Comparative Study of the Kinetics of the Benzidine Rearrangement by Four Electrochemical Techniques D. M. OGLESBY,' J. D. JOHNSON,*
and CHARLES N. REILLEY
Department o f Chemisfry, University of North Carolina, Chapel Hill, N. C. Four electrochemical techniques have been applied to the study of the acid-catalyzed rearrangement of hydrazobenzene. The theory for the study of first-order following kinetics using a reverse-ramp current is developed and verified b y application to the benzidine system. The advantages of using thin-layer potential step electrolysis with integrated current for the study of slow, following kinetics are pointed out and its usefulness i s verified. The first-order rate constants in 35.5% ethanol-water solutions having perchloric acid concentrations ranging from 0.063 to 0.25M were determined and compared with values obtained b y other workers.
T
kinetics of the rearrangement of hydrazobenzene and related compounds in acid media has been widely inveatigated by various techniques and is of current interest (9, 11, 14, 1 6 ) . Recently, the applicability of a step-functional controlled-potential electrochemical method to the study of this system has been shown by Schwarz and Shain (14). Their work not only illustrates the usefulness of the stepfunctional controlled-potential method for the study of first-order reactions follon-ing reversible electrochemical generation but indicates the general usefulness of electrochemical techniques in studying this and similar systems. Electrochemical techniques are particularly suitable for the study of the benzidine rearrangement : HE
@ N = N a
+ 2e-+
STEP CURRENT REVERSAL A t ne---.
B-
k
I
C
A t ne'-B-C
k
'0
time
la
I
I I i I I
-
I
T
I
-
i
T
1 i
E
E
1
1
T
I I
Left. Right.
---
methods have been pointed out (14, 15). The four methods considered here are all two-step methods. Step-reversal chronopotentiometry has previously been applied to the study of the pbenzoquinone imine hydrolysis (15). The reverse-ramp current function, not previously applied to electrochemical
H
A
1%
I
Step-current reversal function Reverse-ramp current function Reverse curve expected when k = 0
2H+4
+
H T h e stable azo compound is used as the starting material and the unstable hydrazo form is generated in situ a t the electrode surface. The products are not electroactive in the potential range employed (+O.l5 to -0.15 volt 2's. S.C.E.). The advantages of two-step electrochemical methods over one-step
REVERSE RAMP CURRENT
studies, appeared to offer the advantage of eliminating the double switching for current reversal, allowing the forward and reverse electrolysis times t o be controlled automatically with relatively simple instrumentation. Figure 1(right) illustrates a typical current program where a is the magnitude of the initial current, b is the rate a t which the cur-
rent decreases, is the transition time, and to is the time a t which the current crosses the zero current axiq. Figure 1(right) shows a typical potential-time plot produced by ramp current electrolysis. The time, to, is a defined time, fixed by the values selected for the initial current, a, and the rate of decrease of current, b. The only measured time is the transition time, 7'. I n the step-current reversal method, accurate measurement of the short transition times encountered in the case of fast kinetics is difficult. To minimize this difficulty, a lower reverse current density can be used. However, lowering the current density also lowers the rate of potential change a t the transition time, and the full benefits desired are not achieved. T h e reverse-ramp current Present address, Department of Chemistry, Old Dominion College, Norfolk, Va.
