Alternating Current Polarography of Electrode Processes with Coupled Homogeneous Chemical Reactions II. Experimental Results with Catalytic Reductions DONALD
E. SMITH
Department of Chemistry, Northwestern University, Evansfon, 111.
b A recently derived equation for alternating current polarographic phase angles with catalytic reductions was subjected to experimental test. Results with the catalytic process occurring when Ti(lV) is electrolytically reduced to Ti(" in the presence of chlorate ion were in excellent agreement with theory. In the supporting electrolyte, 0.200M oxalic acid and 0.0400M potassium chlorate, values of kinetic parameters obtained were kh
= 4.6 i 0.02 X
crn. second-', a: = 0.35 zt 0.03,
k, = 1.02 i 0.03 X
D
= 0.66
lo3 second-',
f0.01 X
R
theoretical equations have been derived describing a x . polarographic phase angle behavior for systems kinetically influenced by preceding (6, 8, 14, 17'1, following ( I ? ) , and catalytic (17) homogeneous chemical reactions coupled with charge transfer. It was indicated (17) that, for many types of electrode processes involving homogeneous chemical reactions, theoretical problems apparently represent little limitation. Experimental tests of these equations have been scarce with experimental observations limited to cases with preceding reactions ( 7 ) . S o phase angle-d.c. potential studies have been reported. Because of the potentialities of a x . polarographic phase angle measurements for studying kinetics of rapid coupled chemical reactions, experi-
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ANALYTICAL CHEMISTRY
USE OF A.C. POLAROGRAPHY WITH
this would involve manipulation of complicated mathematical expressions and would be limited regarding magnitude of charge transfer rates determinable. Theory predicts relatively simple relationships for a x . polarographic phase angles with catalytic reductions (17 ): cot+ =
CATALYTIC REDUCTIONS
Most types of coupled chemical reactions show less influence on d.c. polarographic waves with increasing reaction rate. The potential application of relaxation techniques, such as a.c. POlarography, to rapid reactions falling in
and, a t any frequency, plotting cot+ us. Ed.o. will give a maximum where
second-'
Phase angle behavior observed when hydroxylamine is chemically reduced by electrolytically generated ferrous triethanolamine complex in basic solution were in good qualitative agreement with theory. However, an additional following chemical reaction was detected with this system making quantitative comparison of phase angle data with simple theory unjustified. Applications of a x . polarography to systems involving catalytic reductions are discussed. ECETTLY.
mental investigations have been undertaken in these laboratories with the initial purpose of testing the validity of theory. The present paper reports results obtained with a catalytic reduction.
L
this category is well recognized. However, the inverse is true with catalytic reactions, whose influence on d.c. waves increases with increasing rate. Because no fundamental limitation regarding rate exists for d.c. polarographic studies of catalytic reductions, one is led to conclude that a x . polarography represents no advantage for such systems. This conclusion may be considered justified if it is limited to consideration of measurement of rates of the chemical reaction with simple systems. For determining electrochemical charge transfer rates with catalytic reductions and for studying systems more complex than the usual scheme
(where Z is the chemical oxidizing agent present in large excess) other factors must be considered. Primarily because of theoretical complexity, d.c. polarographic evaluation of charge transfer rates with catalytic reductions has not been reported. I n principle, such measurements are possible utilizing the general theory of d.c. polarographic kinetic currents of Koutecky and coworkers (3,12). However,
where X
=
g = kc/w (5) (khlj/D'/Z)(e--ol + e P 3 ) = (kh/U1'*)(e-aj f e a J ) ( 6 )
j Eri/2 =
(nF/RT)(Ed.o. -
(7) Eo f ( RT / n F )ln(A/fT D , / D o) l i p ( 8) =
D = Do
f
=
DE
=f3:
Er1/2)
(9) (10)
B = l - a
(nutation definitions are given in the appendix). Use of sufficiently high frequencies eliminates influence of the chemical reaction [cot+ = 1 ( ~ W ) ' ' ~ / X ] and evaluation of kh and (Y is most conveniently accomplished under these conditions. However, evaluation of kh, a, and k , a t lower frequencies, where chemical and electrochemical kinetics influence results, does not involve undue difficulty. Enhancement of effects of charge transfer on phase angles with catalytic reductions has been mentioned (17). I n essence, rapid chemical reoxidation
+
of the product of electrolytic reduction drives charge transfer more strongly than does diffusion. This property could be used to advantage in the measurement of very rapid charge transfer rates. Addition of an electrochemically inert oxidizing agent to induce catalytic reduction magnifies charge transfer influence on cot$ us. Edc behavior, enabling measurement of values of kh and LY otherwise inaccessible to conventional a x . polarographic studies. However, the relative scarcity of known catalytic reduction processes and the fact that one cannot always assume addition of chemical oxidizir g agent will not perturb characteristics of the charge transfer process (by complexation or change in double-layer structure) under investigation probably limits application of this effect to a 'em specific systems. Nore complex proce: ses than represented by Equation 1 licely occur occasionally. For example, preceding or following reactions may occur simultaneously with chemical oxidation yielding reaction schemes of the types
Fiyure 1 . Frequency dependence of phase angle with H2C204 solution
AE = 5.00 mv.,
Ed,o,
= -0.290 volt
electrode processes involving catalytic reductions, showing potential advantage in measurements of electrochemical charge transfer rates and in studies of complex processes. (13)
and others. With suck processes, d.c. polarographic detection of the preceding or following reactions and distinction between possible mechanisms could be accomplished by lengthy studies, varying concentrations of 1be appropriate reagents (varying ligand concentration, etc.). Even with these efforts, it is unlikely that d.c. polarographic studies would yield values for all kinetic parameters due to rapidity of reaction or theoretical complexity. Rigorous theoretical derivation of a.c . polarographic phase angles for such processes, considering kinetics of all reactions, is readily accomplished (2 8) and mathematical expressions are not overly complicated, considering thl? nature of the processes under consid2ration. Phase angle theory also predicts relative ease of distinction bemeen different mechanisms-e.g., betwven schemes 13 and 14. TTTOsystems of these types, one mentioned below, are currently under investigation in these laboratories. From the above considerations one can conclude that a x . 3olarography is not without merit in the investigation of
EXPERIMENTAL
The a x . polarograph employed in this work makes use of operational amplifier circuitry (2, 4, 9, 16) for control of applied potential and tuned amplifiers (19) to eliminate extraneous noise and higher harmonic faradaic currents from the fundamental harmonic current signal. Selective amplification of the signal of interest is particularly essential in the present studies because of faradaic nonlinearity associated with the presence of the coupled catalytic reaction. The instrument was substantially identical to one described previously, as were methods of measuring alternating current amplitudes and phase angles (16). One modification was replacement of the commercial signal generator, previously employed, by an oscillator obtained by permitting oscillation in a tuned amplifier. Oscillation is achieved by introducing a small amount of positive feedback by capacitive coupling of the output and positive input of the operational amplifier (capacitive impedance -2 to 5 megohms). Short term frequency instability in many moderately priced commercial instruments introduces significant low frequency (
