Anal. Chem. 1991, 63, 2757-2762
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Kinetic Method Based on Nuclear Magnetic Resonance Measurements Rathindra N. Bose,* Dawei Li, and Shadi Moghaddas
Chemistry Department, Kent State University, Kent, Ohio 44242
A new kinetic method to study redox reactions In soiutlon based on the magnetk susceptlMllty measurements has been developed. The resonance frequency of the H-0-D a n a l of an aqueous solutbn wlth I-5% D20contalnlng Paramagnetic specles depends on the concentration and of unpalred electrons; the frequency-tlme traces constltute the kinetic curves. These rate profiles can be solved by applylng conventional rate laws. I n addltlon to rate constants, these curves readlly yield molar susceptibHnles of intermedlates and products and therefore the oxldatlon states of the same can be determlned by monltorlng the time domain H-0-D signal. For consecutlve first-order reactlons, the sequence of rate constants can be assigned. Furthermore, these traces deal with the redox reactions only and compllcatlons due the secondary wbstltutlon reactlons can be avoided. Thls method has been appiled to four known redox reactions. The frequency-time traces for the oxIdation of homocystelne by the 8-l dichromate Ion ylelded a rate constant of 1.56 X uslng a IO-fold excess of reductant (20.0 mM), which Is In good agreement with 1.63 X I O - ' S - ~ obtalned by the vlslble spectroscopic method. The molar susceptiblllty, 6.23 X cm3 mol-', and a magnetlc moment, 3.84 bB, were also product from the klnetk traces. The evaluated for the Cr( I I I) oxldation of cysteine by the dichromate Ion yielded a rate s-l us~nga 1O-foM excess of reductant constant of 1.2 X (21.0 mM), whlch Is In excellent agreement wIth the value reported by Kwong and Pennlngton. The mdar susceptlblllty (6.98 X I O J an3 mol-') and magnetic moment (4.08 pB)are In keeping wlth the formath of chromlm( III ) products. The secondorder rate constant, 8.5 X I O v 2 M-' s-l obtained for the permanganate ion oxldation of uracil Is also in excellent agreement wlth the llterature values (8.8 X M-l s-l). The magnetic moment, 3.80 pBsupports a predominant Mn( IV) product, In keeping wlth the report by Freeman and coworkers. Finally, the oxallc acM oxldatlon by the dlchromate Ion exhiblts biphaslc klnetlc proflles and the kinetic traces ylelded a magnetic moment, 1.B pB,for the lntermedlate In accord wlth the formation of a translent Cr(V) specles during the reactlon. The rate constants for the formation of lntermediate and Its decomposition were calculated to be 1.8 X and 3.2 X IO-' s-l utlllzlng 5.0 mM Cr(V1) and 50.0 mM oxallc acM. These rate Constants are also in good agreement wlth the values (1.7 X lo-' and 3.6 X IO-' 8-l for the form a t h and decmpodtion of the Intermedlate) obtalned from conventional absorbance-tlme curves. These traces also demonstrate that the rate constant for the formation of the intermediate is larger than that for its decay.
INTRODUCTION Kinetic methods based on NMR measurements such as variation of signal intensity with time, temperature-dependent line width measurements, and more recently self-exchange two-dimensional nuclear Overhauser effect (2DEXSY) ex0003-2700/91/0383-2757$02.50/0
periments are well documented (I, 2). However, none of these methods can be applied to redox reactions involving paramagnetic centers. Here we report a new NMR method based on the magnetic susceptibility measurements in solution (3). This kinetic method yields both rate data and molar susceptibility of the paramagnetic centers (reactants, products, and intermediates). The latter information is valuable for identifying the oxidation states of products and intermediates, especially where more than one oxidation state is possible. Although a kinetic method based on the direct magnetic susceptibility measurements has been reported by Philo and co-workers (4) using a superconducting quantum interference device (SQID) and by Brill et al. (5) utilizing a Rankine balance, methods based on time domain solvent resonance frequency measurements have not appeared.
