Concentration Overpotentials on Antimony Electrodes in DifferentiaI EIectroIytic Potentiometry GLYN D. SHORT’ and EDMUND BISHOP Chemistry Department, The University, fxeter, Devon, England
b Antimony electrodes have been polarized in solutions in equilibrium with oxygen-nitrogen atmospheres in which the oxygen partial pressure was varied from zero to 100%. The nature of the overpotentials and the role of oxygen in their establishment have been elucidated. The polarization has been studied in oxygenated solutions over a range of acid concentrations, both to further understanding of electrode behavior and to provide an experimental basis for testing the theoretical interpretation of polarization phenomena in differential electrolytic potentiometry. A theoretical equation is derived for the differential electrolytic potentiometry of acid-base reactions using antimony electrodes.
0
of this work were to identify the nature of the overpotentials on antimony electrodes measured under the conditions of differential electrolytic potentiometry (DEP) ; to establish the influence of dissolved oxygen on the overpotentials; to provide an experimental basis for a quantitative theoretical interpretation of D E P ; and to develop the theoretical interpretation. By virtue of their fast response to hydrogen ion and their metallic conduction, antimony electrodes have proved best for acid-base titrimetry by D E P (9, I O ) , and useful for a theoretical probe into the fundamentals of the method (28). The situation was obscured by a lack of understanding of the behavior of antimony electrodes under anaerobic conditions. The effects of oxygen on zerocurrent electrodes have been elucidated and the response to both hydrogen ion and molecular oxygen concentration has been established ( 1 2 ) ,but no report has been traced on the influence of oxygen on the potentials or reactions of polarized electrodes. Early assumptions of diffusion control (29) were unsupported and confused by lack of appreciation of the role of oxygen in the electrode reactions. In an endeavor to enter the problem of a theoretical interpretation of D E P , BJECTIVES
‘ Prebent address, Department of Chem-
istry, LIasachusetts Institute of Technology, Cambridge 39, ;\lass.
962
ANALYTICAL CHEMISTRY
Figure 1 . Polarization curves for antimony electrodes of area 0.1 26 sq. cm. in neutral 0.03M potassium chloride under an atmosphere of oxygen
a study was made (28) of the Tafel lines at a number of temperatures for antimony electrodes in partially de-oxygenated unpoised aqueous solutions of pH -7. From a mathematical analysis of the results, empirical equations were derived relating the differential potential, Ea, to the differentiating current, 1 4 , at the equivalence point of a strong acid-strong base titration (28). The treatment was then extended t o pH values diverse from 7 , and an empirical exponential equation was set up, which, when supplied with experimental values of the constants, gave a first approximation description of the complete D E P titration (29). Close examination of the equivalence point region revealed a fine structure wherein the single peak split into two peaks a t high currents. Differentiation of Equation 5 of reference (29), and setting d E a / d [ H + ] = 0 gave a cubic in hydrogen ion concentration confirming the shape, which proved to be a consequence of assuming an exponential concentration gradient in the electrode diffusion layer. By a coincidence, antimony electrodes when starved of oxygen showed an experimental behavior supporting this fine structure ( I O , 27, 29). This is due to mixed potentials arising from a change of electrode reaction when oxygen is progressively withdrawn from the system.
