J . Phys. Chem. 1990, 94, 258-262
258
Neither group has provided for the effects of electrostatic forces in reactions between ions, although Clifford et aL6 have shown that these are important. Zaider and Brenner have also used the IRT method to simulate both electron and proton They used an earlier version of the IRT method in conjunction with their own track structure calculations but made no comment on the problems presented by reactive products, ions, and partially diffusion-controlled reactions. Since they have discussed neither the techniques nor their validation, it is impossible to comment further on their results. Brenner has recently reported simulations of scavenging kinetics, using the same early version of the IRT method.23 However, the results he reports still require a rescaling of the initial G values to bring them into line with experiment. A detailed analysis of the IRT method in scavenging studies will be reported elsewhere together with a discussion of pH effects on radiolysis kinetics.38 VI. Conclusions This paper has concentrated on the application of the IRT method to the simulation of the short-time kinetics in a radiation (38) Green, N. J. B.; Pilling, M. J.; Pimblott, S. M. Manuscript in preparation.
track. The results of the simulation are not readily compared with experimental data, because of shortcomings in the radiation track itself. Once realistic methods are available to assess the excitation cross sections in liquid water and to describe the subsequent presolvation dynamics, then the techniques described here should provide a suitable vehicle for a realistic kinetic simulation. The long-term aim of this research is the provision of a simulation technique for the analysis of experimental data referring to short-time kinetics. It is unlikely that a technique could start from a track section of the type discussed above; rather it would refer to a suitably simplified initial distribution of clusters such as spurs and short tracks. The realization of the kinetics resulting from these simplified distributions must, in turn, be checked against the kinetics of realistic tracks, which will require simulations of the type reported here. Work is in progress on such a description, and we are currently examining techniques for simulating reaction from initially separated Gaussian spurs and in the dense regions found at track ends.
Acknowledgment. We thank Drs. W. G. Burns and G. V. Buxton for helpful discussions. This work was supported by the Office of Basic Energy Sciences of the U S . Department of Energy and AERE, Harwell, U.K. This is Document No. NDRL-3174 from the Notre Dame Radiation Laboratory.
Competltlve Ionic Hydration I nvolvhg Outer-Shell Solvent: Temperature Dependence J. Lee Picosecond and Quantum Radiation Laboratory, P . 0. Box 4260, Texas Tech University, Lubbock, Texas 79409 (Received: March 21, 1989; In Final Form: July 11, 1989)
Retardation of proton dissociation from the excited state of I-naphthol (p&* = 0.4) by added LiCI, MgCI2, and CaCI2 in aqueous solutions is studied as a function of salt concentrationand temperature. The observed “salt effects” cannot be satisfactorily explained by using the bulk properties of electrolyte solutions such as water activity. It is found that near room temperature the proton dissociation is strongly affected by an intermediate hydration region of an ion, which couples the “primary solvation shell” to the bulk region of the solvent. Two concepts are proposed to help classify these imperfectly defined regions: a “relative hydration energy” AE, which is based on the activation energy of kdia,and a temperature-dependent”kinetic solvation number” no, which defines the number of water molecules so strongly bound to the ion that they cannot participate in the proton dissociation process. The analysis of AE as a function of salt concentrationand of n,as a function of both salt concentration and temperature reveals the nature of the important solvation structure of an electrolyte at the molecular level. When comparisons with gas-phase results are made, both types of data indicate a gradual change of hydration energy with increasing hydration number, rather than discrete sets of solvent shell energies.
I. Introduction The Debye-Hiickel theory for electrolyte solutions was first introduced in 1923.’ Since then, chemists and biochemists, on the basis of this theory, have treated these solutions as structureless liquid entities. Averaged bulk properties, such as dielectric constant,2 water activity,’ and steady-state X-ray structure! have been used by theoreticians and experimentalists alike to characterize the solution chemistry of these systems. In spite of valuable past applications of these continuum theories, fast chemical reactions in solution and in biological systems have shown marked deviations from them in some cases.5 A molecular model of these systems seems to be demanded. The most important reason that a molecular level description of these solutions is important and necessary is that they are no longer continuous and structureless in terms of fast chemical ( 1 ) Debye, P.; Hiickel, E. Phys. 2. 1923, 24, 185.
