3301
J. Phys. Chem. 1984, 88, 3301-3305
Temperature-Jump Rate Study of the Chemical Relaxation of Aqueous Boric Acid Solutions G . Waton, P. Mallo, and S. J. Candau* Laboratoire d'Acoustique Mollculaire, Universitt? Louis Pasteur, 67070 Strasbourg Cedex. France (Received: August 1 , 1983)
Measurements of the kinetics of the boric acid-borate equilibrium in aqueous solutions by the temperature-jump method are reported. The results are in good agreement with a two-step model. The influences of temperature, ionic strength, and pH on the rate constants of the slowest relaxation step have been investigated. Knowledge of the kinetic parameters is relevant for the analysis of the acoustical data obtained at high frequencies for the same system.
Introduction Chemical relaxations have been shown to be responsible for excess sound absorption at frequencies below 100 kHz in ocean propagation measurements. In that frequency range, three processes with relaxation frequenciesf, 100 kHz,f, 10 kHz, andf, 1 kHz account for most of the absorption in sea water. The first, involving magnesium sulfate, has been widely investigated in the laborat~ry.'-~The second process has been explored by Mellen et al. in the laboratory and in Lake Tanganyika.e The third relaxation was discovered independently by Thorp9 and by Skretting and Leroy'O through measurements at sea. Laboratory temperature-jump measurements by Yeager et al." showed a single relaxation attributed to the boric acid-borate equilibrium. Further work by S i m m o n ~ ' ~showed * ' ~ the relaxation time measurements are consistent with the two-step equilibrium
-
-
k12
B(OH),
+ OH-%
[B(OH),,OH-]
-
ku 7 B(OH)412
(1)
in which the formation of the borate ion involves an intermediate state and the slow second step causes the sound absorption. In addition, he found bicarbonate produced a marked increase in relaxation frequency, indicating interactions with the pH buffer system in sea water. A detailed study by Mellen et al. using acoustic resonator measurments in synthetic media showed that boron, magnesium, calcium, and bicarbonate were all required to achieve sea-water values of sound ab~orption.6~*.'~.'~ However, the relaxational behavior exhibits extreme complexity and the mechanism remains unexplained. The aim of the present study is to investigate by temperature-jump the stepwise synthesis of artficial sea water. Measurements on aqueous solutions of boric acid in over large range of concentration, pH, and ionic strength are reported. The results are compared with the theoretical predictions of a two-step model involving the boric acid-borate equilibrium. (1) L. N. Liebermann, J . Acoust. SOC.Am., 20, 868 (1948). (2) R. W. Leonard, P. C. Combs, and L. R. Skidmore, J. Acoust. SOC. Am., 21, 63 (1949). (3) G. Kurtze and K.Tamm, Acustico, 3, 33 (1953). (4) 0. B. Wilson and R. Leonard, J. Acoust. SOC.Am., 26, 223 (1954). (5) K. Tamm, G. Kurtze, and R. Kaiser, Acustica, 4, 380 (1954). (6) R. H. Mellen, D. G. Browning, and V. P. Simmons, J . Acoust. SOC. Am., 68, 248 (1980). (7) D. G. Browning, J. M. Gorman, E. N. Jones, W. H. Thopp, and R. H. Mellen, Nature (London), Phys. Sci., 240 (1972). (8) R. H. Mellen, V. P. Simmons, and D. G. Browning, J . Acoust. SOC. Am., 67, 341 (1980). (9) W. H. Thopp, J . Acoust. SOC.Am., 38, 648 (1965). (10) A. Skretting and C. C. Leory, J. Acoust. SOC.Am., 49, 276 (1971). (11) E. Yeager, F. H. Fisher, J. Miceli, and R. Bressel, J. Acoust. SOC. Am., 53, 1705 (1973). (12) V. P. Simmons, Ph.D. Thesis, Department of Oceanography, University of California, San Diego, CA 1975. (13) R. H. Mellen, D. G. Browning, and V. P.Simmons, J . Acoust. SOC. Am., 69, 1660 (1981). (14) R. H. Mellen, V. P. Simmons, and D. G. Browning, J . Acoust. SOC. Am., 70, 143 (1981).
0022-3654/84/2088-3301$01SO/O
TABLE I: Effect of the Ionic Strength upon the Ionization of Boric Acid at Various Temperatures"
DK. I
0 0.1 0.4 0.7
*
4OC
6OC
2OoC
25OC
9.44 9.22 9.10 9.03
9.42 9.21 9.07 9.01
9.28 9.08 8.93 8.88
9.24 9.02 8.89 8.83
31
O C
9.20 8.98 8.85 8.79
"From ref 15.
