N. WINOGRAD, H. N. BLOUNT,AND T. KUWANA
3456 valid because the first is the low, constant field case with Ee IcT and the relaxation time for total alignment of the dipole is not predictable from the Boltzmann region in which there are only minute departures from randomness. If one accepts five fairly discrete component bands in the e-solv spectra for mixed solvents, then each of the correlated species must be fairly well characterized according t o dipole geometry. They cannot preexist and must, therefore, have formed by relaxation prior to observation ( 7)
=
0
(20)
Application of the convolution theorem to eq 12 gives6 Ao(X,t
5
r) =
2 -EO(X)CROa
4;
(21)
and
Ao(X,t
>
2
r) = -eo(A)C~OdB{dt
d71.
- dF-7) (22)
Formation of the ratio The Journal of Physical Chemistry
CRo e r f f p d t }
(18)
1
(27)
and
erf { PdK ]
Consideration of the absorbance parameter A ,,/A f predicts the absorbance ratio Ao(A127) -
At
AO(X17)
=
-
AO(h17)
(28)
which is graphically depicted in Figure 1. Hence the measured absorbance at t = r and t = 27 is sufficient to determine the kinetics of the coupled chemical reaction without consideration of any nondifusing processeslS as long as the step time, 7, and the concentration of catalytic reagent, C,, are known.
Experimental Section A potentiostat similar in design to one previously (16) R. Brdioka and K. Wiesner, Collect. Czech. Chem. Commun., 12, 39 (1947). (17) K. Wiesner, Z . Elektrochem., 49,164 (1943). (18) R. Brdioka and K. Wiesner, Collect. Czech. Chem. Commun., 12, 138 (1947). (19) K. Wiesner, ibid., 12,64 (1947).
SPECTROELECTROCHEMICAL MEASUREMENT OF CHEMICAL REACTION RATES described2 was employed. A Hewlett-Packard Model 467A amplifier served as the booster. I R compensation20was provided by a differential current-measuring amplifier21 rather than a current follower. The potentiostat has a peak output capability of 10 W and a rise time of 2 V/psec was a typical performance into capacitive load. A Hewlett-Packard Model 33003302 waveform generator provided linear sweep and step voltage for driving the potentiostat. A Moseley Model 7035B X-Y recorder, a Tektronix Model 564 storage oscilloscope, and a Midwestern Instruments Model 800R light-beam oscillographic recorder were used for signal-monitoring purposes. Spectral scans were made on a Gary Model 15 spectrometer. For set wavelength studies, a 55-W quartz-iodide tungsten lamp, a Schoeff el monochromator, and an EM1 9592B photomultiplier tube (PMT) in a Pacific photomultiplier housing were mounted in an appropriate configuration and enclosed in a light-tight "black box." The P M T collector current was amplified using an KSL LM201 integrated circuit in the current-follower mode. The box and associated apparatus were all mounted on a Barry Controls vibrationless table. Changes in absorbance of 2 parts in lo5could be detected. A sandwich-type cell' with electrode area of 0.6 cm2was employed. Antimony-"doped" tin oxide glass with a resistance of ca. 6 ohms/square was obtained from Corning Glass Co. All potentials are reported with respect to a saturated calomel reference electrode. Reagent grade chemicals were used. Buffer solutions were made from glycine (0.5 M) and nitric acid. All solutions were made just prior to use. Nitrogen, passed over hot copper turnings, was used for degassing solutions. Temperaturc was maintained a t 25 f 1". Calculations were performed on the Univac 1108 computer.
Results and Discussion The catalytic reaction scheme Fe(CNh4-
I
R 2Fe(CN),3-
O
O
+
Fe(CN),3-
+
e(29)
I
+
2Fe(CN),4-
3459
06b/ 0 51
05
00
10
15
20
P22
Figure 1. Double potential step spectroelectrochemical working curve for pseudo-first-order catalytic mechanism.