Potentials in such media show a poor reproducibility and stability, but polarization in oxygenated solution yields stable and reproducible overpotentials which afford a much more stringent and valid test of theoretical values, and investigation of the characteristics of the single and combined electrodes has permitted identification of the origin of the overpotentials as predominantly concentration polarization. Furthermore, an appreciation of the unique nature of this type of ion combination reaction resulting in the formation of solvent molecules allows certain restraints to be placed on the system ( 2 7 ) , and simplifies the general D E P equation (8) to the concentration overpotential terms ( 9 ) . This permits the derivation from first principles, using theories of linear diffusion, of a general equation for acid-base D E P . This equation is presented with a critical comparison of calculated and experimental results. EXPERIMENTAL
Calibrated rotameters were used to meter the flow of pure oxygen and pure nitrogen (“white spot” grade, British Oxygen Co.) in producing atmospheres of known composition as previously described (12). The preparation of the electrodes, the apparatus, the reagents, the technique, and the methods of measuremeht have been described elsewhere (12, 28). A 2second Cambridge D E recorder was used a t a chart speed of 360 inches per hour for measuring decay curves, and a t 6 inches per hour for observing the equilibration of potentials. Cnless otherwise noted, 6E/6t fell to less than 0.1 mv. per minute in 3 minutes, but potentials were recorded for 20 minutes before final readings were taken. RAproducibility was + 1 mv. over 3 to 10 replications, unless otherwise noted. RESULTS
Polarization in Unpoised Oxygenated Solution at pH 7. Anodic, cathodic (with respect to a similar zero-current electrode) and differential (anode-cathode) potentials produced by scanning t h e differentiating current over the full range are shown in Figure 1 for a vigorously stirred neutral 0.03:M solution of potassium chloride in equilibrium with
l2
Figure 2. Figure 1
F4
LO~,[I,XK)
81
2.2
24
Detail of linear portions of
an atmosphere of pure oxygen. The p H of this solution, measured with a GHS23 glass electrode, u a s 7.0. At high curtents the potentials become unsteady and move toward the decomposition potentials of the solvent: no correction for resistance overpotential has been made. The linear portion of the Tafel lines which is of primary interest is shown in detail in Figure 2, the mean of many determinations of the slope dEa/d loglo Ia was 0.140 + 0.010 volt, the variation occurring with the condition and pretreatment (12) of the electrode surfaces. The cathode slope bvCathode/bloglo la was 0.085 f 0.005 volt, and the anode slope B q A n o d e / b loglo la was 0.050 f 0.005 volt. Polarization in Oxygenated Perchloric Acid Solution. Current scans were repeated under similar conditions in solutions to which increments of standard perchloric acid solution had been added by a calibrated micropipet, with the results shown in Figure 3 . T h e solution p H calculated from the amount of acid added agreed with the values measured by glass electode. The S-shaped curves show inflections a t a current which increases with decreasing pH. At higher
currents, the curves merge with the Tafel line obtained in neutral solution. Iso-current curves, the equivalent of one half of the symmetrical titration curves, can be derived by taking vertical intercepts from the iso-pH curves of Figure 3 and plotting on an axis of volume of acid added or of pH as in Figure 4. At small currents, sharp, low peaks appear in the complete titration curve, and increase in height with increasing current, finally becoming flattened at high currents. Variation of Oxygen Partial Pressure. Typical plots of Ea against loglo p 0 2 a t different fixed currents in neutral 0.08M potassium chloride are shown in Figure 5. The rate of equilibration of the potential increased with increasing partial pressure of oxygen : a t low partial pressures the reproducibility was poor. The general shape of the curves resembles that of
Figure 4. Iso-current (titration) curves, derived from measurements of Figure 3 Current in pa., ( a ) 2.0, ( b ) 1.6, ( E ) 1.26, Id) 1.0, (e) 0.8, ( f ) 0.63, (9)0.50,( h ) 0.40,(i)0.32, (i)
0.20.
Figure 3. Polarization curves for antimony electrodes of area 0.12 6 sq. cm. in 0.03M potassium chloride under an atmosphere of oxygen, after addition of varying amqunts of 0.01M perchloric acid to 150 ml. of solution (a) nil, ( b ) 0 . 0 2 5 mi., (c) (e) 0.20 mi., If) 0 . 3 0 ml.
0.05 mi., (d) 0.10 ml.
I
25
I - 10
1
I
I
""""4"
0
I
1
I
I
10
I
I
20
Figure 5. Potential-log (oxygen partial pressure) relationships a t fixed polarizing currents Antimony electrodes, area 0.12 6 sq. cm., in O.08M potassium chloride, pH = 7
the corresponding zero-current curves ( I d ) in which the potential became constant for oxygen contents above 10%. Here a minimum occurs a t about 10% oxygen, and the potential then increases by about 0.020 volt to a constant value a t higher partial pressures. Current scans a t several fixed oxygen partial pressures gave the anodic and cathodic Tafel lines of Figure 6. Cathodic overpotentials rise toward solvent reduction at low oxygen contents, while at low currents the lines are linear and parallel. Anodic overpotentials are less influenced by change in oxygen content, and show a linear plot over the ranges of current and oxygen partial pressure used. The minima of Figure 5 are reflected in both anodic and cathodic overpotentials. Decay Curves in Oxygenated Solutions of pH 7. Transcripts of strip chart records of the decay in potential after opening the polarizing circuit in 0.08M potassium chloride under oxygen are shown in Figure 7 for anode, cathode, and differential potentials after polarization a t 15 pa. and for the
Figure 6. Polarization curves for antimony electrodes of area 0.12 6 sq. cm. in 0.08M potassium chloride in equilibrium with atmospheres of various oxygen content VOL. 37,
NO. 8 ,
JULY 1 9 6 5
963
Figure 8.