Experimental Section Freshly distilled water and reagent grade boric acid were used. Solutions were prepared by dissolving weighed samples in a volumetric flask and diluting to volume. The ionic strength c~ was adjusted by the addition of NaCl, NaC104, or BaC12. The solutions were carefully decarbonated by first bubbling nitrogen for 10 min and then stirring under vacuum. The pH was adjusted with HCl or HC104and freshly prepared NaOH or Ba(OH), (to avoid COz absorption) and determined with a Tacussel ph meter equipped with a Tacussel glass electrode. There is a disagreement among the reported values of the ionization constant of boric acid. In the present study we have used the apparent ionization constant of boric acid determined by Owen and King15 and defined as
KP = [B(OH)d-I [H+1/ [B(OH)d
(2) where [B(OH),-], [B(OH),], and [H+] represent the molar concentrations of the different species. Table I presents values of the apparent ionization constants at different temperatures and ionic strengths. As the pH is a measure of the hydrogen ion activity we have calculated the activity coefficient of H+ from the Debye-Hiickel limiting law.I6 The values of y may be also obtained from the Davies equation which is more accurate for higher ionic strength than the Debye-Hiickel limiting law but is still limited to fairly low values of p." Therefore [H'] = 1O-pH / y (3) All kinetics runs were carried out on a Joule heating temperature-jump apparatus obtained from Messanlagen Studienge~ e l l s c h a f t . ~A ~ Jchopped ~ heating pulse of 1 MUSwas used for most of the runs. At a potential of 40 kV the temperature jump was 3.8 "C. The temperature in the cell was held constant within f O . l OC. The resultant relaxation curves were visualized on an oscilloscope. The range of accessible relaxation time was 4 ~.lsto 50 ms. (15) B. B. Owen and E. J. King, J . Am. Chem. SOC.,65, 1612 (1943). (16) S. Glasstone, K. Laidler, and H. Eyring, "The Theory of Rate Processes", McGraw-Hill, New York, 1941, pp 427-30. (17) C. W. Davies, "Ion Association", Butterworths, London, 1962. (18) G. Czerlinsky and M. Eigen, 2. Elektrochem., 62,652 (1959). (19) M. Eigen and L. De Maeyer, "Technique of Organic Chemistry", Vol. VIII, Part 11, L. Friess and A. Weissberger, Ed., Interscience, New York, 1963, Chapter XVIII.
0 1984 American Chemical Society
3302 The Journal of Physical Chemistry, Vol. 88, No. 15, I984 TABLE 11: Influence of the Nature of the Supporting Electrolyte on the Relaxation Time" 78,
co mM
NaCl
0.1 0.5 1 2 4 10
859 318 183 94 46 21
0.1 0.4 1 5 10
748 361 181 41 25
1 10
309 46
TABLE 111: Influence of the Ionic Strength on the Relaxation Time for Different Boron Concentrations'
m
BaClz PH 8
Waton et al.
726 320 139 84 46 26
7B3
NaC104
P
976
0.1 0.4 0.7
91 22
pH 8.7
X
308 52
cot mM
318
Thymol blue at a concentration of -2 X M was used to optically follow the relaxation of the solution. To ensure the validity of the experimental results, we performed series of runs on blank systems containing thymol blue and the supporting electrolyte at the same concentration and pH. The measurements have been carried out at temperatures ranging from 4 to 31 "C.
Experimental Results Indicator Effects. The thymol blue exhibits a relaxation in the experimentally accessible time range. The kinetic characteristics for the hydrolysis reaction of this indicator have been determined by T-jump experiments.z0 At a concentration Io = 2 X M, pH 8.75, and T = 4 OC, one obtains T = 17 ps. In aqueous solutions of boric acid containing indicator, the spectrum consists of two exponentials widely separated in time with amplitudes of opposite sign. An example is given in Figure 1, a and b. The experimental relaxation data obtained on a long time scale (Figure l a ) were first analyzed. A single exponential was fitted to the relaxation curve from which the fast rising relaxation mode has been discarded. This allows one to measure the slow relaxation time TB. The part of the curve corresponding to the fast process which can be attributed to the indicator relaxation is then fitted to the following relation:
+c
where T ~ ,is, the fast relaxation time, and A, B, and Care constants. The above relationship represents to a good approximation the sum of two exponentials in the limit t/TB
