ELECTROLYTIC EVOLUTION OF HYDROGEX A N D DEUTERIUM ox IRON
Sox-.. 1961
19-11
COMPARATIVE RATES OF THE ELECTROLYTIC EVOLUTION OF HYDROGEN AND DEUTERIUM ON IRON, TUNGSTEN AND PLATINUM BY J. O’M. BOCKRISAND D. F. A. KOCH John Harrison Laboratory of Chemistry, University of Pennsylvania, Philadelphia 4, Pennsylvania Received February 24, 1961
Methods previously described for the determination of the mechanism of hydrogen evolution and dissolution do not allow the slow electrochemical desorption step to be distinguished from that of proton transfer. The fact that theory indicates a ratio of (io)n,o+/(io)~,o+ characteristic of mechanism is used in this study. The exchange current density for hydrogen evolution has been determined in 0.5 M HCl dissolved in HzO and in 0.5 M DCl dissolved in D10 under conditions of high purity. The ratio of the exchange current densities is 4 for Fe, 8 for W and 3 for Pt. Tafel slopes are the same for both isotopes. The concentrations of the relevant entities present in D-containing solutions are calculated. Equations are derived from which (iO)oao+ can be obtained from the apparent exchange current density in D solution containing a few molecular per cent. of water. Relations are derived for the dependence of the se aration factor, S, on the CD/CE ratio in solution. Limiting values of S exist as CD/CH tends to zero and to infinity, in which l i s simply related to (i~)~,o+/(&)n,o+. Discussion of available values of S, and the exchange current density ratio, gives information on mechanisms following the rate-determining reaction. The theoretical values of exchange current density ratios arising from assumption of a given mechanism depend on the differences in the heat of adsorption of H and D on the metal. Two methods of estimating this are given. The evidence favors a choice of 0.2 kcal. mole-’ for all metals. The results are consistent with rate-controlling proton transfer to iron, electrochemical desorption from tungsten and atomic combination of platinum.
I. Introduction In recent years only two paths have been considered as probable (but cf. Horiuti’) for the hydrogen evolution reaction (h.e.r.) and the reverse hydrogen dissolution reaction (h.d.r.). They are
may clearly occur a t some other conditions (e.g,. of current density) on the given metal. A main difficulty in evaluating a mechanism by application of the results of Table I1 lies in the fact that distinction between (3& and (41)c demands 0 determinations. These often can be made in Discharge (D) alkaline s ~ l u t i o n ,but ~ difficulties are associated If + H + PO- ~- --+ MHadS A (“Catalvtic with their measurement in acid ~ o l u t i o n except ,~ Catalytic (C) path”) for the noble metals.6 Additional methods for 2MHA*, --+ Hz pvl distinction between (3& and (41), are hence desirable.‘ It has been suggested that the plot b4 + H + eoof log io decreases with increase of A H A d s , H for a Electroseries of metals if (41)c is the mechanism but inchemical (E) H + + M H A ~ ~eocreases if (30)cis effective.s An alternative method The behavior theoretically expected for some for distinction has been suggested by Gerischer specific mechanisms is given in Table I2 (with the and Mehl,g but the mechanism-indic ating section experimentally well supported assumption of a of the current density-time relation, which is symmetry factor of When the rate-determin- diagnostic at sufficiently low times, may be obing reaction is the second reaction in a consecutive scured by the rise time of the apparatus. (The series, the preceding reaction is assumed to be in method assumes, further, a negligible H concentraon the electrode a t the commencement of the virtual equilibrium except for mechanisms (41)c, tion cathodic current-time transient.) It may be (21)c, (11)a and (31)~;when the rate-determining step is the first one in a consecutive series, the suc- possible to distinguish bet’ween ( 3 0 ) ~and (411, ceeding is assumed not to be in equilibrium except by suitable analysis’O of galvsnostatic transients, for (ll)c, (3&, (21)aand (41)a. (Earlier calculations3 where the problem of sufficiently fast rise times is neglected mechanisms in which following fast re- less severe. In addition to the difficulty of the e determinaactions were in equilibrium; and distinguishing criteria which arise only if data on the little ex- tions, certain coefficients of Tables I and I1 are difficult to determine in many practical systems. amined h.d.r. are available.) (i) Stoichiometric Number ( v ) DeterminaInspection of Table I1 shows that unique identification of all mechanisms stated can be made in tions.-These depend upon the absence of reacsystems in which the experimental quantities of (3) J. O’M. Bockris and E. C. Potter, J . Electroehem. Soc., 99, 163 the table can be experimentally determined. The (1952). (4) M. A. V. Devanathan, J. O’M. Bockris and W . Mehl. J . Elecusefulness of the pressure coefficients becomes Chem., 1, 143 (1959/1960). apparent (Table 11, 3rd column). Column 4 of troanalyt. ( 5 ) A recent theoretical analysis10 of transient data shows the possiTable I1 has the significance that if the experi- bility of making determinations of coverage with H even on corroding mentally determined values of the coefficients there metals. (6) M. Breiter, H. Kammermaier and C . A. Knorr, 2. Elektrorhem. stated coincide with any unique values (Table I) (1956). for these coefficients, the mechanism is thereby 60,(7)37 (3o)c rate determined by discharge, with following fast elecdetermined. However, the unique values are trochemical isdesorption: (41)cis rate determined by the electrochemicharacteristic of a mechanism a t a given coverage; cal desorption with preceding fast discharge. (8) J. O’M. Bockris and B. E. Conway, J . Chem. Phys., a$, 532 if a unique value is not found corresponding to a certain mechanism and coverage, the mechanism (1967). (9) H. Gerischer and W. Mehl, 2. Elektrochem., 69, 1049 (1955).