(2) Hasted, J. B. Aqueous Dielectrics; Chapman and Hall London, 1973. (3) Robinson, R. A.; Stokes, R. H. Electrolyte Solutions, 2nd revised ed.; Butterworths: London, 1965. (4) Lawrence, R. M.; Kruh, R. F. J . Chem. Phys. 1967, 47, 4758. (5) Simon, J . D. Acc. Chem. Res. 1988, 21, 128.
0022-3654/90/2094-0258$02.50/0
reactions. Experiments carried out on a short time scale, such as NMR,6 picosecond or femtosecond laser spectros~opies,~ etc., become effective tools for revealing the dynamical and structural differences between various electrolyte solutions at the molecular level. Meanwhile, developing a new version of solution theory demands a revolutionary new approach if the modern ultrafast techniques are to gain their maximum utility in the promotion of our understanding of the chemical reactions of ions in solution. Using molecular probes to study fast chemical reactions in solution, such as cis-trans isomerization,8 solvent ~rientation,~ proton dissociation,I0 and electron ejection,” has revealed a great (6) Struis, R. P. W. J.; de Bleijser, J.; Leyte, J. C. J. Phys. Chem. 1987, 91, 6309. (7) Fleming, G. R. Chemical Applications of Ultrafast Spectroscopy; Oxford University Press: New York, 1986. (8) Shank, C . V.; Ippen, E. P.; Teschke, 0.;Eisenthal, K. B. J. Chem. Phys. 1977, 69, 5547. (9) Ben-Amotz, D.; Scott, T. W. J. Chem. Phys. 1987, 87, 3739. (IO) Harris, C. M.; Selinger, B. K. J . Phys. Chem. 1980, 84, 891. Laws, W. R.; Brand, L. J. Phys. Chem. 1979, 83, 795. ( 1 1 ) Robinson, G. W.; Robbins, R. J.; Fleming, G. R.; Morris, J. M.; Knight, A. E. W.; Morris, R. J. S. J. Am. Chem. SOC.1978, 100, 7145.
0 1990 American Chemical Societv
Ionic Hydration Involving Outer-Shell Solvent deal of information about the dynamical solvent structure a t a molecular level. In these experiments, structural information about the solvent is recorded in the kinetic history of the molecular probe. Since the dynamics of the molecular probe occurs in a very short time span, during this time the system only senses the local structure. By monitoring the kinetics of the molecular probe in different solvent environments, one can then probe the microscopic solvent structure. In a previous study, we used a “photon initiated acid”, 2naphthol (2-ROH), to study salt effects on weak acid dissociation.12 We found that proton dissociation from 2-ROH* can be enhanced, retarded, quenched, or inert in the presence of the added salt. Furthermore, the salts LiCI, NaCIO,, NaCl, KCl, MgCI2, and CaCI2, which retard the proton dissociation from 2-ROH*, show a different degree of retardation as a function of the charge and the polarity of the cations. On the other hand, anions do not seem effective in retarding the proton dissociation. Neither do well-known water “structure breakers” such as urea. Such differences cannot be satisfactorily explained by using a continuum concept such as water “activity”. However, they seem to be adequately explained by a “kinetic solvation number” no, which describes the number of water molecules needed for solvation of a cation in the presence of 2-ROH*. 1-ROH, which has a molecular structure and ground-state pK, (=9.8) similar to that of 2-ROH, has a smaller excited-state pK,* (0.4 vs 2.7).13 This difference is partly caused by the fact that, compared with 2-ROH*, there is no activation barrier for the proton dissociation process. In this paper, we will examine proton dissociation from l-ROH* affected by the added salts LiCI, MgCI2, and CaCI,. We will then attempt to correlate the proton dissociation rate kdis with bulk solvent properties such as water activity aw and then demonstrate the superiority of a molecular structural explanation using the proposed “relative hydration energy” and “kinetic solvation number”. Finally, we will compare differences between the ionic hydration picture obtained from the 1-ROH* and 2-ROH* probe studies and ionic hydration in the gas phase studied by Kebarle’s group.I4 11. Experimental Section 1 - and 2-naphthol of 99% purity were purchased from Kodak. LiCl and MgCI2-6H20were obtained from Sigma, and CaCI,. 