EXPERIMENTAL SECTION Reagents. Potassium dichromate and oxalic acid are ACS certified reagents. Other chemicals such as L-cysteine, homocysteine, 6-methyl uracil, trisma, D20 (Sigma),and sodium acetate (Aldrich) were used without further purification. Sodium perchlorate was prepared by NaZCOaneutralization with HC10,. Acetate- and Tris-HC1 buffers of desired pH were prepared by mixing appropriate concentrations of acids and their conjugate bases. Stock solutions of potassium permanganate was prepared, standardized, and stored as described (6). Physical Measurements. Nuclear magnetic resonance measurements were performed on a 300-MHz GE (GN 300) instrument equipped with wide-bore variable-temperature probe heads. The temperatures in the probe were kept constant (f0.1 "C). Deuterium was used as a lock signal. A computer-interfaced double-beam spectrophotometer (Perkin-Elmer Lambda 600) was employed for the UV-visible spectral measurements. Rate Measurements. (i) NMR Method. Reactants of desired concentrations in aqueous solution containing 5% DzO (v/v) were mixed. Aliquots (0.5-1.0mL) of this reaction mixture were then placed in a NMR tube. Alternatively, the reactants are mixed in the NMR tube and then placed in the probe. The mixing time was recorded. Immediately after the sample was placed in the probe, the resonance frequency of the H-O-D signal was measured through a data acquisition subroutine, 'Kinet". The program controls the application of pulse at preassigned time intervals and acquires and stores the free induction decays (FID). A IO-fis pulse (90")was applied for these measurements. Since only the H-0-D signal was monitored, a single scan was sufficient to generate a spectrum with signal/noise > 100. Note that no pulse delay is necessary for this experiment. Usually 20-30-s delays were encountered between the mixing of the reactants and the first data acquisition. This delay time was recorded and accounted for the display of the frequency-time data. The data acquisition time depends on the sweep width and number of data points selected for a single FID. Since only the solvent peak is monitored, usually a 100-Hz sweep width and 256 data points were selected which lead to a 10-ms data acquisition time. Time intervals between the pulses can be set to any number >10 ms. However, if the precision of the resonance frequency is desired within 0.02 Hz, at least 2K data points would be required and the acquisition time will be increased to 80 ms. These acquisition times were negligible in comparison to the reaction time for conventional mixing. Ideally, negligible reaction should take place during the data acquisition and therefore the selection of time intervals must be based on the reaction time. For example, half-lives for the ura0 1991 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 63, NO. 23, DECEMBER 1, 1991
cil-permanganate reaction in our conditions were 3-8 min. A 10-5 time interval was selected for the first 3 min followed by 30-9 intervals for the remainder of the reaction. At the end of the reaction, free induction decays were retrieved and transferred to spectra. Kinetic profiles, frequency of the H-O-D resonance vs time, were then generated. Rate constants and molar susceptibilities were then calculated from these frequency-time curves utilizing appropriate rate equations (see the Results). The rate constants obtained from single-exponential frequency-time curves can be reproduced within 4%. The molar susceptibility in replicate measurements agrees within 5 % . For biphasic kinetic profiles, the errors in rate constants are estimated to be f7% and susceptibility can be reproduced to better than 6%. All commercially available FT NMR instruments are equipped with software to record spectra at a regular time interval and can be utilized for these measurements. (ii) UV-Visible Method. Rates of reactions were also measured by monitoring absorbance with time. For each reaction, at least two wavelengths were selected. Rate constants (ko) for first-order processes were obtained either from computer simulation or semilogarithmic plots according to the equation D , = (Do - D,)e-kd
+D,
(1)
where Do, Dt, and D, are absorbance values at zero time, at time t, and at infinite time. For consecutive first-order reactions h
h
A-B-C the rate constants and the molar absorptivity of intermediates were calculated by using a nonlinear least-squares iterative computer program according to the equation (7,8)
a
200
-1000
-200
0
-1200
Hertz Figure 1. Solvent proton resonances of an aqueous tert-butyl alcohol solution (80% H,O, 10% D,O, and 10% fert-butyl alcohol; v/v) in the presence (outer tube) and absence (inner tube) of K,[Fe(CNb] recwded on a 300-MHz Instrument. The frequency separation for H,O-D,O protons (part a) is 29.1 Hz and that for the methyl resonances of tert-butyl alcohol (part b) Is 29.4 Hz.
Table I. Molar Susceptibility of Selected Transition-Metal Complexes Using H-0-D and tert-Butyl Alcohol as Internal Markers at 25 "C cms mol-' tert-butyl alcohol lit. values marker (11)
l@xMc,
where A. is the initial concentration of A and €1 is the molar absorptivity of the intermediate. The rate constants thus evaluated were compared with those obtained from the frequency w time profiles. The reproducibility of rate constants fom monophasic curves was within 5 % , and that for the biphasic profiles was better than 8%.
