E. GRUNWALD, C. F. JUMPER,AND M. 5. PUAR
492
result suggests that one or more of the rate-controlling steps in the high-temperature radiolytic decomposition involves thermal dissociation in a thermal spike. Acknowledgment. The authors wish to thank Dr. Richard Holroyd of our laboratory for extremely
helpful discussions and criticism of this work. We wish to acknowledge the help of Dr. Trent Tiedeman, also of this laboratory, for his assistance in calculating the activation energies of certain free-radical processes which may occur during pyrolysis of o-terphenyl.
Rates and Solvent Participation in Acid-Base Reactions of Substituted
Phenols and Phenoxides in Methanol'"
by Ernest Grunwald,'b Charles F. Jumper, and Mohindar S. Purlb Bell Telephone Laboratories, Inc., Murray Hill, New Jersey, and Lecks Chemical Laboratories, Brandeis University, W d t h a m , Massachusetts (Received M a y 31, 1966)
The kinetics of proton exchange between methanol (the solvent) and p-nitrophenol or p bromophenol has been investigated by the nmr method in buffered solutions containing phenol and phenoxide and in acid solutions containing phenol and HC1 at -80". Rates of proton exchange are derived from measurements of the CH3- and OH- proton resonances of methanol and of the OH-proton resonance of the phenol. The following processes involving the given numbers of solvent molecules have been identified: (1) base dissociation of ArO-, which involves two solvent molecules, ArOHO(CH3) HOCHI i=2 ArOH (CH3)OH -0CH3; (2) a symmetrical process that involves one solvent molecule, ArOHO(CH3) HOAr + ArOH (CH3)OH -0Ar; and (3) a process that involves one methyloxonium ion, one ArOH, and an unknown number of solvent molecules. Rate constants for these processes and base dissociation constants KBfor reaction 1 are reported. Substituent effects on K B at -80" are nearly equal to those at 25" and are largely entropy effects. Reversal of reaction 1 is fast enough so that this rate could be diffusion controlled even at -80". The self-association of p-nitrophenol was measured at -80" by means of nmr chemical shifts and was substantially that to be expected on the basis of volume fraction statistics. A noteworthy and unsolved problem in the interpretation of the CH3-proton resonance of methanol is that plausible rate laws can be obtained only if values of 1l.r based on the Bloch equations are first corrected by means of an empirical function, + ( T ) , as described in the paper.
+ +
+ +
I n previous papers from these laboratories, nuclear magnetic resonance (nmr) was used to measure rates and solvent participation in acid-base reactions in We now apply water and other hydroxylic the nmr method to the proton exchange reactions of phenols and their conjugate bases in methanol. Our The Journal of Phyeicial Chemistry
+
+
+
+
substrates are p-bromophenol and p-nitrophenol, the reaction temperature is -80", and the pH of the reac(1) (a) Work supported in part by the Petroleum Research Fund of the American Chemical Society. Grateful acknowledgment is made to the donors of that fund. (b) Brandeis University Waltham, Mass.
RATESAND SOLVENT PARTICIPATION OF SUBSTITUTED PHENOLS AND PHENOXIDES
tion mixtures ranges from about +2 (0.01 M HC1) to that of buffers containing both phenol and phenoxide. Under these conditions, we find the following reactions to be kinetically significant. 1 , Reaction of ArOH with Methanol and Methoxide
-
Ion ArOH
ki
+ OH +
c--
I
k-rrkbd
(3%
+ HO + HOCHa
ArO-
I
(1)
CH3 Note that the reverse of reaction 1 is the base dissociation of ArO- as a Br$nsted base (rate constant k ~ ) . 2. Reaction of ArOH with Methanol and ArOArOH
+ OH + -0Ar -%
I
CHI ArO-
+ HO + HOAr
(2)
I CH3 3. Reaction of ArOH with Methyloxmiurn Ion. The number of methanol molecules participating here could not be determined. Some plausible reaction mechanisms are shown below. 4-
CH30H
I
+ OH + OCH3 kt I
I
H
Ar
H
+
CHIO
I
+ HO + HOCHa
H ArO
I
H
+
+ HO + HOCH3 I
CH3
A
l
r
l
(3a)
H
kab
I
H Ar6H
I
H
+ OH + OCHs I
CH3
I
(3b)
H
Reaction 3a represents a symmetrical proton exchange process analogous to reaction 2; reaction 3b is the conjugate of reaction 1 in the sense that the protons move toward rather than away from ArOH. 4. Proton Exchange between CHSO- and Methanol. I n addition, in the buffered solutions there is proton exchange between CH3O- and methan01,~and in the presence of HC1 there is proton exchange between CHaOH2+ and methanol.*
493
Since some of the measurements were made at moderate solute concentrations (up to 0.7 M ArOH), we also measured chemical shifts of solvent and solute protons ~ t as function of concentration in order to elucidate the intermolecular interactions. We found that the self-association of p-nitrophenol, i.e., the probability of formation of adjacent pairs of ArOHeArOH, is substantially that expected for an ideal mixture of ArOH and methanol. Moreover, there was no significant interaction chemical shift when the two solutes, ArOH and NaOAr, were both present in solution. Rate constants have been reported in water at 25' for analogous proton transfer reactions between ArOH and the hydroxide ion, between ArO- and the hydrogen ion, and between phenol, water, and the phenoxide Lifetimes for proton transfer between ArOH and methanol have been reported for o-ClCsH40H in very concentrated solutions.* If these lifetimes may be extrapolated to dilute solution, they probably describe the acid dissociation of ArOH in methanol.
