Chronocoulometry A Convenient, Rapid and Reliable Technique for Detection and Determination of Adsorbed Reactants Fred C. Anson Arthur Amos Noyes Laboratones, D~visionof Chemfstryand Chem~alEngineering,' Calffornla lnstltute of Technology, Pasadena, CA 911% Robert A. Osteryoung Department of Chemistry. Acheson Hall, State University of New York, Buffalo, NY 14212 All of the interesting action in electrochemistry takes place a t the interface between the conducting (usually solid) electrode and the (usually liquid) electrolyte solution. This is where ionic current is transformed into electronic current by an electrode reaction. The electrode/electrolyte interface in any electrochemical cell often exhibits chemical propert~es that differ substantially from those observed in the bulk of the electrode and in the electrolyte solution far from the interface. One particularly interesting property of many electrode1 electrolyte interfaces is their tendency to attract and retain reactants. The phenomenon is often described in terms of the "adsorntion" of reactants at electrode surfaces. Considerable effort has been expended to devise metods for measuring the quantity of any reactant that may be adsorbed a t the electrodelelectrolyte interface. The problem is not trivial because the quantities whose magnitudes it is desired to measure typically lie in the range between 10-l2 to 1 0 - L h o l efor each cm2 of interface. Our interest in measuring the quantities of reactants adsorbed on electrodes was stimulated initially by a publication of Breiter and Gilman (1)in which the amount of a reactant, methanol, adsorbed on platinum electrode surfaces was estimated from the areas under current-ootential curves (voltammograms) obtained when the electrode potential was scanned across the ranre where oxidation of both adsorbed and unadsorbed methanol proceeded. Initially, we also utilized the areas of voltammetric current-uotential curves to measure the quantities of adsorbed reactants ( 2 , 3 )but soon realized that the same information could be obtained more simply, reliably, and rapidly by stepping rather than scanning the electrode potential while measuring the electric charge that flows in response to the potential step (4). Measurement of the time dependence of the flow of charge constitutes the procedure that now is known as chronoconlometry. While the technique has proved useful in a variety of electrochemical measurements besides the evaluation of reactant adsorption (51, we will focus on this single application for which the technique was originally devised. ~
Electrode Reactions Controlled by the Supply of Reactant to the Electrode Surface In Figure 1is shown a typical current-potential curve (recorded under steady-state conditions) for the reduction of a reactant at an electrode surface (extension to oxidation reactions is straightforward). Nu current flows until the potential reaches values near the reduction potential of the reactant whereupon there is a rather sharp onset of current.
Fiaure 1. Tvoicai steadv-state current-ootential curve for the reduction of a ,, reactant at an electrode surface. Reduction currents are plotted upward and the potential becomes more negative to the right.
As the potential is made still more negative, the current eventually levels off at a limiting value where every reactant molecule that reaches the electrode is immediately reduced. At potentials in the plateau region the current is limited by the rate at which the reactant is supplied to the electrode surface. If the experimental conditions are arranged so that the reactant is transported to the electrode surface by means of linear diffusion (i.e., unstirred solution, flat electrode) an equation originally derived by Cottrell (6) can he used to calculate the current that flows a t any time after application of the potential step as a result of the reduction of the reactant. For example, if the electrode potential is stepped from a value (i.e., E l in Fig. 1)where no reaction is proceeding to a value on the limiting current plateau (Ez in Fig. 11, the resulting current is given by eqn. (1):
where F is the Faradav (96.487 coulombs per equivalent). n reactant in the bulk of the solution (mole cm-9, D is the reactant's diffusion coefficient (em2 ss'), and t is the time
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Cottrell current
+ Z W
LZ LZ 3 U I I I I I I I I
O
!
iI
0
'.
i I
(TIME 1''
Figure 3. Chronacoulometric plots of charge versus (time)'? The dashed, horizontal line represents the charge response obtained in the absence of reactant. Line 1 results if the reactant is not adsorbed. Line 2 results with the Same concentration of an adsorbed reactant. The dotted extensions of lines 1 and 2 indicate that the intercepts of chronocoulometricplots are usually obtained by linear extrapolation from the shortest times at which reliable data are available.
C
W
0
u a
I
transported to the electrode surface by diffusion (7). Suppose some of the reactant is adsorhed a t the electrode/electrolyte interface while the electrode is restine at notentialE,..(Fig. " 1). . When the potential is stepped to E2all o? the adsorhed reactant will he reduced essentiallv instantaneouslv because i t is
U
TIME Figure 2. Temporal behavim of me elemode potential, current, and charge in chronocoulometric experiments. (A) The electrode potential is stepped from El to E, at time = (I: (8) The current that flows in response to the potential step (solid curve). The dashed curve is the current obtained when the experiment is repeated in the absence of reactant: (C) The time-integrals of the two curves in 8.