RESULTS I. Selection of an Internal Reference for Susceptibility Measurements in Solution. The difference in frequency, AY, of any resonance of an inert solvent in the presence
compd
H-0-D marker
[Cr(H20)6IC& Na[Mn(EDTA)(H20)] K,[Fe(CN),I
6.07 14.9 2.21
5.96 2.12
Table 11. Rate and Magnetic Susceptibility Data for Various Redox Reactions at 25 O C [oxidant], [reductant], mM mM
rate constants,
l@xMc,
5-1
cm3 mol-l
pel[, pB
MnOL-6-Methyl Uracil Reaction
and absence of dilute paramagnetic substance in a magnetic field (3,9,10)produced by superconducting solenoids can be expressed as
2.7
20.0
1.7 x 10-3
6.07'
3.80'
Cr(V1)-Homocysteine Reaction 2.0
(3) where Y is spectrometer frequency, XM is the molar susceptibility of the paramagnetic substance, XM' is mass susceptibility of the solvent times the molecular mass of the paramagnetic species, and C is the concentration (mol mL-') of the paramagnetic center. The NMR-based magnetic susceptibility measurements in solution are conventionally performed in aqueous organic solvents in coaxial tubes (3);usually, an inner tube contains the solvent, and the solution of the paramagnetic species is placed in an outer tube. The selection of an inert solvent is often a problem. The addition of the organics can be avoided by using 5-10% D20, which can be used as a lock for the high-field instrument, and the proton of the H-0-Dsignal can be measured. The use of DzO as an internal marker can be demonstrated by placing a paramagnetic substance in a mixed aqueous (containing small amount of DzO) organic solvent and measuring the proton resonances of the solution and solvent in coaxial tubes for both the organic substance and aqueous proton. Figure 1shows almost identical AU values
6.15 14.5 2.30
20.0
1.56 X 1.63 x
6.23e
3.86
7.0e
4.11
1.68d 5.ge
3.g
10-3'
Cr(V1)-Cysteine Reaction 2.0
21.0
0.0126 0.0115°
Cr(V1)-Oxalic Acid Reaction 50.0
1.7 X 3.6 X 1.8 x 3.2 X
10-3'*b 10-"'*c 10-3b lodc
19
Rate constants obtained from the UV-vis spectroscopic method. * Rate constant for the formation of the intermediate. Rate constant for the decomposition of the intermediate. dSusceptibilityfor the intermediate. e Susceptibility for the product. fMagnetic moment for the product. #Magnetic moment for the intermediate. (I
for tert-butyl alcohol resonances and for H20-Dz0 resonances for a dilute solution of K,[Fe(CN),] (10 mM) in 10% D2010% tert-butyl alcohol contained in an outer tube and the solvent mixture alone in the inner tube. Table I compares the susceptibility data obtained by using the H-O-D signal and tert-butyl alcohol as internal markers.
ANALYTICAL CHEMISTRY, VOL. 63, NO. 23, DECEMBER 1, 1991 2750
For dilute solutions (1-5 mM) of metal-aqua complexes, the solvent H-0-D concentration is many-fold higher than coordinated water. The latter signal is not observed in our conditions since we collect FID from a single scan only. Further, we expect that the coordinated water signal will be masked under that of H-0-D and should not impose any problem for monitoring the solvent peak with time. 11. Derivation of Rate Expressions. For a first-order reaction, A L B, (representing the molar susceptibility of A and B as x M A and XMB) eq 3 can be rearranged to
( 6-~6B)Coe-kt + 6&0 =
(4)
For reactions where A is the only paramagnetic species, 4~ consists of diamagnetic terms and is very small compared to 4A. Similarly, if the product is the only paramagnetic substance, 4Ais composed of small diamagnetic terms and is small compared to $A. Therefore eq 4 can further be simplified to
depending on whether reactant or product is the only paramagnetic species. Since 1.1.1 depends on concentration and susceptibility, Au-time profiles for redox reactions should afford both molar susceptibility and rate constants. For consecutive first-order reactions kl
A-B-C
kz
the frequency change can be expressed by the conventional double-exponential form (7):
IAvl = ale-klt
+ u2edkZt+ c
(7)
Nonlinear least-squares fits of the double-exponential curves would readily generate values for al, a2, the rate constants. Since $cAo is known, 4Band 4~ can be obtained and hence the molar susceptibilities of the intermediate and products can be calculated. The application of this method is demonstrated in four known reactions described below. 111. Application to Rate Measurements. A. Reactions of Cysteine and Homocysteine with Chromium(V1). The reaction between homocysteine and Cr(V1) was followed by monitoring the change in solvent frequency with time. A total change of 15 Hz was observed by using 2.0 mM Cr(V1) and 20.0 mM homocysteine. In triplicate measurements, the first-order rate constants, (1.56 f 0.05) X s-l, were evaluated from this kinetic curves. The reaction was also followed by an absorbance change at 372 nm. The rate constant, (1.63 f 0.06) X s-l, obtained from the absorbance-time trace is in excellent agreement with that from the NMR method. The uncorrected susceptibility of the product was calculated to be 6.30 X cm3 mol-l, which corresponds to an uncorrected magnetic moment of 3.85 j ~ ~ . Kwong and Pennington (12)proposed a detailed mechanism for oxidation of cysteine by chromium(V1) near neutral pH.
