S. E. KHALAFALLA, A. M. SHAMS EL-DIN AND Y. A. EL-TANTAWY
1252
the system. This relaxation need not have a single cause, but will in general depend on a spectrum of relaxation frequencies (reciprocal relax_ationtimes). Thus the integral diffusion coefficient D(cl,ci; t) can be written b ( c ~ , c d= ) b , ( c ~ , c , )-
$(cI,c2;w)e-ot
do (28)
+
where is the (integral) diffusion relaxation function. Introducing (28) into (22) we find that
As (29) shows AL tells us little about the form of $ but does give us a measure of the mean relaxation time of the various processes affecting transient diffusion. Such information is particularly useful if the magnitude of AL or its variation with the temperature, concentration cl, etc., allows us to identify (or rule out) a given set of relaxation processes. It is now possible for the steady-state of a system to depend on the initial concentration of the diffusing species. Such, for example, is the behavior of a system possessing the diffusion coefficient
Vol. 63
which is a functional of c and t and f(r,t) is an arbitrary function of r and t. From (32) it is clear that the steady-state integral (or differential) diffusion coefficient will in general depend on the initial concentration as well as the history of the system previous to the attainment of its steady-state. It would be of some interest to determine whether the steady-state flux in instances of “non-Fickian” diffusion (say in polymer vapor systems) does indeed depend on the initial concentration of vapor in the membrane. Until further experimental data are available we shall not classify the various steadystate memory effects. We have so far not discussed frame of reference corrections. I n the simplest case where we need only correct for swelling of the membrane the corrections in the time lag, etc., can be carried out as indicated by Barrer and F e r g u ~ o n . ~More generally for diffusion into a deformable medium the diffusion equations written in this paper apply strictly only in a Lagrangian frame of reference. To transcribe the results for a fixed Euleriaii reference frame a general procedure recently used in a different connection by Simmons and Dorng should be applied. (9) J. Simmons and J. E. Dorn, J . A p p l . Phus., 29, 1308 (1958).
STUDIES ON THE ANODIC AND CATHODIC POLARIZATION OF AMALGAMS. PART 111. PASSIVATION OF ZINC AMALGAM IN ALKALlNE SOLUTIONS BYS, E. KHALAFALLA, A. M. SHAMSEL-DINA N D Y. A. EL-TANTAWY Contribution from the Chemistry Department, Faculty of Science, University of Cairo, Egypt ( U.A.R.) Received December 16, 19.58
Anodic polarization of zinc amalgam at constant applied current is investigated in 0.1 M sodium h droxide solution and found to exhibit one step corresponding to the formation of zinc oxide. The potential of this step cianges with the mole fraction of zinc in the amalgam. The mercuric oxide step disappears even with the smallest concentrations of zinc. The quantit of electricity needed t o assivate the amalgam increases with increase of the zinc content and depends on the value o f t h e polarizing current. ?he process of passivation is found t o be essentially diffusion controlled and the diffusing species is proved to be the hydroxyl ion through the hydroxide phase.
The study of the anodic behavior of amalgams has been the subject of a moderate number of articlesl-10 both from the theoretical and the analytical points of view. I n these researches the amalgams were studied in acid or neutral solutions in which the amalgamated metals dissolve as simple ions. The study of the anodic characteristics of (1) J. Heyrovsky and N. Kalousek, CotE. Czech. Chem. Commun., 11, 464 (1939). (2) J . J. Lingane, J . A m . Chem. Soc., 61,779 (1939). (3) M.V. Stackelberg and H. V. Freyhold, Z. EEebtrochem., 46, 120 (1940). (4) J. Heyrovsky and J. Forjet, Z . physib. Chem., 198, 77 (1943). (5) G. Reboul and F. Bon, Compt. rend., 124, 1263 (1947). (6) N. H.Burman and W. C. Cooper, J. A n . Chem. Sac., 78, 5667 11960). (7) A. Hickling and J. Maxwell, Z’rans. Faraday SOC.,61, 385 (1955). (8) A. Hickling, J. Maxwell and J. V. Shennan, Anal. Chem. Acta, 14, 287 (1956). (9) K.W. Gardiner and L. B. Rogers, Anal. Chem., 26, 1393 (1953). (10) J. W.Ross, R. D. DeMars and I . Shain, %bid.,28, 1768 (1956).
amalgams in solutions in which passivity can be established readily has attracted practically no attention. The object of this series is to fill this gap in view of understanding the mechanism by which metals can passivate. The zinc amalgam is first chosen in view of the ease by which it is prepared in a pure state and also because there are enough thermodynamical data for this metal to enable the interpretation of the results obtained. Experimental The electrical circuit used in obtaining the anodic potential-time curves under conditions of constant current was described in Part 1.11 The electrolytic cell has essentially the same features described before except that the anode cup was 1.806 cm.2 in area and was provided with a sealed-in platinum contact. The cathode compartment was situated over the anode and fitted with a sintered lass disc to prevent contamination with the anolyte. Pure iydrogen was used in deaerating the solution and was introduced (11) A. M. Shams El-Din, S. E. Khalafalla and Y.A. El-Tantawy, THISJOURNAL, 62, 1307 (1958).
