June, 1923
I X D USTRIAL AA7D EXGINEERISG C H E X I S T R Y
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T h e Importance of Diffusion in Organic Electrochemistry'3z By Robert E. Wilson and Merrill A. Youtz MASSACHUSBTTS INSTITUTE
OF
TECHNOLOGY, CAFBRIDGE, MASS.
Similar behavior has preCCORDING to the The work described in this paper was undertaken in an effort viously been noted in cergeneral theory of to account for the fact that organic compounds do not in general tain studies of the oxidnelectrode reactions, give clean-cut evidences of depolarization at reasonable current tion3 and reduction4 of orwhich has been substandensities, as do many inorganic salts. ganic compounds, although tiated mainly by work with B y experiments with oarying concentrations of ferrous chloride no such work appears to inorganic compounds, the solution, it is demonstrated beyond question that the rate of diffusion have been done on chloliberation of hydrogen, oxyof the reacting materials to the electrode is lilpdy to be the limiting rination. The peculiar shape gen, or halogen a t an inert factor in determining the rate of reaction at an electrode, especially of the curves has generally electrode cannot take place in the case of organic substances which generally haoe slow rates of been attributed to a very until a, definite potential diffusion and are usually present in comparatively low molecular slow reaction rate between has been exceeded. When concentrations. the nascent hydrogen or a succt:ssively greater elecIt is shown that the obseroed results, which cover a fairly wide oxygen and the organic comtromotive force is applied range of concentrations and temperatures, can be explained quantipound, although Farup,6 and current mlues are tatively on the basis of the known diffusion laws. B y making certain Law,6 and Nernst' have plotted against electrode approximate assumptions, the thickness of the effectivelayer through pointed out that the slowpotentials, a curve of the which diffusion must take place is shown to be about 0.5 mm. in ness of diffusion to the eleccharad eristics indicated by quiet solutions. I t may be reduced to one-ffth of this ualue, trode might well be the conCurve 1, Fig. 1, is obtained, or less, by fairly oigorous stirring. trolling factor in some the intersection of the exA number of expedients are pointed out by which the dificulties cases. Practically nothing, trapolated line with the due to slow rates of diffusion may be overcome in organic electrohowever, has been done in abscissa axis representing chemistry. the direction of distinthe decomposition potenguishing clearly between tial of the solution d u s the over-voltage of the' particular electrode used. If some sub- the two retarding factors, or of evaluat&g the ihickness of stance is present in the solution which can readily be the film through which diffusion must take place under difoxidized, reduced, or halogenated, this material generally ferent conditions. In the hope of clearing up some of these points, a series acts as R depolarizer and allows the current to flow (without the escape of gas) a t much lower voltage than would normally of experiments was made on the chlorination of ferrous be the case, giving a curve such as Curve 2 , Fig. 1. The chloride (or, from an electrochemical standpoint, the oxidaintersection of this line projected to the abscissa axis corre- tion of F e + + to Fe+++), which reaction was found to give a sponds to the oxidation or reduction potential of the material very clean-cut and reproducible depolarization curve. In order to have a definite chlorination potential, the Tali0 bepresent, a t the existing concentrations. The general characteristics of these curves have been ade- tween the concentrations of ferrous and ferric chloride waq quately demonstrated-primarily by experiments on inor- kept constant in all cases. ganic compounds, where it is possible to obtain clean-cut results. In undertaking a fundamental study of the electrolytic halogenation of organic compounds, extensive efforts were made to determine such depolarization curves, using various organic compounds which are known to be readily chlorinated. It is planned to publish the detailed results of these experiments in the near future, but for the present it may be stated that, in spite of using a variety of electrodes ethylene, and a large number of substances-including maleic acid, oleic acid, crotonic acid, benzene, toluene, xylene mesitylene, acetic acid, acetone, and others, generally in the presence of concentrated hydrochloric acid as the electrolyte-it was seldom possible to notice any appreciable variation in the normal current-voltage curve which could be attributed to the presence of these more oq less readily chlorinatable compounds. I n cases where any effect was observed the plotted results had tho general characteristics of the * AFPARATUS AND PROCEDURE dotted Curve 3, Fig. 1, indicating that depolarization was effective only a t very low current densities, although it was The anode used in these experiments was a hollow carbon observed that in general no gaseous chlorine escaped, even cylinder of 25-mm. outside diameter and about 15 cm. high. beyond the point where the dotted line joins the normal It was contained in a porous cup. The cathode was a larger, line for chlorine evolution in the absence of a depolarizer. hollow carbon cylinder, which encircled the porous cup. The
A
1 Presented before the Division of Physical and Inorganic Chemistry a t the 6 l s t Meeting of the American Chemical Society, Rochester, N Y., April 25 to 29, 1921. Received October 21, 1922. 2 Contribution No. 62 from the Research Laboratory of Applied Chemistry, M . I. T.