2 H 2 0 was obtained from Aldrich. All chemicals were used without further purification. Water was distilled, deionized, and passed through a NANOpure three-cartridge system. The measured resistivity of the filtered water is greater than 15 MQ/cm. Salt solutions were prepared in concentrations from 0 to 10 M and were spectroscopically checked between 260 and 600 nm. No impurity was detectabele in either fluorescence or absorption. The concentration of 1- and 2-ROH was around 5 X M. Temperatures between 0 and 60 OC were controlled by a Borg-Warner LHP-150 heat pump and TC-108 controller. For temperatures much higher than 60 OC, 1-ROH was found to decompose too rapidly for convenient measurement. The time-correlated single-photon counting apparatus used for the lifetime measurements has been discussed in detail in earlier work.IS The current system employs an ITT microchannel plate photomultiplier (MCP-PMT, F4129f‘) and a Tennelec constant fraction discriminator (CFD, TC454), which was factory configured to match the rise time of the tube. The MCP-PMT was cooled 40 deg below the ambient temperature with a Products for Research housing (TE271RF). The time resolution of this detection system is nominally about 150 ps. x2 for system lifetimes > 150 ps is typically better than 2, while x 2 for system lifetimes C 150 ps is poor, and the fitted lifetimes involve a lot of uncertainties. For example, the decay lifetime of 1 -ROH in pure water was determined to be 32 ps by using a ( I 2) Lee, J . J . Am. Chem. SOC.1989, 1 I I , 427. (13) Webb, S. P. Picosecond Studies of Excited State Proton Transfer Reaction. Ph.D. Thesis, University of California, Berkeley, CA, 1985. (14) Dzidic, 1.; Kebarle, P. J . Phys. Chem. 1970, 74, 1466. (15) Lee, J.; Griffin, R. D.; Robinson, G. W. J . Chem. Phys. 1985, 82, 4920.
The Journal of Physical Chemistry, Vol. 94, No. I, 1990 259
Wave 1 ength (nm)
Figure 1. Emission spectra of I-naphthol excited at 305 nm in pure water (a), 4 m LiCl (b), and MgCI, (c) solutions at 20 OC.
.i a
m
tL
I
370
I
I
4.10
I
IIXI
510
580
Wavelength (nm)
Figure 2. Emission spectra of I-naphthol excited at 305 nm in 7 M LiCl solution at 0 (a) and 60 OC (b).
streak camera with time resolution of 1 ps,I3 while in our present setup, the measured apparent lifetime varies between 10 and 100 ps. The limitations set by the time resolution of the current system and the salt solubility disallow us to perform accurate and meaningful measurements on 1-ROH in NaCl or KCI solutions in the most interesting concentration regimes, or in LiCl solutions at concentrations lower than 2 M or in MgC12or CaCl, solutions lower than 1 M. 111. Results The emission spectra of 1-ROH in pure water and in 4 M LiCl and MgC12 solutions at 20 OC are shown in Figure 1. For easy comparison, the spectra are normalized to a constant area. Because of the strong acidity of l-ROH* in water, the dominant emission band at 475 nm originates from RO-*. Adding salt causes the deprotonation process to be retarded. As a result, the 475-nm RO-* band decreases, while the 380-nm ROH* band increases. The emission spectra at 0 and 60 OC are shown in Figure 2 for a 7 M LiCl solution. Increasing the temperature is seen to cause the proton dissociation rate to increase. Total decay rates plotted as a function of LiC1, MgCI2, and CaCI2 molality and temperature are shown in Figure 3A-C. Despite the uncertainty at the low-concentration point caused by the limitation of our instrumental time resolution, the following trends in terms of salt concentration and environmental temperature are observed. In all three systems, the concentration effect is very nonlinear, with the decay rate of 1-ROH* converging at high salt concentration to its normal decay ratel6 of 0.1 25 ns-’ in the absence of kdis. The degree of termination of the proton dissociation process varies with salt type as MgCI, = CaC12 > LiCI. Such a dependence on cation charge and polarity is in agreement with expectations gained from studies on the 2-ROH system. However, in contrast to the 2-ROH system, where the (16) Harris, C. M.; Selinger, B. K. J . Phys. Chem. 1980, 84, 1366.