August, 1959
PASSIVATION OF ZINC AMALGAM IN ALKALINESOLUTIONS
through a medium porosity sintered glass disc. The zinc amalgam was prepared electrolytically from a bath which was 2 M in zinc sulfate and 1 N in sulfuric acid. Thus when preparing any of the amalgam anodes studied, 1 ml. of redistilled mercury was introduced into the cup by means of a graduated medical syringe. The proper amount of the zinc sulfate solution was introduced mto the cup and electrolysis was conducted under a fixed current of 250 ma./ electrode. Electrolysis was continued with occasional stirring until all the zinc content of the solution was deposited. This was known by a sudden brisk evolution of hydrogen from the electrode surface; electrolysis was, however, allowed to proceed for a further 15 minute time with vigorous stirring. To ascertain t,he cornpletc depletion of zinc from its solution, a spot test for zinc12 utilizing 8-hydroxyquinaldine in methylated spirit was used. The amalgam was then washed thoroughly with conductivity water for several times and the wash water was drained off by a special pipet and then by small strips of filter paper. Each experiment was carried on a new electrode and a fresh solution. When performing a n anodic experiment, the amalgam electrode, prepared as described above, was introduced in the electrolytic cell containing the deaerated sodium hydroxide solution. In order to reduce any probable oxide on the surface of the electrode, it was subjected to a precathodization period of 30 minutes at a current of 1 ma./electrode. The polarizing current next was reduced to the value a t which the anodic polarization was t o he conducted and then reversed to start the experiment. The potential of the amalgam anode now was followed as function of time. All measurements were carried out in an air thermostat adjusted a t 25 f 0.1’.
Results and Discussion The variation of the amalgam anodic potential with time is shown in Fig. 1 for various compositions of zinc amalgam ranging from 0.1 to 5% and at different currents ranging from 200-500 Fa. From these results, it is seen readily that when forcing the amalgam electrode from the potential of hydrogen (and sodium) deposition to the oxygen evolution potential, only two steps are noticed. The first step observed at the foot of the curve is ascribed by analogy to pure mercuryll to the discharge of the sodium that was previously reduced during the precathodization period. The quantities of electricity consumed in the discharge process were very reproducible and depended on the concentration of zinc in the amalgam. For zinc amalgam electrodes of compositions 0.1, 1.0, 2.3 and 5%, the quantities of electricity consumed in the discharge of sodium from the amalgam were 1408, 1024, 863, 708 mcoulomb, respectively. Comparison of these quantities of electricity with those consumed in its formation (1800 mcoulomb) reveals that the efficiency of reduction of sodium from 0.1 N sodium hydroxide solution is considerably less than loo%, being 78, 57, 48 and 39% for the 0.1, 1, 2.3 and 5% zinc amalgams, respectively. Thus the higher the zinc content of the amalgam, the lower is the efficiency of formation of sodium amalgam. The reason for this may be understood from a consideration of the hydrogen overpotential on both zinc and mercury. It is easier for hydrogen to evolve on zinc than on mercury cathodes. When dealing with a zinc amalgam cathode, the current will distribute itself between the deposition of zinc and mercury. When the zinc content of the amalgam is increased, the ratio of evolved hydrogen to electrodeposited sodium will increase with the result of a decrease in the efficieiicy of the sodium (12) I. I. M. El-Beih and M.A. Abou E l Naga, dual. Ckem. Aetu, 17, 397 (1957).
