I. R. BELLOBONO AND F. MAZZA
2112
Spontaneous Dissolution of Metals in Aqueous Electrolytes.
I. Kinetic
Isotope Effects in the Reaction of Iron with Hydrochloric Acid Solutions in Protium and in Deuterium Oxide by I. R. Bellobono* and F. Mazza Istituto d i Chimica Fisica dell' Universitd e Istituto di Elettrochimka e Metallurgia dell' Universita, 90156 Milan, Italy (Received December 2, 1070) Publication costs borne completely by The Journal of Physical Chemistry
First-order rate coefficients for hydrogen ion disappearance during the dissolution of pure polycrystalline iron at temperatures from 18 to 65" were measured in HzO and in DzO solutions containing 10+ to 1 M HCI or DCl, at constant ionic strength (1.0 M ) . Kinetic coefficients showed an appreciable dependence on pH [(7.163) x 10-6 sec-l at 25", for 1to lo-* 144 HCl, respectively]. Experimental activation energies resulted: 11.3 kcal/g mol (in HzO) and 13.1 kcal/g mol (in DzO). The ratios of rate coefficients (in HzO and DzO) varied accordingly from about 3 at 18" to about 2 at 65". Rates of dissolution in HzO were employed to evaluate corrosion current densities as a function of hydrogen ion activity in the range 0-3.5 pH. Their values were favorably compared with those predicted using a model which considers the reaction of a hydroxide film, formed at the metal-electrolyte interface, with hydrogen ions, as the rate-determining step for the dissolution process. The good agreement between calculated and experimental isotope effects constitutes another argument in favor of this reaction being responsible for the rate of dissolution.
The reaction by which metals evolve hydrogen from aqueous electrolyte solutions is a multistep process. For acid solutions, there is a general agreement1,2concerning the first steps (discharge of hydrated proton and hydrogen adsorption on the metal surface)
11 +Ifn+ e-
+ ne-
+ Has+-+ H(ads)
(1) (2)
but considerable divergences of opinion exist as to step which leads to the formation of hydrogen molecules
+ H(ads) H(ads) + Has+ + eH(ads)
Hdg)
(34
+Hdg)
(3b)
--t
A criterion has been formulated by Bass2 for the stability of metals in aqueous solutions, which implies the conservation of energy when an electron tunnels from the metal to a hydrogen ion adjacent to the metal surface, and reaction 2 determines the overall rate of hydrogen evolution. More recently Pyle and Robertsa have suggested that hydrogen molecules may be directly formed at a metal-electrolyte interface, by the reaction eaq-
4 eaQ- +Hdg)
+ 20H-
(4) [rate constant k4 = (0.45-0.55) X 1O1O M-' sec-' at 20-23" and p H 10.9-13.3435],which has been showne to proceed without the intermediate formation of hydrogen atoms. For metals, which form hydroxides of low solubility, it has been proposed that hydroxyl ions produced by this reaction are adsorbed at the metal surface The Journal of Physical Chemistry, Vol. 76, Yo. 14, I071
and react with formation of a hydroxide film; the dissolution of this latter by hydrogen ions represents the rate-determining step for the whole process. The formation of atomic hydrogen, however, is not entirely prevented. The competition between direct production of molecular hydrogen and the intermediate formation of hydrogen atoms depends, following this scheme, on the concentration of solvated electrons and hydrogen ions, as demanded by reactions 4-6 eas
- + H2O-H
+ OH-
(5)
(rate constant k6 = 16 M-1 sec-I a t p H 8.3-9.0 and 250)' eas-
+ H30+ -+-H + + H2O
(6)
[rate constant ks = (2.1-2.3) X 1Olo A4-I sec-' at 20-23" and p H 2.1-4.761s]. Calculations of the rates of spontaneous dissolution of iron in hydrochloric acid made on the basis of the (1) J. O'M. Bockris, "Modern Aspects of Electrochemistry," J. O'M. Bockris and B. E. Conway, Ed., Vol. I, Butterworths, London, 1954,Chapter IV. (2) L.Bass, Proc. Roy. Soc., Ser. A , 277, 129 (1964). (3) T.Pyle and C. Roberts, J . Electrochem. Soc., 115, 247 (1968). (4) S. Gordon, E.J. Hart, M. 9.Matheson, J. Rabani, and J. K. Thomas, Discuss. Faraday Soc., 36, 193 (1963). (5) M.€3. Matheson and J. Rabani, J . Phys. Chem., 69, 1324 (1965). (6) L.M. Dorfman and I. A. Taub, J . Amer. Chem. Soc., 85, 2370 (1963); cf. J. H.Baxendale, E. .M.Fielden, and J. P. Keene, Proc. Roy. Soc., Ser. A , 286, 320 (1965). (7) E.J. Hart, S. Gordon, and E. M. Fielden, J . Phys. Chem., 70, 150 (1966). (8) J. P. Keene, Rad&. Res., 22, 1 (1964).
