316
J. Phys. Chem. 1986, 90, 316-319
CHEMICAL KINETICS Pulsed-Laser Conductivity Study of Recombination Kinetics of H+ and OH- in AlcohoVWater Liquid Mixtures Gregory R. Phillips and Edward M. Eyring* Department of Chemistry, University of Utah, Salt Lake City, Utah 84112 (Received: June 17, 1985)
The kinetics of the self-ionization of water have been studied in water-rich alcohol/water mixtures (ethanol, methanol, and 1-propanol). A pulsed laser excites overtones of the 0-H vibrations, leading to the dissociative ionization of water and formation of excess hydronium and hydroxide ions. The relaxation back to equilibrium concentrations is analyzed for the recombination and dissociation rates at 25 O C as a function of solvent composition. The recombination rate for ethanol/water mixtures is constant within experimental error between 0 and 4.5 mol % ethanol, and then decreases monotonically as the concentration of ethanol increases to 25 mol %. Methanol and 1-propanol mixtures show an almost identical decrease in recombination rate with mol % alcohol. Dissociation rate constants also decrease with increasing alcoholic content; however, the rate of decrease depends upon the particular alcohol.
Introduction Proton-transfer reactions are an important and widely studied class of chemical reactions. Experiments on a large number of reactions in aqueous solution have led to the generalization that diffusion-controlled proton transfers involve the participation of solvent molecules hydrogen bonded to reactants, forming a bridge by which protons can be transferred by a jump mechanism.' Reactions are much slower in the absence of such a bridge, e.g. in cases where intramolecular hydrogen bonding occurs.2 The role of hydrogen bonding suggests solvent effects should play a prominent role in proton-transfer reactions and has led to a number of studies in aprotic solvents3 Aprotic solvents preclude hydrogen bonding between solvent molecules and reactants (and generally have considerably smaller dielectric constants than water). Alcohol/water mixtures provide a good vehicle for investigating the effect of hydrogen bonding on proton-transfer reactions. Molecules of water and (small) alcohols are similar: both are involved in hydrogen bonding, as donors as well as acceptors, but to differing extents. Variations in hydrogen bonding can be studied in a continuous fashion by measurements over the composition range of the solvent mixture, without dramatic changes in dielectric constant. Properties of alcohol/water mixtures such as viscosity and enthalpy of mixing have been shown to be functions of solvent composition, often exhibiting extrema in the water-rich region. These extrema are usually ascribed to increased water structure. However, these are bulk properties of the solvent and do not necessarily reflect localized physical properties or solvation structure in the vicinity of the reacting species. Kinetic measurements should provide a more sensitive indication of the role of water microstructure in the mechanism of proton-transfer reactions. Kinetic studies of diffusion-controlled reactions in alcohol/water mixtures have received some attention in the past. For example, the proton-transfer rates between dihydrogen phosphate and imidazole in water with small quantities of methanol, ethanol, and dioxane added have been investigated by Schwarz and co-~orkers.~ A sharp maximum in the rate was observed at 0.5% v/v, which was attributed to enhanced hydrogen bonding in the hydration (1) Bell, P R. "The Proton in Chemistry"; Cornel1 University Press: Ithaca, NY, 1973. (2) Hibbert, F. Acc. Chem. Res. 1984, 17, 115. (3) Simmons, E. L. Prog. React. Kinet. 1977, 8, 161. (4) Nicola, C. V.; Labhardt, A.; Schwarz, G. Ber. Bunsenges. Phys. Chem. 1979, 83. 43.
0022-3654/86/2090-03 16$01S O / O
spheres of the reacting ions. Huppert and Kolodney have measured the proton ejection rates from electronically excited aromatic alcohols in aqueous mixtures of methanol, ethanol, and propan01.~ In the course of a pulse radiolysis study6 of the reaction of solvated electrons with CC1, in alcohol/water mixtures, MiEiC and CerEek measured the recombination rate of H+ and OH- in ethanol/water mixtures at 21 OC. While solvent composition was clearly important in the reaction kinetics of all three studies, the differing solutes involved influenced what could be observed. This paper is concerned with the most fundamental of all proton-transfer reactions, the self-ionization of water: k
H20(S) & H+(S) + OH-(S) kr
where S denotes the solvent. Alcohol/water mixtures were used as the solvent, with the concentration of alcohol varying between 0 and 25 mol %. No solutes are present to modify solvent effects on the reaction kinetics. Studies of this kind have traditionally been done using the relaxation techniques of Eigen and co-workers,' the most familiar example of which is the temperature jump method. The present work was done using the laser-induced dissociative ionization reaction of water. In this method, developed by Goodall, Natzle, and co-~orkers,8,~ photons excite overtones of the 0-H vibrations, leading to an enhanced dissociation of water into hydronium and hydroxyl ions. Excess ions generated by the laser pulse decay to equilibrium concentrations by the first-order kinetics common to relaxation methods. Concentration changes are followed by conductivity measurements. The method easily lends itself to signal averaging, small perturbations, and low ionic concentrations (eliminating the need to use activity coefficients in calculations). Experimental Section A block diagram of the apparatus is shown in Figure 1. The sample cell9 consists of a Teflon body with quartz windows and two pairs of platinum electrodes press-fitted into the Teflon body. ( 5 ) Huppert, D.; Kolodney, E. Chem. Phys. 1981, 63, 401. (6) MiEiE, 0. I.; CerEek, B. J . Phys. Chem. 1977, 81, 833. (7) Bernasconi, C. F. 'Relaxation Kinetics"; Academic Press: New York, 1916.
