HENRYN. BLOUNT AND HARVEY B. HERMAN
3006
Conclusions The Brownian model seems to be more adequate for the fused salt than for nonelectrolytes like liquid argon. This result may arise because the tight coupling of the ions by the nondissipative coulomb field through lowfrequency modes causes the high-frequency dissipative oscillations of the ions to be decoupled 'from one another. Thus the ions are probably IocaIized and suffer only very small displacements compared to the
width of the first peak of the radial distribution function during a correlated set of motions. This model is similar in concept to the Einstein model for the solid. Another advantage of the salt system is that the repulsive potential which determines the transport properties is balanced primarily by an attractive coulomb potential which is accurately lmown and does not contribute much to the transport properties. The intermolecular potential can therefore be determined from crystal data with fair accuracy.
Chronopotentiometric Measurements of Chemical Reaction Rates.
11.
Kinetics and Mechanism of the Dehydration of
pHydroxyphenylhydroxylamine1 by Henry N. Blount and Harvey B. Herman Department of Chemistry, The University of Georgia, Athens, G'eorgia 30601
(Received March 86,1068)
Current-reversal chronopotentiometry, chronoamperometry, and chronocoulometry have been applied to the elucidation of the kinetics and mechanism of the dehydration of p-hydroxyphenylhydroxylamine, the reactive intermediate in the p-nitrosophenol system which enjoys widespread use as a model system for verification of ECE theories. Specific acid and general base catalysis were established for the system. Solvent studies, substituent effects, and thermodynamic activation parameters deduced from the temperature dependence of the reaction provided evidence for mechanisms proposed here.
Introduction The ECE mechanism, wherein a chemical reaction is interposed between two charge transfers, eq 1, has been studied by a variety of electrochemical techk
A+nleGB---tC
f n 2 e Z D
(1)
niques.2-s These studies have, in general, used the p-nitrosophenol (PNP) system as a model of this mechanistic scheme. As is seen in eq 2, PNP (I) undergoes
I
N-0 I
$J
'H ' O H
?3H I11
IV
I1
a two-electron reduction to form p-hydroxyphenylhydroxylamine (11), which subsequently dehydrates giving rise to p-benzoquinoneimine (111). This latter The Journal of Physical Chemistry
compound is reduced a t considerably less cathodic potentials than I such that upon current reversal I11 continues to reduce as I1 is oxidized. Some years ago, Stoi'iesov# noted that the magnitude of the polarographic diffusion current for the reduction of o-nitrophenol varied with pH, having a minimum value at an intermediate pH. On the basis of this evidence, he proposed the existence of an acid-basecatalyzed react,ion coupled between two charge-transfer steps. Later Nicholson, et a l l 6solved the expandingsphere problem for the ECE mechanism and applied it to the PNP system. While these authors report the p H dependence of the observed rate constant for the (1) Presented in part at the 164th National Meeting of the American Chemical Society, Chicago, HI.,Sept 1967. (2) G. S. Alberts and I. Shain, Anal. Chem., 35, 1859 (1963). (3) R.S.Nicholson and I. Shain, ibid., 37, 190 (1965). (4) Part I: H.B. Herman and A. J. Bard, J . Phys. Chem., 70, 396 (1966). (6) R. S.Nicholson, J. M. Wilson, and M. L. Olmstead, Anal. Chem., 38,642 (1966). ( 6 ) D.StoEesovh, Collection Czech. Chem. Commun., 14, 616 (1949).
CHRONOPOTENTIOMETRIC MEASUREMENTS OF CHEMICAL REACTION RATES dehydration of p-hydroxyphenylhydroxylamine (PHPHA), the mechanism and exact kinetics of the reaction were yet to be fully understood. Hence, this work was undertaken in an effort to gain more insight into the mechanistic nature of this reaction.