follow in^ the notential steo. Fianre 2A deoicts the notential step that is applied to the eiectride and 2 ~ s h o w thk s current that results. The current is actnallv com~osedof two components: The Cottrell current gi;en b; eqn. (1) plus a "charging current," i,, that flows to charge up the capacitance that is always present in electrode/electrolyte interfaces. The charging current, which can be observed by applying the potential step in the ahsence of the reactant, is shown as the dashed curve in Figure 2B. the charging current decays much more rapidly than the Cottrell current and becomes zero once the interfacial capacitance has become fully charged. The total charge passing through the electrode is the time integral of the two current components: Q = J'FnAcb
D (z) + 112
ddt
Si,dt
(2)
where 0, is the charge flowine into the interfacial canacitance
give rise to an extra burst of charge as soon as the electrode potential is stepped to Ez, hut thereafter the chronocoulometric response will be unaffected by the adsorption of the reactant. Thus, the total charge in the presence of adsorhed reactant will obey eqn. (4) instead of eqn. (3)
);;(Dt
Q = 2FnACb
112
+ Q, + Qads
(4)
where Qads is the extra charge produced by the adsorbed reactant. Under these conditions plots of Q versus (time)l/2 will have intercepts that exceed Q, by an amount of charge equal to Qsds. This behavior is shown in line 2 of Figure 3. The slope is unaffected by the adsorbed reactant. The values of Qads are direct measures of the quantity of reactant adsorhed because of Faraday's Law where r is the quantity of adsorbed reactant in moles. It is this simple, direct relationship hetween the experimentally accessible parameter, Qsds, and the quantity i t is desired to measure, r, that makes the technique of chronocoulometry as attractive as it is. Double Potential Step Chronocoulometry As shown clearly in Figure 3, to obtain Q.a. from the intercept of a chronocoulometric plot of Q versus t'J2 it is necessary to know or measure Q,. This presents no problem when the adsomtion of a readant nroduces little or no change in - thr ~-~~ interfacial capacitance so that the value of Q, measured in a "blank" experiment in the ahsence of reactant (dashed line in Fig. 2C) applies to measurements in the presence of the adsorbing reactant. However, frequently adsorption of a reactant produces significant changes in the interfacial capacitance so that values of Q, evaluated in the absence of the reactant do not apply when the reactant is present. This difficulty can sometimes be overcome by double potential step chronocoulometry in which the electrode potential
-~
response in the absence of reactant. According to eqn. (3), plots of Q versus t1I2 should he linear with intercepts of Q, and slopes proportional to the concentration of the reactant. This behavior is shown by line 1 of Figure 3 and has been observed experimentally in a large number of cases. The charge increases in chronocoulometric experiments with the square root of time because additional reactant is 294
Journal of Chemical Education
Figure 6.Chronocoulometric charge-(time)"2 plots for the reduction of Cd(l1) at a mercury electrode (0.032 cmZ).The suppotting electrolyte was 0.1 FNaN03 for line 1 and 0.5 FNaN03 0.5 F NaNCS for lines 2-4. The concentrations ot Cd(1l) were (1.2) 0.2; (3) 0.5; (4) 1.0; (5) 2.0 mM.
+
TIME Figure 4. Temporal behavior of: (A) potential, (B) cunent, and (C) charge in double potential step chronocoulometry
Flgure 5 Chronocoulometrlc plots for double potential-step chronocoulometry Llnes 1 and 2 correspond to no adsorption of the reactant or product Lmes 3 and 4 correspond to reactant but not product adsorption
Figure 7. Concentration dependence of the adsorption of Cd(l1) on mercury electrodes from 0.5 FNaNO* 0.5 FNaNCS electrolyte. The initial electrode potential was -0.2 V versus a saturated calomel reference electrode.
is returned to its initial value hefore the experiment is terminated ( 8 ) . Figure 4 depicts the potential-, current- and charge-time responses obtained in such a double potential-step experiment for cases where the product of the electrode reaction is re-oxidized when the potential is returned to its initial value. The ~harge-(time)'/~ plot of the data acquired during the first potential step (Fig. 5, line 1) is, of course, identical to that obtained in a single-step experiment. So long as neither the reactant nor the product of the electrode reaction are
adsorbed, the charge, Q,, (Fig. 4) that passes following the second potential step is a linear function of [.r1I2 ( t - T ) ' / ~ - tlJz], where T is the duration of the first step. The corre: sponding plot for data acquired during the second potential step is shown in line 2, Figure 5. In cases where the reactant but not the product of the electrode reaction is adsorbed, for example in the reduction of a variety of dl0 metal complexes to metal amalgams at mercury electrodes (9),the intercept of the chronocoulometric plot for the reverse step (after a
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small wmrctim 1s ;lpp~ic;d111,Il prwides u direct lniusure d with the concentration of Cd(Ii). A plot of Q a d s versus [Cd(II)] Q,.in r l i v p ~~+, i , : h~\ving " ,7967) ,-. ..,. electrolyte. In the mixed nitrate-thiocyanate electrolyte, (11) Anson, F. C., Chriatie. J. H., and Osteryoung, R. A., J El~ctroonal.Chrm., 13, 343 however, there is quite substantial adsorption that increases (1967). ~
~
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