0 1986 American Chemical Society
The Journal of Physical Chemistry, Vol. 90, No. 2, 1986 317
Recombination Kinetics of H+ and OH- in Alcohol/Water
TABLE I: Computed Coefficients for Density, d , in g/mL as a Function of mol % Alcohol, x, at 25
O C
n
d = Cbixi i-0 ~~~
alcohol methanol'
0.9971
-2.8930 X
ethanolb 1-propanol'
0.9971 0.9971
-4.6022 -4.2496
bo
b, X X
b2
b3
2.9907 X lo-' 2.0798 X -4.6263 X lo-'
-6.0876 X -1.0101 X lo-' 4.0238 X lod
b4
5.9438
X loF9 1.6524 X -8.1203 X lo-*
b5
-2.0581
b6
X lo-"
7.1064 X
-2.3200 X lo-]'
'Reference 10. Maximum relative error = 0.08%, mean relative error = 0.04%. bComputedfor less than 30 mol % ethanol by using orthogonal polynomial regression on data from ref 12. Coefficients were retained until the sequential F-test was not significant at the 95% confidence level. Maximum relative error 0.04%, mean relative error 0.02%. 'Reference 11. Maximum relative error = 0.14%. mean relative error = 0.05%.
Bipolar Pulse Generator
+ HV
- HV
Control Logic
Hold +
t
Hold -
9.
I
Lsl ""
IEEE 488
t I I
Figure 1. Schematicdiagram of the apparatus used to measure transient conductivity changes: 01, 0 2 , and 0 3 are LF 156 operational amplifiers; 0 4 and 0 5 are LF 356 operational amplifiers; S/H's are Burr-Brown SHC 85 sample and hold operational amplifiers.
These electrode pairs along with a pair of variable resistors comprise a Wheatstone bridge. A laser beam passes between one electrode pair, generating excess hydronium and hydroxyl ions by the dissociative ionization of water molecules. The other electrode pair is dark and serves as a reference. The transient signal from the conductivity bridge passes through a preamplifier, low-pass filter, and final amplifier. The signal is digitized and averaged on a Tektronix 7D20 digitizer, transferred over an IEEE bus to a DEC LSI 11/2 computer, and displayed on a DEC VT240 graphics terminal. Data are stored on a floppy disk for processing at a later time. Hard copies of raw or analyzed data can be made on a Tektronix 4662 digital plotter. In order to minimize electrolysis due to the high voltage applied to the sample cell, bipolar measurements of the solution conductivity were made, with voltages applied only a small fraction of the total time of the experiment. An AM 9513 System Timing Controller (Advanced Micro Devices, Inc.) coordinates the sequence of events necessary to accomplish this. At a user specified time prior to the firing of the Quanta-Ray DCR-2 Nd:YAG laser, the timing controller triggers a bipolar pulse generator, applying a voltage of f300 V d.c. to the conductivity bridge. The high voltage alternates polarity with each laser pulse and is applied prior to the laser pulse to allow the voltage across the electrodes in the sample cell to stabilize. Shortly before the laser is to be fired, the controller can trigger the digitizer to collect a prelaser pulse base line. For digitizers with a pretrigger capability, such as the 7D20, a photodiode can also provide the trigger pulse. Alternating the polarity of the high voltage inverts the transient signal from the conductivity bridge. To compensate for this, the transient signal is alternately directed through sample/hold amplifiers (S/H) to the inverting and noninverting input of the operational amplifier preceeding the digitizer. Prior to data acquisition, both S/H's are in the sample mode, each one tracking the output voltage of the low-pass filter. Upon receipt of a pulse from the controller, one S/H changes from the sample to the hold mode, locking one input of the differential amplifier at a voltage characteristic of the static conductivity in the sample cell. The other S / H continues to track the output of the low-pass filter, so that the transient signal is automatically corrected for background conductivity. By alternating the S/H which is triggered