Experimental Section Materials. Solvent methanol for most experiments was first dried with magnesium and then doubly distilled, as described previou~ly.~Since the interpretation of nmr spectra in this solvent ran into an unexplained complication (see below) we wished t o rule out the possible presence of kinetically active impurities. We therefore repeated some measurements using a sample of methanol that had been supplied to us by Dr. Calvin D. Ritchie, whose cooperation we acknowledge gratefully. This sample had been dried by Dr. Ritchie with molecular sieves, and acidic or basic impurities had been removed by treatment with ion-exchange resins. The sample was then redistilled by us just before use, the middle fraction being used. Nmr spectra for solutions in this solvent were indistinguishable from those for formally identical solutions in the magnesium-dried solvent,. Eastman White Label p-bromophenol was twice recrystallized from chloroform and dried in vacuo. -~
(2) See, for example, (a) E. Grunwald, C. F. Jumper, and S. Meiboom, J. Am. Chem. SOC.,85, 522 (1963); (b) 2. Luz and S. Meiboom, J. Chem. Phys., 39, 366 (1963); (c) E. Grunwald and M. Cocivera, Discussion8 Faraday SOC.,39, 105 (1965). (3) E. Grunwald, C. F. Jumper, and S. Meiboom, J. Am. Chem. Soc., 84, 4664 (1962). (4) M. Eigen and K. Kustin, ibid., 82, 5952 (1960). (5) 2. Luz and S. Meiboom, ibid., 86, 4766 (1964). (6) For s recent review see M. Eigen, W. Kruse, G. Maas, and L. De Maeyer, Progr. Reaction Kinetics, 2, 285 (1964). (7) Protolysis kinetics of electronically excited ArOH has been reviewed by A. Weller, ibid., 1, 187 (1961). (8) E. Krakower and L. W. Reeves, Trans. Faraday SOC.,59, 2528 (1963).
Volume 71,Number 8 February 1967
E. GRUNWALD, C. F. JUMPER, AND M. S. PUAR
494
For experiments involving very high acid-base ratios, this recrystallized material was further zone refined on a Fisher zone refiner. Fisher White Label pnitrophenol wm twice recrystallized from toluene, air dried, and finally dried in vacuo over Mg(C104)2. Solutions. Solutions were made up from freshly prepared reagents by quantitative methods. Standard solutions of sodium methoxide (for HOAr-NaOAr solutions) or of HC1 were prepared from pure methanol and pure sodium metal or HCl gas in all-glass apparatus. Since some of the phenoxide or HCI concentrations were very low (10-4-10-s M), these concentrations were checked by potentiometric titration of the actual reaction mixtures (which of course also contained HOAr) using methanolic HCl or NaOMe titrants. Furthermore, for the p-nitrophenyl reagents concentrations were also confirmed by spectrophotometry of the reaction mixtures. As a result, we are confident that we know concentrations with an accuracy of at least 2% in even the most weakly buffered of the reaction mixtures. I n order to minimize errors from ion exchange of the sodium or hydrogen ion between weakly buffered reaction mixtures and their glass containers, we prepared all such mixtures twice. The first preparation was used only to establish ionic quasi-equilibrium between the solution and the required containers, including the nmr sample tube. The containers were then rinsed with pure methanol, dried, and used to receive a second, duplicate preparation on which the actual measurements were made. Water content of the reaction mixtures was monitored by Karl Fischer titration after the conclusion of each series of experiments (usually 1 or 2 days after preparation) and was usually less than 0.01 M and always less than 0.015 M. Nmr Measurements. All measurements were made at a frequency of 60 Mc/sec. Most of the measurements were made on Dr. s. Meiboom's nmr spectrometer at Bell Telephone Laboratories;a the rest were made at Brandeis University on a Varian Model HR60 nmr spectrometer equipped with Meiboom's temperature-controlled probe. Experimental techniques followed previous practice. 2a,8 All measurements were made on air-saturated solutions at a nominal temperature of -80". Interpretation of Nmr Spectra In measuring kinetic order with respect to methanol in the proton transfer reactions of pbromo- and p nitrophenol we used a method reported by Grunwald, Jumper, and Meiboom.2a Briefly, we used the CHaThe Journal of Phy&
Chemistry