30
1
20
: a-
a
10
0
0
1000
2000
3000
4000
Time, s Figure 2. Observed (asterisk)and calculated (solM line) Au (of H-0-D signal) vs time for the oxidation of 6-methyl uracil (20 mM) by permanganate anion (2.7 mU) at 25 "C in 0.2 M phosphate buffer (pH
= 6.8). The calculated line is the computergenerated trace utillzlng an iterative nonlinear least-squares program according to eq 4 with k = 1.69 X s-' and +BCo= 19.2.
The Au-time and absorbance-time traces for this thiol oxidation exhibit first-order profiles for which semilogarithmic plots maintained linearity for more than 4 half-lives (using a 10-fold excess of cysteine). A net change of 18.6 Hz for the H U D signal was observed during the reaction using 2.0 mM Cr(V1) and 0.021 M cysteine at pH 7.0. The first-order rate constant, obtained from the Av-time curve, (1.26 f 0.05) X s-l, is in good agreement with the value, (1.15 f 0.05) X s-l, obtained from the absorbance-time profile under identical condition. These values are also in agreement with the reported (12) value, 1.28 x s-l, at 21.8 mM cysteine. The kinetic profile also yielded an uncorrected molar susceptibility, 7.1 X lo9 cm3mol-', for the Cr(II1) product. The magnetic moment (uncorrected) can be calculated as 4.1 ~LB. B. Reaction of the Permanganate Ion with 6-Methyl Uracil To Form Manganese(1V) Species. Freeman and co-workers (13) reported that the oxidation of C=C in uracil and its derivatives by the permanganate ion afforded a manganese product with an average oxidation state of 3.5 X 0.1. On the basis of the UV-visible spectral evidence and titration date, these authors concluded that a soluble manganese(1V) species, perhaps H2Mn03-, is the dominant product. The second-order rate constant for the oxidation of 6-methyl uracil is reported to be 8.8 X lo-* M - ' d in 0.2 M H2P04--HP0,2- buffer (pH = 6.8) at 25 "C. Figure 2 shows the Av-time profile for the same reaction using 2.7 mM MnO, and 20.0 mM 6-methyl uracil at 25 "C. The first-order rate constant, (1.7 f 0.1) x lo4 s-l, was evaluated from the Au-time curves from triplicate kinetic runs. The second-order rate constant thus calculated, (8.5 X 0.3) X M-' s-l, agrees very well with the reported value by Freeman's group (13). The uncorrected molar susceptibility of the products of this reaction is calculated to be 6.20 x cm3 mol-l, which corresponds to a magnetic moment of 3.84 p ~ . C. Reaction of Oxalic Acid with Chromium(V1): Intervention of Chromium(V). Srinivasan and Rocek (14) presented detailed kinetic studies of oxalic acid oxidation by chromium(V1). The reaction passes through a long-lived chromium(V) intermediate which was characterized by EPR spectroscopy. Figure 3 shows kinetic profiles obtained by NMR spectroscopy and by spectrophotometric methods. A
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ANALYTICAL CHEMISTRY, VOL. 63,NO. 23, DECEMBER 1, 1991 0.4
a 0 3 u C
L d
0.2 0
x4
0.1 0.0
2000
0
!/
of
,
0
,
6000
4000
,
,
,
,
,
8000
,
10000
,
IO000
Time, s
Flgurs 3. Kinetic curves for the oxalic acid (50.0 mM) oxidation by the dichromate ion at 25 "C in 0.5 M NaCIo,. (a)Observed (rectangles) and calculated (solid line) absorbance-time profiles using 1.O mM chromium(V1). The calculated line was enerated by computer simulation using eq 2 with k , = 1.52 X lo3 s-', k , = 3.78 X 10" s-', Do = 0.335,and 6 , = 348 M-' cm-'. (b) Observed (asterisk) and calculated (solld line) Av vs time curves using 5.0 mM Cr(V1). The calculated profile was generated utilizing a = -3.25,a 2 =: -33.46, c = 36.9,k, = 1.8 X and k , = 3.2 X lo4 s-' according to eq
,
7.
