Excess Partial Molar Absorptivity of Aqueous Solutions of KCl, KBr, CsCl and CsBr: Are There Three Universal Chromophores in the Excess Molar Absorptivity of the ν ₂ + ν ₃ Band of H₂O for Aqueous Salt Solutions?

Abstract

A new analysis methodology of the ν ₂ + ν ₃ band of H₂O developed by us earlier was applied for aqueous solutions of KCl, KBr, CsCl and CsBr. We isolate the effect of inter-molecular interactions among solute ions and solvent molecules on the near infrared spectra as the excess absorptivity, ε ^E, and then take its mole fraction derivative, $\varepsilon_{\text{S}}^{\text{E}}$ (S stands for the solute). $\varepsilon_{\text{S}}^{\text{E}}$ then signifies the effect of solute S on ε ^E, the transition moment of the ν ₂ + ν ₃ combination band due only to the intermolecular interactions. Together with the earlier similar studies on aqueous NaCl, NaBr, NaI, (CH₃)₄Cl, and (C₂H₅)₄Cl, we found that ε ^E has apparently three universal bands among all the aqueous salts studied so far; a negative band centered at 4873 cm⁻¹, a positive one at 5123 cm⁻¹, and a negative band at 5263 cm⁻¹. They were attributed to “solid-like”, “liquid-like” and “gas-like” H₂O chromophores, respectively, depending on the local and instantaneous completeness of hydrogen bonding. Our recent thermodynamic studies indicated that K⁺, Cs⁺, and Cl⁻ ions are “hydration centers” that are hydrated by a number of H₂O molecules, but the bulk H₂O away from hydration shells is left unperturbed. Br⁻ is a “hydrophile” ion that forms hydrogen bonds directly to the fleetingly and yet permanently existing hydrogen bond network of H₂O, but pins down the fluctuations inherent in pure H₂O. The distinction between Cl⁻ and Br⁻ are apparent only in the behavior of $\varepsilon_{\text{S}}^{\text{E}}$ at the 5123 cm⁻¹ “liquid-like” chromophore band. The quantitative differences in the hydration numbers among Na⁺, K⁺, and Cs⁺ are not conspicuous in either of these three chromophores. We stress, however, that at the ε ^E level there seem to be three bands at 4873, 5123, and 5263 cm⁻¹ that could be universal among aqueous solutions of electrolyte solutes.

Appendix

While the ε ^E (ave.) seems to point approximately to zero at $x_{\text{S}} = 0$ for the 4873 cm⁻¹ (Figs. 4a and 5b) and for the 5123 cm⁻¹ (Figs. 4b and 5b) bands, that for 5236 cm⁻¹, Figs. 4c and 5c, tend to extrapolate to a relatively large positive value at $x_{\text{S}} = 0$. For the NaCl, NaBr and NaI cases studied earlier [2], the ε ^E (ave.) value at 5263 cm⁻¹ showed an initial increase from ε ^E (ave.) = 0 at $x_{\text{S}} = 0$. Thus, the next derivative, $\varepsilon_{\text{S}}^{\text{E}}$, indicates a sharp bend to a lower slope region that was attributed to H₂O-separated ion pairing [16] in the region $x_{\text{S}} > 0.032$ for NaCl, $x_{\text{S}} > 0.036$ for NaBr, and $x_{\text{S}} > 0.040$ for NaI. Here for KCl, KBr, CsCl, and CsBr, however, there are little signs of initial increases from ε ^E (ave.) = 0 at $x_{S} = 0$. We thus leave this set at 5263 cm⁻¹ out of further discussion. It may be probable, however, that H₂O-mediated ion pairing may be occurring at much lower mole fractions just as the case for (CH₃)₄NCl and (C₂H₅)₄NCl [3].

At 4873 cm⁻¹, Figs. 4a and 5a, and at 5123 cm⁻¹, Fig. 4b and 5b, not all of the of ε ^E (ave.) values seem to extrapolate to zero at $x_{\text{S}} = 0$. Judging from the behavior of the equivalent ε ^E (ave.) values for NaCl, NaBr, and NaI, which smoothly extrapolate to zero at infinite dilution [2], we assume for the present study that the ones in which ε ^E (ave.) data do not extrapolate to zero at $x_{\text{S}} = 0$ are due to a constant shift of background and/or the incident beam in the original A data. In order to examine the effect of salt on ε ^E (ave.) of each chromophore, we evaluate the excess partial molar absorptivity, $\varepsilon_{\text{S}}^{\text{E}}$, by Eq. 3. With the above assumption that the baseline is shifted, i.e. the values of ε ^E (ave.) are shifted by a constant amount within a series of a salt, the resulting $\varepsilon_{\text{S}}^{\text{E}}$ would be correct. We drew a smooth curve through the data points as indicated in Figs. 4a, b and 5a,b. We read the data off the curve drawn at the interval of δ$x_{\text{S}} = 0.002$, and approximate the quotient $(\delta \varepsilon^{\text{E}} ({\text{ave.}})/\delta x_{\text{S}}$ as the partial derivative of the far right of Eq. 3 [17]. The results of $\varepsilon_{\text{S}}^{\text{E}}$ are plotted in Fig. 6 for 4873 cm⁻¹ and Fig. 7 for 5123 cm⁻¹.