with each laser pulse, the signal presented to the digitizer is unipolar. After data acquisition on each laser pulse, the high voltage and S/H amplifiers are turned off simultaneously. With the laser firing at a 10-Hz repetition rate, the high voltage was typically on for 3 ms per laser pulse. The sample cell is part of a loop also containing a heat exchanger, an ion-exchange column, a liquid reservoir, and a peristaltic pump all connected by Teflon tubing. The liquid is introduced to the loop through a Pyrex reservoir and dissolved gases are removed by several cycles of evacuation followed by repressurization with argon. Impurity ions are removed by continuously circulating the liquid through the ion-exchange column containing Amberlite MB-1 resin. Flow rates of at least 2 mL SKIfor all experiments were maintained by a Cole-Parmer Masterflex pump. During initial experiments the liquid temperature was measured with an iron-constantan thermocouple, located approximately 7 cm upstream from the platinum electrodes. The liquid temperature was regulated by a Brinkman Lauda K2R-D bath to 25.0'. In the present configuration, an Omega 4200 temperature controller measures the liquid temperature with a resolution of 0.1 OC and automatically regulates the Lauda bath. Deionized water used in these experiments was first distilled in a Corning Mega Pure still and then filtered through Barnstead charcoal and ion-exchange filters. Methanol (Mallinckrodt, spectrophotometric grade), ethanol (U.S.I., absolute), and 1propanol (Mallinckrodt, analytical grade) were used as received. Absorbed CO, from the atmosphere was removed by evacuation and filtering through ion-exchange resin. Density measurements were made on samples withdrawn from the loop. For methanol and propanol mixtures, the equations of Mikhail et al.'oJ1 were used to predict density as a function of alcoholic content. Data from the literature for ethanol/water mixtures'* were fitted to a polynomial in mol %. Coefficients for the polynomial fits are listed in Table I. Measured densities were used with standard numerical techniques to calculate alcoholic content. Each conductivity-time curve was fitted to the three-parameter function y = A exp(-t/r) B
+
by a Levenburg-Marquardt nonlinear least-squares a1g0rithm.l~ T h e y denotes the experimental conductivity and t is the time. Observed relaxation times, 7, were combined into a weighted mean, using the estimated error in 7 to calculate weights. At least seven relaxation times were measured at each solvent composition. A is the transient conductivity arising from dissociative ionization. The parameter B measures the increase in conductivity due to the temperature jump caused by the laser pulses.
Results and Discussion Figure 2 shows typical curves of the transient conductivity in pure H 2 0 and propanol/water mixtures. The rapid increase in conductivity following the laser pulse results from the dissociative ionization of vibrationally excited water. The slower subsequent decay in the conductivity arises from ion recombination to restore equilibrium ionic concentrations. The curves in Figure 2 have ~
~~~
(10) Mikhail, S . Z.; Kimel, W. R. J . Chem. Eng. Data 1961, 6,.533. (11) Mikhail, S . Z.; Kimel, W. R. J . Chem. Eng. Data 1963, 8, 323. (12) "International Critical Tables"; McGraw-Hill, New York, 1982; Vol. 3, p 116. (13) Nash, J. C. J . Inst. Math. Its Appl. 1977, 9, 231.
318
Phillips and Eyring
The Journal of Physical Chemistry,Vol. 90,No.2, 1986
TABLE 11: Computed Coefficients"jbfor pK, as a Function of mol % Alcohol, x, at 25 'C 4
pK, = Cbix' i=n
alcohol methanol ethanol 1-propanol
bo
b,
14.00
1.5147 X lo-* 6.5769 X 8.6776 X
14.00
14.00
b2
-8.2120 -3.2477 -5.8929
X X low3 X lo-'
b3
b4
2.4955 X low5 1.1348 X lo4
-2.7529 X lo-' -1.5025 X lod -4.5349 x 10-6
2.7212 X lo4
Computed by using orthogonal polynomial regression. Coefficients were retained until the squential F-test was not significant at the 95% confidence level. bThe value of x ranged between 0 and 38, 30, and 24 mol % for methanol, ethanol, and I-propanol, respectively.