2 and results are in agreement with Martell, et al.,la who reported the AHz02-catalyzed reaction by ferric ion. This reaction appears quite general for a wide variety of metal ions and metal chelates with AH2.14J5 Because of the stoichiometry, both oxidation steps of ascorbic acid by ferricyanide must be considered, namely AH2
+ Fe(CN)a4- + H f
(31)
+ Fe(CN)sa- -% A + Fe(CN)8*- + H f
(32)
+ Fe(CN)e3--%
AH.
and AH.
where AH. and A are the one- and two-electron oxidation products of ascorbic acid. Since IC2 may be assumed to be much faster than k~ in the above scheme, a steady-state treatment22applied to AH gives
- [Fe(CN)sa-l dt
= 2kl [Fe(CN)s3-][AH%] (33)
Hence the reported rate constant (IC in eq 30) is, in fact, 2k1 where kl is the rate constant for the rate-determining reaction. The oxidation of ferrocyanide in acidic media a t tin oxide otel proceeds a t a diffusion-controlled rate for a potential-step experiment and obeys results predicted by the relationship in eq 1. Cyclic voltammetric i-E curves of ferrocyanide in glycine-nitric acid buffer solutions of pH 2.0 and 2.7 at tin oxide ote are shown in Figure 2. For a double step potential experiment, the light absorbance of ferricyanide followed that predicted by eq 21 and 22. That is, the absorbance is a linear function of .\/t for t 5 7 and a linear function of (dt l/&) for t > 7 . This linearity was obeyed over step times of T from 50 to 1000 msec a t a potential step of 0.0 to 0.5 V and then back to 0.0 V. An example of the absorbance-time (A-t) curve for ferricyanide (double step) is shown in Figure 3. The calculated values of molar absorptivity, BO, equal to 1.02 X loa
-
OH OH ascorbic.acid (AH,) R = CH,CH(OH)
+
2Ht
(30)
where ferricyanide is electrochemically generated from ferrocyanide, was used quantitatively to test the derived relationships. The stoichiometry of reaction 30 was established by potentiometric titrations at pH
(20) E.R.Brown, D. E. Smith, and G. L. Booman, Anal. Chem., 40, 1411 (1968). (21) Suggestions on circuit by A. Pilla, Ft. Monmouth, N.J. (22) J. Koryta, Collect. Czech. Chem. Commun., 19,666 (1954).
Volume 75, Number 10 October 1969
N. WINOGRAD, H. N. BLOUNT, AND T. KUWANA
3460
6 4 0 0 4
L. 10.6
I
.0.2
-0.4
VOLTS
w
.0.0
SC.E.
Figure 2. Cyclic voltammetry at tin oxide ote of: (A) 2.4 mM F e ( C N ) P at pH 2.0; (B) 2.4 mM Fe(CN).'- at pH 2.7; (C) 71 mM AH,at pH 2.0; (D) 71 mM AH, at pH 2.7. All results were obtained in glycine buffers employing an electrode area of 0.6 em' and a sweep rate of 100 m V / m .
Time
(mrecl
Figure 4. Absorban-time behavior for single potential step electrolpis of 2 mM ferrocyanide at tin oxide OTE in glycine buffer of pH 2.2 containing 200 mM AH,. Step amplitude: 0.0to +0.5 V ua. see; 8' = 2.6.
cyanide (5 mM) oxidation in the presence of AHI (100 mM) is shown in Figure 4. A steady-state concentration of the reactive intermediate, in this case femcyanide, is attained after a time as predicted by eq 19. The calculated rate constant by the steady-state method as a function of ferrocyanide and AHz concentration is 13.6 rt 0.2 M-I sec-I and data are summarized in Table 11. The rate constant is independent of varia-
Tabla 11: Evaluation of Rate Constants by the Steady-State Metbod" ~ ~ ~ ~for~ dmhk ~ P - potential 1 i ~ ~ step ~ ~ Figure 3. A l ~ i ~ ~ ~ I Iwluivior
electrolysis of 5 m.11 ferrocyanide at, t i n oxide ole in glycine buffer of pH 2.0. Ordinate: 10-a absorbance unitldiv; abscissa: 20 msecldiv; step amplitude: 0.0 to +0.5 V v8. Sce.
M-I cm-I at X 420 nm and 4 5 = 2.55 X IO-' em =-'/' are in excellent agreement with previous ones.' The quantity A b / A t as defined by eq 23 remained constant over a T variation of 50-1000 msec, verifying the diffusional control of the forward and reverse electron-transfer steps. Data are given in Table I. TableI: As/Alfor Diffusion-Controlled Case"
.*
mwo
1000 500 2.50
100 50
Ab/AC
* * *
0.572 0.006 0.574 f 0.002 0.580 0.003 0.578 f 0.007 0.580 0.005 Av 0.577 0.005
*
'Ferrocyanide cancentration wea 5 mM; HNOrglycine buffer adjusted to pH 2.2.