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L
L
C
Figure 3. Total decay rates as a function of (A) [LiCI], (B) [MgCIJ, and (C) [CaCI,] molality concentrations a t 0 (0). 20 (X), 40 (A), and 60 'C (+). The solid lines are fitted curves.
addition of salt slightly modifies the temperature dependence, the decay rate of 1 -ROH*, which is temperature independent in pure water, becomes temperature dependent upon addition of salt. The barrier in 2-ROH* in pure water is caused mainly by an activation enthalpy associated with the energetics of the proton dissociation and h y d r a t i ~ n , ' ~while , ' ~ the barrier associated with water molecules in the present system is caused solely by an activation energy associated with the solvation shell of the ion. We will discuss this result more fully in a later section. IV. Water Activity Retardation of the 1-ROH* deprotonation process by added NaCl was first reported by Selinger et a1.I6 and was attributed to "disruption of water structure" by the added salt. It was later suggested that kdisfor a series of molecular probes in an electrolyte solution can be simply related to the water activity aw by the following equationl'Js
L A
I Q+
Q
Q p
"IE I
I
J.
+
+ x
+
s
-1040
-780
-520
Log(aw) (X 1000)
-260
L B where k:i8 is the proton dissociation rate in the absence of salt and 9 is a fitting parameter that is equal to the number of water molecules associated with the dissociated proton H+(H20)q. The value of q was found to vary between 6 and 10 for different proton donors, and this number was assumed to remain invariant in different electrolyte solutions. Although the equation was successfully applied to several experimental sy~tems,''-~~ it is hard to understand why q should change for different proton donors but remain constant for different electrolyte solutions. Using a variety of salts, we have shown that eq 1 in fact failed to explain the 2-naphthol data.', Hence, it is of interest to examine the I-naphthol system within the context of eq 1. In Figure 4A we plot log kdisvs log aw for the LiCI, MgCI2, and CaCI, electrolytes at 25 "C. In Figure 4B the same data are plotted for CaCI, at 0, 25, and 40 OC. Instead of a linear relation predicted by eq I , the log kdisvs log aw curves are seen to bend significantly. The effective value of 9 decreases from 4.9 to 1.3 as the water activity decreases or as the salt concentration increases. Furthermore, a large temperature deviation is evident in Figure 4B at low water activity. Consequently, q, as defined in eq 1, is a complicated parameter dependent not only on the molecular probe but also on the water activity, the electrolyte, and the temperature. V. Microscopic Description of Ion Hydration
Since the water activity parameter is not capable of revealing an appropriate kinetic picture of the proton dissociation probe or the solvation of the electrolyte, an alternative approach was sought. In an electrolyte solution, it is generally accepted that the solvation environment of an ion can be divided into three regions: (1) the primary solvation shell, where the solvent molecules are tightly bound to the ion; (2) the bulk region, where the bulk properties of the solvent are preserved; and (3) an intermediate (17) Gutman, M.; Huppert, D.; Nachliel, E. Eur. J . Biochem. 1982, 121, 637. (18) Huppert, D.; Kolodney, E.; Gutman,M.; Nachliel, E. J . Am. Chem. Soc. 1982, 104. 6949. (19) Politi, M. J.; Chaimovich, H. J . Phys. Chem. 1986, 90, 282.
t 8
9
581 m
I1
1
1
-1040
1
1
-780
Log(a,)
1
1
-520
1
(X 1000)
1
-260
1
1
Figure 4. log kdisis plotted as a function of log aw for (A) 1-naphthol in LiCl (0),MgCI, (+), and CaCI2 (X) at 25 "C; (B) 1-naphthol in CaCI, at 0 (0),25 (X), and 40 O C ( 0 ) . The water activity data were obtained from ref 3.
region, which bridges the other two regions.20 In contrast to its simple conceptual definition, the intermediate region is not well defined. None of the experimental techniques ordinarily used to study solvation structure has thus far been able to provide an accurate structural picture of this highly dynamic regime. The difficulties are in fact a result of the complicated dynamic character of this region.,' The experimental technique discussed here is capable of probing the intermediate region,I* and it should therefore provide some important physical insights into the character of this region. VI. Relative Hydration Energy Figure SA-C plots In kdis as a function of 1 / T at various concentrations of LiCI, MgCI,, and CaCI2. The dependence is (20) (a) Harned, H. S.; Owen, B. B. The Physical Chemistry of Electrolytic Solutions, 3rd ed.; Reinhold: New York, 1958. (b) Bockris, J. O'M.; Reddy, A. K. N. Modern Electrochemistry; Plenum: New York, 1970. (21) Anderson, H. C. Modern Aspects of Electrochemistry; Conway, B. E., Bockris, M. O'M.,Eds.; Plenum: New York, 1975; 11, pp 1-31.