0.90-
PL X &'
0.00-
1
0.701
I
I
1
T i m e (microseconds)
Figure 2. Typical transient conductivity curves in (a) pure H2O and (b) 6 mol % 1-propanolin water. Both curves were measured at 25 'C by
using a 532-nm laser pulse and are the average of 250 and 350 pulses, respectively. Both curves have been normalized for laser power; in addition curve b has been magnified in the vertical direction by a factor of
1
A
2.
been normalized for laser power; thus the different amplitudes of the two curves are a reflection of the lower efficiency of dissociative ionization in propanol/water relative to pure water. In addition to the self-ionization of water, two dependent equilibria may be important in aqueous alcohols:
+ H+ & ROHz+ OH- + ROH RO- + HzO ROH
0.4
(2)
0
(3)
The equilibrium constant K2has been measured for methanol ((8 and 1-propanol (2 X ethanol ((3.6 f 0.4) X f 1) X low3),while K3 appears only to have been measured14in methanol (2.1)Aandethanol (0.75 0.15). Following the procedure of MiEiE and CerEek? Kz is considered constant over the range of alcoholic content studied. Clearly, for all three alcohols, equilibrium 2 lies far to the left and the proton is the predominant positively charged species. Equilibrium 3, on the other hand, should be considered in calculating concentrations. Using the Taft equation,I5 K3 = 0.50 is predicted for 1-propanol. For comparison, in ethanol the predicted value (0.70) agrees well with the experimental value (0.75). The reactive species in solution are thus H', OH-, and (to a much smaller extent) RO-. The dependence of the H+ and OH- concentrations on alcohol content are given by the variation in K,. Woolley et al. have developed a potentiometric method for determining the ionization constant for water in aqueous organic mixtures. We have fitted their data for methanol,I6 ethanol,]' and 1-propanol" to a poiy-
*
Fowles, P. Trans. Faraday SOC.1971, 67, 428. (15) Perrin, D. D.; Dempsey, B.; Serjent, E. P. "pKa Prediction for Organic (14)
Acids and Bases"; Chapman and Hall: London, 1981. (16) Woolley, E. M.; Tomkins, J.; Hepler, L. G. J . Solution Chem. 1972, I , 341. (17) Woolley, E. M.; Hurkot, D. G.; Hepler, L. G. J . Phys. Chem. 1970, 74, 3908.
H
5
10
15
20
25
Mole % Alcohol
Figure 4. Semilog plot of the relative recombination rate in methanol/ water ( O ) , ethanol/water (A),and 1-propanol/water (W) mixtures as a function of the mol % alcohol. The dashed line is a least-squares fit of log (k,/k,"'O) vs. x (x > 5%) constrained to pass through the point (0, 1).
nomial in mol %. See Table 11. These equations reproduce experimental data with an error never exceeding 0.07%. The relaxation time, T , is related to the recombination and dissociation rate constants by 7-l
= k,([H+] + [OL-1) + kd kd = krKq
(4) (5)
where L = H, Me, Et, or 1-Pr and Keq = Kw/[HzO]. Because of the small equilibrium constant of HzO, k,([H+] + [OL-1) >> kd, allowing the simplification k, = T - ' / { [ H ' ] + [OL-1)
(6)
Uncertainties in k, and kd are due to errors in both T and K , and are determined by a propagation of errors analysis." Control of the temperature to *O. 1 O C could lead to uncertainties in K , (1 8) Bevington, P. R. 'Data Reduction and Error Analysis for the Physical Sciences"; McGraw-Hill: New York, 1969.
Recombination Kinetics of H+ and OH- in Alcohol/Water
1
A:'
0
1
------e-; - - - - - 4 -- -- -- -- -- _ --------__ _ ----_ AAA - - - -o0- - --------.r
P
1.0
The Journal of Physical Chemistry, Vol. 90, No. 2, 1986 319
0
.A
5
0
AA
IO 15 Mole % Alcohol
20
25
Figure 5. Relative dissociation rate constants in methanol/water (e), ethanol/water (A), and 1-propanol/water (0)as a function of the mol % alcohol. The dashed line is the result of Natzle and Moore (ref 23) for H20/D,0 mixtures.
