Ion Association and Hydration in Aqueous Solutions of LiCl and

9010

J. Phys. Chem. B 2007, 111, 9010-9017

Ion Association and Hydration in Aqueous Solutions of LiCl and Li2SO4 by Dielectric Spectroscopy Wolfgang Wachter, Sˇ arka Fernandez, and Richard Buchner* Institut fu¨r Physikalische und Theoretische Chemie, UniVersita¨t Regensburg, D-93040 Regensburg, Germany

Glenn Hefter* Chemistry-DSE, Murdoch UniVersity, Murdoch, W.A. 6150, Australia ReceiVed: March 28, 2007; In Final Form: May 16, 2007

A systematic study of the dielectric relaxation spectra of aqueous solutions of LiCl and Li2SO4 has been made at solute concentrations of 0.05 e c/M e 1.0 and 2.0, respectively, and over a wide range of frequencies (0.2 e ν/GHz e 89) at 25 °C. The spectra were best described by a superposition of four Debye processes, consisting of the two well-known water relaxations at ca. 8 and 0.5 ps and two ion-pair contributions at ca. 200 and 20 ps, corresponding to the presence of double-solvent-separated (2SIP) and solvent-shared (SIP) ion pairs, respectively. Consistent with spectroscopic studies, no contact ion pairs were detected over the studied concentration range. The overall ion association constants K°A obtained were in good agreement with literature data for both salts. Detailed analysis of the solvent relaxations indicated that Li+ has a significant second solvation sheath although there were differences between the effective hydration numbers obtained from LiCl and Li2SO4, which might arise from competition for the solvent from the anions.

1. Introduction The industrial importance of lithium has undergone a dramatic increase over the last three decades, and it is currently produced on a multi-kiloton scale.1 Lithium compounds are found in numerous industrial applications: for example, lithium stearate is used as a thickener and gelling agent in lubricating greases, lithium hydride (LiH) serves to generate hydrogen for military and meteorological applications, and lithium carbonate is used in the production of special toughened glasses.1 However, perhaps the most intriguing application of lithium salts is their use for the treatment of manic-depressive psychoses; the first such drug to be recognized in 1949 by the Australian psychiatrist John Cade.2 Despite their clinical efficacy, the mechanism of action of lithium salts on the human brain is not well understood but has been postulated to be related to the influence of Li+(aq) on the Na+/K+ and/or Mg2+/Ca2+ balances. The behavior of the lithium ion in aqueous solutions is strongly influenced by its very large energy of solvation (∆hydG° (Li+) ) -481 kJ mol-1), which is more than 100 kJ mol-1 more negative than those of the other alkali metal ions (e.g., ∆hydG° (K+) ) -304 kJ mol-1).3 Given the strong affinity of Li+ for water molecules,4,5 it is not surprising that many simple lithium salts crystallize as hydrates and that the anhydrous salts are often very hygroscopic. Similarly, LiCl and LiBr brines are widely used in dehumidifying and air-conditioning units, due to their outstanding affinity for water. However, in marked contrast to the other alkali metal ions, especially Na+ and K+, solutions of Li+ salts have received limited attention. This is surprising given the physiological activity of Li+(aq).6 As Birch points out in his recent review,2 the physicochemical properties * To whom correspondence should [email protected] murdoch.edu.au (G.H.).