0
60
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180 0 60 120 180 Time (min.). Fig. 1.-Anodic polarization of zinc amalgam in 0.1 N sodium hydroxide solution: (A) 0.1% zinc amalgam, 1200, I1 300, 111 400 and IV 500 pa./electrode; (B) 1% zinc amalgam, I 200, I1 300, I11 400 and IV 500 pa./electrode; (C) 2.3% zinc amalgam, I 200, I1 250, I11 300 and IV 500 pa./ electrode; D) 5% zinc amalgam, 1200, I1 300, I11 400 and I V 500 pa.jelectrode. 120
deposition. In the calc,ulatioii of the efficiency of electro-reduction of sodium ions from solution, it was assumed that the discharge process is purely electrochemical in nature and that the chemical dissolution does not participate to any major extent in the discharge process. The second step in the anodic potential-time curves of Fig. 1 is of some interest. The potential of this step was found to be constant for one and the same amalgam a t different current densities but differed in the different amalgams studied. Table I gives a comparison between the potential of this step and the equilibrium potential of the system Zn/Zn(OH)z a t the corresponding pH value after being corrected for the activity of zinc in the amalgam. TABLE I %
of Zn in the amalgam
0.1 1.o 2.3 5.0
Startinz potentid of 2nd step
Eouilibriuni pdtential of
Zn/Zn(OH)z system
(V.)
(V.1
1.10 1.14 1.15 1.15
1.113 1.142 1.152 1.161
The correction for the activity of zinc in the amalgam was made by applying the Nernst equation and assuming that the activity of zinc is equal to its mole fraction in the amalgam. The very close agreement between the values of potentials obtained from polarization curves and those calculated from thermodynanical data,13 leaves no doubt that this step in the polarization curves correspond to the formation of zinc hydroxide on the surface of the electrode. The quantities of electricity consumed in the second step were found to depend on both the zinc concentration in the amalgam and on the polarizing current imposed. Figure 2 represents the mode of dependence of the quantity of electricity required for passivation on the concentration of the amalgam, For the same polarizing current, the (13) W. N. Latimer, “The Oxidation States of the Elements and their Potentials in Ayiieous Solutions,” Prentice-Hall Ino.. New York, N. Y., 1953, p. 169.
1254 1600
S. E. KHALAFALLA, A. M. SHAMS EL-DINAND Y. A. EL-TANTAWY
I;li
I:
1400 1200
+
1000 800
h
2 600
v
y*
400
2 8 i;
200
a
2
1
3
4
5
Zn, %. Fig. 2.-Quantity of electricity for passivation as a function of the yo of zinc in the amalgam for various olarizing currents: I, 200; 11, 300; 111, 400;IV,500 pa.$lectrode.
1.2
0.8 0.4
3
0.0
4
-0.4
Vol,. 63
-0.8
4 r&
Fig. 4.-Anodic polarization of 1%zinc amalgam in: I, 0.04; 11, 0.05; 111, 0.06; IV, 0.08; V, 0.09; VI, 0.1 N sodium hydroxide solutions a t the current density of 300 pa. /electrode.
0
200
1/ d O H 400
-. 600
800
7 I. d
I
I
2.4 2.5 2.6 2.7 log i (pa.). Fig. 3.-Log T os. log i plot for the passivation of zinc amalgam in 0.1 N sodium hydroxide: % of zinc: I, 5; 11, 2.3; 111, 1; JV,0.1. 2.3
quantity of electricity needed for passivating the electrode increases with increase of the zinc content of the amalgam and also that with low currents, larger quantities of electricity are required to passivate the electrode than with higher currents. After the completion of the zinc hydroxide step, the potential of the electrode changed directly t o oxygen evolution value. The step corresponding to the oxidation of mercury of the amalgam was completely deleted; a zinc concentration as low failed to as O . O l ~ o (mole fraction 3.06 X show any sign for the mercuric hydroxide step. Thus it appears that the presence of zinc impurities changes the electrochemical behavior of the amalgam from that of pure mercury to that of pure zinc electrode. The relation between the polarizing current i and the time taken by the amalgam to acquire passivity T is more quantitatively elucidated from a consideration of the log i-log curves in Fig. 3. For amalgams varying in composition between 1 and 5% in zinc, the log i-log r plots are parallel straight lines with an average slope of -2. This suggests that the relation between the polarizing
1000 -
h
4 X Y
1.14
500 0
1.20
0.02
1.30
0.04
1.12
1.34 1.36
1.38
0.06
0.08
k E
-J
aOH-.