1
+
+
+
+
(1) J. Horiuti, 2. phyaik. Chem., 16, 162 (1958). (2) J. O’M. Bockris and H. Mauser, Con. J . Chem., 57, 475 (1959).
(10)J. O’M. Bockris and H. Kits, J . Electrochem. Soc., 108, 676 (1901).
J. 0’11.BOCKRIS AND D. F. A. KOCH
1942
Vol. 65
TABLE I CRITERIAOF MECHANISM IN THE HYDROGEN EVOLUTION AND DISSOLUTION REACTIONS
TABLE rr MINIMUM EXPERIMEXTAL QUAXTITIES NEEDED TO IDENTIFY CERTAINMECHANISMS IN HYDROGEX EVOLUTION Cathodic Min. quantities needed for identification
Anodic Min. quantities needed for identification
v
a? with b In QHZ or v with e
” or v and 9 ZiGG
1 or . v with e
b7 and b In QH* or Y
a In Q H ~ ’ 3s
* a 3iYK-i
*
b In i’
cathodic cathodic 2,( b In z or anodic
-”-)
_
a In pa2
+_e
&i
” 3 In
and
Q H ~
e
QK?
31(
with either 3 In PHI
cathodi
4 0(&)anodic)
or e
--’7 . ’7 and e b In i’ I? In QK?
(&)cathodic
(a k ) a n o d i c
30( edi& ::)
~. -aq a In i’ b In p~~
a7
b In b
l o ( &)anodic 9 In QHZ
+0
b In i
_
Uniquely diagnostic quantities for reactlon mechanism
v
In i
~’q
Most diagnostic quantities if both cathodic a n d anodic d a t a available
2. a Y and e b In
(A)
anodic
QH%’
b 111 i
tions (e.g., due to adventitious entities which undergo reactions which compete with the reaction under examination), a condition difficult to achieve In acid solution, a t c.d.’s < lo-* amp. most metals dissolve a t low c.d.’s, making determinations impossible if the dissolution rate is comparable with ( i O ) ~ . (ii) .--Pressure sffects are difficult to make because it may not be feasible to obtain cathodic pressure coefficients at c.d.’s sufficiently low so that bubbles (at T ) H ~ * ~atm.) are not formed. In the anodic direction, difficulties associated with dissolution of the metal and passivation arise, particularly for those metals where the data is most needed. Determinations of mechanism in alkaline solutions are easier than those in acid solutions, because the shift of the reversible H2 potential to more negative regions decreases the tendency of the metal to dissolve. Stoichiometric number determinations then become practica1;l’ the double pulse galvanostatic method4 can be used to obtain 8, and pressure effects can be obtained. Measurements of the velocity of permeation of (11) N. Pentland. J. O’XL Bockris and E. Sheldon, J . Electroehem Soe., 104, 182 (1957).
H through metal foils12 distinguish reaction (lo)c from (3& and (41)c(but do not distinguish between (30), and (41)J. This method has the advantage that it is applicable a t potentials sufficiently cathodic to be outside the corrosion region. Were it practical to obtain foils thin enough so that the r.d.s. had become the passage from surface to bulk, then the dependence of permeation upon temperature would give the heat of activation for this process, whereupon an order of magnitude calculation of the rate constant for the process H-+ surface
would be obtainable, and this, together with the experimental permeation rate, would allow calculation of an order of magnitude value of e. In this paper, use is made of the fact that (iO)x/ (&)D can be shown theoretically to depend markedly upon the r.d.s. assumed and the experimental ratios compared with theoretical ones for various r.d.s.’s. 11. Experimental Methods Hbulk
(a) Apparatus.-The electrolysis cell was essentially as described.” The volume of H20 or DzO used per run (including washings) was 100 ml. and the working volume in the cathode compartment, 10 ml. The polarizing current (12) R. Thacker, O.N.R. Report Dec 1959.