Present address, DeDartment of Environmental Science ahd Engineering, University of Pu'orth Carolina, Chapel Hill, S . C. VOL. 38, NO. 3, MARCH 1966
385
function has the advantage of a low current at the beginning of the reverse electrolysis and a higher current density at the transition time. The thin-layer electrochemical technique offers some unique advantages in the study of kinetics ( 5 ) . Fast kinetic processes may be studied by using two working electrodes separated by a thin film of solution (1). I n the study of slow kinetic processes, the reacting species may be generated, allowed to react, and then studied by reverse electrolysis. There is no diffusional loss of the reacting species, because it is confined between the electrode and the opposite boundary. Christensen and Anson (5) used thin-layer chronopotentiometry with current reversal to investigate the p-benzoquinone imine hydrolysis and the rate of attack of nickel(I1) cation on the cobalt(I1)E D T A anion. The equation relating the rate constant to the experimental quantities is implicit, and data are best analyzed with a computer. A simpler procedure is to use a potential-step electrolysis technique, in which a potential appropriate for producing the reacting species is suddenly applied, and the integral of the resulting current is measured. The time required for quantitative production of the reacting species may be less than 1 second for sufficiently thin layers of solution. After suitable reaction time, the unreacted species may be electrolyzed by stepping the potential back to a n appropriate value and the residual quantity of unreacted species determined by the integral of the resulting current. THEORY
The reactions occurring in this study may be represented by the forward electrolysis, Ox
+ 2e- + 2H+
--
B
+ 2e- + 2H+
CR(5,
R
B
=
=
erf k (t.
0
+
7)’”
ANALYTICAL CHEMISTRY
(4)
where a is the initial current and -b is the slope of the ramp function. Therefore,
(1)
A working curve, similar to the one described by Testa and Reinmuth (16), was constructed for calculating the rate 386
(2)
where AC, is the change in surface concentration of component f from its initial value, J , is the flux of component g into the electrode and equals io/ (n,FA), io is the current (positive during reduction) due to the electrode reaction of component g, D is the common diffusion coefficient, no is the number of electrons per molecule lost by component g-Le., the value of n, is positive if g refers to an oxidized species, negative if g refers to a reduced speciesh is a mathematical index, the Kjoh are constants involving only ratios of (pseudo-) first-order reaction rate constants, the k h are constants depending on the magnitude of the reaction rate constants, and p is the Laplace transform variable. The summation over g is taken over all components in the subsystem, and there is one value of h for each component in the subsystem. The desired response function for post kinetics given by Reactions I and I1 is:
i=a-bt
Step - Current Reversal Chronopotentiometry. A constant current is applied for time, t,, a t which point t h e direction of current is reversed, leading to a transition time, T . The solution to this boundary value problem, reported by Dracka ( 8 ) ,is: 2 erf kT1”
kh)-l”
(11)
0 ) = C”
0)
+
The reverse-ramp current, which represents the excitation, is given by:
with the initial conditions that COX(2,
(p
(I)
k
Taking the inverse Laplace, and noting that CR(z, 0) = 0, gives:
-
k
R
and the reverse electrolysis,
Ox
constants from the step-current reversal data. The working curve is a plot T/ta us. kt,. Thus, from the experimental values of t, and 7, k may be determined, Reverse Ramp Chronopotentiometry. The solution to the boundary value problem for the reverse-ramp current function may be derived by application of the generalized approach to chemical kinetics in electrochemical processes, given by dshley and Reilley ( 2 ) . The general equation, in the Laplace plane, relating the net change in concentration of a component to the current excitation function and the system functions is:
The negative sign arises because g refers to the reduced specits (hydrazobenzene). Substitution of J R into Equation 3 and rearrangement yield :
At the transition time, n, the concentration of C R a t the electrode surface is reduced to zero and Equation 7 reduces to a erf(kT1)1’2=
b
l’
[erf(kr)1’2]d~ (8)
Substituting a l t o for b and taking the integral f r o m 0 to instead of 0 to 71 gives :
k is solved by a graphical method. Values of h1are chosen, and the values ) ” ob~ of the error function of ( k ~ ~ are tained from standard tables (IO). Values for the integral were obtained from a table constructed by calculating the value of the integral, (kr1)*
S,
[erf ( k 7 )d ( k r )2 1
for closely spaced, selected values of ( k r J 2 from 0.002 to 10.0. From Equation 9 and these values, a series of values of lit, was tabulated. For a graphical solution of k , a working curve, illustrated by Figure 2, was constructed , the tabuby plotting t o / n us. k ~ from lated values. Hence, from the experimental value of t o / n the value of krl is read from the working curve. The rate constant, k , is then calculated from the known experimental value of 71.