(1900), 533. Haber, I b i d , 4 (1898), 506. Z . physzk. C h e m , 64 (1906), 231; Pharmacia, 3 (1906), 1. J . Chem. SOC.(London), 89 (1904), 1520. "Theoretical Chemistry," 1916, p. 619.
a Dony-Henault, 2. Elektrochem., 6 4 5 6
7
604
INDUSTRIAL AND ENGINEERING CHEMISTRY
cathode and catholyte, and the cup with anode and anolyte, mere contained in a 600-cc. beaker. I n the temperature experiments a glass cooling coil encircled the anode, and the cell was contained in a water bath. A cooling coil also encircled the cathode. The anolyte was a solution of approximately 1.5 molar hydrochloric acid and varying concentrations of ferrous and ferric chlorides, the ratio between which was kept constant (equal equivalents = 3: 2 in mols) in order to keep the theore&l anode potential constant. For measuring the anode potential, a normal calomel electrode was used, connected by a rubber tube to a “search electrode,” or glass tube drawn out to a small diameter and bent a t right angles. This and the ruhber tube were filled with the s o l u t i o n about the calomel electrode, and the capillary tip was pressed closely against the anode. -4 potentiometer, accurate to about one or two millivolts, was used to measure the potentials. Potentials given are referred to the molal hydrogen electrode. No correction was made for liquid potentials between anolyte and calomel electrode solution. These corrections might be quite appreciable, but the observations are consistent with each other and the exact values of the potentials are unimportant for the purpose in hand. I n increasing the applied electromotive force across the cell it is essential that the rate of increase be regular. It was consequently increased by 0.1 volt every 3 min., and the readings of current and anode potential were taken near the end of the period. Temperatures averaged very near to 27” C. for most of the runs. I n the experiments on the effect of temperature, observations were made at 15”,22.5’, and 30’ C., and especial effort was made to prevent variations. DISCUSSION OF EXPERIMENTAL RESULTS SIGNIFICANCE OF THE SHAPEOF THE CURVESOBTAINEDWhen the currents flowing through the cell are plotted as ordinates against the anode potentials as abscissas, curves of the general type shown in Fig. 2 are obtained for moderate concentrations. Point A is the potential characteristic of a ferrous-ferric ion electrode for the ratio of concentrations used. At low concentrations it checked very well with the calculated value of -0.70 volt, assuming equal activity coefficients for F e + +and F e + + +and neglecting any contact potentials. At higher concentrations this point of intersection tended to be lower, as would be expected from the fact that the activity coefficient of Fe+’+ undoubtedly decreases more rapidly with increasing concentration than that of Fe+ L. When the applied electromotive force is increased after point A is reached, a sharp increase in current is observed which corresponds to the oxidation of F e + + to Fe+++, but a t rather small currents, the exact value varying with the concentration of ferrous chloride, the curve bends over rapidly (B) and remains perfectly horizontal, while the anode potential increases by several tenths of a volt. It again rises (D) when the potential corresponding to chlorine evolution a t that current density is closely approached. Even then bubbles of gaseous chlorine are not evolved, since the solution absorbs chlorine rapidly. The normal decompositionpotential curve for hydrochloric acid a t the same electrode is on the same diagram for comparison.