on the order of 1%. This is quite acceptable when compared to changes of 29,84, and 89% in K , between pure HzO and 25 mol % methanol, ethanol, and propanol/water mixtures, respectively. Only Figure 3 shows error bars since the points in Figures 4 and 5 are as large as the standard deviations. Using measured relaxation times and calculated concentrations, we calculated the recombination rate constant from eq 6 . For pure HzO at 25 OC, k, = 1.0 X 10" dm3 mol-' s-', slightly lower than the generally accepted value of 1.1 X 10" dm3 mol-' 8'. Part of this difference could conceivably be attributable to a systematic error in temperature measurement. However, the difference is not large, and the measurements were reproducible, with a relative deviation of 2% between replicate measurements. Recombination rates were measured in several ethanol/water mixtures containing only small quantities of alcohol. It was not practical to examine a range of mixtures containing very small (-0.2 mol %) quantities of ethanol, analogous to the work of S c h w a r ~ .As ~ seen in Figure 3, the recombination rate is constant within experimental error in mixtyres containing less than 4.5 mol % ethanol. Recombination occurs at relatively large distances by the cooperative movement of hydrogen bonds.19 The ratedetermining step is not the proton jump itself, but rather the rotation of solvent molecules into the proper orientation for hydrogen bonding. A constant value of k , suggests the solvation spheres of the hydronium and hydroxide ions (the concentration of the ethoxide ion is negligible) are the same throughout this concentration range. Support for this hypothesis comes from a gas-phase study by Stace and ShuklaZ0on the preferential solvation of the hydrogen ion in mixed clusters of C z H 5 0 Hand H20. Ion clusters of the type {(CzH,OH),-(HzO),))H+ were formed for m n < 25 in a combined molecular beam-mass spectrometer apparatus. By monitoring metastable peaks arising from the loss of either water or ethanol, one can determine which species is more strongly bound
+
(19) Crooks, J. E. In "Comprehensive Chemical Kinetics", Bamford, C. H., Tipper, C. F. H., Eds.; Elsevier: New York, 1977; Vol. 8, Chapter 3. (20) Stace, A. J.; Shukla, A. K. J . Am. Chem. SOC. 1982, 104, 5314.
to the proton. The authors concluded that the proton is more strongly bound to the ethanol molecule than to any of the water molecules in clusters which predominantly consist of water. On a purely statistical basis, solvation spheres in the solvent mixtures described in the preceding paragraph would be predominantly water molecules; thus the presence of an ethanol molecule should be reflected in the recombination rate. At ethanol concentrations greater than 4.5 mol %, the recombination rate decreases monotonically with increasing alcoholic content. Aqueous 1-propanol and methanol show an almost identical decrease in recombination rate with mol % alcohol (see Figure 4). Since experimental equivalent ionic conductivities for OH- and OL- in these aqueous alcohols are unavailable, one cannot fruitfully compare the measured rate constants with those calculated by the Debye equation for diffusion-controlled reactions.z' The only published conductively data for these aqueous alcohols is by M i W and CerEek6 who studied solutions containing >10 mol % ethanol or methanol. Even more troublesome than uncertainties introduced by correcting their estimated conductivities from 21 to 25 OC is the fact that the Walden product varies considerably over the range of alcoholic concentrations studied.zz Thus an extrapolation of the equivalent conductivities of MiEiE and CerEek becomes highly speculative. Without reliable estimates of the ionic conductivities, the estimation of ion recombination distances as a function of alcoholic content also becomes unprofitable. Plots of the dissociation rate as a function of the alcohol mol % are shown in Figure 5. Unlike the recombination rate, the dissociation rate constant decreases over the entire 0-25 mol % ethanol composition range. The dissociation rate constant also depends on the identity of the alcohol present as the cosolvent. The effect of methanol on the dissociation rate is less than that of ethanol, which is less than that of 1-propanol. Included in Figure 5 is the dissociation rate in HzO/DzO mixtures as determined by Natzle and Moore.23 The behavior of methanol/ water mixtures more closely resembles that of HzO/DzO than that of either ethanol or 1-propanol water mixtures. On the basis of the above observations one would expect the ion recombination rate constant in 1-butanol/water or higher alcohol mixtures to be very similar to those observed in methanol/water, ethanol/water, and 1-propanol/water. In l-butanol/water one would expect the dissociation rate constant to be slightly smaller than that in 1-propanol/water.
Acknowledgment. Acknowledgment is made to the National Science Foundation (Grant C H E 82-02740) for partial support of this research. The authors also acknowledge many helpful discussions with Wesley C. Natzle, C. Bradley Moore, and David M. Goodall and the use of a laser generously loaned by the San Francisco Laser Center (NSF Grant C H E 79-16250). E.M.E. carried out preliminary experiments at York University and University of California, Berkeley supported by a John Simon Guggenheim Fellowship. ' H 12408-02-5; OH-, 14280-30-9; Registry No. H20, 7732-18-5; , C2H,0H, 64-17-5; methanol, 67-56-1; 1-propanol, 71-23-8. (21) Debye, P. Trans. Electrochem. SOC.1942,82, 265. (22) Kay, R. L.; Broadwater, T. L. J . Solution Chem. 1976, 5, 57. (23) Natzle, W. C.; Moore, C. B. J . Phys. Chem. 1985, 89, 2065.
