Differential Approach Applied to Spectroscopic Studies on Aqueous Solutions

Eq. (X-1)

CHAPTER X

Differential Approach Applied to Spectroscopic Studies on Aqueous Solutions [X-1] SPECTROSCOPIC VERSUS THERMODYNAMIC STUDIES: INTRODUCTION It has been generally accepted that spectroscopic studies are superior to thermodynamic studies in gaining information about structure or molecular arrangement in aqueous solutions. As we have been demonstrating throughout this book, by obtaining model-free higher-order derivative quantities of Gibbs energy of the system we begin to gain a deeper insight into the molecular level scenario of mixing, mixing scheme, to the same level as, if not deeper than what modern nonlinear spectroscopic studies have provided. From thermodynamic point of view, spectroscopic studies target the nature dictated by the Gibbs energy, G, of the system. G is written down as, G ¼ Gideal + GE ,

(X-1)

where Gideal ¼ NRT fxS ln ðxS Þ + xW ln ðxW Þg is from the mixing entropy in a binary mixture consisting of nS mole of S and nW mole of W, with N ¼ nS + nW and xS ¼ nS =N , etc. GE is the excess Gibbs energy due to nonideality (i.e., reality) arising from intermolecular interactions in the mixture. The important and fundamental question regarding Eq. (X-1) is whether the two terms on the right are actually operating or are written down just for convenience. Recently by Raman hydration shell vibrational spectroscopy and polarization-resolved femtosecond infrared experiment, Ben-Amotz et al. concluded that at least at dilute regions of aqueous mono-ols the issue of hydrophobic hydration is in fact teetering on the edge of random mixing (Ben-Amotz, 2015; Rankin et al., 2015). Fig. X-1 shows the three terms, E Gm, Gideal m , and Gm, in Eq. (X-1) at room temperature against the mole fraction, xTBA for aqueous tert-butanol (TBA). As is evident in the figure, while GEm is positive in the entire mole fraction range, the net Gm becomes negative due to dominance of Gideal m . The findings by Ben-Amotz et al. mentioned Solution Thermodynamics and its Application to Aqueous Solutions http://dx.doi.org/10.1016/B978-0-444-63629-4.00010-9

© 2017 Elsevier B.V. All rights reserved.

353

Fig. X-1

354

2 E Gm

E , G ideal, G (kJ mol−1) Gm m m

ideal Gm

Gm

1

0

−1

−2 0.0

0.2

0.4

0.6

0.8

1.0

xTBA Fig. X-1 Molar Gibbs energies for tert-butanol (TBA)-H2O at 25°C. Gm ¼ GEm + Gideal m . Each term was calculated using the data from (Koga et al., 1990a). (Reproduced from Koga Y. J Mol Liq 2016;219:1006. Copyright (2016), Elsevier).

above then assure that the two terms on the right of Eq. (X-1) are actually operating. What we are interested is to learn the detailed nature of the intermolecular interactions. For that, it is crucial to isolate GEm from Gm. However, at the level of GEm its variation against an independent variable is subtle and not very conspicuous to us, human beings, due to the entropy-enthalpy compensation prevalent in aqueous solutions (Lumry and Rajender, 1970; Lumry, 2003; Starikov and Norden, 2007; Freed, 2011; Starikov, 2013; Mills and Plotkin, 2015; Pan et al., 2015). Thus, we measure or obtain the model-free second, third, and sometimes fourth derivative quantities of G with respect to a combination of independent variables (p, T, ni), and from their variations we have tried to learn the nature of aqueous solutions. We gained much deeper insights than before, as we saw so far in this book. Then, can we not apply the same concept into spectroscopic studies? We introduce below the excess molar absorptivity and its composition derivative, the excess partial molar absorptivity of solute. From their

Eq. (X-2) to (X-4)

355

variations against independent variables, we attempt at learning more about aqueous solutions.