Exponential plots of decay curves
Conditions as in Figure 7 (a)
fa ( t = 0)= 1.5 X
lb)
1.5 X
ampere; dEA/d log f = -0.067volt ampere; -0.066 volt 1.5 X 1 0 - 6 ampere; - 0 , 0 6 3 volt - 0 . 0 4 7 volt 6 X lo-' ampere; -0.026 volt 2.4 X lo-' ampere;
(C) (d) (e)
5
4
3
2
1
0
Ti me, mins. Figure 7. Decay curves for antimony electrodes of area 0.0315 sq. cm. polarized in 0.03M potassium chloride under an atmosphere of pure oxygen [a) Anode decay curve, Ea [ f = 0)= - 2 5 0 mv. (S.C.E). fA (f = 0)= 1.5 X 1 O-s ampere ( b ) Cathode decay curve, Ee (f = 0) = - 4 9 0 mv. (S.C.E.). !A ( 1 = 0)= 1.5 x 1 O-'ampere EA decay curves (c) EA (t = 0)= 3 3 4 mv. f A ( t = 0) = 1.5 X 10-6 ampere (d) EA (f = 0) = 2 0 0 mv. IA (f = 0)= 6 X lo-' ampere (e) E A (f = 01 = 2 3 4 mv. fa (t = 0) = 1.5 X 10-6 ampere
differential potential after polarization under several conditions. Although the instrumentation is not adequate for accurate observation over the first two or three seconds, the decay curves show three portions: a virtually instantaneous drop, a n exponential decay, and a final slow complex fall. DISCUSSION
Nature of the Antimony Overpotential. Three types of overpo-
tential are recognized; activation (q,,), concentration ( q c ) , and resistance (7,). Their origins and the criteria used to distinguish between them have been discussed (S, 6, 1.3, 14, 16, 27, SO). A brief examination of the criteria with reference to the behavior of antimony electrodes follows. E A decreases exponentially with increase in stirring speed, becoming virtually constant above a critical speed (9, 11).
Freshly cut antimony surfaces show a slightly greater overpotential than oxide-coated surfaces, but the latter reach equilibrium more slowly as the thickness of the coating increases. Agar ( 2 , 3) derived values of -0.5 X 10-3 volt deg.-' for ?e and -2.5 X volt deg.-' for q a which should offer a good distinction. The experimental values for antimony electrodes (87) are rather inconclusive, being - 1.7 X 964
ANALYTICAL CHEMISTRY
volt deg.-' for the cathode and - 1.O x volt deg.-' for the anode. Large changes in overpotential on antimony electrodes occur with change in pH. The exponential plots derived from the data of Figure 7 are shown in Figure 8, and their slopes increase with increasing initial current density and with increasing potential intercept of the 0). extrapolated line ( A E , t The decrease of EA with increase of stirring speed, the large changes in overpotential with pH change, and the behavior of the decay curves favor concentration overpotential. This is in general supported by the observations on the effect on overpotential of the condition of the electrode surface. The temperature coefficients indicate mixed diffusion and activation control, the former predominating. I n conjunction with the other evidence and the individual Tafel slopes of anode and cathode, i t is concluded that E A is a consequence of concentration overpotential, but that a measure of activation overpotential is present in the cathode potential. Effect of pH on Antimony Overpotential. At p H 7 the Tafel plot
-
EA =
?Anode
- ?Cathode
=
a
+ b log I A
is linear over a wide current range (Figure 2). In more acid solution, the iso-pH line rises slowly with increasing current, then sharply through an inflection to join the pH 7 line (Figure 3). The value of the current at which the rise occurs increases with increasing hydrogen ion concentration. The oxygen pressure being constant throughout, the waves cannot be due to diffusion limited oxygen reduction (4, 29, 26). The inference that the waves represent hydrogen ion diffusion control is supported by the linearity of the plot of limiting current against hydrogen ion concentration. The successful application of the Nernst diffusion theory for stirred solutions to this situation
(27) adds support to the postulate of diffusion control. The slope Aq/A log la of both anode and cathode lines (Figure 2) should theoretically be RT/F according to any equation for purely diffusion controlled processes. The anode slope of 0.050 volt is in reasonable accord with the nonideal behavior of antimony oxide electrodes (12 ) , but the cathode slope of 0.085 volt is indicative of mixed diffusion-activation control. Similar results have been recorded for copper electrodes (52), and the slopes of Tafel lines for antimony electrodes in buffered solutions of pH 7 have been discussed (11). Role of