nonlinear least-squares fit of eq 7 yielded (1.7 f 0.1) X and (3.2 f 0.2) X lo4 s-' as two rate constants along with the values of the preexponential parameters al and a2 as -3.25 and -33.46. The rate constants, (1.6 f 0.1) X and (3.6 f 0.3) X lO-'s-', evaluated from the absorbance-time profiles are in good agreement with those from the NMR method. By using the values of a, and a2,the uncorrected molar susceptibility of the product can be calculated as 5.9 X cm3mol-', which corresponds to an uncorrected magnetic moment of 3.8 PB.
DISCUSSION The molar susceptibility data obtained by using H-0-D are in good agreement with those obtained by the tert-butyl alcohol marker and with literature values. The use of small amount of D20 to generate an internal marker therefore avoids the use of a second solvent. Secondly, the use of the inner tube (15) which is conventionally used for magnetic susceptibility measurements is not necessary, especially for the newer generation of high-field instruments with superconducting magnets. Since the drift in magnetic field/frequency is negligible during the experiment, the reference solvent signal can be recorded separately. This reference frequency can be subtracted from the frequencies measured at specified time intervals during the kinetic experiment. In fact, the frequency-time curves readily afford the rate constants as well as the frequency at the onset of the reaction (t = 0, at mixing time). The calculated frequency from the kinetic curves can then be compared with the reference frequency measured independently. Since there is a 20-30-s delay between the mixing and data acquisition times, such comparison is important. We find that for systems under consideration, these two frequencies agree with each other to within f O . l Hz. For the static susceptibility measurements, utilizing 2K or higher data points, the frequency can be resolved to within
f0.02 Hz in our instrument, which would correspond to a volume susceptibility of 3 x emu cmS. The other methods (4,5) for direct susceptibility measurements me more sensitive than the present method. However, since reproducibility of the rate constants in 10 measurements is within 5%, such high sensitivity is not required for this kinetic method. Considering a change in frequency of 1 Hz during a kinetic experiment, the lower limit of the concentration of the paramagnetic species undergoing a one-electron change can be set to 0.8 mM. Similarly, for two- and three-electron changes, the lower limits of these concentrations can be set to 0.4 and 0.3 mM. The uncorrected molar susceptibility obtained directly from kinetic curves can be corrected (xMC) by using where xdiais the diamagnetic correction term. Although exact molecular mass and composition are required for these corrections, we note that xM0 and x& partially cancel, since both are essentially diamagnetic terms but carry opposite signs in eq 8. The residual correction factor usually accounts for no more than 5% of the susceptibility for magnetically dilute paramagnetic substances, even with one unpaired electron. For kinetic experiments, the molecular mass and composition are not generally known; yet the magnetic moment calculated from the uncorrected values (ILeff = 2.83(x~.T)'/*) should not differ more than 2% from the actual moments. Such calculated values would not impose any problems in distinguishing alternatives among paramagnetic species containing one, two, or more unpaired electrons. Since xM0 > xb, the actual molar susceptibility should be less than the uncorrected values. Therefore, a magnetic moment slightly higher than actual values would emerge from kinetic curves if uncorrected susceptibilities are converted to magnetic momenta. The magnitude of the correction factor can be addressed by examining the chromium(VI)-cysteine reaction. The uncorrected molar susceptibility was evaluated to be 7.1 X lo9 cm3 mol-' from the Av-time profile. The magnetic moment based on the uncorrected value amounts to 4.1 pB, a value not much different from that expected for Cr(II1) complexes with three unpaired electrons. The chromium(II1) product for this reaction has been characterized (12) as Na[Cr(~ysteine)~]. 2H20.By using this formulation, we calculate (16)x M 0 and xdiaas -2.15 x lo4 and -0.99 X lo-' cm3mol-'. The corrected susceptibility can be estimated as 6.98 X cm3mol-', which corresponds to a magnetic moment of 4.08 pB at 25 "C. Formation of a dominant manganese(1V) product, presumably HMn03- was suggested for the permanganate-uracil reaction. From our kinetic traces we estimated an uncorrected molar susceptibility of 6.20 x cm3 mol-', which corresponds to a magnetic moment of 3.84 pB. This moment is within the values expected for a Mn(1V) product with three unpaired electrons. The susceptibility for an intermediate obtained from the biphasic kinetic curves depends on the ordering of the rate constants (18). For example, for the Cr(VI)-oxalic acid reaction, if we assume the rate constant for the formation of the intermediate is larger than that for its decay, 1.73 X cm3mol-' can be calculated as xM'for the intermediate which corresponds to a magnetic moment of 1.9 pug. If the sequence of the rate constant is reversed (i.e. the rate constant for the formation of the intermediate is smaller than that of its decay), the uncorrected susceptibility is evaluated to be 8.29 X cm3 mol-' with a magnetic moment of 4.46 p~ at 25 "C. Since the later situation does not correspond to a magnetic moment for any intermediate oxidation studies of Cr (Cr(V) and Cr(IV)), we chose the former sequence as the correct ordering of the rate constants. Taking the formulation of the intermediate (20) as Cr Na[Cr(O)(~xalate)~], we calculate the