Xov., 1961
ELECTROLYTIC EVOLUTIOX OF HYDROGEN A N D DEUTERIUM ox IRON
was supplied by a Dresden-Barnes Regulated Supply. Currents from 10-2 to 10-5 amp. were measured with a to 10-9 amp. on an electrometer. microameter and from loW6 Potential measurements were made to =k 1mv. (tube potentiometer). ( b ) Preparation of Cell and Solution.-The electrolysis cell was in contact with a 1:1 mixture of nitric-sulfuric acid for three hours after each run, and then was washed successively with many changes of distilled and conductance water beforch the next run. Conductance water of K 95y0 D substituted) was held in a flask a t 1 atm. pressure and passed in a stream of helium through the traps into the cell. Helium used was purified by passing it through hoopcalite, sodalime, copper on diatamaceous earth a t 400 , anhydrous CaSOc, and three traps containing charcoal a t liquid nitrogen temperatures. Hz and DZ were passed through a similar train, in which platinized asbestos was substituted for copper. (c) Preparation of Electrodes.-All electrodes were prepared by heciting a wire of the metal (0.05 cm. diam.) in Hz, D z or He and sealing into a glass bulbI3 which was broken in the cell immediately before the electrode was used. The electrodes were heated a t 800" for 15 minutes in a wire-wound silica tube which was jointed onto the glass bulb through a graded seal and, after heating, the electrodes were drawn into position in the bulb with a magnet. (Iron wire was joined to platinum and tungsten electrodes.) The gases, He, Hz and Dz, used in electrode preparation were recycled through a purification train using a pulsating mercury pump. Liquid air traps and gold foil decreased the possibility of contamination with mercury vapor. Spectroscopically pure iron wire was flame-welded to tungsten. The electrodes were electropolished in 1:3 phosphoric acid t o remove oxide near the weld. A glass sheath was sealed onto the tungsten and extended over the joint. The electrodes then were treated as described above; platinum 99.9570 \vas sealed to tungsten and then heated in H z or He. S o significant difference in parameters was observed for surfaces prepared with either gas. Tungsten electrodes were prepared by cleaning 99.9570 W wire with molten sodium nitrite and then sealing a glass sheath over a section of the wire to provide a metal glass seal. The oxide formed in this step was removed by a further cleaning with sodium nitrite and the electrodes were then thoroughly washed in conductivity water and dried with filter paper prior to the heating in hydrogen or deuterium as described for iron. The bulbs were sealed to tubes which fitted corresponding tubes in the head of the cathode compartment. They (five) were moved into solution when required. (d) Procedure.-Part of the HC1 or DC1 solution was introduced from the anode to the cathode compartment; pre-electrolysis was carried out on an electrode (0.2 area) of the metal concerned a t 3 ma. for 20 hours. Helium was bubbled through the anode and cathode compartments during pre-electrolysis and the gas was changed to hydrogen or deuterium 15 minutes prior to commencement of measurements. Solution from the cathode compartment was passed into Ihe reference electrode (platinized Pt) compartment and H2, or Dz bubbled through this. Electrode bulbs were broken in hydrogen or deuterium a t the top of the cathode compartment and introduced into solution with potential applied to prevent the electrode dissolving. The potential was read for a series of currents first with increasing c.d. in the case of P t and W and then with decreasing current density. For iron, the first Tafel curve was with decreas(13) J. 0'11,Bockris and B. E. Conway, J. Sci. Instr., 2 6 , 283
(1948).
1943
ing c.d. to minimize surface changes due to dissolution. All electrode potentials showed a negative drift with time but two complete traverses of the current potential curvep, taking 10 min., showed a drift of overpotential a t a given current density of less than 5 mv. In some instances, it greater drift was noted for platinum and when this occurrd only the first "up" curve was taken.