Experimental Section Controlled-potential coulometric experiments utilized a conventional potentiostat’ coupled with a chopper stabilized integrater. The disappearance of P N P during the course of the electrolysis was followed by conventional dc polarography, while the formation of paminophenol was monitored by voltammetry with a rotating platinum electrode. The electrolysis product was isolated by extraction of the electrolyzed solution followed by solvent stripping and sublimation. The product was then identified by its infrared spectrum and melting point and comparison of these with authentic samples. Current-reversal chronopotentiometric measurements were made using a hanging mercury drop working electrode formed by a Metrohm extruder, an isolated platinum counter electrode, and a saturated calomel reference electrode equipped with a Lugin capillary. Switching was accomplished using the circuit already reported.* Experiments were initiated by making a connection to the input of the constantcurrent amplifier, rather than by unshorting the working and auxiliary electrodes (see Figure 1, ref 7). Potential-time curves were recorded on a Tektronix 564 storage oscilloscope and were photographed with a C-27 oscilloscope camera. Current programs were selected which facilitated the most precise determination of transition time ratios. Chronocoulometric and chronoamperometric data were obtained simultaneously through the use of a Tektronix Type 3872 dual-trace amplifier and the oscilloscope and camera already described. I n all experiments except concentration studies, the concentration of nitrosophenol was maintained a t 1.0 mM. Dielectric constant measurements were made with a Sargent Model V chemical oscillometer. The p-nitrosophenol was obtained as the sodium salt from Eastman and was purified according to Alberts and S h a h 2 Substituted nitrosophenols were prepared by direct nitrosation of the corresponding phen01.~ These bromo, chloro, methoxy, and 2,6-dimethyl phenols were obtained from Aldrich and K & K Laboratories. The 2-methyl-4-nitrosophenol was obtained (technical grade) from Aldrich and was purified by recrystallization from benzene under an inert atmosphere. Synthetic products were analyzed by ir and highresolution nmr spectroscopy. Buffer solutions were prepared from reagent grade acids, which were neutralized to the appropriate p H with carbonate-free sodium hydroxide. Ionic strengths were adjusted to 1.0 M with reagent grade potassium
3007
nitrate. Solvents were purified by fractional distillation, except dioxane which was used as reagent grade, Determinations of p H were performed using a p H meter comprised of a Sargent electrode (No. S-30070-lo), a high input impedance Philbrick Researches operational amplifier (No. SP2AU) powered by a modified Heathkit IP-20 power supply, and a James G. Biddle potentiometer. The estimated accuracy of this in0.005 p H unit. Standardizations strument was were made using buffers prepared according to the National Bureau of Standards scale.l0 Dissociation constants for acetic, citric, phosphoric, and phthalic acids were determined by potentiometric titrations of samples of the above acids with 20% ethanolic sodium hydroxide. The ionic strength of each sample was adjusted to be 1 M a t half-titration, the total change in ionic strength not exceeding 3%. The titration data were fitted to equations predicting the ionic equilibria involved after the manner of Fleck.ll Hydrogen ion concentrations were obtained from hydrogen ion activity measurements by the determination of the p H of a series of solutions of known hydrogen ion concentrations a t fixed ionic strengths of 1.0 M . The least-squares slope of a plot of log [ H f ] vs. log (apparent H+ activity) was then taken as the activity-to-concentration conversion factor. The concentration autoprotolysis constant for water in 20% aqueous ethanol at 1 M ionic strength was deby measurements of the termined to be 2.67 X hydrogen ion concentrations in a series of solutions of known hydroxyl ion concentrations. In every case, the solid nitrosophenol was preweighed and introduced into a measured volume of degassed buffer solution. All measurements, kinetic and otherwise, were made in jacketed cells maintained a t the desired temperature, 0.05”, by a thermostated reservoir. All measurements were made at a total ionic strength of 1.0 M . The solvent composition was maintained at 20 vol yo ethanol, except in solvent-effect studies. All kinetic parameters were determined a t 25.0”, except for temperature-dependence studies for the evaluation of thermodynamic activation parameters.