be addressed. E-mail: (R.B.) and g.hefter@

determining the action of lithium on the human organism are almost certainly less complex than those of organic drugs. Thus, understanding the physicochemical properties of Li+(aq) may be of particular value in the understanding of fundamental processes in drug-receptor interactions. Dielectric relaxation spectroscopy (DRS), which measures the response of a sample to an applied electromagnetic field,7 is a powerful technique for the study of ion-ion and ionsolvent interactions. Complex permittivity spectra ˆ (ν) ) ′(ν) - i′′(ν) obtained as a function of the field frequency, ν, provide unique insights into the nature and dynamics of electrolyte solutions.8-10 Accordingly, this work presents a dielectric relaxation study of aqueous solutions of LiCl and Li2SO4. These salts were chosen as typical representatives of 1:1 and 1:2 lithium electrolytes with potentially very different behavior in aqueous solution. A number of previous DRS studies of LiCl(aq) have appeared, but the measurements were made only on rather concentrated solutions and over a limited range of frequencies. Thus, David and Henry11 determined permittivities at just one frequency (5 GHz) over the approximate concentration range 0.2 e c/M e 9. Ermakov et al.12 studied solutions in a similar concentration range (0.2 e c/M e 5) at four frequencies over the range 3.7 e ν/GHz e 7.5. Barthel et al.13 investigated 10 solutions in the range 0.5 e c/M e 13.0 at 3 frequencies (8.3, 10, and 12 GHz). In a more recent study, Wei and Sridhar14 used a much wider frequency range (0.05 e ν/GHz e 20) in the range 0.55 e c/M e 13.38 but at an unspecified temperature. More importantly, the numerical data of Wei and Sridhar are not accessible and the Cole-Cole fitting model used by them exhibits marked and systematic deviations from their data even at low concentrations. Apart from the mundane observation of a shift of the water relaxation process to higher frequencies with increasing solute

10.1021/jp072425e CCC: $37.00 © 2007 American Chemical Society Published on Web 06/30/2007

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Figure 2. Dielectric loss spectrum of 0.8 M Li2SO4(aq) at 25 °C. Experimental data (symbols) are described by a superposition of four Debye processes (4D model, eq 2, solid line).

Figure 1. Dielectric permittivity (a) and loss (b) spectra for LiCl(aq) at 25 °C and concentrations c/M ) 0.05, 0.09, 0.10, 0.15, 0.22, 0.30, 0.40, 0.49, 0.67, 0.79, and 0.99 (top to bottom).

concentration, few insights into the nature of LiCl(aq) can be gained from these pioneering studies.11-14 The only previous DRS study of Li2SO4(aq), to the best of our knowledge, was by Lileev et al.15 These authors investigated seven solutions at 0.2 e m/(mol/kg) e 3 at five frequencies in the range 7 e ν/GHz e 25. However, no relaxation process other than that due to bulk water was detected. Clearly, a thorough reinvestigation of the DR spectra of the solutions of these two electrolytes using modern equipment and covering a wide range of frequencies and concentrations is desirable. 2. Experimental Section Solutions were prepared gravimetrically without buoyancy corrections. However, for data-processing purposes, all concentrations are expressed in moles of solute per liter of solution (M). The densities required for the interconversion were obtained from the ELDAR database.16 Both salts were commercial analytical reagents: LiCl (BDH Chemicals, England, 99%) and Li2SO4 (Sigma-Aldrich, USA, 99%), which were used without further purification. These salts were dried under vacuum (∼1 mbar) for at least 48 h at 180 °C (LiCl) and 150 °C (Li2SO4), respectively, using P2O5 (Sicapent, Merck) as a desiccant. Dielectric spectra were recorded at νmin e ν/GHz e 20 at Murdoch using a Hewlett-Packard model 85070M dielectric probe system based on an HP 8720D vector network analyzer (VNA), as described previously.17 The temperature was controlled by a Hetofrig (Denmark) circulator-thermostat to (0.02 °C, with a NIST-traceable accuracy of (0.05 °C. The value of the minimum frequency of investigation, νmin, was determined by the conductivity contribution to the loss spectrum. As such, it varied with concentration and the salt but was typically in the range 0.2-0.4 GHz. All VNA spectra were recorded using at least two independent calibrations, with air, water, and mercury as the references. Higher frequency data for selected LiCl(aq) solutions were recorded at Regensburg using four interferometers: X-band (8.5 e ν/GHz e 12), Ku-

band (13 e ν/GHz e 17.5), A-band (27 e ν/GHz e 39), and E-band (60 e ν/GHz e 89). The operation of these instruments is described in detail elsewhere.9,18 Temperature control and accuracy were similar to those at Murdoch. The ˆ (ν) data for LiCl(aq) from the X- and Ku-band instruments were found to be in very good agreement with the overlapping VNA spectra. Hence for Li2SO4(aq), only A- and E-band data were recorded for all solutions. Typical spectra and the corresponding fits (see below) are shown in Figures 1 and 2; all fitting parameters are given in Table 1. 3. Data Analysis For an electrolyte solution of conductivity κ, DRS determines the relative dielectric permittivity, ′(ν), and the total loss, η′′(ν), which is related to the dielectric loss ′′(ν)