111. Results Departure from linearity of the Tafel curves for hydrogen and deuterium evolution in 0.5 N acid on iron occurred when oxide was present, or when the temperature at which the surface had been prepared mas raised over 800'. Parameters are in Table 111. Platinum electrodes prepared in helium or hydrogen showed a time-dependent overpotentinl and were irreproducible. The Tafel relations showed two slopes, one of about 0.04 a t low c.d.'s (< 10-z5 amp. and the other of about 0.13 at c.d.'s between loF2 and Reproducib!e values were obtained by anodic activation of the electrode a t amp. em.+ for 10 seconds (Table 111). (This increase in reproducibility obtained by anodic activation was earlier reported by Bockris, Ammar and Huqi4). The log i - 77 curves for tungsten shoned two slopes in both hydrogen and deuterium. The results in hydrogen are similar to those publishcd by Bockris, Ammar and Huq14 except that the lower slope now recorded begins at a slightly higher overpotential than that formerly observed The ( i o , ~ ) h values f were obtained by referenre to the reversible deuterium electrode. Consvaylj has given the potential difference between the normal reversible hydrogen and deuterium potentials as -0,009 v. after correcting for the liquid junction potential (Table IV). IV. Discussion (1) Effect of Water Content on the Evaluation of (a) Calculation of Species Present in Solutions.-The weight per cent. of H in the mizture solutions used in the present work1e 's 3, giving an atomic ratio (H to D) of 3/48.5. Using this value and the equilibrium constants (Kirchenbaum,17 Schwarzenbach'*) shown above together with a total acid concentration of 0.5 N it is p ssible to calculate the concentrations of the individual species by successive approximation. TI e concentrations obtained in this manner are shon n in Table V. Deu(b) Evaluation of (~o)D,o+from ( i O pin) ~ terium-containing Solution.-The measured value of io in the deuterium oxide solutions, (&,D)M cannot be directly compared with the ( i O ) ~ , o + measured in the aqueous solutions, because the measured exchange current density represents the net effect of discharge from D30+,HODl+, DOH?+, etc., whereas, to compare directly with ( i O ) ~the s~+, (iO)~,o+ value must be evaluated from ( 1 0 ~ ) h f . The dependence of io for a given ionic species upon the concentration of this species depends upon (14) J. O'hi. Bockris, I A Ammar and A K \f S Huq J Phvs Chem , 61, 879 (1957). (15) B. E. Conway, Proc. Roy. Soc. (London), A247, 400 (1958) (16) Determmed b y a mass spectrographic method (17) I Kirschenbaum, "Physical Properties and Analysis of Heavy Water " hIcGraw-Hi11 Book Co , New York, N. Y . , 1951, p 54. (18) G Schaarzenbach, 2. Electrochem, 44, 47 (1938)
J . 0’11, BOCKRIS AND D. F. A. KOCH
1941
1-01, 65
TABLE I11 TAFEL CONSTANTS AND CORROSION POTENTIAL IN HYDROGEN A N D DEUTERIUM I N 0.5 .V HCl F: b -log io corr. KO of Tafel lines No. of electrodes
Hydrogen
Den teriiini
0.133 f 0.004 5.18 f .IO 0.203 f .007 12 12
0.134 0.004 5.77 i .14 0 . 2 1 7 f .004 7 7
0.029 f 0.003 3.33 i .14
0.026 f 0.006 3.62 i .45
18 9
18 9
Hirher nlppe
0 112 i 0.009 6 :30 i . 2 3
Deuterium Lower slope Hixher slope
0.059 f 0 006 5.34 k .27
0.101 =k0.004 7.10 f .42
13 7
TABLEI V Fe, Pt
W (Lower) W (Higher)
Hydrogen
0.070 f 0.005 7.87 zt .31
( ~ o ) A ? o +A N D ( i 0 . p ) ~FOR
Fe Pt
-
Deuterium
No. of electrodes
(i0)HIO
Pt
DC1
Hydrogen
Lower slope
h -log io corr. KO.of Tsfel lines
OR
AND
inH/ (Z’oD)M
(~o,D)M
+
6 5 k 0 . 8 X 10-6 5.1 f 1.7 X 10-4 1.51 0.45X 10-8
2 . 2 f0.8 X 2.6 h O . 8 X 4.37zt 1.2 X 5.01 i 1.15 X 10-7 7.94 k 3 . 2 X
*
TABLE
W
10-6 3.0 f 1 1 10-4 2.0 f 0.9 10-9 3.4 f 1 0 10-8 6.3 i 2.80
v
CONCENTRATIONS OF H AND D SPECIES PRESENT Ix EXPERIMENTAL SOLUTIONS HOD = 5 37 m./1000 g. DsOf = 0.368 m./1000 g. H20 = 0.170 m./1000 g. HDzO+ = 0.108 m./1000 g. DzO == 43 9 1 m./1000 g. €&DO+= 0.0234 m./1000 g. HaOt = 0.0015 m./1000 g.
where CI
N , = ___
CifC,+Ck$
..