*
Results and Discussion The over-all electron change in the reduction of P N P was determined by controlled potential coulometry to be 3.99 f 0.05, which is in good agreement with reported results.2 The identity of the product was reaffirmed as p-aminophenol. l2 Total conversion to the amino compound was established by voltammetry (7) W. M. Schwars and I. Shain, Anal. Chem., 35,1770(1963). (8) H. B. Herman and A. J. Bard, ibid., 37, 590 (1965). (9) R. K.Norris and S. Sternhell, Aust. J . Chem., 19, 841 (1966). (10) R. B. Bates, “Determination of pH,” John Wiley and Sons, Ino., New York, N. Y., 1964,p 76. (11) G. M. Fleck, “Equilibria in Solution,” Holt, Rinehart, and Winston, Inc., New York, N. Y., 1966,p 105. Volume 79,Number 8 August 1868
HENRYN. BLOUNT AND HARVEY B. HERMAN
3008
chronocoulometric16 measurements in very acid media. on a platinum electrode in the gross electrolysis cell. Moreover, a heterogeneous oxidation-reduction reacNo detectable side reactions occurred at P N P concention between the mercury electrode and P N P becomes trations below ca. 20 mM. At somewhat higher conthermodynamically more favorable as the reduction centrations, coupling reactions were observed which potential of P N P approaches the oxidation potential gave rise to highly colored products. of mercury. Hence measurements in solutions of high Current-reversal chronopotentiometric measurement of the kinetics of dehydration of PHPHA in equimolar acidity were made with minimum time lapse between acetic acid-sodium acetate in 20% aqueous ethanol electrode extrusion and the onset of the experiment. (pH 4.92) gave rise to a rate constant of 0.42 i 0.03 sec-l, which is in good agreement with other published Table I: Dependence of Observed Rate Constant for the result^.^-^ Variation in P N P concentration over a Dehydration of PHPHA on pH a t 25' (Ionic Strength = 20-fold range showed no second-order contributions 1.0 M in 20 Vol % Ethanol) to the observed rate constant. No trend was present in the observed rate constant over a wide range of forward electrolysis times, except in the case of very fast 1.11 0.88 f 0.15 measurements where adsorption becomes i m p ~ r t a n t . ~ 1.54 0.64 zk 0.11 Correction of the transition-time ratio for monolayer 2.22 0.49 f 0.04 coverage of adsorbed material was made on the basis 3.15 0.43 zk 0.05 0.39 f 0 . 0 3 3.75 of the perturbation treatment of Deron and Laitinen.13 0.42 =IC 4.92 0.03 Values of the surface excess were determined by current 5.50 0.50 zk 0.03 reversal chronopotentiometry. l4 An adsorption model 6.10 0.78 f 0.06 incorporating simultaneous formation of the monolayer 1.28 f O . 0 9 6.37 and electrolysis of the diffusing species was chosen 6.80 2.48 zk 0.09 7.08 4.8 f 0 . 3 because of the absence of both chronopotentiometric and polarographic prewaves in the P N P reduction. After correction for adsorption, short-time kinetic Generally, the first-order rate constant for a catalyzed parameters agreed with all others. Corrections for reaction can be given byle nonsemi-infinite linear diffusion to the spherical electrode were also made on the basis of the Deron-Laitinen ko ~ H + [ H + ]~oH-[OH-] kobsd perturbation treatment. la CkHAi[HAi] -k Ckai[Ai-I (3) The observed rate constant for the dehydration of i i PHPHA was indeed seen to be a function of p H as is where contributions from all acids and bases in solutions shown in Table I. Such behavior is indicative of acid are taken into account. For a single conjugate and and base catalysis. A cathodic shift in the reduction acid-base pair, eq 3 reduces to potential of P N P of about 59 mV/pH unit prevented the acquisition of current-reversal chronopotentiokobsd = ko -k ~ H + [ H + ] ~oH-[OH-] metric data below ca. p H 2. In more acidic media, ~ H A [ H Af] ka-lA-1 (4) the proximity of the mercury oxidation wave rendered the reverse transition indiscernible. Therefore, kinetic which can be represented by data were obtained from chronoamperometric and
+
+
+
+
+
where
2.0 I 89
1 3 9 I
and 1-7
1:6
+
1.5 1.4
(12) H. V. K. Udupa and M. V. Rao, Electrochim. Acta, 12, 353 (1967). (13) S. Deron and H. A. Laitinen, Anal. Chem., 38, 1290 (1966). These authors derive for the adsorption correction ( ~ ~ / t f ) ~=b ~ d (Tr/tf)true(! +.{[2(If I ~ ) * I / [ I f w f Ir)I)(&ads/Iftf)] and for the { [?rl/z spherical-diffusion correction (Tr/tf)obad = ( d t f ) t r u e(1 (If rr)w[1,ve(21~ I ~ ) ~ / 1z(DVZ I tfvvr)). (14) H. B. Herman and H. N. Blount, Abstracts, 162nd National Meeting of the American Chemical Society, New York, N. Y.,p 24B. (15) H. B. Herman and H. N. Blount, 1987,unpublished results. (16) R. P. Bell and E. C. Baughan, J. Chem. Soc., 1947 (1937).