Equation 18 predicts the absorbance to follow a dependenceof (I/S)erf{S V-t) during a single potential step for a catalytic scheme. The A-l curve for femThe J a r d of Phy.*d Chntidry
lIC*Fe(CNld-I,
mM
2.07 2.06 2.06 4.96 4.98 5.02
IAwrbio Acidl. mM Ab.orbmcs
50 100 200
50 100 200
0.00652 0.00457 0.00326 0.0158 0.0109 0.NXO
5.m-1
k, M - l
0.678 1.38 2.70 0.667 1.40 2.67
13.6 13.R 13.5 13.4 14.0 13.4 Av 13.6f. 0.2
-
MO-I
* 45 = 2.55 X lo-' em sec-'/*; e 1.02 X 10' 1. mol-' om-'; HNOrglyune buRer adjusted to pH 2.2. tiona in ferrocyanide and AH, concentrations over a wide range. It should be emphasized that the present optical technique allows the following: (i) Z or Z' components may be undergoing faradaic electmntransfer reactions but do not interfere if the concentration of Z is not appreciably altered in the reaction layer and the electrode products of Z and Z' do not enter into the catalytic reaction; (ii) conventional optical apparatus (ie., spectrophotometer) can be employed for measuring absorbance to determine fast kinetic rates using the steady-state method. Experimentally, the current due to the oxidation of AH, becomes a p preciable a t E > +0.6 V and values of the observed rate constants vary. However, the value of 8' remains invariant of E steps between +0.4 and +0.6
SPECTROELECTROCHEMICAL MEASUREMENT OF CHEMICAL REACTION RATES
3461
Table 111: Evaluation of Rate Constants by Double Step Method" T,
maec
[Ascorbic eoidl, mM
A(?)
A@?)
see-1
B2.
k, M
-1
sec-1
1000 500 250 500 250 100 250 100 50
50 50 50 100 100 100 200 200 200
0.0117 0.00935 0.00794 0.00815 0.00745 0.00500 0.00576 0.00451 0.00312
5 mM [Fe(CN).P] 0.0022 0.00261 0.00272 0.00152 0.00206 0.00179 0.00109 0.00143 0.00111
0.698 0.355 0.143 0.70 0.35 0.13 0.69 0.24 0.13
0.695 0.710 0.730 1.40 1.40 1.30 2.76 2 -40 2.60
13.8 4 0.6 14.2 ?C 0.3 14.6 4 1.1 14.0 4 0.3 14.0 4 1.1 13.0 4 2.5 1 3 . 8 4 0.8 12.0 11.8 13.0 i 2.1
500 250 100 250 100
100 100 100 200 200
0.00375 0.00299 0,00216 0.00545 0.00402
2 mM [Fe(CN#-] 0.00065 0.00079 0.00077 0.00109 0.00125
0.765 0.340 0,133 0.640 0.26
1.53 1.36 1.33 2.56 2.60
15.3 4 2.1 13.6 f 1 . 2 13.3 4 2.2 12.8 4 1.8 13.0 f 3 . 1
' "03-glycine
buffer adjusted to pH 2.2.
V and under the conditions of AH,:ferrocyanide concentrations of 50: 1 where the current due to AH2 oxidation was ca. 3 times greater than that for ferrocyanide oxidation at +0.6 V. It is fortunate that the electrooxidation of AH2 is sufficiently irreversible (see AH2 i-E in Figure 2 ) a t tin oxide compared to the quasireversible behavior ( E A H=~ +0.22 V) a t HgS2* This allows the selective oxidation of ferrocyanide in the presence of AH2. The double potential step method (eq 28) predicts an absorbance ratio from which k can be determined. The data for AH2-ferrocyanide are summarized in Table I11 for 2 and 5 mM ferrocyanide concentrations over a wide range of r times. The values of k are in good agreement with those obtained by the single-step method. The most precise kinetic parameters are found for values of p2r in the range 0.3-0.8, and r can easily be adjusted to fulfill this condition. The dependence of the rate constant on pH was examined, and the results are shown in Figure 5 . The observed rate constant is linearly dependent on [H+]-', which indicates that the monoanion AH- is the reactive species. Martell has shown13that if the neutral species and monoanion react independently with oxidizing agent, the observed rate constant may be expressed as (34) where AH^ and AH- are the rate constants for the reaction of AH2 and AH- with the oxidizing agent and K1 is the first dissociation constant of AH2. Equation 34 is graphically shown in Figure 5 , and a least-squares fit of the data shows that AH, = 6.7 f 0.5 while AHreacts with a bimolecular rate constant of 434 f 15 M-l sec-' a t the 95% confidence level.