proton resonance of methanol to evaluate proton exchange rates in the spin-coupled OH group of methanol; and we used the OH-proton resonance of the ArOH-CH30H proton system (which collapses into a single line at fast exchange rates) to evaluate proton exchange rates in the OH group of ArOH. OH-Proton Exchange Rate of Methanol. The calculation of proton exchange rates in the OH group of methanol from slow passage nmr spectra of the spincoupled CHa group has already been described in detail.' We now wish to report a complication that had not been envisaged in the previous work. We cannot give a theoretical explanation of the complicating p h e nomenon, but we shall try to characterize it empirically. In the following report we shall use the notation of ref 3. The slow passage nmr spectrum of the CHI protons of methanol is regarded as a function of two characteristic times: the transverse relaxation time, Tz,of the CHa protons and the time, r, between proton spin inversions in the OH group. OH-proton spin inver1/T =
2(rate of OH-proton spin inversion/ [MeOH]) (4) sion is assumed to occur by two parallel mechanisms, TI relaxation and chemical exchange (which proceeds at a rate of R g-atom/l. sec-I). On the basis of a large
+
1 / ~ = (~/TI)oH R/[MeOHI
(5)
body of data for proton exchange in methanol at -80" we find, however, that we cannot derive plausible rate laws unless we add an empirical correction, 9, as in
+
1 / ~= ( ~ / T I ) o H 447)
+ R/[MeOHl
(6)
eq 6.1° This correction is a function either of T or R-we cannot decide empirically because ( T l ) 0 ~ ,on the basis of spin-echo measurements, varies relatively little in the experimental range. All our evidence indicates, however, that @ does not depend on the nature of the solutes or the rate law for R. For convenience ) values of 4 at -80" are plotted we shall write 4 ( ~and vs. 1 / ~in Figure 1. As shown below, these values were obtained from slow passage CH3-proton spectra for a single system, p-nitrophenol-p-nitrophenoxide ion in methanol, under conditions where the rate law (9) We gratefully acknowledge the help of Dr. S. Meiboom with construction and installation. (10) After completion of this manuscript A. Allerhand, H. S. Gutowsky, J. Jonas, and R. A. Meinser have published a critical enalysis of errors in nmr measurements of chemical exchange rates [J. Am. Chem. SOC.,88, 3185 (1966)l. However none of the errors described by them could have been large enough in our experiments to account for . $ ( T ) . I n particular, the theoretical line shapes used for evduating T were based on density-matrix line shape equations, see ref 3.
RATESAND SOLVENT PARTICIPATION OF SUBSTITUTED PHENOLS AND PHENOXIDES
495
t
3.0
0.01
I
2
4
6
10
20
40
60
I
100
I/? (sec-')
Figure 1. Plot of the empirical function +(T) in eq 6 for CHa-proton resonance of methanol a t -80'. The smooth curve is a plot of 1 1 7 ~ / ( 1 4789).
+
for R is simple. Although our method of evaluating r# involves an arbitrary assumption, it accomplishes the following result. Without the 4( T ) correction, slow passage CH3-proton spectra of methanol at -80' lead to implausible rate laws for solutions of the following acids and their conjugate bases: benzoic acid, acetic acid, pbromophenol, p-nitrophenol, and trimethylammonium ion. On applying the 4 ( ~ )correction shown in Figure 1 the kinetic behavior of all of these substrates becomes entirely rational. Let us give an example. In previous workzs on benzoic acid-benzoate buffers in methanol at -80', we calculated R on the basis of eq 5 and obtained the rate law
R = kl[HBz]
+ k2[HBz][NaBz] + Ica[HBz]l/'[NaBz]l"
The third (square root) kinetic term seemed implausible because we could not make it consistent with any theory that conformed to (i) the mass law of chemical reaction rate, (ii) microscopic reversibility in chemical systems a t dynamic equilibrium, and (iii) stability principles of molecular structure. However, when the same data are recalculated on the basis of eq 6, taking $J(T) from Figure 1, the implausible (square root) kinetic term becomes insignificant and can be dropped from the rate law. t$(~) in eq 6 for the CHa-proton resonance of methanol at -80' was evaluated using our extensive slow passage nmr data for pnitrophenol-p-nitrophenoxide buffers in methanol. Experimental results for 1 / ~ at [ArOH]/[NaOAr] ratios ranging from 90 to lo00 depend accurately on a single variable, the concentration product [ArOH][NaOAr]. This suggests that reaction 2 is the only reaction that is kinetically significant under these conditions. If in first approximation we calculate R on the basis of eq 5 and if we then calculate an apparent rate constant j2 according
I/Z (sec-'1
Figure 2. Histogram showing jz (eq 7) rn a function of 1 / for ~ pnitrophenolpnitrophenoxide solutions The ratio [ArOH]/[NaOAr] in methanol a t -80'. ranges from 90 to 1000 in these experiments.