2
4
6
8
[HPO~]XIOz-
Figure 1. Effect of the buffer concentration of the observed rate constant a t pH 6.40. The J o u r n a l of Physical Chemistry
+
+
+
-
CHRONOPOTENTIOMETRIC MEASUREMENTS OF CHEMICAL REACTION RATES
"'I
TI
1$0
3009
Table 11: Catalytic Constants" for the Dehydration of p-Hy droxyphenylhy droxylamine Species constant
Technique of evaluation Regression analysis Graphical analysis
0.3 f0.1 8.4 f 0.3 (3.0 f 0.1) X lo7 (0.08 f 0.04) 0.22 f 0.03 (6.2 f 0.4) x los 0.16 rt 0.06 0.4 f 0 . 1
0 . 3 =k 0 . 1 5.3 f0.5 (3.1 f 0 . 1 )
x
-
107
'All constants have units of M-' sec-1 except the intrinsic rate constant, which has units of sec-1.
Figure 2. Variation of the zero buffer concentration rate constant with the hydrogen ion concentration for the determination of kH+and ko.
Thus by maintaining the ratio [HA]/ [A-] constant so that the pH of the solution remains invariant and noting the value of the observed rate constant as a function of the conjugate base concentration, one obtains a linear relationship, the slope of which is a and the intercept of which is k'. If this procedure is repeated for several values of [HA]/[A-], a series of simultaneous equations is generated which can then be solved for best-fit values of the catalytic constants ICHA and k ~ - . If the intercept values (k') of these determinations are then treated as a function of hydrogen or hydroxyl ion concentration, one is able to observe the dependence of the observed rate constant on these concentrations at zero buffer-component concentration. The slopes of these latter linear dependencies are measures of the catalytic constants k ~ and OH-, respectively, and the intercepts are measures of the noncatalyzed or "intrinsic" rate constant, ICo.
Experiments of the above nature were performed over a wide range of pH values in a variety of buffer systems of constant ionic strength where both acid and base catalysis had been observed. A typical determination of a and k' is shown in Figure 1. The nonzero slopes of such plots in several buffer media in the pH range where base catalysis is important indicate that the dehydration of PHPHA is general base catalyzed. However, no effect on the observed rate constant with a variation in the conjugate acid concentration in the pH range where acid catalysis is important was taken as an indication of the specific acid catalysis. The dependence of IC' on hydrogen and hydroxyl ion concentration is shown in Figures 2 and 3, respectively. Experimental values of ICO, k ~ +and , ICOH-, as determined by these graphical techniques, are shown in Table 11. While the technique described above is clearly applicable to monobasic acid buffer systems, it is somewhat less than desirable for treatment of results obtained in polybasic acid buffer systems. I n the latter case, there is no a priori way of assigning catalytic + activity to a given species if more than one is present. Taking the results shown in Figure 1 as an example, the catalytic species in this plot could just as easily have been designated H&&- or PO**-, since their concentrations can be related through equilibrium expressions. In order to circumvent this difficulty, eq 2 was written in an expanded form to embrace all species present in solution. Each individual determination of the observed rate constant can thus be expressed by the expansion of eq 2 which has the form
Y = -40
+ -41x1+
-42x2
+
4 4 x 4
A
0.0
2
4
6
8
[0H-]x1O8
-
IO
12
74
Figure 3. Variation of the zero buffer concentration rate constant with the hydroxyl ion concentration for the determination of kOH- and ko.