The Journal of Physical Chemistry, Vol. 94, No. I , 1990 261
Ionic Hydration Involving Outer-Shell Solvent
Figure 5. In kdir is plotted as a function of I/T(K-'). The solid lines are fitted result. (A) LiCl of 3.19 (A),4.35 (X), 5.56 (O), 6.83 (+), 8.17 (O), (*I, and 12.63 (a) m. (B) MgC& of 2.1 (*), 3.24 (A), 3.84 (0),4.46 (X), 5 . 1 1 (+),and 5.78 (0) m. (C) CaCI, of 2.11 (*), 3.28 (A),4.55 (X), 5.95 (0), and 7.49 (+) m.
9.58
I
1
X X
TABLE I: Critical Molalities for 1-Naphthol in LLCI, MgCI,, and CaCI, Solutions at 0, 20, 40, and 60 "C LiCl MgC12 CaCI,
t
f
X
Q
I
I
6
I
I
12
I
I
18
I
I
24
I
n
Figure 6. Activation energy of kdisis plotted as a function of an averaged hydration number n for various salts: LiCl (O),MgCI2 (+), and CaCIz (X).
seen to be linear. The slope of this straight line provides an activation energy AE, which increases as the salt concentration increases in a very nonlinear manner. Because of the zero activation energy for kdisof 1-ROH* dissolved in pure water, this induced activation energy from added salts must be caused by the hydration energies of the solvated ions. It is therefore natural to relate the induced A E to the hydration energy of water molecules bound to the ion. For each salt concentration m, we define an average number of water molecules n = 55.56/m in the neighborhood of an ion. In a dilute solution, n is large. In this concentration regime, most of the water molecules probed by I-ROH* are very far from any ion and thus maintain bulk water properties: The AE for kdis is close to zero as in pure bulk water. As m increases, n decreases, and the water molecules probed by I-ROH* become closer to an ion and are less free. Thus AE increases with increasing salt concentration as observed. The hydration energies of different water molecules can be correlated with A E by varying the salt concentration. Figure 6 plots AE(n) for LiCI, MgCIz, and CaC12 systems. Three conclusions can be drawn. (1) The MgCI, curve 1s very nearly coincident with the CaCI, curve. Within current experimental error, no distinct differences between these two salts are observable. (2) The AE value for n < 18 is larger for MgCI, and CaCI, than it is for the LiCl system. This result is consistent with the fact that Mgz+ and Ca2+carry twice the charge of Li+. (3) All curves bend upward for small n and merge together at large n. Such a nonlinearity is expected for a system with Coulomb force interactions. The smaller the n, the shorter the distance of the charge-dipole interaction between the ion and water and the stronger the Coulomb force. The general trend in Figure 6 is in agreement kith the hydration enthalpies of alkali-metal ions in the gas phase.I4 In contrast to steady-state ion hydration, in both gas and solution phases the hydration enthalpy continuously decreases from the inner shell toward the outer shell, showing no discrete drop at the "shell boundary". However, a direct correlation between gas and solution
0
20
40
60
16.55 8.85 8.83
17.54 10.21 9.94
18.74 11.19 11.25
19.40 12.13 12.66
phases requires a certain caution. First of all, the enthalpies for clustering in the gas phase are not a correct representation of the hydration enthalpies in the liquid phase. Many-body interactions in the liquid phase tend to lower the ionic hydration energy and more effectively screen the Coulomb force field in comparison with the gas-phase result. Second, since the ionic hydration energy of Figure 6 is probed by a molecular probe, the thermodynamic properties of this probe make an important contribution to the hydration energy determination. For example, the 2-naphthol probe gives a AE associated with its proton dissociation process in bulk water. It does not provide useful information about the hydration energy of the added ions.lZ Hence Figure 6 reflects a relative ionic hydration energy, rather than one in absolute terms.
