recommended to switch back and forth between intermittent and dc operation. In the intermittent mode, the lamp is operated for only a short time, nt, typically 20 X 0.01 sec = 0.2 second for the results in Table 11. We found that the light output is the same and so is the stability if n and t are changed within limits to maintain the product constant. For example, if instead of twenty 15-msec pulses, sixty 5-msec pulses are used, output signal is nearly the same value and stability is constant. For short ON-times of less than 2 msec, time delay problems in lamp response and power supply responses can lower reproducibility. In our case, a 4-15 msec ON-time per period proved to be the most appropriate. Measurement Conditions. It is important when making measurements with the hollow cathode lamps to operate under experimental conditions so that sufficient photons are
incident on the photomultiplier cathode during the measurement period (12). For example, if a relative standard deviation of 0.1 % is desired for each integration of n pulses, then 106 photon counts must be obtained for the selected hollow cathode time. Thus, the optical throughput and the product nt must be sufficient to provide the required number of photons for the desired precision.
RECEIVED for review July 6, 1972. Accepted September 15. 1972. Work supported in part by NSF Grant GP 18910. Presented in part at the Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, Cleveland, Ohio, March 1972. (12) H. V. Malrnstadt, M. Franklin, and G. Horlick, ANAL.CHEM., 44 (8), 63A (1972).
Comparative Spectroelectrochemical, Stopped-Flow Kinetic, and Polarographic Study of the Titanium( III)-Hydroxylamine Reaction M. Petek,’ T. E. Neal,2R. L. McNeelj~,~ and Royce W. Murray Department of Chemistry, Unicersity of North Carolina, Chapel Hill, N.C. 27514
Spectroelectrochemical theory for diffusion layer absorbances in current step experiments is developed for the reversible EC, irreversible EC, and catalytic coupled chemical reaction cases. Using an Au minigrid optically transparent electrode, and detection of Ti(lll) at 410 nm, the current step experiment is tested with a catalytic system, the reaction between hydroxylamine and electrogenerated Ti(lll). This reaction is also assessed by the non-electrochemical stoppedflow kinetic spectrometry technique. Appreciable kinetic sensitivity to solution pH and ionic strength, and sensitivity of reaction stoichiometry to solution composition, was noted during the study. For similar solution conditions, both methods give kinetic results in excellent agreement with previous electrochemical reports.
A CATALYTIC REACTION, in the context of an electrochemical experiment, refers to a post-electron transfer chemical event which regenerates the original electrochemical reactant: O+ne+R
R + Z k / O + P
(1 1 (2)
It is possible to elicit the rate of Reaction 2 by several electrochemical techniques. It is also possible, by transmission spectrophotometry of the diffusion layer at a n optically transparent electrode (OTE), t o utilize the absorbance-time response for species R for this kinetic determination. Theory and experimental details for spectroelectrochemical measurements on catalytic reactions have been presented by Kuwana and coworkers ( I , 2) for controlled potential experiments. Present address, Department of Chemistry, State University of New York, Buffalo. N.Y. 2 Present address, Textile Research Laboratory, E. I. du Pont de Nemours and Company. Wi!mington, De!. Present address. Department of Chemistry, University of Tennessee, Chattanooga, Tenn. J
( I ) N. Winograd, H. N. B!ount, and T. Kuwana, J . Phys. Cheni., 73, 3456 (1969;.
32
The Au minigrid electrode has certain advantages for controlled current electrolysis and has recently been shown to be suitable for semi-infinite linear diffusion transmission spectroelectrochemistry (3). This report will describe theoretical relations for current step spectroelectrochemistry with couplec chemical reactions, and a n application of the Au minigrid electrode to the determination of catalytic electrode reactior kinetics. In spite of the extensive electrochemical evaluations 01 charge-transfer-coupled chemical reactions, it has been quite rare that kinetic results of any electrochemical, or spectro. electrochemical experiment have been compared t o those oj independent, non-electrochemical methods. Given the facts that electrochemical methods have in general a greater rate than mechanistic sensitivity, especially where multiple reac. tion path possibilities are concerned, and that effects of ad. sorption and surface reaction catalysis on kinetic determina, tions are incompletely understood, we contend that suck comparisons should be useful and more commonplace. IF line with this contention, then, a second aspect of this reporl is a n illustration of the elementary ideas involved in applying stopped-flow kinetic spectrometry to kinetic and mechanistic studies of electrochemically germane chemical reactions. The illustration is the stopped-flow kinetic characterization of the same catalytic electrode reaction selected for current step spectroelectrochemical study. The one-electron reduction of titanium(1V) in aqueous oxalic acid medium in the presence of hydroxylamine is an electrochemical catalytic reaction which has served as a “model” for evaluation of a number of kinetically-sensitive electrochemical approaches, including polarography (41, (2) H. N . B!ount. N. Winograd, and T. Kuwana, ibid., 74, 3231 (1970). (3) M. Petek, T. E. Neal, and R. W. Murray, ANAL.CHEW,43, 1069 (1971). (4) A. R!ai!ek and J. Koryta, Collect. Czech. Chem. Comrn~m.,18, 326 (1953).