Oxygen. If the overpotentials are normally due t o diffusion of hydrogen ions (and of hydroxyl ions in the opposite direction), t h e nature of the electrode surface and the formal potential and electrode reaction are governed by the concentration of dissolved oxygen. The situation has been clarified for zerocurrent electrodes (1$), but electrode processes under anaerobic conditions are ill understood (24, 31). Cathode. At very low oxygen partial pressures, the oxide film is reduced without replenishment, resulting in a bare metal surface at which the ultimate reaction can only be reduction of hydrogen ions or water molecules, as illustrated in Figure 6 . T h e point of transition from oxide reduction to solvent reduction depends on current density and electrode pretreatment as well as on the partial pressure of oxygen in the atmosphere in equilibrium with the solution. As the oxygen partial pressure increases, the rate of diffusion of molecular oxygen to the electrode surface becomes sufficient to maintain an adequate coating of oxide, and the potential controlling reaction is reduction of both oxide and oxygen. The potential becomes invariant with oxygen concentration .at partial pressures above about 20% (Figure 5): oxide reduction now controls the potential, the electrode surface being
fully coated with oxide and saturated with oxygen doublets. A tentative explanation of the minimum is that oxide reduction is accompanied by some activation overpotential, so that as the oxygen partial pressure is increased the contribution of oxide reduction to the overall reaction increases, so increasing the overpotential to a final constant level. Anode. T h e potential change at a given current from maximum t o minimum oxygen partial pressure is a b o u t 0.070 volt, a b o u t t h e same as for the zero-current change (12). This is consistent with the view that oxygen affects the anodic reaction only indirectly by regulating the proportion of oxide on the electrode surface and hence the ratio of cathodic to anodic sites (21). Reaction Scheme. On t h e foregoing basis a sequence of reactions a t each electrode can be constructed according t o t h e magnitude of t h e polarizing current a n d t h e partial pressure of oxygen.
Cathode
show that Sb204disproportionates under all conditions in aqueous media. hlthough SblOb exists at high potentials, such conditions have not been encountered in this work. The physical state of the anode surface is complex and in a state of flux rather than equilibrium, best described by the corrosion theory of Gatty and Spooner (211, THEORETICAL
Principles and Conditions. Passage of current causes discharge of hydroxyl ion a t the anode with consequent ionization of the solvent t o produce hydrogen ion, so t h a t t h e hydrogen ion concentration a t the anode surface, [H+]A,is greater than t h a t in the body of the solution, [H+]B. The electrode responds to hydrogen ion concentration, and, assuming the validity of the Nernst relationship, will display a potential, EA,positive to that of a zerocurrent electrode, E, in the body of the solution. Analogously at the cathode
T
The precise formulation of (1), (2), and (2a) will depend on the p H of the solution. At low currents and high oxygen concentrations, (1) is potential controlling. At lower oxygen partial pressures, around lo%, in the region of the minimum in Figure 5, (1) and (2) share control. At low oxygen contents and high currents, the reaction is independent of oxygen and (3) and (4) become potential controlling (26). Anode. Oxygen has a secondary influence in controlling the a m o u n t of oxide on the electrode surface, a n d a simplified scheme is adequate, precise formulation again being dependent on t h e p H of the solution. 2Sb Sb&
where hydrogen ion is discharged, the hydrogen ion concentration at the cathode surface, [H+]c, will be smaller than [H+]B,and the cathode potential, Ec, will be negative to E. The differential potential will then be
EA = EA- Ec
=
Anode and cathode titration curves are superimposable on the zero-current curve (9), therefore there is no shift in
+ 3Hz0 e Sb203 + 6 H + + 6e + 2H20 e SbpOs + 4 H + + 4~ 2Hz0 + 4 H + + 46 0 2
Oxidation of Sb203to Sb204and SbzOS has been postulated (19, 20) from a study of the discharge curves of anodically polarized antimony electrodes, but potential control by higher oxides is unlikely (31). Such a postulate would be inconsistent with the potential-pH relationships reported by Pourbaix (25) for antimony, which
+
EOA
(5) (6)
(7)
formal potential of the electrodes and E~A = EOC, and 2 303RT log,, f [H+]A (9) EA = [H I C