ANALYTICAL CHEMISTRY, VOL.
corrected susceptibility to be 1.68 X cm3 mol-'. The corrected magnetic moment, 1.9 pB, is in keeping with a Cr(V) intermediate containing one unpaired electron. The salient features of this method can be summarized as follows: (i) The procedure is simple, and no internal refrence in a coaxial tube is needed. Only 1-5% D20 is sufficient to generate enough H-0-D signal which can be conveniently followed. (ii) The Au-time profiles readily yield rate constants according to the conventional rate laws for first-order, second-order, or any other reactions. (iii) Molar susceptibilities of intermediates and products will emerge from kinetic curves, and therefore the number of unpaired electrons (oxidation states of paramagnetic metal centers) in the intermediates and products can be established. These intermediates and products include EPR-active as well as EPR-silent paramagnetic substances. (iv) Since AYdepends primarily on the concentration and number of unpaired electrons, kinetic curves will provide information of the primary redox reaction only. This offers an additional advantage since secondary substitution reactions sometimes complicate the rate profiles of the primary redox reactions. (v) This method is equally applicable to reactions where little or no absorbance change is associated with the redox reactions. (vi) For consecutive rate processes, the sequences of the rate constants can be established where other conventional methods fail. However, an unequivocal assignment of these rate constants cannot be made if the intermediate exhibits cooperative phenomenon or exists as a mixture of two or more oxidation states. (vii) When anomalous magnetic susceptibilities of the intermediates and products are obtained from kinetic curves, temperature-dependent kinetic experiments can be performed and therefore the possible existence of the cooperative phenomenon can be explored.
ACKNOWLEDGMENT We thank Professor E. S. Gould for valuable suggestions and Dr. Mahinda Gangoda for technical assistance to maintain a constant temperature in the NMR probe. APPENDIX A. Derivation of Equation 3. The difference in frequency, Au, of any resonance of an inert solvent (usually aqueous organic) in a magnetic field in the presence and absence of a paramagnetic center is related to its mass susceptibility (3) by
3Au
xg=
2*vm + xo + xo,
do - d,
In this equation, xg and xo are the mass susceptibility of the paramagnetic species and solvent, m is the concentration (g mL-l) of the paramagnetic ion, and doand d, are the densities of solution and solvent. Live and Chan (9) and Becconsall (10) independently have shown that for a cylindrical sample placed in a superconducting solenoids, the polarizing magnetic field is along the long axis of the sample and the effective magnetic field along this axis is given by
where xv is the volume susceptibility of the sample. Taking this modification into consideration, neglecting the third term of eq 1' in dilute solution, and expressing the concentration in mol mL-' (C), we obtain
(3) B. Derivation of Equation 4. This equation can be derived readily by using
63,NO. 23, DECEMBER 1, 1991
b'l = IAvAl + IAYBl
2761
(44
CA = Coe-kt (4b) C B = (1 - Co)e-kt (44 where IAYAIand IAuB(are the change in frequency for A and B, CA and CB are the concentrations of A and B at any time, and Co is the initial concentration of A. Combining equations 4a, 4b, and 4c, one obtains
lAYl = ($A +~BCO (4) C. Derivation of Equation 7. In this expression, the change in frequency, Au, is contributed by all species, A, B, and C, such that IAul = IAuAl + IAYB~+ lAucl where IAYA~= $AIAo]e-klt
It follows then
LITERATURE CITED (1) See, for example: (a) Espenson, J. H. Chemlcal Kinetics and Reaction Mechanisms; McQraw-Hill: New York, 1981;pp 188-190. (b) Atwood, J. D. Inorganic and Orgenometallic Reaction Mechanisms; BrooksICole: Monterey, CA, 1985;pp 26-27. (c) Drago. R. S. physical Methods in Chemistty; Saunders: Philadelphia, 1977; pp
253-267. (2) (a) Rahman, A. One and Two Dimensional NMR Spectroscopy; Elsevier: New York, 1989;pp 369-371. (b) Crans, D. C.; Rithner, C. D.; Theisen, L. A. J . Am. Chem. Soc.1990, 772, 1901-1908 and references therein. (c) Ni, J.; Kubiak. C. P. Inorg. Chem. 1990, 29.