ANALYTICAL CHEMISTRY, VOL. 45, NO. 1, JANUARY 1973
Table I. Literature Results for Reaction of Ti(I1I) with Hydroxylamine in 0.2M Oxalic Acid [S042-l,M [Cl-],M Temp., “C uk, M-l sec-’ Method none 0.004 25 42.1 f 1.5 Polarography (4, 5)e 0.05 0.025 0.006 25 40.8 Potential-sweep chronoamper0.1 0.05 0.006 25 44.3 ometry (IO) 0.2 0.1 0.006 25 39.7 0.1 (pH 1.1) 0.10 25 46.1 Double potential step chrono0 . 2 ( p H 1.0) 0.20 25 41 .O coulometry ( I I ) b 0.005 none 0.004 25 44.8 Chronopotentiornetry(6), 0.008 none 0.004 25 46.8 second-order conditions 0.010 none 0.004 25 45.9 0.49 0.002 0.49 30 30 Chronopotentiometry ( 5 ) 1.46 0.002 1.46 30 0.01 none 0.01 23 23c Cyclic chronopotentiornetry(8) 0.1 none 0. I 27d 33.3 Reverse current chronopotenti0.2 none 0.2 27 37.0 ometry (9) 0.25 25 32.3 Chronopotentiornetry (7), mern1.00 25 29.4 brane electrode E,,$ = 7.9 kcal/mole. b E,,% = 17.2 kcal/mole. This value calculated in Reference 9. d This value cited in Reference 11. [NH30Ht],M 0.03-0.18
0
chronopotentiometry in several forms (5-9), potential sweep chronoamperometry (IO), and double potential step chronocoulometry (11). Based on a report by Davis et al. (12), the titanium reaction is usually written as Ti(1V)
+e
--f
Ti(II1)
stoichiometric factor u, where u has a value somewhat less than two. Reaction 4 has also been employed as a source of amino radicals for various purposes, including polymer initiators (15, I 6 ) , reaction with unsaturated compounds (17-19), and ESR studies (20). Variation of u from 0.6 to 2.0 with scavenger additions has been observed (19). The kinetic results of previous electrochemical studies of the titanium-hydroxylamine reaction are summarized in Table I. Discrepancies evident for the chronopotentiometric methods have been attributed, variously, to poor transition time definition (5),reaction complexities (8),and double layer charging effects (9). The polarographic, potential sweep chronoamperometric, and chronocoulometric results are fairly consistent, and appear to represent an accurate assessment of the product uk for Reaction 4. The seemingly adequate characterization of the titaniumhydroxylamine reaction led us to select it for our current step spectroelectrochemical evaluation and stopped-flow kinetic comparison. While the reaction did serve that purpose, it also exhibited some previously unrecognized kinetic features which were further explored using the polarographic method. The third point of this report is a description of these features.