'I'
I
0
1
I
I
2 l/[HY
1
I
I
3
4
5
x Figure 5. Plot of k&sd as determined by the steady-state method vs. (l/[H+]) X 10%. Step amplitude: 0.0 to +0.5 V us. sce; [Fe(CN)e4-] = 2.4 mM; [AH21 = 59 mM. Slope = 0.0396 (=k0.0014), intercept = 6.69 (10.45); standard deviations are for 95% confidence limits.
Summary The technique of spectral determination of the kinetics of coupled catalytic reactions by the use of ote affords precision comparable to the double potential step chronocoulometric technique described by Christie, et al.,6,E as long as the reactive intermediate possesses a sufficiently large molar absorptivity. The maximum first-order rate constant which can be measured with a 90% confidence limit is given by (23) L. Meites, "Polarographic Techniques," 2nd ed, Interscience Publishers, New York, N. Y., p 679.
Volume 73, Number 10 October 1969
DOUGLAS P. FAYAND NEIL PURDIE
3462
p = 5€t(X)C?
(35)
based on an absorbance sensitivity of 2 X lo+. I n addition to the advantages of ratio measurement inherent in double potential step chronocoulometry, the spectral approach has the additional attributes of direct observation of the reacting species, insensitivity to “nondiffusing” electrochemical effect^,^ and freedom from the restriction of complete electroinactivity of the catalytic agent, Z. The theoretical relationships presented here have been verified using the ascorbic acid-ferricyanide catalytic system. The powerful generality of spectral methods lies in the fundamental statement of the absorbance of the reactive species in the transform plane, namely (11’) Hence this technique is applicable to any kinetic scheme for which the transform of the reacting species, Ct(z,s), can be written.
The case of overlapping _ _ - spectral bands which complicate the measurement of the absorbance due to the reactive intermediate has been discussedz4 and this effect has been quantitatively evaluated. The extension of the spectral technique to much faster reactions through the use of internal reflection spectroscopy (irs), as well as further application of the transmission techniques discussed here, is presently being pursued. Acknowledgments. The authors gratefully acknowledge the financial support provided by Grant No. GM14036 from the Research Grant Branch of the National Institutes of Medical Science, National Institutes of Health, and by National Science Foundation Grant No. GP9306. N. W. gratefully acknowledges support by the National Institutes of Health for a predoctoral fellowship, 1968-1969. The authors also appreciate the interest of R. Van Duyne during the initial stages of this work. (24) G. Grant and T. Kuwana, J . Electroanal. Chem., in press.
Calorimetric Determination of the Heats of Complexation of the Lanthanide Monosulfates LnSO,+ by Douglas P. Fay and Neil Purdiel Department of Chemistry, Oklahoma Stale University, Stillwater, Oklahoma 74074
(Received March 17, 1060)
Heats of complexation of the 1:1 sulfate complexes of the trivalent rare earth ions and yttrium have been measured calorimetrically at 25” using the known stability constants. The conditions were corrected to zero ionic strength using an extended form of the Debye-Huckel equation, and the results are compared with values obtained in a 2.0 M perchlorate medium. A linear correlation is observed between log k , the first-order rate constant for complex formation, and log K , the over-all stability constant for the members Ce(II1) through Ho(II1). This observation is taken as being indicative of a dissociative mechanism.
Introduction Recently the rates of formation of the trivalent rare earth monosulfate complexes were measured by the pulse technique of ultrasound absorption.zJ Experiments are in progress in which the temperature dependence of the rates of formation are being ~ t u d i e d . ~It has been suggested5 that if the mechanism for a ligand substitution reaction is dissociative or SN1, there may be a linear correlation between the free energy of activation AG* and the standard free energy change AGO for the reaction in a series of similar ligand-substitution equilibria. The linear correlation has been observed The Journal of Physical Chemistry
for acid hydrolysise in the series of cations Co(NH3)5X2+ over a wide range of leaving groups X-. Analogous correlations between A S and the partial molal entropy
*
(1) To whom communications should be directed. (2) N. Purdie and C. A. Vincent, Trans. Faraday SOC., 63, 2745 (1967). (3) D. P. Fay, D. Litchinsky, and N. Purdie, J . Phys. Chem., 73, 544 (1969). (4) D.P. Fay and N. Purdie, submitted for publication. ( 5 ) C. H. Langford and T. R. Stengle, A n n . Rev. Phys. Chem., 19,193 (1968). ( 6 ) C.H.Langford, Inorg. Chem., 4,265 (1965).