4345-4374. (3) Evans, D. F. J . Chem. SOC.1959, 2003. (4) Philo, J. S.; Fairbank, W. M. Rev. Sci. Instrum. 1977, 4 8 , 1529-1536. Philo. J. S. Roc. Natl. Acad. Sci. U . S . A . 1977, 74, 2520-2623. ( 5 ) Brill, A. S.; Hartog, H. N.; Legallais. V. Rev. S d . Instrum. 1958, 29, 383-391. (6) Skoog, D. A.; West, D. M. Fundamentals of Analytlcal Chemistry, 4th ed.; Saunders: New York. 1978;p 756. (7) Wilkins. R. G. The Study of Kinetics and Mecahnism of Reactions ol Transffbn Metal Complexes; Allyn -nd Bacon: Boston, 1974; pp 22-23. (8) (a) Bose. R. N.; Viola, R. E.; Cornelius, R. D. J . Am. Chem. SOC. 1984. 706. 3336-3343. (b) Easom, K. A.; Bose, R. N. Inwg. Chem. 1988, 27, 2331-2334. (9) Live, D. H.; Chan, S. I. AnaiChem. 1970, 42, 791-793. (10) Becconsall, J. K.; Daves, G. D.; Anderson, W. R. J . Am. Chem. SOC.
ln70. ... .. 92. .- . 430. .. (1 1) Earnshaw, A. Introduction to Megnetochemistry; Academic Press: New York, 1968;p 35. (12) Kwong, D. W.; Pennington, D. E. Inwg. Chem. 1984, 23, 2528-2532. (13) Freeman, F.; Fuselier. C. 0.;Armsted, C. R.; Dalton, C.E.; Davldson, P. A.; Karchesfski, E. M.; Krochman, D. E.; Johnson, M. N.; Jones, N. K. J. Am. Chem. Soc. 1981, 703, 1154-59. (14)Srinivasan, V.; Rocek. J. J . Am. Chem. SOC. 1974. 96, 127. (15) The use of an inner tube for kinetic experiments is not recommended for the following reasons. First, for smaller Av values at the beglnning
or at the end of the reaction (depending on paramagnetic or dlamag netlc products). separate resonances may not be observed. This Is due to the fact that the line widths of h s e resonances may be iargec or comparable to Av values. Secondly, for hlgh-field instruments, a small field gradient between the tubes may cause an artiflcially large frequency separation, and higher molar susceptibilities may thus be obtained from the kinetic curves. This field gradient would not affect the rate of the reaction, however. (16) The values of xa are calculated by using Pascal's constant ( 17). xMo is calculated by multiplying the solvent susceptibility of water ( 77), -0.72 X lo-' cm3/g, by the molecular mass of the complex under consideration. (17) O'Connor, C.J. In Rogress in Inorganic Chemistry; Lippard, Ed.; WC ley: New York, 1982;Vol. 29,pp 209-211 and 227. (18) I t is recognized that any rate profile dealing with the buildup and decay of an intermediate by firstorder processes can be described by a pair
Anal. Chem. 1993, 63,2762-2765
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of algebraic solutions ( 19) having the same numerical values of the rate constants but with assignments reversed. The molar absorpthrltiy of the Intermediate will be different when the assignment is changed. For example, the t, value for the absorbance-time trace shown in Figure 3 was calculated to be 348 M-' cm-' when the rate constants for the formation of the intermediate and Its decay were 1.52 X and 3.76 X I O * s-'. The molar absorptivity of the same was caiculated to be 399 M-' cm-l when the assignment for the rate constant was reversed.