From Figure 2 we see that for small values of k~~ the value of to/T1 approaches 0.666. The time from t , to T I is one half the time from t = 0 to to for the special case where k is zero and the rate of removal of R is strictly diffusioncontrolled. This same result may be obtained by substituting k = 0 in Equation 3. When krl is greater than 10, Equation 9 reduces to kt, = k n - 0.500, and the value of IC can be determined directly from
0.500
-
a
p2(p
71
+
-
to
If an accuracy of 1 or 2% is sufficient, Equation 10 can be used for ICn values above 5 .
Considering the time, t,, when Cox (0, tj becomes zero and rearranging terms gives :
0.6
o
1.0
2.0
4.0
3.0
7.0
6.0
5.0
8.0
kr Figure 2. Working curve first-order kinetic studies
for
reverse-ramp
The right side of this expression is identical to that for the transition time, obtained when a constant current equal to a is used for electrolysis. Therefore:
current,
t
Because b/a = l / t o ,
0.4
q o’6
’0.2
(t,)’/2
j - 2(r, 3t” 3/2
(~aj1’2
(14)
A consideration of the possible roots to Equation 14 shows that Cox (0, t ) = 0 when t, = t,/2. Xow to may be expressed in terms of by substituting t,/2 for t, in Equation 13. Upon simplification, this gives: -0.41
0
to = 4.5T,
w :
I , 5
10
15
20
65
60
70
Thus, t o should not be greater than 4.57.. In practice, to is made somewhat less than 4.57,. Thin-Layer Chronopotentiometry. T h e theory for the thin-layer chronopotentiometric kinetic study has been
TIME (seconds)
Figure 3.
Thin-layer chronopotentiogram of azobenzene
Constant current for time f j Current off for time td td Current reversal at time t j T. Time required for oxidation of unrearranged hydrazobenzene
+
To minimize charging current effects, the number of coulombs passed for the Faradaic electrolysis should be maximized. For this reason, a should be as large and b as small as possible. However, a requirement is imposed by the assumption of 100% current efficiencyLe., that a forward transition time must not occur. If the value of a is too large or b too small, the concentration of Ox at the electrode surface will reach zero before the current reaches zero. When this occurs, the current mill seek a path in addition to the electrolysis of Ox. A convenient method of choosing a n appropriate value of b for a given value of a i b to consider the relationship between to and the transition time one would obtain for constant current electrolysis, using a current equal to a. Because it is desired that Cox (2,t ) reach the minimum practical value, consider the expression for Cox (2,t ) . This may be obtained by setting k of Equation 6 equal to zero and taking the inverse Laplace transform, yielding:
150
(15)
..
0
5
IO
TIME (seconds)
90
95
100
IO!
Figure 4. Integrated current-time curve for thin-layer potential-step electrolysis of azobenzene and unrearranaed hvdrazobenzene
hr. Coulombs passed for reduction of azobenzene hh Coulombs passed for oxidation of unrearranged hydrazobenzene tl.
Reaction time
VOL. 38, NO. 3, MARCH 1966
e
387
given ( 5 ) . The relationship between the rate constant, k , for a first-order following reaction and the experimental quantities, 7, t d , and t / , illustrated in Figure 3, is given by
This equation is best solved for k with the aid of a computer. This relationship is valid so long as homogeneous mixing within the volume element occurs during times t i , t d , and T ! which means that it is primarily useful for the study of slow kinetics. Thin - Layer Potential Step Electrolysis. The necessity for a n iterative solution for k is eliminated and the relationships are made much simpler if one uses t h e thin-layer potential-step electrolysis technique to study slow kinetic processes. The theoretical time required for nearly total depletion of a 2.0 x 10-3 cm. layer of solution is less than 1 second (7), using potential-step electrolysis. If the reaction to be studied is sufficiently slow, the reacting species may be rapidly generated by means of a potential step and allowed to react for a time much longer than that required for its generation, and then the potential may be stepped to the value required for reverse electrolysis of the unreacted species. If the integral of the current passed is recorded, as shown in Figure 4,the ratio of the coulombs for the forward electrolysis to the reverse, h,/hb, will be the ratio of the initial concentration to the final concentration of the reacting species. Thus, a plot of ln(h,/hb) us. the reaction time, t,, will give, for a first-order process, a straight
Table 1.