(3)
+ NHzOH+ & Ti(1V) + HzO i-NH2. NH2. + H2C204fast- NH3 + products
Ti(II1)
(4) (5)
The oxalic acid component of the medium acts, ostensibly, as an amino radical scavenger, and also imparts electrochemical reversibility to Reaction 3 (13). The results of Davis (12) and an amperometric titration, at elevated temperature, by Blaiek (14) indicated that the Ti(III)/NH30H+ reaction stoichiometry is overall l/l-e.g., that the amino radical is completely consumed by Reaction 5 and that further rapid consumption of Ti(II1) by the reaction Ti(II1)
+ NH2. + H+
last
Ti(1V)
+ NH,
(6)
is insignificant. Saveant and Vianello (IO), from titrimetric and supplemental NH,. scavenger (ethyl alcohol) experiments, concluded on the other hand that in 0.2M oxalic acid, the reaction stoichiometry is actually somewhat less than 2/1 (e.g., that Reaction 6 does participate). From the lack of any discord between potential sweep experiment and theory, these authors also concluded that both Reactions 5 and 6 are sufficiently fast that the measured rate is a simple product of the second-order rate constant k of Reaction 4 and a (constant)
CURRENT STEP SPECTROELECTROCHEMICAL THEORY We consider here three cases of charge transfer-coupled chemical reactions : the catalytic reaction as expressed by Reactions 1 and 2, and the allied cases of reversible and irreversible “EC” reactions
+ ne +R ; 0 + ne -+ R ;
0 ( 5 ) P. Delahay, C. C. Mattax, and
T.Berzins, J. Amer. Chem. Soc.,
76. 5319 (1954). (6) 0. Fischer, 0. Drafka, and E. Fischerova, Collect. Czech. Chem. Commun., 26, 1505 (1961). (7) Zbid., 27, 1119 (1962). (8) H. B. Herman and A. J. Bard, ANAL.CHEM., 36, 510 (1964). (9) J. H. Christie and G. Lauer, ibid., p 2037. (10) J. M. Saveant and E. Vianello, Electrochim. Acta, 10, 905
(1965). (11) P. J. Lingane and J. H. Christie, J. Electronanal. Chem., Znterfacial Electrochem., 13, 227 (1967). (12) P. Davis, M. G. Evans, and W. C. E. Higginson, J. Chem. SOC., 1951, 2563. (13) R. L. Pecsok. J . Amer. CIwm. Soc., 73, 1304 (1951). (14) A. Blatek, Chem. Listy, 47, 1003 (1953).
+ Z k/_ P (Irreversible EC) kf R +Z P (Reversible EC)
R
(7)
(8)
kb
(15) T.Kakurai, T. Sugata, and J. Noguchi, Kobunshi Kugaku, 274,
120 (1968). (16) E.Howard, U.S.Patents 2,683,140,July 6,1954, and 2,567,109, Sept. 4, 1951. (17) F. W.Hoover, U. S. Patent 2,983,758,May 9, 1961. (18) H. Seaman, P. J. Taylor, and W. A. Waters, J . Chem. Soc., 1954,4690.
(19) C. J . Albisetti, D. D. Coffrnan, F. W. Hoover, E. L. Jenner, and W. E. Mochel, J. Amer. Chem. Soc.. 81,1489 (1959). (20) D. J. Edge and R. 0. C. Norman, J . Chem. SOC.B, 1969,182.
ANALYTICAL CHEMISTRY, VOL. 45, NO. 1, JANUARY 1973
33
Table 11. Current Step Spectroelectrochemical Relations K = B/kb; p = kj[Z]; OR = 1O3eR/nFA;Bp = 10%p/nFA Absorbance-time relations Limiting (long time) relations
Reaction case Diffusion-only O+ne+R Reversible EC 0
AR = 0 ~ i t
+ ne +R
AR
=
0 ~ i Kr t 1 +
fii
R + Z S P kb
Irreversible EC
The reversible EC case, Reaction 8, is a generalization of relations for the three cases. Access to the C R ( z , ( )and Cp(z,f) this case is through solution of the Fick’s law expressions
under the conditions
Figure 1. Theoretical absorbance-time responses for current step spectroelectrochemistry Curves A-E general to Equations 17, 19. Curve D also represents AR for catalytic and irreversible EC reactions (Equations 21,25) The kinetic conditions will be pseudo-first order-e.g., [ R ] and a pseudo-first order forward rate constant
P
=
kLZ1
[ Z ] >> (9)
The pertinent absorbance-time relations will be those for species R ( A R ) and P ( A p ) . Since the optical absorbance of the entire diffusionlayer a t the optically transparent electrode is t o be monitored during the current step experiment, we can identify the absorbance-time relations for R and P with their Beer’s law-converted concentration-distance integrals r m
A p = lO%p
l=
Cpc,,t)dx
(11)
where E , and e p are the molar absorbance coefficients of R and P in M-l cm-l, respectively, concentrations are in moles/cm3, and the factor l o 3 is included for dimensional consistency. 34
This solution follows conventional Laplace Transformation paths and will not be detailed here, It is convenient during the solution t o carry out the integration and absorbance conversion of Equations 10 and 11 while in the Laplace plane ( I ) . The absorbance-time relations for AR and A P which result from the above theoretical formulation for the reversible E C reaction are presented in Table I1 as Equations 17 and 19. The irreversible EC Reaction 7 is a subcase treated by setting kb = 0 in Equations 17 and 19, giving Equations 21 and 23 in Table I1 for AR and A p . The concentration distance profile for species R in a catalytic reaction is identical t o that of an irreversible E C reaction; Equation 25 of Table I1 is, thus, identical to Equation 21. The absorbance-time transient in all three reaction cases is characterized by a decaying exponential term; the resulting long-time limiting expressions are Equations 18, 20, 22, 24, and 26 of Table 11. The behavior of the absorbance-time responses is further summarized in Figure 1 where curves A-C represent A,-t responses for the reversible EC reaction a t several equilibrium constants b/kb, curve D is the limiting kb = 0 response for A,-r (irreversible E C and catalytic reactions), and curve E is a general form of the A,-t response for reversible and irreversible EC reactions. We now consider more specifically the theoretical Relations 25 and 26 for the catalytic Reaction 1,2. It is clear from these relations and Figure 1 that the absorbance of the electrolysis product R achieves a time-independent level, ARSs, a t which point the rate of consumption of R by Z has exactly compensated for the constant current generation of R.