(19) See, for example: Alcock, N. W.; Denton, D. J.; Moore, P. Trans. Farahy Soc. 1970. 80, 2210. Frost, A. A,; Pearson, R. G. Kinetics and kchenism; Wiley: New York, 1961; p 187. (20) Farrell, R. P.; Judd. R. J.; Lay. P. A.; &amby. R.; JI, J.-Y. I W g . Chem. 1988, 28, 3401-3403.
RECEIVED
1991.
for review July 1, 1991. Accepted September 10,
Indirect Electrochemical Determination of L-Tyrosine Using Mushroom Tyrosinase in Solution Gustavo A. Rivas and Velia M. Solis* Instituto de Inuestigaciones en Fisicoquimica de Cdrdoba (INFIQC), Departamento de Fisicoquimica, Facultad de Ciencias Quimicas, Uniuersidad Nacional de Cdrdoba, SUC. 16, C.C. 61,5016 Cdrdoba, Argentina
An electroanalytical method for quantifying L-tyrosine Is described. Thls technique le based on the measurement of the reduction current of dopachrome, which is formed in solution as a product of the oxidation of L-tyrosine by oxygen catalyzed by the enzyme mushroom tyrosinase also present in solution. The effect of ascorbic acid as cofactor is analyzed and optimal experimental conditions are determined. A vitreous carbon electrode activated in alkaline solution was employed. The method proposed Is a new applkation of the use of tyrosinase for the determination of tyrosine using voltammetric techniques and is an alternative to the amperometrlc tyrosine determination technique.
Scheme I
0 0 dopaqvinone
INTRODUCTION The amino acid L-tyrosine is electrooxidizable on carbon, platinum, and gold electrodes a t high positive potentials through a complex process ( I ) . The irreversibility of the oxidation wave and the complexity of the follow-up chemical reactions make the direct electrooxidation of L-tyrosine a poor method for its direct quantification. The electrochemical mechanism is clearly different from metabolic oxidation in tissues. Some metabolic routes start with the enzymatic ortho-hydroxylation of the aromatic ring, giving ~-3,4-dihydroxyphenylalanine (L-dopa) (2,3) which is oxidizable a t a much lower potential than that for L-tyrosine (2). The electrochemical hydroxylation of L-tyrosine is very difficult to achieve, although yields of 10% of L-dopa obtained by electrolysis in strong acid media have been reported (3). The aim of this work was to develop a suitable electroanalytical method for quantitative determination of L-tyrosine in the presence of tyrosinase, taking advantage of the high specificity of the enzymatic hydroxylation process and the electrochemical response of the o-quinone couples (2). The vitreous carbon electrode is very convenient for this purpose and has been widely used in the electrochemical analysis of various catecholamines (4-6). Nevertheless, the strong dependence of the electrochemical response on the surface state of the electrode is a disadvantage and many physical, chemical, and electrochemical pretreatments have been performed in order to improve the electrocatalytic performance of the electrodes. The reproducibility of the results is dependent upon the extent to which the activating procedure is exactly reproduced (7). The reasons for the electrocatalytic improvement are not completely known ( 5 ) although many explanations have been 0003-2700/91/0363-2762$02.50/0
0
melanic products
-0
A
dopachrome
suggested. There is general agreement with respect to changes in the nature of surface functional groups which might serve as mediators for the electron-transfer reactions (8). Phenolic, carboxylic, and quinone groups have been detected by different chemical, electrochemical, and spectroscopic techniques (7). Kepley and Bard (6) and Beilby et al. (9) have reported the formation of an anodic film of graphite oxide on pretreated surfaces, actually a complex mixture of different oxidized aromatic compounds including acidic functional groups. Although electrochemical activation is very effective for increasing the reversibility of the electrochemical response of many substrates, undesirable side effects have been observed such as the increase in background currents and the enhancement of substrate accumulation on the surface that lower the sensitivity and the specificity of the electrochemical response. These side effects were greatly reduced when the activation procedure was carried out in alkaline solutions, as previously stated by Anjo et al. (10). These authors reported excellent results for the electrooxidation of catecholamines, even in the presence of ascorbic acid, and they explained the improved response in terms of the high solubility of the oxide film in alkaline solutions. 0 1991 American Chemical Society