and for dilute solutions is the ionic fraction of the isotopic series, i. (It easily can be shown that there is no effect of the partial pressures of gases the rate determining step effective. If this is ariring from i,,ik, etc., on these equations.) (3& or (4dC(Table I), then It is necessary to estimate io values for HOD2+ and DOHz+, during H discharge and D discharge from each, respectively. Considering the discharge of H + from HODZ+, in termq of a potential Hence energy profile diagram,19 it is clear that the poten&, = K’aB+(1-8) tial energy profile for the final state for the reaction HODz+ eo-+H.hd, DzO is the same as that Or, if (20), is rate determining eo- + H A d . H20. The potential for H 3 0 + io = K‘ (2 ) energy curve of the initial state is changed only (1) and (2) refer to systems which contain ions by a shift of the solvation energies, but tkis is at concentrations sufficiently high to give d&/ compensated by an equal and opposite change’j d In a H + -+ 0, where 42-b is the potential of the in the zero point energies of the comparable ions, Gouy-Helmholtz boundary, and to avoid the at- e.g., H30+, HODz+. The bond undergoing rupture taining of limiting current densities by any species in HOD2+ eo- + HA^^ D 2 0 has the same for the current densities used in the measurements zero point energy as that in H30+. Hence, the (this requirement is satisfied in the systems dis- io value for HODz+ discharging to give H should cussed here, except for H30+ in the deuterium-con- be almost the same as that for H 3 0 + in a, simihr taining solutions; the contribution to io,^ of the discharge, except that for HOD2+ the proton haq latter ion hence will be neglected). probability of discharge of 1/8rdof that in H30+. Consider the discharge of a given isotopic ion, i, Hence in a solution in which it is the only discharging species. Then, for a “standard” concentration of this ion, csi, for which a “standard” value of io, is known
++
+
(io,i)ca,i =
kic6.i
exp[-8 In c.,J
+ +
+
(3)
Consider now the corresponding value of (io3i)cj, for a solution in which i has a concentration ci, and in which are other isotopic species of concentrations cj, Ck, etc. The standard reversible potentials for the reaction concerned being Vo,i, Vo,j, V 0 , k , etc., respectively.
(19) J. O’hl. Bockria. “Modern Aspects of Electrochornistry,” Vol. I, Rutterworths Scientific Publications, 19.54, p. 23 5 .
ELECTROLYTIC EVOLUTION O F HYDROGEN AND DEUTERIUM G N
Nov., 1961
1945
IRON
is large compared with the contributions made to io,^)^ by other species. Hence, the combination of discharged D, e.g., from HODz+, will be with D. Thus, the rate-determining reaction is identical with that for D from D30+, and therefore ( ~ O , D - H O D ~ + ) ~= . 2/3(i0,D-DDsO+)~a. Other relations are as above. For reactions in which the rate-determining reaction is (ZO),, the equation corresponding to (6) is Taking Cs,i as 0.5 M , the concentrations of the indicated species and the values of io,^)^ and ($H~O+ for Fe from Table IV, one obtains
which is not significantly different to the (&,D)M/ ( i o ) ~ratio s~+ given in Table IV so that the effect on entities other than D,O in the case of Fe is negligible. I n the case of tungsten the measured ratio is
lf01H3E = 6.33 (Table IV) (iO.D)M
Assuming a slow discharge mechanism as before we obtain (io)D;o+ =
3.10 X 10-8 amp. cm.-*
and hence
which is much higher than any ratio predicted theoretically in the following section and also appears anomalous when it is remembered that the separation factors on tungsten are not very different from those on iron.20 Correspondingly, without correction for the effect of H-containing ions, the value of ( ~ o ) H ~ o + / io,^)^ = 6.33 for tungsten leads to unlikely values for the difference in heats of adsorption of hydrogen and deuterium, if discharge is ratedetermining. It is worthwhile therefore to consider the possibility of a slow electrochemical desorption mechanism in this case. The effect of proton concentration on io,^)^ is here more complex than for simple discharge, since it is probable that H + discharges onto D.4ds rather than HAds from solutions containing D : H in the mole ratio 48.5:3. Consequently the rate of the H reaction would be that of H+
+ hIDAds + eo-
= HD
which will be expressed as ( i O ) ~ ~-o + D and would be in magnitude between (&)H&+ and io^)^. Assuming ( i O ) ~ ~-o +D is the mean of these two values (iO)H$O+-D
(13)
= (io,i)adVi'
(io.i)ai
where Ni is the ionic fraction of the species i.
Terms dependent upon concentrations of HzOD+ may be neglected since they will be negligibly small when squared. Assuming ( ~ o . H ~ o-+ H) = (+,H~O+ - D), and using the values of io,^)^ and ( z ~ ) H ~ oin + Table IV and concentration terms in Table V, equation 14 gives (iO)Da+
= 2.1
x
10-4
Assuming ( & ) H ~ O +- D for combination between H and D is the arithmetic mean of ( i o ) ~ ~-o + H and ( ~ o , D ) M Both corrections do not significantly alter the ratios for Pt. measured (~O,D)M(&)H,O+ (2) The Exchange Current Densities of Isotopic Ions and the Separation Factor.-The separation factor for H and D is defined by18 i
s=--=
(CH /CD) gas
i(H)
(a/cD)mIn
(2)wln
-'-
(15)
E icn)
where ci is the concentration of the given entity in the given phase (independent of the species in which it exists), and ii is the total current density of evolutions of the indicated species. Utilizing equat,ion 6 which applies when the Tafel slope is 2RT/F and 0 = 1/2 one has
and consequently
1
5 (&)HgO+-H For iron this gives Sp.