[X-2] EXCESS MOLAR ABSORPTIVITY, εE, AND EXCESS PARTIAL MOLAR ABSORPTIVITY OF SOLUTE S, εES , IN AQUEOUS SOLUTIONS Consider a binary mixture consisting of nS mole of S and nW mole of W in volume V through which a beam of light with wavenumber, ν, is passing with the resulting absorbance, A. Instead of the classical Beer-Lambert law, we write down the concentration dependence of A as, following the solution thermodynamic tradition (see Eq. (II-63), for example) (Koga et al., 2009, 2013; Sebe et al., 2012, 2015; Li et al., 2008), A=l ¼ εðN =V Þ ¼ ε0S ðnS =V Þ + ε0W ðnW =V Þ + εE ðN =V Þ,

(X-2)

where l is the path length, ε0S and ε0W are the molar absorptivity of pure S and W. With the molar volume Vm ¼ V/N, Eq. (X-2) is rewritten as, ðA=l ÞVm ¼ ε ¼ ε0S xS + ε0W xW + εE :

(X-3)

ε is the excess molar absorptivity of the system due to nonideality arising from complex interactions among solute and solvent molecules. As such, we accept nonlinear dependences of nS and nW in εE. This is where we divert from the treatment by Beer-Lambert law. The conventional approach in spectrum analysis is to regard the total molar absorptivity as a linear sum of those of putative species that obey the Beer-lambert law. Namely, E

ðA=l ÞVm ¼ ε ¼ Σxi ε0i ,

(X-4)

instead of Eq. (X-3). xi and ε0i are the mole fraction and the molar absorptivity of the putative ith species. In this treatment, i stands for such putative species of S(H2O)m type (Chapados and Max, 2001; Max et al., 2002), or the putative H2O molecules distinguishable by the number of hydrogen bonds to the adjacent H2O molecules (Fornes and Cahussidon, 1978; Saitow et al., 2004). This approach assumes that as a result of intermolecular interactions such species exist and as such they act as an ideal mixture. In our approach based on Eq. (X-3), on the other hand, there are no a priori assumptions, and the effect of intermolecular interactions is lumped together into εE which is accessible experimentally.

356

Fig. X-2(A) to X-2(B)

In order to investigate its concentration dependence, we define and evaluate the excess partial molar absorptivity of solute S, εES , as (Koga et al., 2009, 2013; Sebe et al., 2012, 2015; Ikehata, 2010a,b),

εES  N @εE =@nS ¼ ð1  xS Þ @εE =@xS : (X-5) εES thus defined signifies the effect of solute S on the nonideality of the mixture in terms of the excess molar absorptivity, εE, or the transition moment of the vibrational excitation due only to nonideality of the mixture at each wavenumber. Eq. (X-5) follows from the definition of the partial molar quantity of an intensive mother function (Koga, 2012a, 2015a), since εE defined by Eq. (X-3) is an intensive quantity.

[X-3] SPECTRA OF EXCESS MOLAR ABSORPTIVITY, εE, AND EXCESS PARTIAL MOLAR ABSORPTIVITY OF SOLUTE, εES , FOR AQUEOUS SOLUTIONS OF ACETONITRILE (AN) AND ACETONE (AC) Using a home-assembled NIR spectrophotometer (Saitow et al., 2004), we determined NIR spectra of the combination band (ν2 + ν3) of H2O (Koga et al., 2009) for aqueous solutions of acetonitrile (AN) and acetone (AC). The resulting absorbance spectra are shown in Fig. X-2A–C. Following Eq. (X-3), we evaluate εE by using the Vm data for AN-H2O (Handa and Benson, 1981) and for AC-H2O (Boje and Hvidt, 1971). The results are plotted in Fig. X-3A–C. For both aqueous solutions of different nonelectrolyte solutes, there are two bands: a negative band at 5020 cm1 and a positive one at 5230 cm1 in spectra of εE. On addition of AN or AC, the excess (nonideal) part of the ν2 + ν3 NIR band of H2O, or the εE spectra, decreases at 5020 cm1, while that at 5320 cm1 increases. It is the transition moment at each excitation energies that changes due only to intermolecular interactions. Since the NIR spectra for ice peaks at about 5000 cm1 and that for liquid at about 5200 cm1 (Fornes and Cahussidon, 1978; CzarnikMatusewicz and Pilorz, 2006), we assign the negative chromophores at 5020 cm1 in εE spectra to be ice-like and the positive one at 5230 cm1 to be liquid-like. This assignment is in line with the mixture model of liquid water (Roentgen, 1892) followed recently by many (Bassay et al., 1987; Vedamuthu et al., 1994, 1995). See Section [IV-3] for detail. To proceed further in our analysis, we evaluate the values of εE of two chromophores. For this, we take the average value in the slit of 20 cm1 instead of a common practice of integrating deconvoluted bands. We prefer the present