SPONTANEOUS DISSOLUTION OF METALS IN AQUEOUS ELECTROLYTES above model3 showed good agreement with observed This model substantially parallels that proposed by Bockris, Drazic, and Despicg on the anodic dissolution of iron
rates.
+ OH- +FeOH(ads) + eFeOH(ads) FeOH+ + e-
Fe
__
-3
FeOH+
Fez+
+ OH-
(7)
(8) (9)
with the difference that in the Bockris model reaction 8 is considered to be rate determining. Conway and RlacKinnonlO have shown many thermodynamic and kinetic difficulties which arise in most cases of metal dissolution, when hydrated electrons are supposed to be the direct precursors of molecular hydrogen evolved. Notwithstanding that the role of solvated electrons at the metal-electrolyte interface may be seriously questioned, the model of the hydroxide film adsorbed on the metal surface, as representing the slow step of the dissolution reaction, deserves adequate testing. I n order to investigate further the experimental aspects of this problem and their interpretation, a study has been undertaken of the kinetics of dissolution in acid solution of metals that form hydroxides of low7 solubility in water. The present paper deals with kinetic isotope effects in the dissolution of pure polycrystalline iron in acid solutions of ionic strength maintained practically constant during each experiment: in these conditions the metal was dissolved at its corrosion potential. Kinetic measurements of this kind had been already effected by Podesth and Arvla'l only in ordinary mater. A technique similar to that described by these authors was employed both in protium and in deuterium oxide solutions.
Experimental Section Materials. Triply distilled water, free from oxygen and carbon dioxide, as well as from any organic contaminant, was used throughout. Deuterium oxide and concentrated [2H]hydrochloric acid in deuterium oxide were supplied by Merck: minimum isotopic purities were 99.7 and 99.5%, respectively (ir and nmr spectra). Solutions, containing 0.001-1 14 HCl (or DC1) in protium (or deuterium) oxide were prepared in a nitrogen-filled glove box. The ionic strength of these solutions was corrected (when necessary) by addition of KCI, to the same final value (1.0 A I ) in all experiments. Iron foil (99.998%) was an Alfa-Inorganics product. It was degreased with boiling chloroform, washed first with ethyl alcohol, then repeatedly with triply distilled mater, and finally dipped into a solution having the same composition as that to be used in the kinetic runs. Glassware and the electrode cell were heated at 220" for several hours, before preparation of D20solutions. paH Measurements. A Radiometer pH meter, Type T T T l C , was used with glass and saturated calomel electrodes. By means of a scale expander, Type pHA 630
2113
TA, pH values could be read directly to two places of decimals. A jacketed electrode cell of about 120 om3 was used, kept at a constant temperature of =k0.lo by circulation of thermost ated liquid. A polyt etr afluoroethylene cover was placed on top, to hold the electrodes. The iron foil, conveniently folded, was completely immersed in the solution, suspended by a glass hook. A tube, with sintered glass at the end, was used to agitate the solution with nitrogen. The inert gas was previously saturated with vapor by bubbling it through a solution of the same composition and temperature as that employed in the kinetic experiment. The saturated calomel electrode was placed in a glass sleeve ending in a U-shaped capillary tip. I n each experiment, the sleeve was filled with the solution used for the kinetic measurements, thus preventing any diffusion of chloride ion from the reference electrode to the bulk of the solution. For measurements in DzO solutions the reference electrode was filled with a saturated KC1 solution in DzO and the experimentally determined value of ApH (e.q., 0.405 a t 25") was added to pH meter readings in order to obtain pa^ values (on a molarity scale), following the recommended procedure.l2,l3 The ApH values varied slightly with temperature. l4 The glass electrode was conveniently calibrated in the range of pH and temperature at which experiments were run. Kinetics. All kinetic operations mere carried on inside a glove box, with careful air exclusion. The PUH change of solutions during each run was never greater than 0.3 units and the surface of the metal was not appreciably altered. Experimental results were obtained at temperatures between 18 to 65". An example of some individual runs in deuterium oxide solutions is shown in Figure 1, where the pa^ is plotted as a function of time. Each run was repeated an average of five times. Linear dependence of paH (or ~ U D on ) time was always observed, within the limits of experimental errors, if the range of ~ U (or H ~ U D )variations was sufficiently narrow. Rate coefficients have been calculated on the basis of a firstorder rate equation. The ratio (0.10 cm) between the volume of electrolyte (usually 50 ml) and the apparent surface of the iron foil was always the same in all experiments. Results and Discussion The rate of dissolution of iron can be calculated either by the kinetic parameters related to the dissolution (9) J. O'M. Bockris, D. Drazic, and A. R. Despic, Electrochim. Acta, 4, 325 (1961). (10) B. E. Conway and D. J. MacKinnon, (1970).