η′′(ν) ) ′′(ν) + κ/(2πν0)

(1)

where 0 is the permittivity of free space. Each VNA spectrum at each concentration was analyzed separately to determine ′′(ν) and the slightly calibration-dependent effective conductivity κ. The resulting κ values are generally 1-2% smaller than conventional (low frequency) conductivity data16 with slightly larger deviations at high electrolyte concentrations. Provided the κ values so obtained were sufficiently reproducible ((2 % for at least two measurements), the averaged VNA spectra were combined with the relevant interferometer data. As can be seen from Figures 1 and 2, there was in general a seamless fit between the low- and high-frequency data although, as is usually observed for electrolyte solutions, the noise increased with increasing solute concentration (conductivity).17,19 The fitting of dielectric relaxation spectra requires care, especially in the presence of weakly formed ion pairs. Our general approach to this problem has been outlined in detail in our previous papers,20,21 and thus, only a brief description of the procedures is given here. The combined ˆ (ν) data were analyzed by simultaneously fitting the in-phase (′(ν), see, for example, Figure 1a) and out-of-phase (′′(ν), Figure 1b) components to various relaxation models consisting of n distinguishable relaxation processes. Although many other plausible models were investigated, it was found that the DRS data for those of the present solutions that were investigated over our full frequency range (0.2-89 GHz) were best described

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TABLE 1: Concentration, c, Conductivity, K,16 Dielectric Permittivities, E, E2, E3, E4, and E∞, Relaxation Times, τ1, τ2, τ3, and τ4, and Reduced Error Function, χr2, for Aqueous Solutions of LiCl and Li2SO4 at 25 °Ca c

κ

0

0

0.0498 0.0879 0.0995 0.149 0.217 0.298 0.396 0.487 0.669 0.786 0.985

0.515 0.871 0.977 1.42 1.99 2.65 3.41 4.09 5.36 6.13 7.36



τ1

2

τ2

χr2

3

τ3

4

τ4

∞

78.32

8.32

5.87

0.264

3.48

77.54 76.79 76.66 76.14 74.36 71.18 68.81 68.37 64.05 60.48 58.03

8.52 8.41 8.44 8.37 8.33 7.97 7.83 7.95 7.75 7.37 7.32

6.83 6.04 6.59 6.17 6.02 5.42 5.30 5.55 6.30 5.45 5.58

0.5F

4.35

0.5F

4.61

0.5F 0.5F

3.78 2.88

0.5F

4.81

0.01 0.09 0.01 0.01 0.01 0.02 0.02 0.07 0.04 0.03 0.10

76.01 74.19 67.34 63.51 57.37 49.59 37.75

8.35 8.40 7.94 7.98 7.93 7.71 7.36

6.05 6.72 5.64 6.34 6.97 7.17 7.66

0.32 0.5F 0.5F 0.5F 0.5F 0.5F 0.5F

3.4F 1.60 5.83 4.84 3.42 4.42 3.93

0.07 0.07 0.07 0.09 0.10 0.13 0.06

LiCl(aq) 77.86 77.30 77.26 76.64 75.61 74.91 73.25 72.00 69.86 68.10

327 220 252 206 156 238 158 140 240 276

75.81 74.60 73.79 72.55 71.22 69.16 67.90 65.59

17.5F 17.5F 17.5F 17.5F 17.5F 17.5F 17.5F 17.5F Li2SO4(aq)