?L
+ + ... +
-43x8
-4Jt
(8)
where Y is the observed rate constant, A . is the intrinsic rate constant, and A t represents the catalytic constant of the ith species in solution whose concentration is X g . Such a series of simultaneous equations is amenable to treatment by multiple linear regression analysis. This analysis was performed using a modified version Volume 72,N u m b 8 August 1068
3010
HENRYN. BLOUNTAND HARVEY B. HERMAN
of an IBM Scientific Subroutine Package1' program and an IBM System 360/65 computer. Results of kinetic determinations in acetate, citrate, phosphate, and phthalate buffer media1*are shown in Table 11. Since the previously described graphical technique for the evaluation of catalytic constants indicated that all changes in the observed rate constant with changes in conjugate acid and base concentrations were due to catalysis, negative regression coefficients from the multiple linear regression analysis were taken as insignificant. Of the species tabulated in Table I1 which exhibit a catalytic effect, the catalytic constant for molecular acetic acid is the least significant on the basis of computed t values. It is also of interest t o note that, in general, those species in each buffer system which exhibited the greatest catalytic effect were the strongest bases, which is in accord with the proposed mechanism for base catalysis. The values of ICo, k ~ +and , OH- obtained in this study are in good agreement with those published by Nicholson and coworkers.6 Substituted 4-nitrosophenols were prepared by direct nitrosation of the correspondingphenol. l9 Substituents included the 2-chloro, 2-bromo, 2-methyl, 2-methoxy1 and 2,g-dirnethyl derivatives. Melting points and polarographic half-wave potentials are summarized in Table 111. Correlation between the observed rate constants for the dehydration of the substituted PHPHA and Taft ortho-substituent constants20-2a was noted and is reflected, for example, in Figure 4. Furthermore, the slope of this Hammett-type plot, p, was observed to change with pH, as is shown in Figure 5. Not only do the base catalytic terms in eq 2 become more important with increasing pH, but also the effects of substituents of the same electron donor and steric properties are reversed. Such behavior was taken as an indication of the fact that different mechanisms are operative a t sufficiently separated pH values. Herman and Bard4 and later Nicholson, et a l l s suggested mechanisms for the acid-catalyzed dehydration of PHPHA which were generally of the form
PH
?H
r\
OH
P
Compd
M~oor (obsd), 'C
2-H 241 2-Br 2-Me 2-Me0 2,6-Me
133-133.5 145-146 155-156 134-135 169-170 170-171
Mp (lit.),
m/n, (V U8.
OC
sed'
12gC 145d 156d 134"
-0.075 -0.067 -0.064 -0.108 -0.131
170-171b
-0.080
"J. L. Bridge and W. C. Morgan, Amer. Chem. J., 20, 766 (1898). K. von Auwers and Th. Markovits, Ber. Deut. Chem. Ges., 41,2335 (1908). ' J. L. Bridge, Ann. Chem. Liebigs, 277,85 (1893). d H . H. Hodgson and L. E. Nicholson, J . Chem. Soc., 811 (1940). 'pH 4.92 in 20 vol % aqueous ethanol, T = 25.0'.
'
Taking k~ to be rate determining, we have rate = kl(PH+)
(11)
rate = klK1(P)(H+)
(13)
but
Thus In the above mechanism, a rapid protonation equilibrium precedes the rate-determining loss of water,
-
ob
01
0.2
03
0.4
%;THO--
Figure 4. Substituent effect of the observed rate constant at pH 2.25 in phosphate buffer.
the latter being followed by a rapid proton loss. Such a scheme is, as experimental results show, first order in substrate and first order in proton. This mecha-
I
H
Table I11 : Properties of p-Nitrosophenols
PH'
(17) IBM Application Program H20-02062, White Plains, N.Y., 1967, p 290.
(18) Dissociation constants for these various acids and the autoprotolysis constant of water in 20% aqueous ethanol at the ionic strength of this study were determined potentiometrically. (19) H. H. Hodgson and D. E. Nicholson, J . Chem. SOC.,810 (1940). (20) R. W. Taft, Jr., J. Amer. Chem. SOC.,74,2729 (1952). (21) R. W. Taft, Jr., ibid., 74,3120 (1962). (22) J. Hine, "Physical Organic Chemistry," 2nd ed, McGraw-Hill Book Go., New York, N. Y., 1962, p 98.
The Journal of Physical Chemistry
3011
CHRONOPOTENTXOMETRIC MEASUREMENTS OF CHEMICAL REACTION RATES
in dioxane-water mixtures. The latter anomalous results were attributed to the use of unpurified dioxane, which was shown to contain considerable impurities. The presence of electron-withdrawing substituents was observed to increase the rate of the base-catalyzed reaction and to decrease the rate of the intrinsic reaction, as reflected in Figure 5. Thermodynamic activation parameters were determined for both the base-catalyzed and intrinsic reactions. The results of these determinations are shown in Table IV.