ANALYTICAL CHEMISTRY, VOL. 45, NO. 1, JANUARY 1973
Table 111. Reaction Stoichiometry at 25 "C by Amperometric Titration Moles Ti(III)/ [HzCZO~I, moles M Titrant Sample NHaOH+ 0.20 0.0483M NH30H+ 0.0139MTi(III) 2.04 0.75 0.0483M NH30H+ 0.0139M Ti(II1) 2.00 0.20 0.0453MTi(III) 0.0194MNH30H+ 1.18 0.75 0.0461M Ti(II1) 0.0194M NH30Hf 0.93
0
There are two paths for extracting the kinetic parameter /3: (a) Direct calculation from A R S S Equation , 26. This approach requires explicit knowledge of e R but offers the advantage that substantial instrumental damping of the absorbance response becomes permissible for dealing with very small absorbance signals; (b) Use of the approach to steady state. A working S Pt can be employed, or a plot made accordplot of A E / A R Scs. ing to a combination of Equations 25 and 26
t
1
=
- - I n [l
P
2.0
1.0 1. see
Figure 2. Current step spectroelectrochemical response of Ti(II1) at 410 nm in the presence of hydroxylamine [Ti(IV)] = 10.0mM; [H&04]
=
0.75M;"[a-
OH+] = 0.0773M; [S04z-] = 0.0386M; i = 3.28 mA/cm2; electrode area = 0.306 em2; damping time constant = 10 msec; photomultiplier out-
put zero suppressed by 9.414 volts Curve A. PMT output Curve B. Minigrid electrode potential Curve C. Steady state PMT output
- AR/ARSs]
A third approach to the rate assessment does not employ the relations of Table I1 but simply uses the current step as a means of generating an observable level of absorbance for R. The current step is then removed, and the time required for A R to diminish to one-half its value at the time of current cessation is measured. This reaction half-life is related to pseudo-first-order rate by
The current cessation approach is exceedingly simple but, being single valued, is less accurate than those above. All three of these data analysis methods will be used in the current step spectroelectrochemical experiments on the titanium("-hydroxylamine reaction. EXPERIMENTAL Chemicals. Oxalic acid (Mallinckrodt) was recrystallized from water, hydroxylammonium sulfate (Matheson, Coleman & Bell) from water-ethanol mixtures. Solutions of Ti(", prepared from 20 % aqueous solutions (Fisher) and handled and stored under nitrogen at all times, were analyzed for Ti(II1) on the day of use by titration with standard Fe(II1) solutions [prepared from Fe("4)2(S04)2, KzCrzOi mixtures] using KSCN visual indicator. Solutions of Ti(IV) were prepared by exhaustive air oxidation of standard Ti(II1)-oxalic acid solutions. Concentrations of titanium employed were 5 or 10mM. Spectroelectrochemical Measurements. The kinetic spectrometer, optically transparent electrode (OTE) cell, and associated equipment were as previously described (3). T o minimize shadowing effects (3), the maximum Au minigrid mesh size, 2000 lines/inch, was employed. The OTE cell was thoroughly flushed with sample solution (introduced from a closed system reservoir) to remove any initial oxygen or gas bubbles and before each current step measurement. The area of the minigrid OTE was determined by current step oxidative spectroelectrochemistry of o-tolidine (3). The diffusion-only Equation 16 (Table 11) modified by a factor of two (since the minigrid OTE is two-faced) applies to this experiment. Needed e values for Ti(II1) were then determined by current step spectroelectrochemistry and Equation 16, reducing Ti(1V) in the absence of hydroxylamine and monitoring the 410-nm band maximum of the stable Ti(II1) prod-
