1712
Fueno et al.
Temperature-Jump Rate Studies of the Association Reactions of Boric and Benzeneboronic Acids with Hydroxide Ion 0. Kajimoto, T. Saekl, Y. Nagaoka, and T. Fueno* Department of Chemistry, Faculty of Englneering Science, Osaka University, Toyonaka, Osaka 560, Japan (Received March 1, 1977)
The second-order rate constants k for the additions of hydroxide ion toward boric acid B(OH)3and ringsubstituted benzeneboronic acids XC6H4B(OH)2 in 0.1 M aqueous KCl medium at 25 and 35 "C were measured by the temperature-jump relaxation method. The reactions were found to be activation-controlled processes with k being of the order of M-'s- The empirical activation energy for the boric acid reaction was 4.4 kcal/mol. Benzeneboronic acid showed a greater reactivity than did boric acid. The effects of ring substituents on the reaction rate of benzeneboronic acid proved to obey the Hammett relationship log k X / k H= pfu with pf = 1.18at 35 "C. It is suggested that the *-electronic charge on the boron atom in the acids is a factor governing the relative heights of the activation barrier.
Introduction Several have demonstrated that boric acid in an aqueous medium undergoes complex equilibria with borate and polyborate ions. In boric acid solutions having a total acid concentration of less than 0.01 M, the equilibrium B(OH),
+ OH'
+ B(0H); -1
is known to be the only important 0 1 1 8 . ~ 9 ~ At higher acid concentrations, boric acid enters into the formation of polyborate i ~ n s l - ~ 2B(OH),
+ B(0H);
2
+ B,O,(OH);
t 3H,O
(2)
and 2B(OH),
3
+ B,O,(OH);
+ B,O,(OH);
t 3H,O
(3)
In the boric acid concentration range 0.06-0.6 M, Eyring et al.4 investigated the temperature-jump relaxations of the polymerization equilibria 2 and 3. At pH 7.4, the relaxation times observed were 2-15 ms; the rate constants for forward processes 2 and 3 were 2.8 X lo3and 2.0 X lo2 W2s-l, respectively, at 25 "C. They noted that, under their conditions, reaction 1 should have a characteristic relaxation time much shorter than the resolving time (10 ps) of their instrument and that the association reaction would probably be a diffusion-controlled process (kl lolo M-' s-l). We have investigated the temperature-jump relaxation of boric acid equilibrium 1 in far more dilute (2 X to 1.5 X M) acid solutions. The forward rate constant Itl has been found to be 1.5 X lo7 M-ls-l at 25 "C. The activation energy was found to be 4.4 kcal/mol, a result which indicates that the association reaction is "activation controlled". Motivated by the above finding, we have further studied the reaction rates of several ring-substituted benzeneboronic acids: XC,H,B(OH),
+ OH'+
4
XC,H,B(OH);
(4)
-4
where X = p-CH3, m-CH3, H, m-CH30, p-C1, and m-C1. The rate constants k4 for the forward processes were found to be of the order of M-l s- at 35 "C. The substituent effects on the rates proved to conform to Hammett's The Journal of Physical Chemistry, Vol. 81, No. 18, 1977
relationship log k4X/k4H= pfu with pf = 1.18. The equilibrium constants K4 = k 4 / k 4 were also correlated with u ( p = 2.00). Clearly, the electronic effect of substituents plays a dominant role in governing the rate of the forward as well as the backward process of reaction 4. Experimental Section Materials. Boric acid of reagent grade was recrystallized from water. Its melting point, 185 "C (with decomposition), checked with the literature datum. Benzeneboronic acid and its p-CH3, m-CH3, m-CH30, p-C1, and m-C1 derivatives were all synthesized according to the method of Branch et al.6,7 Thus, trimethyl borate was allowed to react with appropriate phenylmagnesium bromide at -60 "C, followed by decomposition with dilute sulfuric acid. Benzeneboronic acids thus formed were purified by successive recrystallizations from benzene and water, and dried under a ventilated atmosphere. All the boronic acids were identified by 'H NMR spectroscopy and elemental analyses. The OH proton chemical shifts (in acetone at 25 "C) were as follow: p-CH3, 6 6.99; m-CH3, 6 7.13; H, 6 7.13; m-CH30, 6 7.09; p-C1,6 7.24; and m-C1, 6 7.41. The acids were all subject to dehydration on heating, as reported previously.8 Their melting points checked well with the literature data8 for anhydrides: p-CH3, 260 "C (lit. 259-260 "C); m-CH3,162-163 "C (lit. 160-161.5 "C); H, 214 "C (lit. 214-216 "C); m-CH30, 158 "C (lit. 159 "C); p-C1, -260 "C (lit. 261-262.5 "C); and m-C1, 183 OC (lit. 179 "C). Acid Ionization. The ionization constants of boric acid and various benzeneboronic acids in aqueous 0.10 M KC1 were determined by the standard procedure described by M with Albert and SerjeanLg Sample solutions, 1.0 X respect to the acid, were titrated with 0.01 M NaOH under a nitrogen atmosphere. A Hitachi-Horiba pH meter Model F-5 with a scale expander was used for pH measurements. Our pK, values thus obtained are based on the proton activity in 0.10 M KC1. Hence, they are uniformly greater than the standard concentration-based pK, values by a constant factor of -log Y H = 0.08, where Y H = 0.83 is the activity coefficient of H+ in an aqueous KC1 solution of ionic strength 0.10 M.l0 Temperature-Jump Experiments. The temperaturejump apparatus constructed in this laboratory is essentially the same as that described by Kresheck et al.ll Details of the specification of our apparatus have been delineated previously.12 The theoretical temperature rise was calculated to be ca. 7 "C with a rise time of 6 ps.