0.0747 0.149 0.298 0.494 0.785 1.17 1.90

1.12 1.95 3.26 4.71 6.22 7.49 8.39

78.95 78.26 76.52 73.87 69.86 65.34 57.96

222 163 140 130 125 130 142

74.24 71.70 69.15 65.80 61.30 53.43

45.2 23.7 28.8 30.0 27.4 26.0

a The data for pure water was taken from ref 24. Parameter values followed by “F” were fixed during the fitting procedure. Units: c in M, κ in Ω-1 m-1, τ1, τ3, τ3, and τ4 in 10-12 s.

overall by a superposition of four Debye processes (the 4D model):

ˆ (ν) ) ∞ +

 - 2 2 - 3 3 - 4 + + + 1 + i2πντ1 1 + i2πντ2 1 + i2πντ3  4 - ∞ (2) 1 + i2πντ4

In eq 2, ∞ is the infinite-frequency permittivity and τj is the relaxation time for the jth dispersion step (j ) 1 ... 4). In principle, ∞ reflects only contributions from intramolecular polarizability that could be obtained from dielectric measurements in the terahertz region.22 Since this is outside our frequency range, ∞ was treated as an additional fitting parameter in the analysis of ˆ (ν). Note that Sj ) j - j+1 is the amplitude (relaxation strength) of the jth dispersion step and  ) ∞ + ΣSj is the static (zero-frequency) permittivity of the solution. For those LiCl(aq) spectra where no interferometer data were recorded (Table 1), a 3D model without the fast mode (S4,τ4) was used to describe the data since process 4 makes no measurable contribution to the spectra at ν e 20 GHz. Even with state-of-the-art apparatus, such as that employed here, amplitudes of j2 are difficult to detect for processes that are close to the dominant water relaxation. For this reason it is important not to over-interpret the present data, particularly for LiCl, where the amplitudes of the solute-related processes 1 and 2 are very small and process 2 is very close to the water relaxation process 3. However, an unconstrained 4D fit for LiCl yielded physically reasonable amplitudes for process 2 at most concentrations. As the values of τ2 obtained from these fits showed some scatter, but no significant dependence on concentration, τ2 was fixed at the average value of 17.5 ps and all LiCl(aq) spectra were refitted with that constraint for consistency. As would be expected, this procedure resulted in slightly increased values of the reduced error function, χr2,20 but, more importantly, a smoother variation of the parameters 2 and 3 with concentration. The analysis of the Li2SO4(aq) data are much less affected by the proximity of the dominant water relaxation because the

amplitudes of processes 1 and 2 are higher. Only at very low electrolyte concentrations (c e 0.1 M), where ion pair concentrations are also low, was S2 too small to be detected, i.e., eq 2 was reduced to a 3D model. The parameters produced from the 4D (or, where appropriate, 3D) model are given in Table 1. As well as providing a set of self-consistent permittivities and relaxation times for each dispersion step, the fitting model used gave smaller values of χr2 than any of the other models tried. Process Assignment. For the purpose of assigning the four observed processes, it is convenient to consider the data for the solutions of both salts together. As the higher-frequency relaxation processes 3 and 4 are very similar to those observed for pure water,22-24 they can be attributed with confidence to the solvent. Process 3 (τ3 ≈ 8 ps), which is the major feature of all the spectra recorded in this work, reflects the cooperative relaxation of the hydrogen-bond network of bulk water.20,23 Process 4, which is barely detectable in the present spectra at ν e 89 GHz, is a small-amplitude very fast relaxation centered at ∼600 GHz. This process is thought to be related to the reinsertion of a “free” water molecule into the H-bond-network and to memory effects associated with dielectric friction.22 Even though this process makes only a small contribution to the DR spectra at ν e 89 GHz, its neglect led to significantly larger values of χr2. Accordingly, its relaxation time τ4 was fixed at 0.5 ps.25 The magnitude of the relaxation time of process 1 (τ1 ≈ 200 ps) and the dependence of its amplitude S1 on concentration indicate that it is solute-related and arises from the tumbling motion of an ion pair (IP). The decrease in S1 and the simultaneous increase of the amplitude of process 2, S2, with increasing electrolyte concentration c strongly suggest that process 2 arises from the presence of a second type of ion pair, as has been observed for Na2SO4(aq).19 In contrast, if process 2 was not due to IPs, this would imply, in contradiction to Le Chaˆtelier’s principle, that the overall IP concentration decreased with increasing c. These findings are in marked contrast to the earlier, far more restricted, DR data for these two systems. This is mostly a reflection of the technological difficulties (largely