that a t each electrode the coulometric generation or consumption of active ion is in equilibrium with the dispersion of the ion by diffusion or electromigration. Rate of production = rate of diffusion electromigration (10)
+
From this, the values of [H+]Aand [H+]c can be calculated in terms of the known quantities IAand [H+]B. I n evaluating Equations 9 and 10, the following conditions prevail: Although the balance of evidence favors certain paths provided the solution is in equilibrium with an atmosphere containing more than 10% of oxygen, the exact choice of electrode reaction is unimportant because the number of electrons transferred per hydrogen or hydroxyl ion is always unity and the current yield for coulometric generation is identical for all feasible reactions. The validity of the Kernst potential equation, and a current efficiency of 1 0 0 ~ oare assumed, although deviations from the theoretical zero-current slope (12),or lower current efficiencies affect only the magnitude of EAand not its mode of variation. The solution contains sufficient supporting electrolyte ( 2 0.03M potassium chloride or sulfate) so that any change in ionic strength does not affect the value of EA, and that transport of active ions by electromigration can be neglected. The rate of stirring of the solution is fast enough so that any variation in stirring speed does not affect EA,and so that the Nernst theory of diffusion is valid. It is also assumed that the thickness of the diffusion layer is the same at both electrodes, and is independent of concentration ( 1 ) . Limitations in the concept of the diffusion layer have been discussed (1, 3, 5, 18, 23, 27). The concentration gradients, ([H+]B - [H+Ic)/dx and (["]A [ H + ] ~ ) / d x ,are assumed t o be linear over the distance dz. Concentration terms are used in place of activities, because the media are of constant ionic strength in the region of importance. Calculation of Concentrations at Electrode Surfaces. I n Equation 10 electromigration can be neglected, and the diffusion term embraces, in acid-base reactions, t h e diffusion of hydroxyl ion toward and of hydrogen ion away from the anode. If DOH and D H are the diffusion coefficients of hydroxyl and hydrogen ions, dx is the thickness of the Nernstian diffusion layer, and AA is the area of the anode, then when the rates of generation and dispersal are in equilibrium,
The overpotentials, ? A = EA - E and ?C = E - Ec,are stable and reproducible a t given values of p H and l a , and come to equilibrium rapidly, so VOL. 37,
NO. 8,
JULY 1965
965
Substituting [OH-IB = K,/[H+]B and[OH-] A = K,/[H+]a, andmultiplying through by [H+-]adx/AaD~,
formula solution of which gives the concentration of hydrogen ions a t the anode surface in terms of known constants and the parameters [ H f I B and la. Analogously a t the cathode,
F
-
ax
([0H-lc
- [OH-IB)
+
0
Figure 9. EA - pH curves computed from Equation 15
dxRT F 2 A K w " 2 ( D ~ DOH)
+
available. The values of the constants used for the following results were,
whence
[H+]a)[H+]c
- -- 0 (14) DH
and again formula solution gives the hydrogen ion concentration a t the cathode surface Calculation of Ea. Substitution of the values of the surface concentrations from Equations 12 and 14 into 9 gives the required value,
The remaining unknown in Equation 15, dx, was checked by substituting series of known values of I&, [ H + ] B and EA and solving for &. The found value of 3 X 10-3 cm. is the same for anode and cathode, is invariant with current density and concentration, and is in agreement with expectation (6, 18). Subject to the limitations of the conditions outlined above, and to the nonideal behavior of antimony electrodes, this equation should yield results capable of comparison with experimentally determined Tafel lines and titration curves. Evaluation of EA. Manual manipulation of Equation 15 being tedious, the calculation was programmed for an electronic digital computer, so that [ H + ] A ,[H+lc, E , E A , Ec, t ~tlc, (see below) Ea or any combination thereof could be computed for series of supplied values of I*, the constants and either the volumes of titrant added or the pH of the solution, and either Tafel lines or titration curves could be drawn Sum-checked tapes of the program ( 7 ) in Elliott 803 autocode >lark I11 or in binary machine code are 966
4 5 6 7.8 9 PH