Eq. (X-5)

357

6 xAN

A/l (mm−1)

4

0.0999 0.2001 0.3001 0.3801 0.4998 0.7001 0.7996 0.9002 0.9702 1

2

0

4600

4800

(A)

5000

5200

5400

5200

5400

n (cm−1) 7

6

A/l (mm−1)

5

4

xAN 0 0.008173 0.01011 0.01996 0.03980 0.06978 0.09988 0.2001

3

2

1

0 4600

(B)

4800

5000 n (cm−1)

Fig. X-2 (A) Absorbance divided by the path length, A/l, for acetonitrile (AN)-H2O at room temperature. (B) Absorbance divided by path length, A/l, for aqueous acetonitrile (AN)-H2O for a low mole fraction region of AN, xAN, at room temperature. (Continued)

Fig. X-2(C) to X-3(B)

358

6

xAC 5

0.05000 0.1100 0.2000 0.3800

4

0.5500 0.6900 0.8800

A/l (mm−1)

0.9500 3

0.9790 0.9960 1

2

1

0

−1 4600

(C)

4800

5000

n

5200

5400

(cm−1)

Fig. X-2, cont’d (C) Absorbance divided by the path length, A/l, for acetone (AC)-H2O at room temperature. (Reproduced with permission from Koga Y, Sebe F, Minami T, Otake K, Saitow K-I, Nishikaw K. J Phys Chem B 2009;113:11928. Copyright (2009), American Chemical Society).

procedure, since the εE spectra that we obtained are the results of subtracting two similar values by Eq. (X-3) ending up with an order of magnitude smaller values. Hence, the relative uncertainties in εE is sizable, particularly so toward skirt regions of a band. Furthermore, there is no a priori knowledge about the band shape for each chromophore. The peak regions in εE, on the other hand, suffer less from such short comings. The resulting average values

359

40 Acetonitrile

xAN

e E (mm−1 cm3 mol−1)

30

20

10

0.09988 0.2001 0.3001 0.3801 0.4998 0.7001 0.7996 0.9002 0.9702

0

−10

−20 4600

(A)

4800

5000 5200 n (cm−1)

5400

5000 5200 X axis

5400

12 10

e E (mm−1 cm3 mol−1)

8 6 4 2

Acetonitrile

xAN 0.008173 0.01011 0.01996 0.03980 0.06978 0.09988

0 −2 −4 −6 4600

(B)

4800

Fig. X-3 (A) Excess molar absorptivity, εE, for acetonitrile (AN)-H2O at room temperature. (B) Excess molar absorptivity, εE, for acetonitrile (AN)-H2O in a low mole fraction range at room temperature. (Continued)

Fig. X-3(C) to X-4

360

50

xAC

40

0.05000 0.1100 0.2000

Acetone

0.3800 0.5500

e E (mm−1 cm3 mol−1)

30

0.6900 0.8800 0.9500 0.9790

20

0.9960

10

0

−10 4800

(C)

5000

5200

n

5400

(cm−1)

Fig. X-3, cont’d (C) Excess molar absorptivity, εE, for acetone (AC)-H2O at room temperature. (Reproduced with permission from Koga Y, Sebe F, Minami T, Otake K, Saitow K-I, Nishikaw K. J Phys Chem B 2009;113:11928. Copyright (2009), American Chemical Society).

of εE thus evaluated are plotted against the mole fraction of solute in Figs. X-4 and X-5. For both solutes, AN and AC, the values of εE at xAN and xAC ¼ 0 and 1 are properly zero within the estimated error bars, since Eq. (X-3) is based on the symmetric reference states. We then draw smooth curves through all the data points in Figs. X-4 and X-5 and read the values of εE off the smooth curves at the mole fraction interval of 0.02 for dilute range and 0.04 otherwise. We calculate εES (S ¼ AN or AC) by Eq. (X-5). The results are shown in Fig. X-6A for AN-H2O and in Fig. X-6B for AC-H2O.