J. Phys. Chem., 74, 3663
(11) J. J. Podestb and A. J . Arvia, Electrochim. Acta, 10, 159 (1965). (12) R. Gary, R. G. Bates, and R. A. Robinson, J. Phgs. Chem., 68, 3806 (1964). (13) P. K. Glasoe and F. A . Long, ibid., 64, 188 (1960). (14) I. R. Bellobono and P. Beltrame, J . Chem. Soc. B, 620 (1969).
The Journal of Physical Chemistry, Vol. 76, N o . 14, 1971
I. R.BDLLOBONO AND F. MAZZA
2114 ~
~
~
Table I : Kinetic Coefficients for the Spontaneous Dissolution of Iron at Various Hydrochloric Acid Concentrations, in Protium and Deuterium Oxide
291.2 291.2 298 2 298.2 298 2 298.2 303.2 313.2 323.2 338 2 I
I
I
a
4.59 f 0.56 13.2 f 0 . 8 7.11 dz 0.65 28.3 f 1 . 6 49.6 f 3 . 8 62.9 f 5 . 9 10.7 k O . 6 18.7 f l . 1 36.5 2 ~ 2 . 9 67.9 rt6.1
1.00 0,100 1.00 0.100 0.010 0.001 1.00 1.00 1.00 1.00
Initial concentrations.
b
0,35i 0.15 1.28 f 0.10 0.35 f 0.13 1.25dzO.10 2.18 f 0.08 3 . l O k 0.14 0.38 f 0.10 0.31 f 0.12 0.36 f 0.15 0.36 i 0.10
1.49 rt 0.25 4.46 i 0.45 2.55 & 0.18 9.18 i 0.76 4.11 f 0.38 6.27 k 0.54 14.4 f 0 . 7 34.0 1 2 . 4
* 0.04
0.64 1,73 0.75 1.65f
0.09 0.15 0.10
3.08 2.96 2.79 3.08
0.65 dz 0.15 0.73 zk 0.13 0.80 f 0.15 0.76 i 0.15
2.60 2.98 2.53 2.00
Mean value and maximum range of variation during kinetic runs.
kinetic coefficients ~ H ( D (sec-l) ) by the equation
io
20
30
40
the, min
Figure 1. Decreasing rate of hydrogen ion activity in deuterium oxide containing 1.00 M DC1 (initial concentration), at various temperatures: plot according to a first-order rate equation (the zero of the time scale does not correspond exactly to the beginning of the run).