For systems in which the Tafel slope is RT/BF the atomic combination reaction may be rate determining. The values of (i&* required in the correction equation may be obtained as follows. In the deuterious solutions, the discharge of D30+ (20)
B. Topley and H. Eyring, J . Chem. Phys., 2, 217 (1934).
= 6.9
and for tungsten, assuming (&)H,O+-D
- -1 (io)"
2 (&)DsO+ S, = 7.87
(&)DaO+
When the Tafel slope is RT/ZF we have from equation 13
194G
J. 0'11. BOCKRIS AND D. F. A. KOCH
~701.65
+
A sharp increase in S for CH/(CH CD) < 0.4 is observed on the curve for platinum (Fig. 1) calculated by equation 17. The concentration terms in this equation are squared so that any error in the values of the equilibrium constants would be magnified. Condensing (16), is it clear that
SCH/CD+O
=
~o.H~o+
It can be seen from the values of ( i o ) ~ 3 ~ + / that S lies between 1.2-10.8, 1.3-12, and 0for iron, tungsten and platinum, respectively. O l I I I The exchange c.d's determined in nearly pure 0 0.2 0.4 0.6 0.8 1.o DzO and nearly pure H20are, therefore, consistent CH/(CH + CD). with the experimental data measured in mixtures Fig. 1.-Calculated separation factor as a function of of HzO and D20 containing excess H20.21-23 CH/CH CD. Fe values are based on a slow proton transfer mechanism and Pt values on a slow recombination mechaFrom (18) and (19), it can be seen that separanism. tion factor determinations in limitingly high R values give ( i J ~ , o +directly, ( i o ) ~ * obeing + known. The results of Post and H i ~ k e yfor ~ ~ ioH/ioD on mercury is 3. This is in fair agreement with the slow discharge mechanism. The separation factor, however, is also 3 and the calculations and assuming shown above indicate that for slow discharge in (i0)H3OC-D - 1 (i0)H30t-H These solutions of lorn D content, S = 3(iaH/iaD). calculations however assumed that the discharge (iO)DaO+ 2 (iO)D30t of protons and deuterons occurred by the same S P t = 3.5 both in pure and mixed solutions of The separation factors here have all been cal- mechanism H and D. This is not necessarily the case and it culated for a 0.5 ill acid solution using the concen- will now be shown that the reaction path may trations shown in Table V. In view of the ap- determine (ioH)/ioD in mixed solution. pearance of the concentration terms in the expres(a) Slow Discharge-Fast Electrochemica1.sion for S it is of interest to determine the effect In a pure solution the reaction steps for D? evcof CH/CD on X. Let cH/cn = R. As R varies, the distribution lution are D + + eo- + M = ? r l D ~ d ~ of H and-D among the various species varies hlD,d, + D + + eo- = DP + ?vi and hence Zil(R)/Zil(D)varies. Calculations have been carried out for ( c H / c D ) ~ ~(mole ~ ~ ratios) from and analogous steps mould apply to hydrogen 0.01 to 100, the latter corresponding to water con- evolution. taining 1% D. Knowing R, the corresponding In a solution containing an excess of H over D, C H ~ O ,CD,O and CHOD (moles 1.-') can be calculated; however, the deuterons would discharge more thence, using the ratios of the equilibrium con- rapidly onto an adsorbed hydrogen atom than onto stants described in IV, 1, the concentrations of the the bare metal (remembering that the electrovarious ions for a solution of given R can be cal- chemical step is faster than discharge). Conseculated. Utilizing those values in (16) and (17), quently the relevant value of io, would be that together with the (io,Jc0 values stated above, S for the reaction has been evaluated as a function of R. Results D + + MH,d, + eo- = HD + M are shown in Fig. 1. The calculations of the limiting values of S for and therefore variations in R have been carried out using the O D pure solu O D mixed saln exchange c.d.'s for Fe and Pt of this paper. However, the results are not sensitive to values of the exchange c.d., but upon the distribution of H and so that D among the various ionic species, and the relative exchange c.d.'s of H30+ and D30f. The calculations are influenced by the dependence of (io,,),, a result consistent with that on mercury. upon c i . Figure 1 has been calculated using (16) (b) Slow Discharge-Fast Catalytic.-In this and (17). The separation factor for Fe is little case if the discharge reaction is faster than a dependent upon R for CHICH C D > 0.3, in possible electrochemical step (the effect of heating which range most experimental determinations (21) H. A. Smith, C. 0. Thomas and J . C. Posey, J . Electrochem. have been made (a similar conclusion would be 106, 576 (1959). reached for W ) . The fair concordance of results Soc., (22) Y.Takahashi, S. Oka and h i . Oikawa, Bull. Chem. SOC.J a p a n , for S determined in solutions without attention S1, 220 (1958). being paid to CH/CD is therefore understandable. (23) B. Post and C. F. Hiskey, J . Am. Chem. SOC.,72, 4203 (1950). (io)D,Ot
(F)
+
>(?)