EXPERIMENTAL
Instrumentation. A three-electrode system was used for all the studies. The desired instrumentation was accomplished with K2-P chopper-stabilized K2-W operational amplifiers and UPA-2 operational amplifiers, powered by a R-300 power supply (amplifiers and power supply manufactured by G. A. Philbrick Researches, Inc., Boston, Mass.). N o s t of the necessary input and feedback circuits have been described ( I S ) . The reverse ramp current function was generated by placing the desired initial charge on the O.l-bfd., 200-volt, 1% capacitor of an integrator. This was accomplished by connecting a variable secondary voltage across a 10-meg. resistor to the summing point, with a 10-meg. resistor also connected between the summing point and the output. This voltage souice, along with the 10-meg. feedback resistor, was switched off a t the same instant the constant potential of opposite sign, to be fed into the input of the integrator, was switched on, thus generating a reverse ramp potential function a t the output of the integrator. (The input resistances, which could be seIected, were 10 meg., 1.0 meg., or 100 K, giving RC time constants of 1.0, 0.10, or 0.01 second.) Also a t the same instant, via a triple pole-double
Thin-Layer Chronopotentiometric Determination of Rate Constant of Rearrangement of Hydrazobenzene in 38.5% Ethanol at 25' C.
0.2531 HC104; 0.0.11 h'aC104 k x 10'2, t ~ sec. , ld, sec. 7 , see. see.-' 3.8 14.9 0.0 3.7 2.2 14.2 9.6 5.0 4.6 13.5 0.0 14.5 4.6 14.4 0.0 19.4 4.8 13.5 29.5 0.0 19.6 5.0 2.5 14.4 24.9 0.0 5.0 14.9 Av. 1 4 . 3 0.15031 HC104; 0.1N NaC104 9.8 4.9 4.6 6.32 14.6 0.0 7.5 6.26 15.0 5.0 5.9 6.24 8.8 5.98 19.7 0.0 7.1 5.94 20.0 4.9 0.0 9.3 6.69 29.8 29.6 5.3 7.1 6.66 9.9 6.17 29.9 0.0 29.7 9.9 5.9 6.33 Av. 6.29
388
line with a slope of k . Also, when &/ha = 2, one half of the generated species has reacted. The reaction time then represents the half life of the reaction, and the following relationship between the reaction time and the firstorder rate constant may be used to determine k:
ANALYTICAL CHEMISTRY
0.0997J1 HC104; 0.15M NsC104 k X t f , see. t d , see. 7 ,see. set.-' 14.8 4.9 9.0 2.99 14.8 10.0 8.1 2.83 14.9 15.0 6.1 3.54 19.9 0.0 12.8 2.74 20.1 9.6 3.02 10.0 19.6 15.0 8.5 2.91 24.9 0.0 13.1 3.50 24.7 15.1 9 .0 3.23 3.10 0.0629X HC104; 0.187Jf ZiaC104 14.9 11.9 1.69 0.0 14.9 1.41 10.0 10.8 15.3 10.3 1.43 14.9 19.8 1.51 9.9 13.3 20.0 11 9 1.13 30.0 19.8 9.8 1.29 39.8 24.9 25.1 13.9 1.32 24.9 10.0 1.36 49.8 1.39
throw witch, the output potential of the integrator was applied to the input of the current generating amplifier. For chronopotentiograms longer than about 5 seconds and for the thinlayer controlled-potential studies, the follower output was recorded with a Ssrgent Model SR recorder, using a chart speed of 12 inches per minute. A Sanborn Model 151-100.1 singlechannel recorder with a Model 150400 drive amplifier and power supply and a Model 15-1600 stabilized DC preamplifier was used to record the shorttime chronopotentiograms. Cell and Electrodes. .i mercury pool working electrode was used for the reverse-ramp and the step-reversal controlled-current studies. The pool was contained in a Teflon cup mounted on a glass J tube. T h e Teflon cup was filled to the same point each time, giving an electrode area of about 1.27 sq. em. S.C.E. reference electrode, used for all the studies, was inserted into a piece of 10-nim. glass tubing having a fine glass frit in one end. The flit v a s then inserted directly into the bolution to be studied, and the tube was also filled rvith the qolution to be