Fig. 5.-Variation of the quantity with: I, the reciprocal of the square of hydroxyl ion activity; 11, the reciprocal of the square root of zinc ion activity; 111, hydroxyl ion activity.
current and the passivation time is of the form i ~ ' / a = constant. I n the first part of this series we have drawn attention to the similarity between the above observation and the results obtained from the equations of electrolysis at constant
PASSIVATION OF ZINC AMALGAM IN ALKALINE SOLUTIONS
August, 1959
current14 where the supply of reducible material is controlled by diffusion to the electrode surface; the transition time in these equations is replaced by the passivation time. This proves conclusively that the process of passivation of the zinc amalgam in sodium hydroxide solutions is diffusion conbrolled. It becomes necessary to determine the diffusing species which brings about passivation. There are three possibilities for a diffusion process to occur in the solution phase: (1) diffusion of the OH ions from the bulk of the solution to the solutionhydroxide interface; (2) diffusion of zinc ions through the hydroxide phase to the zinc hydroxidesolution interface; and (3) diffusion of hydroxyl ions through the hydroxide layer to the hydroxideamalgam interface. The diffusion of hydroxyl ions from the bulk of the solution to the solution-hydroxide interface is ruled out since the solution isrelatively concentrated in these ions and they can reach the interface mostly by migration rather than by diffusion. If the zinc ions were the diffusing species through the oxide film according to the second possibility then Sand's equation for electrolysis under conditions of constant flux, could be written as +/z
nFD'/zn'/s E
(ab
- ad
where (ab - ai) represents the activity (concentration) gradient causing diffusion, Ub being the initial activity where diffusion starts, ai the boundary activity where diffusion terminates and D is the diffusion coefficient of the diffusing species. To test this possibility we used the same amalgam concentration (1%)in solutions of different normalities in sodium hydroxide. The anode potentialtime curves obtained are shown in Fig. 4 in different concentrations of sodium hydroxide using the same current density of 300 pamp. throughout. It is evident' that a b is here a constant representing the activity of zinc ions in the surface of the amalgam and ut represents the zinc ion activity in the hydroxide-solution interface and could be replaced by X / U ~ O H - where S is the solubility (activity) product of Zn(OH)z and UOH- is the activity of OH ions. The plot of ir*/zagainst l / a 2 0 ~did - not give a straight line as shown in curve I, Fig. 5. This eliminates the possibility of the zinc ions to be the diffusing species through the oxide. If the hydroxyl ions were the diffusing species through the hydroxide layer, then a b in Sands equation will represent the bulk activity of OH- and uf could be set equal to (S/uzn++)'/z. The plot (14) P. Delahay, "New Instrumental Methods in Electrochemistry," Interscience Publishers, Inc., New Yolk, N. Y.,1954, p. 184.
1255
of the product ir'lt for the different amalgams against the reciprocal of the square root of the zinc ion activity gave the straight line I1 showii in Fig. 5. The slope of this line is expected t o be - 1/2(nFD1/2~'/2SI/zX and should make an intercept with the ordinate of '/2(nFD'/2r1/2 X 0.0766 X where the factor is used t o convert activities into moles per ~ m and . ~0.766 is taken as the activity coefficient of OH- in 0.1 M sodium hydroxide solutions. The slope divided by the intercept should give the value of S'/z/0.0766 enabling the determination of the solubility (activity) product of zinc hydroxide. From the parameters of this line, the activity product is calculated to be 1.5 X 1O-l' which compares with satisfaction The to the value 4.5 X 10-17previouslyreported. uncertainties in the data used for the plot of this line may be due to the fact that the zinc ion activities were calculated from the measured potentials where every 0.03 volt represents a tenfold change in the zinc ion activity. If instead of using different amalgam concentrations, we used the same amalgam with different concentrations of sodium hydroxide, then Sand's equation will assume the form i#/a
=
nFD'/rn '/laon. 2
& - nFD1/i?r'/z 2 a.w+%
The change in the product ir'12 with UOH- is linear as shown in line I11 Fig. 5, and proves the pretext that OH- is the diffusing species through the oxide layer. The ratio of the intercept to the slope of this line gives us -S'/z/aZn++'/2. Data for this line lead to the valde 1.01 X lo-" for the activity product of zinc hydroxide. The possibility of the hydroxyl ions to be the diffusing species through the oxide film was qualitatively presented in Part Ill of this series. Thus for the passivation of pure mercury in sodium hydroxide solution, it was observed experimentally that the passivating oxide film grows from the inside rather than from the outside, In part (11),16 which dealt with pure mercury in ammonium hydroxide solution the above argument was further substantiated by calculating the diffusion coefficient of the species undergoing diffusion and comparing it with the available data for the diffusion coefficients of metal atoms or ions through their oxides, where it was found to deviate considerably. The above arguments show that the hydroxyl ion is the diffusing species during the process of passivation and not the metallic atoms or ions as was believed before. ( I n ) Reference 13, p. 168. (16) T H I 0 JOURNAI, 63, 1224 (1959).