Vol. 15, No. 6
The flatness of the horizontal portion of the curve (B-D) is quite remarkable as long as steady conditions are maintained, although stirring or other disturbances cause it to rise sharply for a time and then return to normal. After due consideration of various possibilities, the following appears to be the only reasonable explanation for the shape of the observed curves. Between A and B enough ferrous ions are diffusing in to take care of all the current sent through the cell by the imposed voltage., As point B is approached, however, the curve begins to round off, probably owing to the fact that the diffusion of ferrous ions cannot quite keep up with their rate of oxidation, and the ratio between ferrous and ferric ion a t the electrode surface becomes so much lower than that in the solution that the anode potential begins to rise quite rapidly. By the time a point shortly beyond B is reached, the anode oxidation potential ha9 ceased to be the real controlling factor, and the amount of current flowing is determined solely by the rate a t which ferrous ions diffuse to the electrode surface and take up their additional charge. The rate of diffusion, and hence the amount of the current flowing, thenceforth remains constant, regardless of the applied voltage, over a wide range of anode potentials. The amount of current corresponding to the flat portion of the curve is therefore a direct and accurate measure of the rate of diffusion of ferrous ions to the anode, and, if the coiicentration and specific rate of diffusion of these ions is known, it is possible to calculate the effective thicknesss of the stationary film through which diffusion is taking place. On the outside of this stationary film the concentration of F e + + is substantially that of the solution as a whole, while at the electrode the concentration is substantially zero. When the point D is approached, the curve bends upward and gradually merges into the normal curve for chlorine evolution in the absence of a depolarizer. The rise in the curve before reaching the normal point for chlorine evolution may be due to any one of several causes, of which the most probable is that some chlorine is dissolving and diffusing away from the electrode until it meets s o m e ferrous ions. Some current is therefore consumed in this way, even before the voltage is reached a t which chlorine would be evolved a t atmospheric pressure. Even when the solid curve has entirely joined the normal chlorine-evolution curve, gaseous chlorine is not evolved as such, undoubted19 because it is very rapidly absorbed by the ferrous chloride solution-in other words, the sphere of 8 Actually, the region around the electrode may be divided into three layers. ( a ) an inner layer, where there is no convection, and a uniform concentration gradient which forces the F e + + t o diffuse in a t a definite rate, ( b ) an intermediate layer, where diffusion is more and more aided by convection, and the concentration gradient therefore gradually decreases; and (c) the main body of the solution, where convection currents are sufficient t o keep the concentration uniform throughout. The “effective thickness” of the stationary film, or diffusion layer, is defined as “the thickness of a perfectly stationary layer which would interpose the same resistance t o diffusion as the above-mentioned combination.” Physically i t is equal to the true stationary layer plus possibly one-third to one-half of the hazy intermediate layer in which slight convectioii aids diffusion
June, 1923
I N D U S T R I A L A N D ENGINEERING C H E M I S T R Y
the reaction has been changed from a two-dimensional surface to a three-dimensional region surrounding the anode, and the amount of current which can be taken care of without evolving gaseous chlorine is correspondingly greatly increased. If the foregoing reasoning is correct, several predictions may be made as to the effect of concentration, temperature, stirring, etc., on the position of the curve. For example, the height of the horizontal portion should be directly proportional to the concentration of ferrous chloride, and should increase very rapidly with stirring and less rapidly with increasing temperature. EFFZCT OF CONCENTRATIOIi-Fig. 3' shows the results obtained with five different concentrations of ferrous chloride varying from M / 2 to M/32. It will be noted that the flat portions of the curve are, within the limits of experimental error, directly proportional to the concentration, as was predicted.
605
a cross section of 1 sq. cm. if the concentration gradient were equal to unity c1 = concentration at outer boundary of the diffusion layer in equivalents per cc. cz = concentration a t the other boundary I = thickness of the layer in cm.