0.E
T 0.4 0.2 OSC
1-0.; Q .
I
-0.4
-0.6
-0.8
Table IV : Thermodynamic Parameters
1
-1 OC 3
4 ,-
5
pH
6
F *,
*,
Reaction
H $, kcal/mol
kcd/mol
cal/mol deg
Intrinsic Base catalyzed
11.8 f 0.4 16.2 f 0.4
18.0 f 0 . 6 6 . 3 =k 0 . 6
-21 f 1 33 i 1
bs
7
--+
Figure 5. Dependence of the reaction constant, on p H for the dehydration of PHPHA.
p,
nism is consistent with that proposed for the rearrangement of phenylhy d r ~ x y l a m i n e . ~ ~ It can be seen from Table I that two other pH regions are mechanistically important, namely the region wherein base catalysis is pronounced and the region wherein neither acid nor base catalysis is relatively important. In this latter pH region, ko, the intrinsic rate constant, is essentially the sole component of the observed rate constant. As can be seen in Figure 6, both the intrinsic and the base-catalyzed reaction rates were increased by increasing the dielectric constant of the solvent. Acetone-water and ethanol-water mixtures exhibited the same effect, while indeterminant results were obtained
Definitive results concerning the effects of ionic strength on the reaction rates were not obtained. This was due to the fact that the concentration range for quantitative description of ionic-strength effects was exceeded in order to maintain appreciable buffer capacity in relation to the substrate concentration. In the case of the noncatalyzed reaction, the following mechanistic scheme is suggested.
9-
AOH
H
P
!2
Taking lc2 to be rate determining, we have rate = k2(P*)
(16)
but 0,oL
60
65
-
70 DSOLVENT
75
80
(17)
I
Figure 6. Effect of the dielectric constant (E) of the solvent on the observed rate constants for PHPHA dehydration: 0, ethanol-water, base-catalyzed reaction, 15 and 30 vol %; 0, acetone-water, base-catalyzed reaction, 15 and 30 vol %; 0, ethanol-water, intrinsic reaction, 15 and 30 vol %; 0, acetone-water, intrinsic reaction, 15 and 30 vol yo.
Thus rate = kzK2(P) (18) The above rate expression is in agreement with the experimental results. The enhancement of the (23) H. E. Heller, E. D. Hughes, and C. K. Ingold, Nature, 168, 909
(1961).
Volume 72,Number 8 August 1968
3012
H ~ N RN. Y BLOUNT AND HARVEY B. HERMAN
reaction rate by electron-donating substituents is felt to manifest itself in the transition state, in that the elimination of water is rendered more facile. The entropy of activation shown in Table IV reflects the increased solvation (order) of the transition state, a fact which is also shown through enhancement of the reaction rate by increased solvent polarity. Furthermore, solvents of increasing polarity tend to favor the dipolar zwitterion structure in the prior equilibrium, an effect that would also appear as rate enhancement. In the case of the base-catalyzed reaction, a suggested mechanism is
P\OH
H
P
P\
H OH P-
Taking Fca to be rate determining, we have rate = ka(P-) but
Hence
(23) This rate expression is also in agreement with the experimental results, namely first order in the hydroxyl ion and first order in the substrate. The effect of electron-withdrawing substituents manifests itself to a great extent in the prior equilibrium, in that the phenolic proton is made more labile, thereby increasing Ka. Increased solvent polarity also tends to enhance K8, hence the observed rate constant, the latter being the product kaKa. Although the activation entropy is felt to be rather large for the hydroxyl-catalyzed case, its sign and the activation enthalpy for the reaction have precedent in mechanistic schemes of this type wherein an acid-base equilibrium is followed by a rate-determining decomposition of an ion into an ion and a neutral molecule.24 While mechanisms are not conclusively proven, it is felt that the results obtained in this and other s t ~ d i e stend ~ ~ ~to support the mechanistic pathways proposed here. rate = k&(P)(OH-)
Acknowledgment. This work was supported in part by grants from the Petroleum Research Fund (No. 488-G2) and the National Science Foundation (No. GP-6596). (24) W.E.Jordan, H. E. Dyas, and D. G. Hill,J . A m . Chem. SOC., 63,2383(1941).