to eq 7, we obtain the result shown in Figure 2. It
j2 =
[T-'
-
( T ~ ) o H -[MeOH]/ ~] [ArOH][NaOAr] (7)
is seen that j 2 is constant within experimental error when 1/r > 40 and that j2 increases significantly as 1 / goes ~ to lower values. We have been unable to reconcile this variation of j2 with any plausible reaction mechanism. To calculate 4 / ( ~ )we assume that j2 approaches k2 in the limit as 1 / ~becomes large. In Figure 2, we have taken this limit to be 4.28 X los sec-l M-l. We then calculate + ( T ) from eq 8. The resulting values and estimated standard errors are plotted in Figure 1. 4(T)
=
7-l
- (T1)OH-l
-
k2 [ArOHI [NaOAr]/ [MeOH] (8) The smooth curve in Figure 1 is a graph of the empirical eq 9, which fits the values satisfactorily. Accordingly, I$(T)-*~
=
+478~~)
117~/(1
(9)
$ ( T ) at -80' approaches zero at both large and small values of 7 and goes through a maximum a t 1 / ~= 21.9 sec-l. This maximum very nearly coincides with that value of 1 / ~a t which the CHBresonance of methanol just fails to be a resolved doublet. As 1 / ~increases above 21.9 sec-' @ ( T ) rapidly becomes of the order of the experimental error in 1 / ~amounting , to 10% of 1 / at ~ 26 sec-l and to 5% at 43 sec-l. On the other hand, as 1 / ~decreases below 21.9 sec-l + ( T ) gains progressively in relative importance, amounting to 25% of 1 / at ~ 4 sec-l.
Volume 71, Number S February 1067
E. GRUNWALD, C. F. JUMPER, AND M. S. PUAR
496
The physical significance of $(7) is obscure to us. The effect cannot be ascribed to an impurity in the methanol solvent because of its high reproducibility, considering that the solvent was prepared by two different methods and in many independent batches. For a given value of 7, the effect is independent of pH and, apparently, of the nature of the solutes. Thus everything indicates that $ ( T ) is a characteristic property of the solvent, methanol. Perhaps $(T) represents a mechanism of OH-proton spin inversion that is triggered by proton exchange in a nonspecific way so that the effect depends only on the total rate of exchange. (In that case we should write $ ( R ) rather than $ ( T ) . ) It is more likely that there is a flaw in the equations that were used to calculate theoretical nmr spectra for methanol as a function of 7.11 This explanation is suggested by the fact that (6(7) goes through a maximum near the "coalescence point" of the CHs doublet. Cocivera, in spin-echo measurements of T1,has obtained evidence for cross relaxation of magnetization between CHB and OH protons of the sort described by Solomon and Bloembergen.I2 His work is relevant because a term for cross relaxation was not included explicitly in the theoretical equations.'* However, that sort of cross relaxation is a t a maximum when 1 / ~= 6, whereas our effect is at a maximum when I/? E= J/&. ( J = spin coupling constant, 6 = difference in chemical shift.) Note that for methanol a t -80" 6/J E= 30. Note also that in the present as in previous work, spin-echo measurements on a representative number of solutions indicate that (1/ T1)oH varies only slightly, and approximately linearly with solute concentration, in the experimental range of 1 / < ~ 100 sec-'. OH-Proton Exchange Rate of ArOH. I n some experiments we measured the OH-proton resonance of ArOH under conditions of lifetime broadening; in others we measured the coalesced OH resonance of ArOH and methanol. The interpretation of these nmr spectra was analogous to that of C02H-OH proton spectra for benzoic acid solutions in methanol.28 l/Tl for the phenolic OH protons was measured by rf saturation of slow passage spectra and was found to be 6.0 sec-' for p-bromophenol and 6.7 sec-l for p-nitrophenol at -80". The chemical shift between the two kinds of OH protons was 4.07 ppm for pbromophenol and 5.27 ppm for p-nitrophenol a t -0.1 M [ArOH] and -80".