I n this case
dS
is measured dt
directly by the magnitude of
the current passing and c2 can be considered negligible, since the ions which diffuse in are almost immediately oxidized on this horizontal portion of the curve. Making these substitutions and solving for 1, Equation 1reduces to
where C = the molal concentration of ferrous chloride I = the current in amperes, on the flat portion of the depolarization curve obtained with the concentration C
The value of D for ferrous chloride is not given in the literaEFFECTOF TEMPER- ture, but that for the F e + + ions may be calculated from the ATURE-The influence mobility of the ions involved, by Nernst's formula: of temperature was investigated by experiD = - (2.361 X 273 u+v ments a t 15", 22.5", and 30" C., using a where U = mobility of Fe-- a t a given temperature V = mobility of C1- a t a given temperature solution M/12 in ferT = absolute temperaturc rous chloride, M/18 in ferric chloride, 3 M / 2 The mobilities U and V are found by: in hydrochloric acid. 1.036 x u x 10-13 It was difficult to obu = -9650 tain an entirely satisfactory curve :at other than room tenipera- where u = equivalent conductance of F e + + ture, on account of conv = equivalent conductance of C1vection currents, but This formula can only be used with exactness in very diby surrounding the cells by a large bath lute solutions. At the concentrations used the per cent the curves in Fig. 4 ionization is well below 100, but undissociated ferrous were obtained. Ap- chloride is undoubtedly diffusing in as well as the Fe++ ions. parently, the rate of diffusion would be about doubled .4s a n approximation, then, it is assumed that the diffusion for a n increase of 25 degrees. This compares well with constant of ferrous chloride is independent of the concentrathe observations of Springg on the solution velocity of tion or the degree of ionization. The movement of the F e + + marble in hydrochloric acid (a heterogeneous reaction where due to electrolysis is neglected, because practically all the rate of diffusion is the determining factor) that a n increase current is carried by Hfand C1- ions. On the basis of these approximations, D = 0.96 a t 27" C . This value is quite of 20 degrees doubles the rate of solution. EFFECT OF STIRRING-The difficulty of getting accurately possibly 10 per cent too high on account of these approximareproducible curves a t other than room temperature, and the tions. * By substituting the value of D calculated for the temoccasional failure even a t that temperature, was laid to the slight stirring induced by convection currents. I n support perature in question in Equation 2 above, the following reof this, the horizontal portion of the curve for a M / 3 2 solution sults were calculated: 2 of ferrous chloride was raised from 0.04 ampere to 0.20 Expt. Concn I in T,emp. Calcd ampere when vigorous agitation with a motor stirrer was NO. of F e + + Amps. C. D Cm. carried. on during the experiment. M CALCULATION OF THICIWESS OF DIFFUSIOK LAYER By employing the Nernst'O formula and making certain approximate assumptions, it is possible to calculate with a reasonable degree of accuracy the effective thickness of the diffusion layer under various conditions. The fundamental equation for the rate of diffusion is:
Effect of Concentration
10
Z.physik. Chem., 1 (18771, 209. "Theoretical Chemistry," 1916, pp. 153 and 621.
I165 64 81
Effect of Temperature
where dS = amount of substance transferred in time dt q = area through which diffusion occurs in sq. cm. (G6 in these experiments) D = diffusion constant of the substance; the number of equivalents per day which would diffuse through
E 1 ::
Effect of Stirring
1I 83 184 68
4
M --
8 M 16
M 32 M 12 M 12 M 12 M 32
0.355
27
0 96
0.0498
0.177
27
0.96
0 0499
0.081
27
0.96
0,0544
0 038
27
0 96
0.0581
0 104
22.5
0.86
0.0502
0 078
15
0.71
0.0559
0 119
30
0.99
0.0551
0.198
27
0.96
0.0112
It is gratifying to note that over the entire range of temperatures and concentrations used, the average deviation of the
* Note t h a t two equivalents of F e + +must diffuse in for each of oxidation a t the anode.
equivalent
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calculated thicknesses of the diffusion layers from the mean value of 0.533 n m . is oiily 5 per cent. This agreement is considered remarkable in view of the difficulty of controlling small cpvection currents and the approximations made in the calculations. It will be noted that by fairly vigorous stirring i t is possible to reduce the film thickness to about one-fifth of its value in a quiet solution. I n view of these facts, the explanation offered for the shape of the curves must be considered as established beyond much question, and it appears that the effective thickness of the stationary film through which diffusion must take place is about half a millimeter in a quiet, solution, though i t can be very greatly reduced by stirring.