reaction, or by the corrosion electrochemical parameters associated with the cathodic and anodic processes. I n the present work, it was preferred to evaluate rates of dissolution (1') and corrosion current densities (i) directly by means of kinetic coefficients for the spontaneous dissolution of the metal. Rates of dissolution of iron (referred to its apparent surface) are related to The Journal of Physical Chemistry, Vol. 76,No. 14, 1971
where v is the volume of electrolyte solution (cm3),s the apparent surface of iron (cmz), and U H ~ the ) activity (equiv/l.) of hydrated proton (or deuteron). I n a narrow range of pH variation, ~ H ( D may ) be considered to be approximatively independent of pH, as it was in fact observed, and eq 10 treated as a first-order rate equation. First-order rate coefficients k ~ p a) t temperatures between 18 and 65" were measured in protium or deuterium oxide solutions containing hydrochloric acid (HCl or DCl). Most of the runs were followed in 1.0 M HCl (or DC1) solutions (cf. Figure 1); but experiments in a wider p H (or pD) range ( ~ U H0.3-3; PUD 0.6-1.6; initial value) were also carried out, mainly a t 25". I n this latter case, potassium chloride was added in order to obtain the same initial ionic strength (I = 1.0 M ) , which was approximatively constant, since the pH (or pD) change during each kinetic run was moderately small. Mean values of ICH(D) and their standard deviations, a t the various hydrochloric acid concentrations examined, as well as experimental k H / k D ratios, are given in Table I. As the ratio between the volume of solution and the apparent surface or iron was held constant in all experiments, rate coefficients k H ( D ) , simply expressed in second-' units, were employed to calculate the activation energy, by Arrhenius plots (Figure 2). Experimental activation energies for the corrosion process occurring in protium and in deuterium oxide media resulted: 11.3 f 0.6 kcal/g mol, in HzO, and 13.1 0.6 kcal/g mol, in DzO. As it clearly appears from Table I, kinetic coefficients showed an appreciable dependence on p H (or pD) of solutions, beyond the limit of experimental errors. Rates of dissolution in protium oxide were employed to calculate corrosion current densities a t various p H values. The logarithms of corrosion
*
SPONTANEOUS DISSOLUTION OF METALS IN AQUEOUS ELECTROLYTES
2115
when the amount of adsorbed hydroxyl ion is low, the massive presence of chloride ions exerts an inhibiting effect;18 consequently the slope of the log i profile
I
L
28
3A
3.2
30 WT)
io3(OKit)
x
Figure 2. Arrhenius plot of kinetic coefficients k~ ( 0 )and k~ (0)in protium and in deuterium oxide, respectively.
I
I
(cf. Figure 3) tends towards a zero value (independence of corrosion current density from hydrogen ion activity). This fact is conveniently accounted for in the Pyle and Robert's model, on one side by the low ratio, exhibited by iron, betweeii the concentration of solvated electrons a t the inner Helmholtz plane and the Concentration of sites, and on the other by the competition between metal hydroxide and water molecules in the surface film. The close agreement between absolute rates for the spontaneous dissolution of iron, predicted by the simple model proposed by Pyle and Roberts (when employing the value of 11.4 kcal/g mol for activation energy), and experimental results has been already pointed out, and is favorably confirmed by the present measurements. On the basis of this model, it should be the removal of the hydroxide film by the reaction
Fe(OH)&, film)
-8
i
1 1 0
+ Haq+
Fe(0H) +
+ HzO
(11)
that determines the rate of dissolution. Consequently the activation energy for forward reaction 11 should be approximatively equal to the activation energy for the iron dissolution process. As activation energy of reaction 11 has not been measured the energy of the dissociation re action I
1
I
2
I
3
I
4
1
PH
Figure 3. Comparison of calculated* (0)and experimental rates of dissolution of iron a t 300°K: (I), ref 11; (O), ref 15; (e), present work. Dependence of log i (i = corrosion current density) on p H a t 300°K and ionic strength 1.0 M .
current densities, a t 300"K, as a function of pH, are reported in Figure 3, together with values calculated by Pyle and Roberts,3 and other experimental values taken from the literature.">'6 A slope of about -0.8 is found in the linear range of the plot of log i vs. pH. However, if experimental values at pH < 1 are also considered, the slope may vary up to about -0.5, A similar slope was obtained for the corrosion current densities by Bockris, Drazic, and D e s p i ~ ,who ~ employed sodium sulfate, while a slope of -1 resulted in the case of sodium perchlorate This difference of behavior was attributed to a specific effect of the different anion^,'^-'^ a greater adsorption occurring in the presence of chloride ions, as compared with that of perchlorate ions." If this is so, the increase in absolute value of the slope, with increasing pH, towards the limiting value (-1) shown by the kinetic equation for hydrogen evolution on iron, would indicate that, when the hydroxyl ion concentration increases, these ions would preferentially cover the metal surface. At low pH, on the contrary,