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J. Phys. Chem. B, Vol. 111, No. 30, 2007 9013

overcome with modern instrumentation) faced by previous workers rather than any criticism of their pioneering efforts. Further support for this assignment of process 2 comes from its relaxation times (τ2 ∼ 18 ps for LiCl(aq) and τ2 ∼ 30 ps for Li2SO4(aq)), which are similar to those obtained for the second IP process of Na2SO4(aq). It is possible that process 2 might arise from the presence of “slow” water,20,26 which has a similar relaxation time. However, slow water has to date only been observed in solutions containing large hydrophobic ions,20,26 which are very different from the ions present in LiCl(aq) and Li2SO4(aq). 4. Results and Discussion 4.1. Solute Relaxation and Ion Pairing. Before discussing the solute-related processes of LiCl(aq) and Li2SO4(aq) in detail, it is useful to briefly summarize current views on ion pairing in solution.27 For strongly hydrated ions (such as Li+ and SO42-), Eigen and Tamm28 proposed a three-step association mechanism by which free hydrated ions Xx+(aq) and Yy-(aq) initially associate to form double-solvent-separated ion pairs (2SIPs) with their hydration sheaths essentially remaining intact. According to Eigen and Tamm, the intervening water molecules are then subsequently lost to form, sequentially, solvent-shared ion pairs (SIPs) and contact ion pairs (CIPs). This mechanism is summarized in equilibrium scheme 3: yx+ yXx+ aq + Yaq h [X ‚OH2‚OH2‚Y ]aq h free ions 2SIP [Xx+‚OH2‚Yy-]aq h [Xx+‚Yy-]aq (3) SIP CIP

with the stepwise association constants

K12 )

c2SIP cSIP cCIP ; K23 ) ; K34 ) c+cc2SIP cSIP

(4)

The existence of this mechanism has been demonstrated for many systems by ultrasonic29 and dielectric relaxation19,21,30,31 measurements and (in part) by Raman spectroscopy.32 The thermodynamically determinable equilibrium in such a system is y(x-y)+ Xx+ aq + Yaq h XYaq

(5)

where the species on the right-hand side of eq 5 represents all ion pairs of 1:1 stoichiometry regardless of their degree of hydration.32 The overall association (ion pairing) constant corresponding to eq 5 is

KA )

cIP c+c-

(6)

where cIP ) c2SIP + cSIP + cCIP is the total ion-pair concentration. It is readily shown that

KA ) K12 + K12K23 + K12K23K34

(7)

Note, however, that not all of the three association steps proposed by Eigen and Tamm have to be present (or, more precisely, detectable) in every system. In aqueous solution, the strong hydration of Li+ 4,5 implies that contact ion pairs will only appearsif at allsat very high electrolyte concentrations. As already noted in section 3, the magnitudes and the relaxation times of process 1 for LiCl(aq) and Li2SO4(aq) are

typical of solute relaxations related to the presence of ion pairs.10 Furthermore, the decrease of S1 and increase of S2 with increasing electrolyte concentration strongly suggest that process 2 is due to the presence of a second IP species. The question then is: which types of IPs are present? Possible combinations are 2SIP/SIP, SIP/CIP, or, less plausibly, 2SIP/CIP. The magnitude of τ1 (Table 1), the variation of S1 with the salt concentration, and the strong solvation of the ions are all consistent with process 1 being due to the presence of 2SIPs. Additionally, the relaxation times of τ2 ≈ 30 ps for Li2SO4(aq) and τ2 ) 17.5 ps for LiCl(aq) are similar to that assigned to SIPs in Na2SO4(aq).19 Further support for these assignments comes from a comparison of the observed relaxation times (Table 1) with estimates of the rotational correlation time, τ′, of model ion pairs at c f 0. These can be obtained with the modified Stokes-DebyeEinstein equation33

