. The electrolyses described were carried out at 18.ooC. with solutions of copper sulphate in maximum-conducting sulphuric acid. To secure uniform fluid friction over the whole surface of the revolving cathode, the latter was mounted on a vertical shaft between two auxiliary electrodes of the same dimensions; to secure a uniform electrolytic field, the three electrodes were supplied with currents of the same intensity; only the central cathode was connected to the oscillograph. The rate of revolution of the cathode-shaft was recorded on the oscillogram, and an empirical relation was established between the limi ting-current, the rate of revolution, and the concentration of the electrolyte. From this relation, if the diffusion-constant of the copper be known, the equations of “The mathematical theory of the changes of concentration at the electrode” can predict the time that must elapse before hydrogen will be liberated by a known current passing through a solution of known concentrafion into a cathode revolving at a known rate. Assuming k = 4.0 X IO-^, these predictions agree with the time intervals recorded by the oscillograph within the limits of experimental error. Results of electrolyses between flat copper electrodes were also in accordance with the predictions. The effect of unequal friction between the electrolyte and different parts of the same cathode surface is discussed, and evidence adduced that errors from this source have been avoided in the apparatus employed. The apparatus described has grown out of that employed by Mr. L. V Redman in this laboratory in 1907-10; it has been rebuilt, tested, and re
ELECTROLYSIS O F ACID COPPER SULPHATE SOLUTIONS
413
modelled many times since then. I wish to express my obligations to Professor W. Lash Miller under whose direction this series of investigations has been carried out, to Mr. L. V. Redman from whom I received my first instruction in the technique of these measurements, to Mr. H. A. G. Willoughby, Mr. A. D. Hone and Mr. H. R. Brant, who worked with me in constructing and improving the complicated apparatus, to Dr. S. Dushman for assistance in the earlier measurements and t o Mr. A. R. Gordon for cooperation in the final determinations. The University of Toronto; Electrochemical Laboratory, December, 1926.