uct. The results for e were identical in 0.2M and 0.75M oxalic acid but did depend slightly on the sulfate concentration (e = 410 M-lcm-l with no added sulfate, 360 M-km-l with 0.5M sulfate). These data were spot-checked and confirmed by conventional spectrophotometry of Ti(II1). The Ti(1V) reduction wave is quite near to the hydrogen background on Au in these solutions (see Figure 8 in Reference 3). A loss of 100% current efficiency occasioned by background proximity is reflected, in the determination of ET^ (1x1) under various conditions, by an apparent decrease in €Ti(IIIj cited with increasing applied current (3). Values of CT~(III) above are limiting ones at low applied currents. The current steps employed for the Ti(II1)-hydroxylamine rate measurements, to obtain readily measurable Ti(II1) absorbances, were 5-1OX larger than these limiting low current values. Accordingly, in the calculation of uk from A R S Sdata (Equation 26), values of apparent CT~(III)corresponding to the actual current levels employed were used. The difference is small, amounting to approximately 10-1 5 %. Stopped-Flow Kinetic Measurements. The stopped-flow system (Atom-Mech Machine Company) employed is similar to that described by Dulz and Sutin (21). Its eight-jet Teflon (Du Pont) mixing chamber has a specified mixing time of 2 rnsec. The system and experimental technique were checked using the reaction of Fe(phen)32+with Ce(IV) in 0.25M HzS04; the second-order rate constant obtained (1.42 X lo5 M-lsec-l; average deviation of nine determinations, 1 . 7 x ) duplicates the literature values (21). The concentrations of the Ti(II1)-oxalic acid and hydroxylammonium sulfate solutions employed in the stopped-flow kinetic measurements were chosen to duplicate those in the electrochemical experiments; reaction half-lives of this reaction are in the range of several hundred milliseconds. The solutions, as were those in the polarographic and spectroelectrochemical experiments, were thermostated at 25 "C. Reaction Stoichiometry. The stoichiometric factor of the Ti(II1)-hydroxylamine reaction was evaluated by titration of Ti(II1) solutions with hydroxylamine, and rice cersu. The titration was followed with the anodic polarographic diffusion current of Ti(II1). The results, presented in Table 111, are discussed later. Polarographic Measurements. Measurements of Ti(II1)hydroxylamine reaction rates are polarographically accomplished by comparisons of Ti(1V) limiting currents in the (21) G. Dulz and N. Sutin, h r g . Chem., 2,917 (1963).
ANALYTICAL CHEMISTRY, VOL. 45, NO. 1, JANUARY 1973
35
~~~
Table IV. Kinetic Results for the Ti(II1)-Hydroxylamine Reaction [HzCzOd, ["30H+l, [S042-1, Temp, ak,a M M M PH "C. Detn. M-1 sec-' 0.20 0.097 0.048 1.4 25 6 41.3 f 0.6 1 44.7 0.75 0.0773 0.0387 0.7 25 3 20.3 f 0.3 2 20.0 f 0 . 5 1 20.7 0.75 0.290 0.145 0.7 25 3 21.4 f 0.5 1 21.7 0.75 0.482 0.241 0.7 25 2 20.0 i. 0 . 9 1 17.1 62.1 3.9 0.10 0.0496 0.0248 25 4 42.1 zt 0.6 0.050 1.4 25 5 0.20 0.101 41.7 0.20 0.134 0.067 1.4 25 3 1.1 42.1 f 1.3' 0.20 0.147 0.073 1.4 25 4 0.20 0.147 0.073 1.4 15 2 15.7 f 0.2' 111 f 2' 0.20 0.147 0.073 1.4 35 2 0.714 0.0993 0.0496 25 4 17.1 f 1.2 a uk is k f , evaluated from observed pseudo-first-order rate p by Equation 9. Current step spectroelectrochemistry, steady-state absorbance analysis, Equation 26. Current step spectroelectrochemistry, current cessation, Equation 28. Current step spectroelectrochemistry, absorbance plotted by Equation 27. e Stopped-flow kinetic spectrometry, data analysis by Equation 30. A plot of these data, In (uk) us. l/T, gives energy of activation E,,$ = 17.0 kcal/mole.