τ′ )

3Vf⊥Cη kBT

(8)

where V is the ion-pair volume, η is the solution viscosity, and f⊥ is a shape factor that can be calculated from the ion-pair dimensions. C is a parameter describing the effective friction acting on the rotating dipole. Its theoretical limits are C ) 1 for stick and C ) 1 - f⊥-2/3 for slip boundary conditions.33 Neglecting hydration effects, the value of V can be approximated as a prolate ellipsoid of semiprincipal axes a ) r+ + r- + 2nrs and b ) c ) r-, where r+ and r- are the radii of the cation and the anion, respectively, and rs is the radius of a water molecule (all radii were taken from the work of Marcus34); n is the number of water molecules separating the ions (CIP n ) 0, SIP n ) 1, 2SIP n ) 2). For rotation on a molecular scale, hydrodynamic boundary conditions are likely to be closer to slip than to stick.33 For both Li2SO4(aq) and LiCl(aq), the τ′slip values obtained for 2SIPs and SIPs (Table 2) are broadly similar to the experimental relaxation times τ2 (Table 1). The differences between the observed and calculated values are similar to those obtained for Na2SO4(aq)19 and arise from the approximate nature of eq 8, especially concerning the estimation of V, f⊥, and C,33 and from the experimental uncertainties. All of these arguments, along with the results obtained with eq 10 (see below), suggest that the presence of 2SIPs and SIPs is the most likely explanation of processes 1 and 2. Ion-pair concentrations ci can be obtained from the amplitudes S1 and S2 of the relaxation processes 1 and 2 using the generalized Cavell equation35

3( + (1 - )Ai) kBT0 (1 - Rifi)2 Si ci )  NA µ2

(9)

i

where Ri ) R+ + R- + nRs is the polarizability, fi is a reaction field factor, and Ai is a shape factor of the ion pair i. The last two of these quantities can be calculated from the radii of the ions and of water as described previously,19 while the polarizabilities of the ions, R+ and R-, and of the solvent, Rs, were taken from literature sources.34,36 Calculation of the dipole moment, µi, for the various ion-pair types from the ionic and water radii is straightforward for LiCl(aq). However, for the charged ion pairs formed in Li2SO4(aq), an assumption must be made about the pivot of ion-pair rotation. Limiting cases for the pivot are the center of mass (CM) and the center of hydrodynamic stress (CHS).35 As it is not obvious which of

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TABLE 2: Molecular Volume, V, Shape Factor, f⊥, Rotational Correlation Times, τ′slip and τ′stick, Polarizability, r, and Dipole Moments, µ, for the Model Ion Pairs CIP, SIP, and 2SIP for Aqueous Solutions of LiCl and Li2SO4 at 25 °Ca electrolyte ion pair LiCl(aq) LiCl(aq) LiCl(aq) Li2SO4(aq) Li2SO4(aq) Li2SO4(aq)

CIP SIP 2SIP CIP SIP 2SIP

V

f⊥

34.3 53.8 73.4 93.6 133 173

0.0912 0.452 0.979 0.0667 0.285 0.595

τ′slip

τ′stick

2.28 28.4 17.7 63.9 52.4 123 4.55 75.0 27.7 137 75.1 229

R

µ

3.788 5.228 6.668 6.328 7.768 9.208

9.07 23.23 35.45 11.84b 11.96c 30.99b 33.40c 48.04b 51.86c

a Units: V in 10-30 m3, τ′slip and τ′stick in 10-12 s, R in 10-30 × 4π0 m3, µ in D (1 D ) 3.336 × 10-30 C m). b For CM as the pivot. c For CHS as the pivot.