APPLICATION OF RESULTS TO
ORGA4XIC. ELECTROCHEMISTRY
Once the foregoing facts are clearly established, the reason for the failure to obtain clean-cut depolarization curves in studying the chlorination of organic compounds becomes fairly obvious. I n organic electrochemistry thc molal concentration of the organic compound in the electrolyte is usually rather low, and the specific rate of diffusion is also generally low because of the high molecular weight. It is therefore difficult to secure clear evidence of depolarization except at very low current densities, even if the reaction rate at the electrode surface is sufficiently rapid. This reasoning does not, of course, apply to cases such as strong acetic acid solutions, etc., where the molal concentrations of the organic compound may be very high. I n order to indicate the magnitude of the current densitier involved, it should be noted that even in a M/4 ferrous chloride solution, the current density corresponding to the maximum 0 355 rate of diffusion in still solutions is only = 0.54 ampere 0.66 per square decimeter, which is far lower than what is generally considered commercially practicable. The great importance of speeding u p diffusion in most organic electro-
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CHEMISTRY
Vol. 15, No. G
cheniicnl processes therefore becomes obvious. As indicated, the factors which tend to increase the specific rateof diffusion are: (a)high concentrations, (b) low molecular weights, ( e ) rapid stirring, (d) high temperatures, (e) low viscosities. The use of spongy electrode surfaces does not appear promising in view of the relatively great thickness of the stationary diffusion layer. In many cases, however, the adoption of all these expedients to the maximum degree feasible in a particular case does not carry on the desired reaction with reasonable current efficiency a t current densities high enough to be commercially practicable. I n these cases an expedient which is frequently very helpful is the use of rapidly diffusing carrying agents, which in effect extend the zone of a reaction from a surface to a volume of solution surrounding the electrode. Such carrying agents are generally inorganic salts which form very active oxidation or reduction products at the electrode and then diffuse into the main body of the solution and react with the organic compound. Examples of materials successfully employed in such operations are salts of manganese, cerium, vanadium, and titanium, which can exist in two or more stages of oxidation. It should be pointed out, however, that the mere fact that the depolarization curve soon joins the normal curve for chlorine evolution, as in Fig. 1, does not mean that the desired reaction with the organic compound may not still be proceeding to a very large extent, even a t much higher current densities. I n some cases this may be accounted for by the formation of intermediate compounds-as, for example, hypochlorous acid-which diffuse away from the electrode and react with the organic compounds, but in many cases it appears to be primarily due to the increase in diffusion caused by the very effective disruption of the stationary film which results from the evolution of a few gas bubbles. It is therefore impossible to judge the probable success of organic electrolytic reaction by the amount of depolarization shown in curves such as that in Fig. 1.
Dr. Moore Joins Staff of The Dorr Company are vital links, and it is of these that Dr. Richard Bishop Moore, chief chemist and Moore will have charge. mineral technologist of the United States Bu, Dr. ,Moore’s work at Washington has inreau of Mines, has resigned his position and cluded general supervision of all the chemistry on June 1 will take charge of the Developwork of the Bureau of Mines, with direct ment Department of The Dorr Company, charge of the work in nonmetallics, ceramics, Engineers, with headquarters a t its New rare metals, helium, and some of the alloys. York office. He will also act as consulting ’ He built and operated the government raengineer in the many phases of the company’s dium plant a t Denver, and during the activities, where his wide experience and outGreat War was in charge of the construction standing professional reputation will be of and operation of three government helium great value to its clients. plants and of the field work on helium. The Dorr Company is to be congratulated His many other achievements are well known on this important addition to its growing staff to men of science the world over. and on the expansion which is ever bringing He was educated in England and was assoit into contact with a wider range of indusciated with Sir William Ramsay, under whose tries and industrial problems. Beginning in inspiration he decided to make chemistry his metallurgy, its specialization in the handling life work. From 1896 to 1904 he was instrucand treatment of finely divided solids susR. B. MOORE tor in chemistry a t the University of Missouri, pended in liquids has brought it into close and from 1904 t o 1911 professor of chemistry a t Butler College. contact with practically all the great producing industries, and In 1911 and 1912 he was associated with the Bureau of Soils has necessitated a continually broadening field of activity. In of the Department of Agriculture, making a special study of this work the search for new applications of the basic printhe fertilizer resources of the United States. In 1912 he joined ciples of Dorr equipment, the improvement of existing methods and the development of entirely new methods and processes, the Bureau of Mines where he has remained until now.