*
absence and presence of hydroxylamine tively), and the use of the relation (22) iklid
(id
and it, respec-
= +(Ptd)
(29)
where +(h) is a tabulated function and t d is the time of instantaneous current measurement (drop time). CURRENT STEP SPECTROELECTROCHEMISTRY
Figure 2 shows a typical response for the 410-nm absorbance of the Ti(II1) diffusion layer generated by a current step reduction of Ti(1V) at a 2000 line/inch minigrid OTE in the presence of hydroxylamine. Concentrations are chosen such that [NH30H+] >> [Ti(III)] (first-order conditions). The form of the response is qualitatively that expected from Equation 25. A quantitative assessment made by a plot according to Equation 27 is shown in Figure 3 and reveals an excellent correspondence of theory and experiment. The 2000 linelinch Au minigrid OTE had been shown earlier (3) to adhere to linear semi-infinite diffusion theory for a diffusion-only electrode reaction and electrolysis times exceeding 10-20 milliseconds. The result of Figure 3 shows that the legitimacy of linear diffusion theory for the minigrid OTE is maintained in the presence of a coupled chemical reaction. Equation 26 shows that, given the value of E for Ti(III), rate data can be calculated directly from the steady state absorbance response A R S S . The required values of E were determined by current step reduction of Ti(1V) in the absence of hydroxylamine as described in the Experimental section. The use of Equation 26 is advantageous since noise in the steady state absorbance can be heavily damped. (The total absorbance change in Figure 2, for example, amounts to only 0.015 absorbance unit.) Values of uk obtained from A B S s measurements are presented in Table IV along with that resulting from the analysis of Figure 3. It should be noted that the A R S Smeasurements were conducted over a range of current from 1-4 mA crn-2 with no observed variation, or trend, of uk with current, as prescribed by Equation 26.
_(22) J. KouteckL, Collect. Czech. Chem. Commuri., 18, 311 (1953). 36
Method SP-EC ( A R s ~ ) ~ SP-EC (ti,z)c SP-EC ( A ~ a * ) b SP-EC ( i i , z ) C SP-EC (pl0t)d SP-EC (A~*a)b SP-EC ( t i / z ) c SP-EC (Ans")" SP-EC (tl/.i)c S-Fe S-Fe S-F" S-F' S-F" S-Fe S-F"
A series of rate determinations was effected by the current cessation approach, in which the current step is removed after observable Ti(II1) absorbance is generated (and generally after A R S Sis attained), and the half-life of Ti(II1) absorbance decay measured. These data, converted to uk using Equation 28, are also given in Table IV. Comparison of the Table I V values of uk from the three data analysis approaches shows a very acceptable consistency. In general, the experimental findings indicate that the current step spectroelectrochemical method with the minigrid OTE functions satisfactorily in application to chemical kinetic determinations. It is worth re-emphasizing that this type of controlled current experiment avoids the afflictions of transition time measurements borne by conventional controlled current chronopotentiometric methods. The only concern that the spectroelectrochemical experiment has with transition time is that the optical absorbance measurements must be accomplished at times not exceeding that quantity. Comparing now the kinetic data with previous controlled potential electrochemical results (Table I), we see good accord with our kinetic values in 0.2M oxalic acid medium. The results of Table IV at 0.75M oxalic acid, by lack of dependence on hydroxylamine concentration, verify that the reaction is first-order in hydroxylamine, but at the same time reveal by their diminished magnitude a considerable and previously unrecognized dependence of ak on oxalic acid concentration. STOPPED-FLOW KINETIC SPECTROMETRY
We consider now the stopped-flow kinetic spectrometry experiment in which the effluent of a chamber efficiently mixing two fast-flowing reactant solutions is observed after abrupt flow termination. The practical requirement for applying the stopped-flow experiment to the chemical step(s) of an electrochemical process is that we be able to isolate the chemical step from its electrochemical context. This reaction isolation is possible whenever the electrochemical process involves a chemical reaction between an electrochemical charge transfer-generated species and a deliberately added (or otherwise controllable) reaction substrate. In the stopped
ANALYTICAL CHEMISTRY, VOL. 45, NO. 1, JANUARY 1973