the p H 7 curve, and of the other curves after they have merged with the p H 7 curve, is exactly 2.303RT/FJ which is included in the equation, whereas the experimental slope is about 20% higher, possibly because of the contribution of activation to the experimental cathodic overpotential: At currents below about 10+ ampere the Tafel line a t pH 7 is no longer linear. The deviation is similar to that found experimentally (16) and theoretically (16) for activation overpotential and theoretically for concentration overpotential (6). At very low currents E A becomes linear instead of exponential to current, as shown in Figure 12, in agreement with expectation (6). Confirmation is afforded by differentiation of Equation 15 with respect to current,
ANALYTICAL CHEMISTRY
DH = 9.34 X 10-5cm.2sec.-1 DOH = 5.23 X cm.2 sec.-l dx = 3.0 X lO+cm. K, = 1.008 X mole2 AA = Ac = 0.126 cm.2 T = 298.16' A = 8.3147 joule deg.-l mole-' R = 9.6493 X lo5 amp. sec. F RESULTS
(16)
Substitution of values in (16) gives the slope of 10 x lo5volt amp.-' compared with 8.5 X lo5 volt amp.-' from Figure 12. Variation of Overpotential with pH. T h e anode overpotential for any given value of l a and [ H + ] Bis ?A
=
EA- E =
Variation of Ea with pH. I n Figure 9 a family of curves for dif-
ferent values of IA are shown plotted on a p H axis instead of a volume axis so t h a t the equivalence point region is expanded. These agree closely with the experimental curves in oxygenated solution (Figure 4), and with full titration curves (IO),the increase in height and breadth of the peaks with increasing current being clearly shown. The flat top to the peak occurs when the current is so high that small changes in solution pH in the equivalence point region do not affect the concentration gradient a t the electrode surface; Cosijn (17) has made similar observations with platinum electrodes. The close agreement between theoretical and experimental curves is illustrated in Figure 10. Variation of Ea with I d . Plots of E a us. log,, lafor a number of pH values are shown in Figure 11 and compare excellently with the experimental curves (cf. Figure 3). That the waves were due to hydrogen ion diffusion and not to molecular oxygen is substantiated, since only ionic diffuqion has been incorporated in Equation 15. However, the slope of the linear portion of
and the cathode overpotential is -7c
=
E - Ec
=
Substitution of [ H f I Bfor the denominator in Equation 15 gives the value of V A and substitution of [ H + ] B for the
7
6
5
Figure 10. Comparison of theoretical and experimental titration curves (a)
(b) (E)
Atmosphere of ordinary grade nitroqen, current density 6.3 X ampere cm.-l [compare reference ( 2 9 ) ) Atmcrphere of pure oxygen, current density 1.30 X ampere cm.-* Computed from Equation 15, current density 1.30 X 10-6 ampere cm.-*
3
I
I
I
I
Combining (19) with (9),
10RlO K d (21) Differentiating (21) with respect to [H+]B,and applying (20),
dEa ~-
-
~[H’]B 2 X 2.303RT . ~ 1 . _d[H+]A _ _ -F [H+]A ~ [ H + ] B (22)
therefore a t
Figure 1 1 . EA-log IA iso-pH curves, computed from Equation 15 (Compare Figure 3)
numerator gives the value of -qc, so the individual overpotentials are readily accessible. The variation of and -TC with p H at a current of 5 x ampere is shown in Figure 13. This does not perfectly match experimental results, because experimentally -7c a t p H 7 is greater than T A , but does indicate the titration behavior. As the p H increases on addition of base to acid, the cathode overpotential first rises sharply, because the hydroxyl ions produced in excess a t the cathode affect p H more in acid solution than will the excess hydrogen ions produced at the anode. The steep rise occurs at a p H value dependent on current density: here it is at pH 5.5, and shows a maximum a t p H 5.9. At this point the hydroxyl ion production has overcome the residual hydrogen ion activity furnished by the solution and the p H a t the cathode surface enters the alkaline region. Thereafter the overpotential falls more gradually as solution p H overtakes that on the cathode surface. The converse effect occurs at the anode, whose overpotential shows a maximum a t p H 8. I n principle a sharper titrimetric end point than the usual one a t EA,,,, will be indicated by the point where ? A = -qc, if equality of overpotential is assured by adjustment of electrode area. Displacement of End from Equivalence Point. T h e end point-$he midpoint of t h e peaks in Figure 9 or t h e intersection of anode and cathode curves in Figure 13-is at p H 7.12 f 0.01, slightly on t h e alkaline side of the theoretical value of p H 6.998. This displacement is due to the difference in diffusion coefficients of hydrogen and hydroxyl ions. At the end point T A = -?CJ so
EA,,,
Differentiat’ing (12) with respect to [H+]Band simplifying, at EA,,,
Since [H+]Acan never be zero, at R.