these two assumptions is more realistic, both values for µIP were used for further processing. Using eq 6, the overall association constants KA can be calculated for all possible IP combinations: 2SIP/SIP, 2SIP/ CIP, and SIP/CIP. For convenience, these constants are fitted to a Guggenheim-type equation37,38

log KA ) log K°A -

2ADH|z+z-|xI 1 + AKxI

+ BKI + CKI3/2

(10)

to obtain the standard (infinite dilution) overall association constant, K°A (Figure 3). In eq 10, ADH is the Debye-Hu¨ckel constant (0.5115 L1/2 mol-1/2 for water at 25 °C), XK (X ) A, B, C) are adjustable parameters (AK was fixed at 1.00 M-1/2 throughout), and z is the charge number of an ion.38 The ionic strength, I, is expressed as I ) c - ∑ci for 1:1 electrolytes like LiCl and as I ) 3c - 2∑ci for 1:2 electrolytes like Li2SO4. Due to the small amplitudes of the solute-related relaxation processes, the extrapolation of eq 10 to I ) 0 is not very accurate and the obtained K°A have a large uncertainty. Nevertheless, a clear assignment of the low-frequency modes to specific ionpair species is possible from the data. For both LiCl(aq) and Li2SO4(aq), only the 2SIP/SIP combination yields physically reasonable values for K°A. For the other combinations, SIP/CIP and 2SIP/CIP, the association constants obtained from eq 10 using the present DRS results are unrealistically large (SIP/ CIP yields smaller, but still unrealistic, values with K°A(LiCl) ) 35 ( 28 and K°A(Li2SO4, CHS) ) 46 ( 3) and are at variance with the results reported using other methods. For the 2SIP/SIP combination, the K°A values are listed, together with BK and CK, in Table 3. Within experimental accuracy there is agreement between K°A values obtained using either the CM or the CHS as the rotational pivot for LiSO4-(aq). Although both Li2SO4(aq) and LiCl(aq) are nominally strong electrolytes, some level of ion pairing has long been suggested for them. Consistent with the present data and the strong hydration of Li+,4,5 the formation of CIPs is regarded as unlikely, at least up to moderate concentrations at ambient temperatures,39 although it may be noted that one Raman study40 detected CIPs in very concentrated LiCl(aq). For LiCl(aq), values of the association constant K°A reported from conductivity measurements are 0.8141 and 2.75,42 while a molecular dynamics simulation yielded a result of 2.45,39 all of which agree within the error limits with the present value of 1.5 ( 1.3. Other computational studies have yielded widely divergent results, with Harsa´nyi and Pusztai43 suggesting no IPs even at very high concentrations using a reverse Monte Carlo analysis while Degre`ve and Mazze´44 claimed from their molecular dynamics simulation of 1.0 M LiCl(aq) that 77.3% of