Fe(OH)2
Fe(0H) +
+ OH-
(12)
was used instead of it, by Pyle and Roberts, and the mean value of 11.4 kcal/g mol a d ~ p t e d . ~This value is remarkably close to the experimental ones (11.5 kcal/g mol;ll 11.3 lrcal/g mol, present work). However, the choice of 11.4 lrcal/g mol as the free energy of reaction 12 may be critically discussed. The equilibrium constant for reaction 12 can be calculated using the values determined by Gayer and Wootnerlg or by Leussing and Kolthoff20 for the equilibrium constant of reaction 13 a t 25" Fez+
+ HzO
Ih(OH)+
+ H+
(13)
(1.20 X lo-* M;19 5 X 10-9 M z O ) , and the solubility products of Fe(OH)2.20 The values of (9.7 f 3.6) X 10-lo or (4 1.5) X 10-lO M are obtained, respectively. Even with a large margin of error, the free energy of reaction 12 may be expected to lie within the range.12.2-13.3 kcal/g mol, which would give rates of
*
(15) A. P. Bond, Sc.D. Thesis, Department of Metallurgy, Massachusetts Institute of Technology, Cambridge, Mass., 1958. (16) G. M. Schmid and N. Hackerman, J . Electrochem. SOC.,107, 647 (1959). (17) Ja. M. Kolotyrkin, ibdd., 108, 209 (1961). (18) F. Mazza and N. D. Greene, Ann. Univ. Ferrara, Sez. 6 , 401 (1966). (19) K. H.Gayer and L. Wootner, J. Amer. Chem. SOC.,7 8 , 3944 (1966). (20) D. L. Leussing and I. M. Kolthoff, ibdd., 75, 2476 (1953). The Journal of Phyadeal Chemistry, Vol. 76,No. 14, 1971
2116 dissolution differing of one or two orders of magnitude from those calculated with an activation energy of 11.4 kcaljg mol. Greater differences result if the value of 4.6 X ALLfor the equilibrium constant of reaction 13, as determined by Wells and Salam,21is adopted. (There is a considerable disagreement on the literature values of the equilibrium constant for reaction 13. For a critical discussion, see ref 21.) I n the calculation of rates of dissolution of metals following the model of Pyle and‘Roberts, there is consequently a great uncertainty in the value used for the free energy of reaction 12, which has been chosen arbitrarily as a measure of the activation energy for the dissolution process. A better choice would be to employ activation energy of reaction 11, if available. The use of an experimental value, directly determined for the reaction of metals with acids, would of course completely resolve the problem, because by this way all effects, including the possible anion inhibition,18 would be taken into account. I n fact, the calculated curve of Figure 3 must be considered as the result of a computation employing the experimental value of activation energy for the spontaneous dissolution of iron in hydrochloric acid solutions. Furthermore, a close analogy, oxidation states apart, between reaction 11 and the rate-limiting step during anodic dissolution (reaction 8) may be observed. Another point, which deserves attention and constitutes another argument in favor of reaction 11 being responsible for the rate of dissolution, is the examination of isotope effects. If reaction 11 represents the rate-determining step, measured kinetic isotope effects should substantially correspond to those of forward reaction 11 and should consequently be related to isotope effect of equilibrium 11. The following equation must hold
The Journal of Physical Chemistry, Vol. 76,N o . 1 A 1071
I. R,.BELLOBONO AND B. MAZZA
where ~ H ( D )and ~ c H ( D ) ’denote rate coefficients for forward and backward reaction 11, respectively, and ApK ( ~ K D- pKH) is equal to log (KHIKD),K H and KD being the acid dissociation constants of Fe(0H) + in protium and in deuterium oxide
The value of ApK is not known, but it can be evaluated if the correlation between pK and ApK given by Bel122-24is assumed to be generally valid, at least in a first approximation. The equilibrium constant KH can be calculated from literature data:19t20 it = (1.04 k 0.39) X or (2.5 b 0.9) X at 25”. The corresponding ApK should thus be about 0.50. Calculation of kinetic isotope effect kH’j1cD’ by means of the Eyring-Cagle e q ~ a t i o n ,using ~ ~ , ~for ~ Fe(0H) + the O-H stretching vibration of hydrated Fe(OH)s (3300 ~ m - ’ ) ,yields ~ ~ the value of 9.12 at 25”. By eq 14, k H j k D = 2.88, in excellent agreement with the experimental value a t 298.2”K (see Table I).
Acknowledgment. Financial support by Consiglio Nazionale delle Ricerche is gratefully acknowledged. (21) C. F.W’ells and M.A . Salam, Nature, 205, 690 (1965). (22) R. P. Bell, “The Proton in Chemistry,” Cornel1 University Press, Ithaca, N. Y.,1958,p 188. (23) R. P. Bell and A. T. Kuhn, Trans. Faraday SOC., 59, 1789 (1963). (24) A. 0.McDougal and F. A. Long, J. Phys. Chem., 64, 188 (1960). (25) H.Eyring and F. W. Cagle, Jr., ibid., 56, 889 (1952). (26) Cf.L.Melander, “Isotope Effects on Reaction Rates,” Ronald Press, New York, N. Y.1960, p p 17, 21, 35. (27) 0.Glemser, Nature, 183, 943, 1476 (1959).