VII. Kinetic Solvation Number The proton acceptor for 1- and 2-naphthol has been identified ~ ~ walk ~ ~(transfer ~ ~ ~ ~ ~ ~ to be a water ~ 1 ~ ~ t Byeuser of .a random matrix) method, a rate scheme involving water cluster configurations has been formulated, and a cluster containing at least four water molecules has been shown to be the effective proton ac~ e p t o r . ' ~ In ~ ~this * - scheme, ~~ the final state of the hydrated proton is (H904+),,.2z The requirement of such a water cluster for weak acid dissociation causes kdis to be nonlinearly dependent on the water concentration in water/alcohol mixed solvent systems. The same kind of rate scheme can be applied to the current system. A total decay rate k = ko kdk = 31.25 ns-I was used for the pure water config~ration.'~In the case where the four-water cluster cannot be formed, kdisis absent and k = ko = 0.125 ns-'.I6 A "kinetic solvation number" no proposed by Taube and coworkersz4can be formulated for the current model. The parameter n, in our system is related to a "critical" molality mo of the salt: n, = 55.56/mo, at which concentration all the solvent molecules are tied up with the ions and the proton dissociation process is completely stopped; i.e. kdis= 0 when m 2 mo. For electrolyte concentrations m < mo, there is a fraction of "free" water [H2OIf (=1 - m/mo) that can participate in the proton dissociation of the molecular probe. With these assumptions, a distribution of pure water configurations and the other mixture configurations can be set up for the transfer matrix. The quantity mo, and thus no, as one expects, is a function of the ionic charge, polarity, and the temperature; moreover, it is dependent on the reaction system. A detailed description of this kinetic model has been discussed
+
(22) Robinson, G. W.; Thistlethwaite, P. J.; Lee, J. J . Phys. Chem. 1986,
90. - , 4224 .-- ..
~
(23) Lee, J.; Robinson, G. W.; Webb, S. P.; Philips, L. A.; Clark, J. H. J . Am. Chem. SOC.1986, 108, 6538. (24) Swinehart, J. H.; Rodgers, T. E.; Taube, H. J . Chem. Phys. 1963,38, 398.
262
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The Journal of Physical Chemistry, Vol. 94, No. I , 1990
I
*
In-
to
an anion already have the proper orientation and can therefore accept the H+ probably as well as bulk water. Second, the diffusion or the exchange time scale of water molecules around an anion is comparable to or shorter than the proton dissociation time scale of 1- and 2-ROH.6 Finally, in the 2-ROH experiments, NaCl and NaC103 showed no apparent difference.',
-
+X
9-
-
0 0
m-
Q
Q
I
I
I
I
I
I
I
I
I
Figure 7. Kinetic solvation number n,as a function of 1/T (K-') for LiCl ( O ) , MgCI, (+), and CaCI2 (X).
in the previous 2-naphthol work.', Using the proposed matrix scheme, one can calculate the proton dissociation rate of I-ROH and thus determine the critical molality mo for each electrolyte at each temperature. The solid lines in Figure 3A-C give the calculated total decay rates k of I-ROH*, and Table I summarizes the critical concentrations mo for LiCI, MgCI2, and CaCI, a t 0, 20, 40, and 60 OC. It is worthwhile to point out that the only unknown quantity in calculating k in the matrix scheme is mo. This quantity is determined from the data fitting. Note particularly from Table I that, as the temperature is raised, there is a continual increase in the number of water molecules around the ions that can participate in the hydration competition with the proton, even including what would normally be thought of as inner-shell waters of hydration. This latter effect is exactly what would be expected from the continuous change of hydration energies discussed earlier.