studied. This arrangement minimizes contamination of the solution by chloride from the reference electrode. The auxiliary electrode was a 1-sq. cm. platinum foil fused to a platinum wire lead sealed in a piece of 6-mm. glass tubing. For diffusion-controlled studies, a 100-m1. jacketed cell, equipped with a Teflon stopper in which holes were provided for the electrodes and the nitrogen inlet , was employed. Temperature control of this cell was maintained a t 25.0' =t0.1' C. by circulating mater from a therinostated bath through the jacket of the cell. The buret stand, holding the cell assembly, was mounted on a layer of foam rubber, a poicelain slab, and another layer of foam rubber to isolate the cell from vibrations. The thin-layer cell with a mercurycoated platinum electrode has been described (18). Chemicals. Eastman white label azobenzene was recrystallized twice from hot 95% ethanol and found t o have a melting point of 68.0' C. All other chemicals were reagent grade, used without further purification. The solutions to be studied were prepared by dilution of: the desired amount of aqueous, standard perchloric acid solution; the amount of 0.5X SaCIOl necessary to give a total ionic strength of 0.25; 10 ml. of 0.025-11 azobenzene in 95% ethanol; and 100 ml. of 95% ethanol. Upon dilution to 2.50 ml., this resulted in an azobenzene concentration of l O - 3 X . As a precaution against the photooxidation of azobenzene, the solutions were prepared immediately before use and the stock solution of azobenzene was kept in the dark. S o precautions were taken to prevent the photoisomerization of azobenzene. The solutions were deaerated with Seaford grade nitrogen, which had been
0
1
0 TIME (soc.), to
Figure 5. Kinetic d a t a from step-current reversal chronopotentiometry of azobenzene
passed
through a 0.25111 NaC104-
407, ethanol solution.
Procedure. T h e solution t o be studied was deaerated for 10 minutes and alloxed 30 minutes t o reach constant temperature. .S. fresh mercury pool was used for each series of runs on a given solution. T h e stepcurrent reversal d a t a were taken using a current of 100 pa. This allowed forward electrogeneration times, t,, of up to 30 seconds. A series of stepreversal chronopotentiograms with t, varying from 30 seconds down to about 1 second mas taken for each solution, giving values of t, well on each side of the half life of the reaction a t each acidity studied. For the reverse-ramp studies, two initial currents were used in each series of chronopotentiograms obtained. For those Ivith t o longer than 10 seconds a n initial current of 200 pa. was used, and for those with t o less than 10 seconds a n initial current of 300 pa. was used. Values of t o from 35 seconds (slightly less than 4.5 times the 8.5 second transition time obtained with a constant current of 200 pa.) down to 2 seconds were chosen. The techniques for using the mercurycoated thin-layer electrode have been discussed ( 2 2 ) . The Teflon collar of the electrode was slipped down slightly past the electrode face to decrease the amount of diffusion into and out of the thin layer of solution a t the edge. The solution thickness used was 2.07 X cm.; the electrode area was 0.278 sq. cm. For the thin-layer chronopotentiometric studies, a current of 5 pa. was used for both the forward and reverse steps. The current was manually switched cathodic for a time, t,, and then reversed, giving a back-transition time, T , or the current was stopped before reversal for a time, t d ( 5 ) . The specific times used for the study of each bolution are given in Table I.