the anions and 66.7% of the cations form “clusters”. Such diversity of conclusions probably says more about the built-in assumptions of such models rather than the real nature of LiCl(aq). Similarly, the claimed absence of ion pairing in LiCl(aq),45 based on its colligative properties, is unconvincing because, for weakly associating electrolytes such as LiCl(aq), the results obtained are highly dependent on the theoretical model adopted, none of which is strictly applicable at the concentrations to get measurable effects.27 For Li2SO4(aq), the values of K°A ) 5 obtained from osmotic coefficients46 and 5.9 ( 0.7, calculated47 using the dissociation constant of KSO4- are in good agreement with the present values of 6.4 ( 1.4 (assuming µIP (CM)) and 7.6 ( 1.2 (assuming µIP (CHS)). The value 10.4 ( 0.6,48 obtained from conductivity measurements, is slightly higher but it is wellknown that the interpretation of conductivity data for nonsymmetrical electrolytes, especially if they are weakly associated, is strongly dependent on the conductivity and activity coefficient equations adopted.8 The lower value for KA of LiSO4(aq) obtained using Raman spectroscopy49 cannot be compared with the present results or those obtained by classical methods. This is because Raman measurements do not in general detect 2SIPs and/or SIPs and so do not produce thermodynamically meaningful association constants for systems containing such species.32,50 Note that, in contrast to the common spectroscopic techniques, the sensitivity of DRS to ion-pair species increases with increasing dipole moment, i.e., from CIP to SIP to 2SIP.10 Interestingly, the present values of K°A(LiSO4-) are essentially the same as those reported for NaSO4- from potentiometric measurements (6.82 ( 0.08)51 and DRS (6.7 ( 0.3)19 where the latter study also suggested a 2SIP/SIP equilibrium. Simple charge considerations would predict K°A(LiSO4-) > K°A(NaSO4-) as has been found for the association constants of Li+ and Na+ with many other anions.52 The fact that this does not hold for sulfate “complexes” is probably a reflection of the strong hydration of the ion pairs attenuating the charge effect. Although the K°A values for LiSO4-(aq) and especially for LiCl0(aq) are small, Figure 4 shows that the relative ion-pair concentrations ci/c are nevertheless considerable. For both systems, 2SIPs are the dominant associated species only at low salt concentrations (c j 0.2 M). At higher solute concentrations, c2SIP either approaches zero (LiCl) or decreases strongly (Li2SO4), while the relative concentrations of SIPs rise to about 15 % (LiCl) or 10 % (Li2SO4). How far the decrease of cSIP/c at high c (Figure 4) reflects so-called “redissociation”21 due to increasing charge crowding or hints at the presence of (undetected) CIPs or larger aggregates cannot be decided from the present data. It is also not clear whether the direct anion-cation contacts detected at very high concentrations of LiCl(aq) by Raman spectroscopy40 and scattering experiments53 would contribute to the DR spectrum of such solutions. To show up in DRS, the rotational correlation time, τ′, of a dipolar species has to be of similar order of magnitude to the ion-pair lifetime. Because the expected τ′ for CIPs is rather small (Table 2), such a process might well be hidden under the much larger water relaxation. Even so, a shoulder or similar distortion of the dominant water band would be expected. No such feature is observed at high concentrations in the published spectra of Wei and Sridhar14 nor those of the other more limited studies.11-13 Thus, it appears that, at concentrations sufficiently high to force direct cation-anion contact, the dielectric behavior of LiCl(aq) may be more like that of a molten salt than of a typical electrolyte solution.53,54 The decrease of cSIP/c is then mostly just a reflection of the

Aqueous Solutions of LiCl and Li2SO4

J. Phys. Chem. B, Vol. 111, No. 30, 2007 9015

Figure 3. Overall ion association constant, KA, as a function of the ionic strength, I, of (a) LiCl(aq) (9) and (b) Li2SO4(aq) (9 CHS model, b CM model) at 25 °C. Lines were calculated with eq 10.

TABLE 3: Standard Association Constants, K°A, and Empirical Parameters BK and CK from Eq 10, Assuming AK ) 1.00a electrolyteb

K°A

BK

CK

LiCl Li2SO4 (CM) Li2SO4 (CHS)

1.5 ( 1.2 6.4 ( 1.4 7.6 ( 1.2

- 3.0 ( 1.2 - 0.30 ( 0.19 - 0.47 ( 0.09

3.3 ( 1.4 0.059 ( 0.076 0.11 ( 0.03

a Units: K°A and BK in M-1, CK in M-3/2. b CM: centre of mass, CHS: centre of hydrodynamic stress as the pivot (see text).

deficiency of water and competing Coulombic interactions between proximate ions. 4.2. Solvent Relaxation. Process 3 which, as noted above, is the dominant relaxation in all the present dielectric spectra (Figure 2), is due to the cooperative relaxation of bulk-water molecules. This process, centered on 18 GHz in pure H2O, plays a major role in all aqueous electrolyte solutions.10 Process 4, which makes a minor contribution to the present spectra, is thought to reflect the reorientation of “free” water molecules into new H-bond configurations, as well as small memory effects associated with dielectric friction.22 As this process is centered on ∼600 GHz, it is difficult to resolve in, and has little effect upon, the present spectra (Figure 2). Accordingly, its relaxation time was fixed at τ4 ) 0.5 ps throughout.25 As both processes 3 and 4 arise from the H-bonded water network, it appears reasonable to use a combined bulk-water amplitude Sb ) S3 + S4 ) 3 - ∞ for further processing.30 For ∞, the value of pure water obtained from THz data, ∞(H2O) ) 3.48,22,24 was used throughout. This is justified because the estimated variation of ∞ with c, obtained from the polarizabilities of the ions and water, should be