Reactions of Boric and Benzeneboronic Acids wHh Hydroxide Ion The temperature-jump relaxation measurements were carried out with 1.5 mL of each sample solution in the pH range 8.1-8.9. Sample solutions were 0.10 M in KC1 and 0.25-1.5 mM in the acid. Temperature jump was effected by discharging a 0.1 fiF capacitor charged to 25 kV through a cell. Relaxation courses were traced by monitoring the absorption at 565 nm of cresol red (1.0 X M) used as an indicator. Relaxation profiles were recorded on an Iwatsu 5505 oscilloscope and photographed. The relaxation times were evaluated from the slopes of the semilogarithmic plots of absorbance vs. time. Blank experiments involving only the indicator gave no observable relaxation in the time region (30-400 ps) of interest. Relaxation Rates. The temperature-jump relaxation observed under our conditions is probably due to the following set of reversible reactions B
+ OH-
5
BOH-
(5)
-5
1713
Flgure 1. Typical oscillographic record of the relaxationai response: wdinate (abswbanceat 565 nm), 10 mVldiiision; abscissa (time), 100 M; cresol red. 1.0 X lO-'M: medium. -/division; baic aca. 1.0 X 0.10 M KCI; pH, 8.49 temperature, 25 "C;7 = 144 JLS. Moving upward on the record corresponds to an increase in the In2-absorption.
6
HIn- + OH- 3 In2- + H,O
(6)
-6
with the equilibrium constants K5 = k5/k-5 = [BOH~]e/[B]e[OH~le K6 = k6/k-6 = [In'-]J[HIn~].[OH~].
(7)
(8)
where B denotes either boric or benzeneboronic acid, and HIn- is the acid form of the indicator (cresol red) anion. The relaxation equation pertinent to this coupled reaction scheme is
-A dt
(A[HIn-] A[B1 )
=~
~ ~ H Ie nk5[B].) TC' - ]
(9)
where A[B] and A[HIn-] are the respective deviations of instantaneous concentrations of B and HIn- from equilibrium while r5 and T~ are the constants defined as 7;' 7;'
+ [OH].) + k-5 = k6([HIn-]. + [OH-].) + 12-6
= k,([B].
(10) (11)
where K, is the ion product of water and KHInis the ionization constant of HIn-. At 25 and 35 "C, the pK, is 14.00 and 13.68, respectively." The KHlnof cresol red is 8.20 at 25 OCO ' and is estimated to be 8.15 at 35 "C. The HIn- equilibrium concentration can be expressed as [HW.
=Io/(l
+ K,[OK]e)
(16)
I, being the total concentration of the indicator used. Thus, the factor f is a function of only Io and [OH-], at a given temperature, and tends to decrease with increasing I, and decreasing [OH-], Under the present experimental M, f conditions in which Io has been fixed at 1.0 X varies from 0.338 to 0.851 at 25 "C and from 0.513 to 0.929 at 35 'C as the pH of the sample solution is changed from 8.1 to 8.9. Results (A) Boric Acid. The equilibrium constant K, for reaction 1 in 0.10 M KC1 can be evaluated from the acid dissociation constant K. and the ion product of water K , in the same medium: K I = [B(OH),IJ[B(OH)3l.[OH-l.
= K ~ H (17) G
The coupled relaxation time T of interest is given as the reciprocal of the smaller eigenvalue of the relaxation matrix appearing in eq 9.13 Evidently, T