For the thin-layer potential step electrolysis study the azobenzene in the volume element was reduced by stepping the potential from $0.15 to -0.15 volt us. S.C.E. The potential was held at the latter value for a time, t,, and then stepped back to f0.15 volt, reoxidizing all of the unreacted hydrazobenzene. The time required for complete reduction of the azobenzene and complete oxidation of the unreacted hydrazobenzene was longer than would be espected from theory (approximately 5 seconds rather than the expected 1 second). This was probably caused by the I R drop, resulting from the increased isolation of the volume element by slipping the collar down and from lower electrical conductivity caused by the alcohol content of the solvent. The effect of this on the chosen reaction time, t,, is largely cancelled by the method of selecting t,, as shown in Figure 4. RESULTS AND DISCUSSION
Step-Current and Reverse-Ramp Current Methods. T h e step-current reversal method !vas applied t o solutions of azobenzene containing 0.150, 0.175, 0.200, 0.225, and 0.250V perchloric acid. For each solution, different values of t, were used and t h e corresponding values of 'T were measured. From the working curye, described above, the values of kt, were deduced. A plot of the kt, values os. t, should have a straight line of slope k . The k values found a t each level of perchloric acid are given in Figure 5 . The reverse-ramp technique was applied to the same solutions of azobenzene. For each solution, different values of to were employed and the resulting values of T~ were recorded. From these and the working curve for this technique, the values of krl were
obt'ained. X plot of J2r1 os. T ~ shown , in Figure 6, should be a straight line of slope k. The values of k for each solution are given in the figure. Least squares lines through the experimental points in the plots of kt, os. t, do not extrapolate to the origin, but have a t , intercept of -2 seconds. This discrepancy niay be accounted for by considering the effect of adsorption of hydrazobenzene (11) on the rate of the benzidine rearrangement. The rate of rearrangement of the adsorbed species is espected to be much slower than that of the solution species, causing the back transition time, T , to be longer than in the absence of adsorption. This results in a slight increase in the slope of the plot of kt, e's. t, and a positive t , intercept. *in increase of only 0.13 second in T for step current reversal with an applied current of 100 pa. is sufficient to account for the observed positive intercept. When 0.13 second was subtracted from each value of T and a new plot made of kt, z's. t,, the intercepts were found to average 0.0 & 0.2 second and the rate constants were changed by less than 3c0.This amount of charge, 13 pcoul.. corresponds to -0.5 X mole [electrode a,rea = 1.27 sq. em.), or approximately 437, of a theoretical monolayer coverage. Of course, this method of correction for adsorption is not rigorously correct and is presented only as a correction for firstorder effects. The 13-pcoul. correction may be made in either of two ways for the reverse-ramp data, depending on the assumed order of reosidation of the two forms of hydrazobenzene (adsorbed and solution species). If it is assumed that all of the adsorbed species is reoxidized first,, near to, the "corrected" value of k is twice the value of k s h o r n in Figure 5 and the k r l us. ' T ~intercepts at negative values of 'T]. On the other hand, if it is assumed that the adsorbed species reacts last, near ' T ~ , the corrected value of k is within 1% of the value in Figure 5, and the intercept is esjentially unchanged. For these calculations, the adsorbed form of hydrazobenzene is assumed to be produced near time zero while the current is near its maximum value a. The calculations indicate that a mechanism in which adsorbed generated first and agreement with the observed positive intercept of the kt, us. t, plots, the essentially zero intercept observed for the k r l cs. ' T ~plots, and the agreement between the apparent rate constants obtained with the two techniques. Thin-Layer Methods. Thin-layer chronopotentiometric d a t a were obtained for azobenzene solutions having perchloric acid concentrations of 0.250, 0.150, 0.0997, and 0.0629V. From the VOL. 38, NO. 3, MARCH 1966
389
0.250 I 11.14.1 I
0
5
IO
15
25
20
30
35
40
45
5,(sec.)