Fig. 6

a The excess partial molar absorptivity of the salt, $\varepsilon_{\text{S}}^{\text{E}}$, of the 4873 cm⁻¹ band for KCl–H₂O and KBr–H₂O, b the excess partial molar absorptivity of the salt, $\varepsilon_{\text{S}}^{\text{E}}$, of the 4873 cm⁻¹ band for CsCl–H₂O and CsBr–H₂O

Fig. 7

a The excess partial molar absorptivity of the salt, $\varepsilon_{\text{S}}^{\text{E}}$, of the 5123 cm⁻¹ band for KCl–H₂O and KBr–H₂O, b the excess partial molar absorptivity of the salt, $\varepsilon_{\text{S}}^{\text{E}}$, of the 5123 cm⁻¹ band for CsCl–H₂O and CsBr–H₂O

The 4873 cm⁻¹ chromophore in the ν ₂ + ν ₃ combination band of H₂O was attributed as an “ice-like” portion of H₂O [1–3], following from the NIR spectrum of solid ice and in comparison with that of liquid H₂O [7]. According to Fig. 6a, b, the effect of addition of salt on ε ^E (ave.) is approximately constant and independent of $x_{\text{S}}$ within the mole fraction range studied. This was also the case for NaCl and NaBr [2]. Furthermore, the value of $\varepsilon_{\text{S}}^{\text{E}}$ for S = NaCl was about −500 ± 60 cm²·mol⁻¹, while −600 ± 60 cm²·mol⁻¹ for KCl (Fig. 6a) and −400 ± 60 cm²·mol⁻¹ for CsCl (Fig. 6b). From our previous 1P-probing studies, all the ions involved here, Cl⁻ [8], Na⁺ [8], K⁺ [13], and Cs⁺ [13], were found to belong to “hydration centers” that are hydrated by 2.3 ± 0.6, 5.2 (standard), 4.6 ± 0.8 and 1.1 ± 0.5 molecules of H₂O, respectively, and leave the bulk H₂O away from hydration shells unperturbed. This observation could be closely related to our findings that this 4873 cm⁻¹ chromophore comes from “ice-like” patches of bulk liquid H₂O that are left unperturbed by the presence of ions belonging to a “hydration center” [8]. The Br^– ion, on the other hand, belongs to “hydrophile” that forms hydrogen bonds directly to the fleetingly and yet permanently existing hydrogen bond network of bulk H₂O, but pins down the degree of fluctuation inherent in liquid H₂O [8]. Now, Fig. 6a, b indicate that the values of $\varepsilon_{\text{S}}^{\text{E}}$ for KBr and CsBr are constant at about −600 ± 60 cm²·mol⁻¹. The same value was also obtained for NaBr [2]. This finding seems to be consistent with our earlier finding that a hydrophilic solute has no effect on the “ice-like” chromophore [1, 3], just as was found for NaBr [2].

Figure 7 shows the $\varepsilon_{\text{S}}^{\text{E}}$ results at 5123 cm⁻¹ for S = KCl, KBr, CsCl and CsBr. This chromophore was attributed to the “liquid-like” portion of H₂O [1–3], again judging from the NIR spectra for ice and liquid H₂O [7]. We earlier observed that the values of $\varepsilon_{\text{S}}^{\text{E}}$ for NaCl stayed constant at about 1000 cm²·mol⁻¹ while those for NaBr and NaI decreased from about 3000 cm²·mol⁻¹ and 4000 cm²·mol⁻¹, respectively, as $x_{\text{S}}$ increased [2]. The same trends together with the similar values of $\varepsilon_{\text{S}}^{\text{E}}$ are shown in Figs. 7a, b. Thus, the qualitative difference in their effects of Cl⁻ versus those of Br⁻ and I⁻, i.e., “hydration center” versus “hydrophile”, manifests itself in this 5123 cm⁻¹ chromophore. Here, with the cation fixed, the difference of the effect of Cl⁻ and Br⁻ is also apparent only at this band at 5123 cm⁻¹ for the present investigation of the Br⁻ salts of K⁺ and Cs⁺. Thus, from the $x_{\text{S}}$-dependence of $\varepsilon_{\text{S}}^{\text{E}}$, we confirmed that the 5123 cm⁻¹ chromophore is the target band to elucidate the difference between the ions belonging to “hydration center” and to “hydrophile”.