flow experiment, the substrate solution becomes one of the reactant solutions mixed. The second reactant solution is that of the charge transfer-generated (or otherwise chemically preparable) species, which must, of course, exhibit sufficient stability in the absence of substrate for storage and manipulation in the stopped-flow sample introduction system. Many electrochemical reactions of the catalytic, EC, and ECE types contain such potentially isolatable chemical steps and exhibit kinetic control on time scales within the kinetic domain of the stopped-flow experiment. (The short time limit of that domain is determined by the flow-system mixing time, typically a few milliseconds.) Three useful features of stopped-flow kinetic study of a chemical step of an electrochemical reaction can be cited: (i) the independent kinetic and mechanistic determination aids evaluation of the correctness of postulating that chemical step as a kinetically influential subcomponent of the electrochemical reaction and also provides insight into the efficacy of the electrochemical techniques and approaches employed in proposing the chemical step; (ii) heterogeneous charge transfer steps following the primary chemical step in the electrochemistry are voided in the stopped-flow experiment. The importance of alternative subsequent homogeneous charge transfer routes can thereby be explicitly examined (e.g., mechanistic choice between an ECE and an ECC scheme); (iii) involvement of (electrode surface) heterogeneous catalysis in the chemical step becomes revealed by comparing stopped-flow and electrochemical kinetic data. Isolation of the chemical step in the catalytic system considered here is an elementary matter, as reactant solutions of Ti(II1) and hydroxylamine are readily preparable. Their reaction can be followed by observation of the Ti(II1) absorbance at 410 nm in the flow-mixed solution. Analysis of the Ti(II1) absorbance decay is by a conventional first-order kinetic expression, which written in terms of initial (lo),timedependent ( I t ) , and terminal (I,) kinetic spectrometer beam intensities is
In [In ZJZJ
= Pt
- In [In Zo/Zm]
(30)
Experimental plots of Ti(II1) absorbance decay curves according to Equation 30 are linear for approximately two reaction half-lives, thereafter curving toward slower reaction rate. The curvature, which indicates some reaction complexity not evident in the electrochemically based experiments, is more pronounced and evident at shorter times in the reaction at lower oxalic acid concentrations. [Long time deviations were earlier noted in cyclic chronopotentiometric experiments (81.1 Rate constants derived from the linear first half-life of the rate plots are given in Table IV. In the solutions containing 0.2M oxalic acid, the stoppedflow rate data agree both with the spectroelectrochemical and the previous controlled potential electrochemical results. This agreement confirms the electrochemical techniques’ efficacy as applied to chemical processes of this type in eliminating the following conceivable complications : (i) the chemical process is solely a homogeneous one; no surface catalysis occurs; (ii) any adjustment in the coordination of the electrochemically generated Ti(II1) species must be rapid in comparison to the half-life of its reaction with hydroxylamine; (iii) the electrode reaction “2.
+e+
“2-
(31)
must be unimportant in the electrochemical measurement of uk. Some further words of comparison of stopped-flow and spectroelectrochemical (and other electrochemical) methods
1 , sac.
Figure 3. Plot of Figure 2 according to Equation 27 Absorbance values for times 0.2, 0.4, 0.6, 0.8,1.0,1.2, and m seconds are 0.00426, 0.00744, 0.00947, 0.010, 0.0122, 0.0131, and 0.0153,respectively
I
I
I
0.2
0.4
1 06
[Ethyl Alcoholl
,M
08
1.0
Figure 4. Depression of the polarographic catalytic current for 1.00mM Ti(IV), 0.105M hydroxylammonium sulfate by addition of ethyl alcohol
4 0.75M HzCz04 0.20M HtC204 -X0.1OM HzC204 -A-
are in order at this point. There do not seem to be any outstanding differences in reproducibility of kinetic determinations by the two classes of methods. There are likewise no particular convenience differences among the methods in terms of man-hours required for a series of determinations. (This, of course, presumes pre-existing instrumentation and some experience with each method.) The authors’ experience in this and other on-going studies does suggest that, for a reaction to which the stopped-flow kinetic and a spectroelectrochemical (or electrochemical) methods are both applicable, the stopped-flow method will provide more sensitive detection of changes of order or mechanism as a reaction progresses. This is simply a consequence of the absence of mass transfer kinetic effects in the stopped-flow data output and a greater ease in following the reaction over several half-lives. DISCUSSION OF REACTION KINETICS
The preceding results fulfilled this study’s aims with respect to “model reaction-method testing.” Results in Table IV also reveal, however, a substantial solution compositional sensitivity of the Ti(II1)-hydroxylamine reaction kinetics. The reaction was accordingly further explored to uncover, at least in part, the origin of the observed kinetic effect. An obvious possibility for variation of uk with oxalic acid concentration is a variation of the relative efficiencies of Reactions 5 and 6 (e.g., variation of u). This possibility was explored using the approach of Saveant and Vianello (IO), in which polarographic determination of uk is carried