Figure 6. Kinetic data from reverse-ramp current chronopotentiometry of azobenzene
experimental values of ti, t d , and 7 the values of k , given in Table I, were calculated from Equation 1 by means of a n iterative computer proaoram. The thin-layer potential step method was applied to azobenzene solutions having perchloric acid concentrations of 0.0997 and 0.0629V. The plot of ln(h,/hb)us. t, and the values of the rate constants based on the slope of these plots are given in Figure 7. The values obtained by the thin-layer electrochemical studies are in good agreement with those obtained by the two diffusion-controlled methods (Figure 8). I n the thin-layer technique, all of the hydrazobenzene generated is trapped nithin the thin layer of solution. X monolayer of adsorbed hydrazobenzene would represent only about 6%
of the total hydrazobenzene generated (6% based on electrode area = 0.278 sq. em., C = 10-6 mole per cc., and solution thickness = 2.07 X em.). Factors Governing Lower Limits of k. Accurate measurement of the rate constant a t low acidities by diffusioncontrolled methods is difficult because the ratios of t G / T and & / T , approach that for nonkinetic systems a t low values of t,. Larger values of t, are limited by the onset of convective mass transfer. The thin-layer studies not only support the validity of the diffusion-controlled data but also enable determination of the small rate constants obtained a t low acidities. T o standardize the medium for these studies, only perchloric acid was used as the source of protons for the rearrange-
I
ment. This imposed a lower limit on the acidities which could be studied, hecause the ratio of perchloric acid to azobenzene had to be high enough to assure adequate adherence to pseudofirst-order kinetics. Suitable buffer systems could be chosen for the study of the rearrangement rates a t lower acidities. -4practical lower limit to the rates which may be determined by the thinlayer electrochcinical technique is governed by the magnitude of the edge effect. This effect, which is primarily an elect'rode design problem, has been discussed (12). -4s longer reaction times are required, before rererse , more of the electrogenerated reacting species will diffuse from the thin layer of solution into the bulk solution a t the edge. Also, when the thin-layer potential step method is employed, more of the reacting bpecies is being generated during the reaction time because of th-, diffusion of electrolyzahle ipecies into the thin layer of solution a t the edge. This is illustrated in Figure 6 by the continuous rise in the integrated current-time curve during the reaction time, t,. Comparison of Rate Constants. The rearrangement of hydrazobcnzene exhibits a second-order dependence on the hydronium ion concentration (6), and a plot of -log k z's. -log [H+] should have a slope of 2 . The rate data from each of the four techniques, shown in Figure 8, illuhtrate this dependency. The rate of rearrangement' has also been shown to be dependent on the ionic strength of the solution and the di-
Figure 8. Rate data obtained by four electrochemical techniques
-
Theoretical slope of - log k VI. log [H+] = 2 Step-current reversal data, slope 2.0 0 Reverse-ramp current data, slope 2.1 0 Thin-layer chronopotentiornetric data, slope 1.7 A Thin-layer potential-step data, slope 1.8
0
390
ANALYTICAL CHEMISTRY
electric constant of the solvent (6). Because these factors, as well as the acidity of the solution, markedly affect the rate of t h e reaction, comparison of our data with those of Schwarz and Shain (14) or those of the classical methods is not entirely straightforward. Schwarz and Shain’s studies were made a t much higher acidities than used in this and in other ethanol-water solution studies. Their comparison of electrochemical results to classical studies was based on estimating a value of k a t an acidity studied by Croce and Gettler (6) from a plot of log k us. the Hammett acidity function. They then corrected Croce and Gettler’s value for the difference in the dielectric constant of the solvent with 60% ethanol (used by Croce and Gettler) and that with 50% ethanol (used by Schwarz and Shain). A comparison of our data with those of other workers is based on similar estimates. The solution conditions used by Blackadder and Hinshelwood (S), ionic strength of 0.25 -11 and 44y0 ethanol more nearly resemble those used for this study, ionic strength 0.25M and 35.5y0 ethanol. Blackadder and Hinshelwood report a value of k = 2.9 X set.