Results Rate Constants. We shall use the symbol k with a superscript to denote a phenomenological rate constant The Journal of Physical Chemistry
in an empirical rate law and k with a subscript to denote an actual rate constant for a particular reaction. The OH-proton exchange rate of methanol, R, was measured in the near-neutral to alkaline pH range. The data for p-bromophenol are consistent with the rate law, eq 10. The data for p-nitrophenol are con-
R
=
kl[ArO-]/[ArOH]
+
k*[ArO-]
+ k**[ArOH][ArO-]
(10)
sistent with the same rate law except that the term k* [ArO-] is insignificantly small. Rate constants are listed in Table I. Table I: Rate Constants for Proton Exchange of p-Bromophenol and pNitropheno1 in Methanol" Kinetic COnRt8nt
k' = kMeO-KB k* = 3kbd k** = k2 k*' = kbd k**' = k2 k" = ka
Value and std dev f o pBromopheno1, pNitrophenol, -81.6' -80.00
(1.08 f 0.1) X 10' (9 =k 2 ) x 104 ( 1 . 4 3 f 0 . 1 5 ) X lo6 ( 3 =k 1) x 104 ( 1 . 5 2 f 0.10) X lo6 (21 f 4) x 104
p
42 =k 2
b 4 . 2 8 X 10' C
c
( 0 . 9 4 rt 0.1) x 104
' All kinetic constants are based on the second as the unit of time and the mole per liter (at the reaction temperature) aa the unit of concentration. Too small to measure ( < 2 x 1 0 4 ) . Not measured.
The OH-proton exchange rate of ArOH, R', was measured for p-bromophenol both in the near-neutral and in the distinctly acid pH range. The data are consistent with the rate law eq 11. For pnitrophenol
R'
=
k*'[ArW]
+
k**'[ArOH][ArO-]
+ k"[ArOH] [MeOHz+]
(11)
R' was measured only in the distinctly acid pH range where only the last term of eq 11 is significant. Rate constants are given in Table I. Because of their concentration dependence and for reasons stated below, we believe that kinetic terms can be identified with chemical reactions as follows: (a) k1 [ArO-]/[ASH] = k~,o-[MeO-], proton exchange between methoxide ion and methanol. Hence, k1 = kMeO-KB, where KB = [ArOH][MeO-]/[ArO-]; (b) k* and k*' with reaction 1; (c) k** and k**' with reaction 2; and (d) k" with reaction 3. (11) See ref 3 and literature references cited therein. (12) (a) M. Cocivera, Bell Telephone Laboratories, private communication; (b) I. Solomon, Phys. Rev., 99, 559 (1955); (c) I. Solomon and N. Bloembergen, J. Chem. Phya., 25, 261 (1966).
RATESAND SOLVENT PARTICIPATION OF SUBSTITUTED PHENOLS AND PHENOXIDES
The rate laws, eq 10 and 11, were established with high statistical probability on the basis of an extensive series of measurements covering a wide range of all relevant concentrations. All told, the measurements of R involved 41 separate solutions for p-bromophenol and 35 for p-nitrophenol; those of R' involved 15 separate solutions for p-bromophenol and 7 for p-nitrophenol. The complete data are made available elsewhere.13 Solvent Participation. The number of methanol molecules participating in a given kinetic process can be deduced from the ratio of rate constants for corresponding kinetic terms in the rate laws for R and R' (eq 10 and 11).28 Thus, for the kinetic term proportional to [ArO-1, k* = 3k*' within experimental error. Since the rates are measured at dynamic equilibrium, the corresponding reaction must be such that in each reversible cycle three methanol molecules exchange an OH proton for every ArOH molecule that exchanges an OH proton. Furthermore, the forward reaction of the reversible cycle must be formulated so as to be kinetically of the first order in [ArO-1. A reversible cycle consisting of reaction 1, first from right to left, then from left to right, will fit these requirements. To predict the three-to-one ratio, we count the protons that enter a given state in one cycle, regardless of where they come from.14 In reaction 1 from right to left, one proton enters the state "methanol" and one proton enters the state "ArOH." In the reverse of this reaction, two protons enter the state "methanol" and zero protons enter the state "ArOH." If this interpretation be granted, then k*' must be identified with kbd.
For the kinetic term proportional to [ArOH][ArO-1, k** = k**' wit