Xov., 1961
ELECTROLYTIC EVOLUTION OF HYDROGEX AND DEUTERIVM o s IROX
1947
4. Effect of Heat of Adsorption of H and D on Theoretical Values.-The values of the theoretical ratio to be expected can be calculated with significance depending on the chosen model only. Limits to the value of AAHA~, may be estimated theoretically, upon the basis of alternative extreme assumption concerning the degree of coverage. and Such estimates are orientive only. s=3 (i) If the interaction in the surface is neglected, an absolute upper limit, for the heat of adsorption as has been shown for iron. of H or D on the metal may be calculated. This is Consequently the determination of the separation given by8 factor a t undetermined CH/CD is not diagnostic of the r.d.s. but together with (iOx/ioD), which is diagnostic, may shorn both the slow step pure (20) solution and the reaction path. where Do is the heat of dissociation and X the 3. Numerical Values Consistent with the Ratios of Exchange c.d. for h.e.r. and d.e.r. as a Function electronegativity. Since X is the same for isoof Mechanism.--A crude approximation to a topes calculation of the ratio of io’s of isotopic species 1 A H M - H - A H M - D = - (DH,O - Dn2O) (21) was carried out by Bockris.19 Conway and Bock2 ris24 pointed out later that this ratio would depend =0.9 kcal. mole‘ significantly on the mechanism assumed and (ii) A more realistic model for the surface must detailed numerical calculations were carried out take into account interactions between the adby Conway.15 I n the present work, a A A H A d s sorbed atoms. It may be assumed that (where A A H A d , is the difference in heats of adAHe-e a(1 - 0) (22) sorption of H and D on the metal) value of 0.2 kcal. mo1e-l was assumed and, taking into account where A H s - 0 is the heat of adsorption when the the increase in the difference of heats of activation degree of coverage is 8. for the isotopic reaction due to a difference in Then the shapes of the Morse curves of the M-H and ill-D A H s a = AHsco [ l - 0) (23) molecules (ratio of Morse constants U M - H ~ M - D 1 .’.(AHe)a - (AHe)D = 2 (1 - 0)(DHZo - DD,O) (24) is calculated to be 1.017), (iO)HaO+/(iO)DaO+ mas found to be 6 for the slow discharge mechanism. In the case of the electrochemical desorption For all mechanisms of the h.e.r. the surface is mechanism, the same method of calculation as covered with either water or H. It appears that of ConwayZ4 was used except as follows: therefore that the appropriate value for e used (i) differences in the shapes of the Morse here is 0 + 1 in all cases. Thus (AH& - (AHO) curves for Hz and DZ were taken into account. + 0. Thus, the theoretical estimates allow a variation The dataz5show that a H 2 / a D 2 = 1.005 and taking this factor into account appreciably reduces the of AAH from 0.0 to 0.9. A decision as to the choice / ( i ~within ) ~ s ~these + limits may be made by reference theoretically expected value of ( i o ) ~ a ~ +(e.g., from 26 to 20 for AAH = 0.2 kcal. mole-’). t o the experimental work of Rozenthal, Dolin and (ii) The two cases in which H on the surface is Erschler,26who measured AAH by means of A.C. mobile or immobile are distinguished, since if H measurements on Pt. On the basis of a Langmuir and D on the electrode surface are mobile the value adsorption isotherm, a value of 0.2 kcal. mole-1 is of the partition function ratio is 2 and if immobile obtained from their results for A A H a d s . The use it is 1. H adsorbed from the gas phase in W is of a Langmuir adsorption isotherm would be conmobile.25 The introduction of adsorbed water sistent with the assumption of a fairly low (Le., on the surface will tend to reduce the mobility. < 10%) degree of coverage with H on Pt and this Conversely, the effective hI-H bond strength is consistent with the values measured tiy BreiteF will be weakened and mobility thus made more for smootli Pt. 5. Mechanistic Conclusions.-Comparison of the likely. theoretical expectation in Table 1-1 with the 9 summary of calculated ( i o ) ~ , ~ + / ( i o ) p , ~ for + an arbitrary value of A A H a d s (see below) is shown results for Pt is consistent with slow combination as a rate determining step. This conclusion is in Table VI’. consistent with AAH values of about 0.5 or less. TABLE VI It is widely agreed that the mechanism on Pt in THEORETICAL ( ~o)H,o+/(~o)D,o+FOR VARIOUSMODELS aqueous acid solutions ( b = 0.029) involves a r.d.s. AAHkds = 0 2 kcal. mole-’ of the combination reaction and it seems reasonable Slow discharge 6 therefore to allow the assumption of this mechSlow electrochemical immobile 7 anism, together with the observed value of ( i o ) ~ ~ o + j mobile 13 (iO)~~o+, to suggest a AAH of about 0.2 (cf. the
on iron already discussed suggests this) the rate ratio in pure solutions would apply to mixed solutions since the rate-determining step for both H and D would be discharge in both cases, Le.