VIII. Salt Effects It has been seen that there is no marked difference between the effects of using MgCl, and CaCl,, while LiCl exhibits a reduced degree of retardation of the proton dissociation. The singly charged ion Li+ ties up fewer solvent molecules than the doubly charged ions Mg2+ and Ca2+. Thus, mo is larger for the LiCl system than for MgCl, or CaCl,. This observation is also in agreement with the previous 2-ROH result.I2 However, mo for I-ROH is consistently greater than it is for 2-ROH in the corresponding electrolyte. This is caused by the stronger acid character of I-ROH*, which allows its more highly energetic dissociated proton to be better capable of competing with the ion for water molecules. In other words, the overall free energy change guides the dynamics. On the other hand, the existence of the large activation barrier for proton dissociation from 2-ROH* causes its dissociation proton to be less energetic and thus more restricted in its ability to become hydrated. As a result, 1-ROH* is more capable of probing solvation structures closer to the ion than is 2-ROH*, giving rise to the larger mo. In the current analysis, no is assumed to be independent of the electrolyte concentration. It is treated as a primary solvation number. In spite of the oversimplified assumptions, the calculated data agree reasonably well with the experimental data throughout the concentration range studied, from 2 to 12 m. In other words, the solvation structure adjacent to the ion is not affected to first order by the ionic strength. Concentrated or dilute electrolyte solutions can be treated equivalently. The participation of anions in the 1- and 2-ROH deprotonation processes has been neglected for the following three reasons. First, solvation of H+ requires the oxygen atom of a water molecule to be directed toward the H+. Water molecules hydrated around
IX. Temperature Effect It is a well-known fact that the hydration number of an electrolyte decreases as the temperature increases.20 The thermal energy is capable of weakening the binding of solvent molecules around the ion. Temperature-dependent mo (or 4)was noticeable but was not so obvious in the 2-ROH system,I2 because the large internal activation barrier (2.6 kcal/mol) overwhelms the temperature dependence of mo. In the case of 1-ROH, where there is no inherent activation barrier, the temperature dependence of mo is quite obvious (Figures 3A-C and 5A-C, Table I). Shown in Figure 7 is no as a function of 1/T for the L E I , MgCI,, and CaC1, systems. The dependence is near linear within the temperature range studied, and the slopes for MgClz and CaCI2 are about 3.5 times steeper than that for LiCI. Although a larger number of water molecules are bonded to Mg2+ and Ca2+ than to Li+, the binding energy for these outer-shell waters is weaker for the large doubly ionized cations than for Li+. As a result, no is more sensitive to temperature variations for Mg2+ (or Ca2+) than for Li+ in the corresponding shell studied. It is worthwhile to point out that such a linear relation between no and 1 / T is accidental and will undoubtedly break down if a wider temperature range were experimentally feasible. In other words, if we expand the range of no for MgC1, to that for LiCI, we would expect a shallower slope and a smaller temperature dependence for MgC1, than for LiCI.
X. Conclusions Combining picosecond laser spectroscopy, a fast molecular probe technique, and a matrix-formulated generalized rate scheme, we have been able to study weak acid (1- and 2-ROH*) dissociation influenced by an added salt. These studies reveal the interesting microscopic structure and dynamics of an electrolyte solution. The proton acceptor for these two weak acids in LiCl, MgCI,, and CaCI2 electrolyte solutions is found to be a cluster composed of a minimum of four water members. Correlation between the proton dissociation rate and the water activity of the electrolyte solution is poor and incapable of explaining the observed results. On the other hand, a molecular level description of an electrolyte solution using a "relative hydration energy" and a "kinetic solvation number" provides a more realistic picture, revealing important information about the solvation of ions. Perhaps the most important conclusion in this regard is that, at least for ultrafast hydration/dehydration kinetics, the concept of solvent shells breaks down. As the temperature is raised, ion dehydration becomes continuously easier, with water molecules ordinarily thought to belong to the "inner shell" participating in the hydration competition with the proton. The concept of a solvation shell thus seems to be more of a structural than an energetic parameter. Acknowledgment. The author is grateful for Dr. G. Wilse Robinson's valuable discussions and comments. Without his constant encouragement and support, none of this work would have been possible. Financial support at the PQRL has been shared by the Robert A. Welch Foundation (DOOOS, 54%, and D-1094, 7%), the National Science Foundation (CHE8611381, 25%), and the State of Texas Advanced Research Program ( 1 306, 14%). Registry No. LiCI, 7447-41 -8; MgCI2,7786-30-3; CaCI2, 10043-52-4; 1 -naphthol, 90- 15-3.