ANALYTICAL CHEMISTRY, VOL. 45,
NO. 1, JANUARY 1973
37
Table F7. Polarographic Kinetic Results, 25 "C [HX2041, M
[",OH+], M
[sO~2-l, M
0.200
0.040
0.25
0.096
0.042
0.021 0.081 0.181 0.28 0.38
uk,
pH
M-1 sec-1
1.40 1.10 0.90 0.68 0.58 1.32 1.34 1.48 1.41 1.42
37.8 36.4 29.4 22.7 18.6 83.0 74.9 68.7 69.1 65.5
out in the presence of ethyl alcohol as a supplemental amino radical scavenger. Results are shown in Figure 4. A depression to ix/(2)1'2(or 71 of il) is expected if ethyl alcohol effects a conversion from a 2/1 to a l j l reaction stoichiometry. The results in 0.2M H2C204confirm the earlier conclusion that Reaction 6 dominates in this medium (u close to 2) (10). Increase of [H2C204]to 0.75M makes Reaction 5 more competitive but does not lower the Ti(II1)-hydroxylamine reaction stoichiometry completely to unity. The results in 0.1M HzC204, surprisingly, show an apparent diminution to u < 1, an effect noted in previous ethyl alcohol scavenger experiments (19). Appearance of a second, more cathodic, titanium catalytic wave upon addition of ethyl alcohol in this medium suggests partial conversion of titanium to a new species. The sensitivity of the reaction stoichiometry to solution conditions is further brought out by the titrimetric stoichiometric assay of Table 111. These results clearly show that competition between Reactions 5 and 6 can vary depending on whether NH,. is generated in a [Ti(III)I-rich or a [NH3OH+]-rich environment. Table 111 would, by itself, suggest that u = 1 in the electrochemical experiments, but the obvious great sensitivity of u to concentration levels makes direct extrapolation of the titrimetric results to the conditions of the kinetic determinations an unsafe argument. The fact that u can vary with concentration levels offers a probable explanation of the long-time kinetic deviations observed in the stopped flow kinetic measurements; a lowering of instantaneous [Ti(III)] and [NH2.]as the reaction progresses would gradually attenuate the participation of Reaction 6, lowering the value of uk. The variation of uk with [H2C20n]cannot be entirely laid to alterations in the reaction stoichiometry, of course, since uk is observed to change by more than a factor of two (com-
38
pare 0.1 and 0.75M oxalic acid in Table IV). Additional polarographic kinetic data, given in Table V, showed that the residual variation is actually a pH effect. Thus, the value of uk in 0.2M H2C204 is lowered to almost exactly that of a 0.75M H2C204solution by simple adjustment of pH to that of the latter solution. The manner in which [H+] exerts this kinetic control is not understood, although two possibilities could be eliminated. A change from the 2/l oxalate coordination (13) of Ti(II1) is not expected as the free [C2042-]over the pH range of Table V varies by less than 15 and the spectrum of Ti(II1) is invariant over 0.2 to 0.75M oxalic acid. Second, postulation of NHzOH as a kinetically more reactive species than NH30H+, although leading to qualitatively consistent predictions, cannot be confirmed by linearity of uk us. [H+]l-. (A plot of uk us. [H+] is linear with negative slope.) Results by Taube et al. (23) on a Cr(H20)62+ reaction also suggest that the reactant is NH30H+. Several early sets of polarographic determinations suggested that uk decreases with increasing [NH30H+]. Closer inspection showed that this effect was due, in part, to a minor change in pH occasioned by acid dissociation of NH30H+ and also to a sensitivity of rate to the sulfate concentration [hydroxylamine is added as (NHaOH+)2SOd]. The latter effect is illustrated in Table V for solutions where the pH has been maintained approximately constant. Although the sulfate rate variation is consistent with that expected from a purely ionic strength effect [increasing ionic strength should diminish uk for a cation (NH30HT)-anion (Ti(C204)2-) reaction], it is also probably a reflection of a Ti(II1)-sulfate interaction (recall spectral sensitivity of ET~(III)to [S04*-]>. It is interesting to note in this connection that sulfate was absent from the solutions used in the discordant chronopotentiometric studies of Table I. In summary, some further details of the reaction of Ti(II1) with hydroxylamine were offspring products of our use of this reaction as a method-testing system. A more complete understanding of the reaction will undoubtedly require a better picture of the Ti(II1) coordination chemistry in these solutions than is at present available. RECEIVED for review June 9, 1972. Accepted September 7, 1972. This research was supported by the Air Force Office of Scientific Research under Grant AFOSR-69-1625 and by the U.N.C. Materials Research Center under Contract SD100 with the Advanced Research Projects Agency. (23) W. Schmidt, J. H. Swinehart, and H. Taube, Inorg. Chem., 7, 1984 (1968).
ANALYTICAL CHEMISTRY, VOL. 45, NO. 1, JANUARY 1973