(2)
SLOWcatalytic
3
(24) B. E. Conway and J. O‘M. Bockris, Can. J . Chem., 36, 1124
(1957). (25) 0. Beeck, Adaances in Catalysis, 2, 151 (1950).
(26) K. I. Rozenthal, P. I. D o h and B. V. Erschler, Acta Physicochzm. U R S S., 18, 74 (1940). (27) M . Breiter, “Symposium on Electrode Kinetics,” Philadelphia. May 1959.
1948
J. 0’11.BOCKRIS AND D. F. A. KOCH
TTol. 63
Russian value of 0.2). One would expect this under Contract A F 33(616)-5681, SA KO. 6, to he largely unchanged for the other metals. and discussion with Dr. It. Barton of the The AAH value expected from bond strength data Wright Air Base. They are grateful to Dr. M. (which refers efyectively to an empty surface) Enyo for theoretical discussion, to Mr. N. Nordin is about 0.5-0.8 kcal. mole-l for a number of metals, for help with the experimental work on Fe and Pt, and the reduction to the value of about 0.2 would to Mrs. V. Drazic and Mr. S. Srinivasan for carryarise from the effect of adsorbed water in lowering ing out a major portion of the experimental work on the adsorption heats. This effect would be ex- W, and to the Executive of the C.S.I.R.O. (Auspected to be about the same for all metals. tralia) for granting leave of absence to one of us The present results are not consistent with the (D.F.A.K.). view that the 1i.e.r. on noble metals measured Appendix under the conditions used here is controlled by Calculation of AHO,D* - A H o , ~ from * Potential diffusion of molecular H2 away from the electrode initial and final state surface.6 The rate of the diffusion of H2 and D2 Energy Diagrams.-The in aqueous solution would depend upon interaction potential energy curves for H and D are shown with the solvent, and not involve vibrational schematically in the following figure states in H2 and D2, so that no isotopic effects D n D\ H \, ,’ H would be expected (cf. Table VI). The experimental value of the ratio of the io’s for Fe of 4 is in fair agreement with slow discharge control if the AAH value is about 0.2, when ioH/& = 6. The values for Fe are inconsistent with the requirements of electrochemical discharge with mobile H, and are consistent only with the unlikely case of immobile H. The observed ratio for W of 8.3 is in reasonable agreement with the expectations of the electroIn order to calculate the relative rates for HI chemical rate control for AAH of about 0.2 (which and D2 evolution it is necessary to know the difindicates a ratio of 13 for a rate-determining elec- ferences in activation energies for these two trochemical mechanism and mobile H). processes (AHo? * - AHor-r*). The present results offer clear evidence against In the first instance, neglecting the zero point the tunnelling of protons as a rate-controlling energy differences of the initial state, the following mechanism as the h.e.r. Thus, the Tafel slope geometric relationships can be obtained from the expected from this mechanism would differ for the above figure. H and D evolutions,28 but no such difference is A”* = a - b - p Q observed on the three metals studied. AH~*=a-bb+P-P=a-b-(l-+)P The conclusion concerning the mechanism on Fe is :tt variance with that suggested earlier for where /3 is the symmetry factor and Q and P are the the mechanism on this metal from a consideration differences between the minima of the PE curves ~ when the of hydrogen and deuterium species for the final of the log io - A H A ~relation,* apparent trend of the log io values for a number of and initial states, respectively. Thus AHD* metals to decrease with increase of AHads was in- A“* = /3Q ((3 - l)Pand with /3 = l/2. terpreted to indicate the rate-determining electroAHD* - A“* = l/p(Q - P) chemical desorption for metals showing this behavior. W fell upon a section of the proposed Nom correcting for the zero point energy of the relation corresponding to relatively high A H a d s , ~ initial state the required activation energies are values and it may be that the position of certain AHOH* A”* - (z.p.e.)H of the metals in the intermediate part of the log AHoD* = AHD* - (z.p.e.)D iO-AHsds graph is better interpreted as an extension of the section of the log io-AH,ds correspond- AHo,a* - AHo.B* = l/?( Q - P ) 4- ( 8 . p . e . ) ~- (z.p.e.)D ing to the log & - A H a d s , ~relation. This value has been corrected for the difference Acknow:edgments.-The authors wish to ac- in slope of the H and D curves by the appropriate knowledge the support of the U. S. Air Force “a” constant of the Morse curve ns described in the paper. (28) B E. Conway, Can. J . Chem., 37, 178 (1959).
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