-Omax
[HflB=
[%
112
(25)
‘
Figure 13. Cathodic and anodic overpotential changes during titration, computed from Equation 15
(12) Bishop, E., Short, G. D., Talanta 11, 393 (1964). (13) Bockris, J. O’M., “Electrical Phenomena at Interfaces,” Chap. VII, J. A. Y. Butler, Ed., Methuen, London, _ ^ _ _
Substitution of known values for Don. ._ DH,and K , in (25) gives a value for the pH at the end point Of 7.11, is in agreement with the value from Figure 13. Such a small displacement from true equivalence is neither detectable or significant.
lY51.
(1) Agar, J . N., Discussions Faraday SOC. 1, 26 (1947). (2) Zbid., p. 81. (3) Agar, J. S . , Bowden, F. P., Proc. Roy. Soc. 169A, 206 (1938). (4) Azzam, A. M., Bockris, J. O’M., Conway, B., Rosenberg, H., Trans. Faraday SOC.46, 918 (1950). ( 5 ) Bircumshaw, L. L., Riddiford, A. C., Quart. Rev. Chem. Soc. 6 , 157 (1952). (6) Bishop, E., Proc. SAC Conference, Nottzngham, 1965, p. 50. (7) Bishop, E., Elliott 803 A 3 program D E P 4/3, University of Exeter. (8) Bishop, E., Dhaneshwar, R. G., Short, G. D., Proc. Feigl Symposium, Birmingham, 196‘6, p. 236, Elsevier, Amsterdam, 1963. (9) Bishop, E., Short, G. D., Analyst 87, 467 (1962). (10) Zbid., 89, 415 (1964). (11) Bishop, E., Short, G. D., A s . 4 ~ . CHEM.36, 730 (1964).
(14) Bockris, J. O’M., “Modern Asuects of Electrochemistry,” vol. 1, Bitterworths, London, 1954. (15) Bockris, J. O’&l,, Potter, E. C,, J . Chem. Phys. 20, 614 (1952). (16) Bockris, J. O’M., Potter, E. C., J . Electrochem. fhc. 99, 169 (1952). (17) Cosijn, A. H. hI., J . Electroanal. Chem.. 3. 24 (19621. , (18) Deiahay, P., “Xew Instrumental Methods in Electrochemistry,” Chap. 9, Interscience, New York, 1953. (19) El Wakkad, S. E. S., Hickling, A., J . Chem. SOC.1950. 2894. (20) El Wakkad, S. ’E. S.,Hickling, A,, J . Phys. Chem. 57, 207 (1953). (21) Gatty, O., Spooner, E. C. R., “The Electrode Potential Behavior of Corroding Metals in Aqueoiis Solution,” Oxford University Press. London and New York. 1938. (22) Hickling, A , , Salt, F. W., Trans. Faraday SOC.37, 319 (1941). (23) Ibl, N.,VIIIth meeting, C.I.T.C.E., 1956. (24) Ives, D. J. G.,,;Janz, G. J., “Reference Electrodes, Academic Press, S e w York, 1961. (25) Pitman, A . L., Pourbaix, >I J..N., de Zoubov, S . , Trans. Electrochem. Soc. 104, 595 (1957). (26) Sawyer, I). T., Interrante, L. V., J . Electroanal. Chem. 2, 310 (1961). (27) Short, G. D., Ph.D. Thesis, Uni-
4
J . Chem. SOC.1952, 2626. (32) Timer, D. R., Johnson, G. R., J . Electrochem. Soc. 109, 798 (1962). RECEIVEDfor review Jiine 15, 1964.
LITERATURE CITED
O
-
/”
I
I
I
I
I
I
I
\ - - -
and for maximum EA,
VOL. 37, NO. 8, JULY 1965
e
967