-' in 0.075M HC1, 0.175M NH4C1, and 44% ethanol at 25’ C. From the -log IC us. -log [H+]plot in Figure 8 the estimated values of k at 0.07551 HClO, for each technique are: 10.2 X set.-' by step-current reversal 10.7 X 10-3 set.-' by reverse-ramp current 18.6 X l o w 3 sec.-l by thin-layer chronopotentiometry 11.7 X lop3 set.-' by thin-layer potential step With the exception of the value obtained by thin-layer chronopotentiometry, these values are reasonably consistent but are greater than that of Blackadder and Hinshelwood by somewhat more
than a factor of 3. Only part of this difference may be accounted for by the difference in the dielectric constant of the solvent. A comparison has been made by using Croce and Gettler’s ionic strength and dielectric constant data at 0.0931M H f and correcting for the dielectric constant of the solvent. From a plot of log k us. the ionic strength and a plot of log k us. 1/D (D = dielectric constant), the value of k a t 0.0931iM H + from Blackadder and Hinshelwood’s data and the values of k at 0.0931 M H + from Figure 8 were estimated. These are shown in Table I1 along with our data and Schwarz and Shain’s estimated value at 0.0931M H’. ACKNOWLEDGMENT
The authors acknowledge the assistance of L. B. Anderson. LITERATURE CITED
(1) Anderson, L. B., Reilley, C. N., J . Electroanal. Chem. 10, 295 (1965). (2) Ashley, J. W., Reilley, C. N., Zbid., 7,253 (1964). (3) Blackadder, D. A., Hinshelwood, C., J . Chem. Soc. 1957,2898. (4) Carlin, R. B., Nelb, R. G., Odioso, R. C., J . Am. Chem. Soc. 73, 1002 (1951).
Table It. Comparison of Pseudo-FirstOrder Rate Constants for Rearrangement of Hydrazobenzene in 50% Ethanol, 0.093M H+, and 0.25M Ionic Strength a t 25” C.
[Estimated corrections for differences in ionic strength and dielectric constant based on data by Croce and Gettler ( 6 ) ] k X 10+3,
see. -l Values of k fron mated for 0.093) By reverse-ramp current By thin-layer chronopotentiometry By thin-layer potential step Value from Blackadder and Hinshelwood (3) (estimated for 0.093M H + and 5070 EtOH) Value from Schwarz and Shain (14) (adjusted to 0.25.V ionic strength from author’s set.-' value of 2.4 X at 0.093M H + ; determined in 507, EtOH) Value from Croce and Gettler ( 6 ) (estimated for 5070 EtOH and 0.25Jf ionic strength; determined in 60Y0 EtOH and 0.093M H + )
5.3 5.6 10.0 5.9 3.3
5.0
3.6
( 5 ) -Christensen, C. R., Anson, F. C.,
ANAL. CHEM.36, 495 (1964). (6) Croce, L. J., Gettler, J. D., J . Am. Chem. SOC.75, 874 (1953). (7) De Vries, W. T., Van Delen, E., J . Electroanal. Chem. 8. 366 (1964). (8) Dracka, O., Collection Czech: Chem. Communs. 25, 338 (1960). (9) Ingold, C. K., Boll. Sci. Fac. Chim. Ind. Bologna 21, 34 (1963). (10) Natl. Bur. Standards, “Tables of
the Error Function and Its Derivative.” Applied Nathematics Series, p. 41,
1954. (11) Nygard, B., Arkiv. Kemi 20, 163 (1963). (12) Oglesby, D. M., Omang, S. H., Reilley, C. N., ANAL. CHEM.37, 1312 (1965). (13) Operational Amplifiers Symposium, Ibid., 12, 1770 (1963).
(14) Schwarz, W. hl., Shain, Irving, J . Phys. Chem. 69, 30 (1965). (15) Testa, A. C., Reinmuth, W. H., ANAL.CHEW32, 1512 (1960). (16) Tecera, M., Chem. Listy 52, 1373 (1958).
RECEIVEDfor review July 29, 1965. Accepted December 15, 1965. Division of Analytical Chemistry 149th Meeting, ACS, Detroit, llich., April 1965. Research supported in part by the Advanced Research Projects Agency. One of the authors (D.XI.0.) thanks the American Viscose Corp. for financial assistance provided in the form of a research fellowship. Nachine calculations carried out a t the Duke University Computing Center.
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