361

40 Acetonitrile

e E (mm−1 cm2 mol−1)

30 5230 ± 15 cm−1

20

10

0 5020 ± 20 cm−1 −10

−20 0.0

0.2

0.4

0.6

0.8

1.0

xAN

(A) 20 Acetonitrile

e E (mm−1 cm3 mol−1)

15

10 5230 ± 15 cm−1 5

0 −5 −10 0.00

5020 ± 20 cm−1

0.05

0.10

0.15

0.20

xAN (B) Fig. X-4 (A) The average value of excess molar absorptivity, εE, of the negative 5020 cm1 band and the positive 5230 cm1 band for acetonitrile (AN)-H2O at room temperature. (B) The average value of excess molar absorptivity, εE, of the negative 5020 cm1 band and the positive 5230 cm1 band in a small mole fraction region for acetonitrile (AN)-H2O at room temperature. (Reproduced with permission from Koga Y, Sebe F, Minami T, Otake K, Saitow K-I, Nishikaw K. J Phys Chem B 2009;113:11928. Copyright (2009), American Chemical Society).

Fig. X-5 to X-6

362

60 Acetone 5230 ± 15 cm−1

e E (mm−1 cm3 mol−1)

40

20

5020 ± 20 cm−1

0

−20 0.0

0.2

0.4

0.6

0.8

1.0

xAC

(A) 30 Acetone

e E (mm−1 cm3 mol−1)

20

5230 ± 15 cm−1

10

0 5020 ± 15 cm−1 −10 0.00

(B)

0.05

0.10

0.15

0.20

0.25

xAC

Fig. X-5 (A) The average value of excess molar absorptivity, εE, of the negative 5020 cm1 band and the positive 5230 cm1 band for acetone (AC)-H2O at room temperature. (B) The average value of excess molar absorptivity, εE, of the negative 5020 cm1 band and the positive 5230 cm1 band in a small mole fraction region for acetone (AC)-H2O at room temperature. (Reproduced with permission from Koga Y, Sebe F, Minami T, Otake K, Saitow K-I, Nishikaw K. J Phys Chem B 2009;113:11928. Copyright (2009), American Chemical Society).

363

150

X

Y

Acetonitrile Error

eE (mm−1 cm3 mol−1) AN

100

5230 cm−1 5020 cm−1

50

0

−50

II

III

−100 0.0

0.2

0.4

0.6

0.8

1.0

xAN

(A) 300

Acetone

eE (mm−1 cm3 mol−1) AC

250 5230 cm−1

200

5020 cm−1

X 150

Y

100

III

II I

50 0 −50 0.0

(B)

0.2

0.4

0.6

0.8

1.0

xAC

Fig. X-6 (A) Excess partial molar absorptivity of acetonitrile (AN), εES (S ¼ AN), in AN-H2O at 5020 cm1 and 5230 cm1. I, II, III, X, and Y are the mixing schemes and the boundary region X and Y between Mixing Schemes I and II, as discussed in Chapter VI. (B) Excess partial molar absorptivity of acetone (AC), εES (S ¼ AC), in AC-H2O at 5020 cm1 and 5230 cm1. I, II, III, X, and Y in the figure are the mixing schemes and the boundary region X and Y between Mixing Schemes I and II, as discussed in Chapter VI. (Reproduced with permission from Koga Y, Sebe F, Minami T, Otake K, Saitow K-I, Nishikaw K. J Phys Chem B 2009;113:11928. Copyright (2009), American Chemical Society).

364

Fig. X-7(A) to X-7(B)

As we discussed in Chapter VI, acetonitrile (AN) has its hallmark as a hydrophobe and acetone (AC) that as a hydrophile, at least in the mole fracE tion dependence pattern of the enthalpic solute-solute interactions, HSS , although AC is an amphiphile by the 1-propanol probing methodology discussed in Chapter VII. In Fig. X-6, the loci of point X and Y, the start and the end of the boundary region from Mixing Scheme I to II, and also the regions in which Mixing Scheme II and III are operative are shown (see Table VI-2 (p. 207)). Thus, Fig. X-6A indicates that it is at the 5020 cm1 solid-like chromophore that shows a sharp increase in εEAN below point X, while Fig. X-6B shows a sharp decrease in εEAC at the 5230 cm1, liquid-like chromophore below point X. Namely, for further elucidation toward more detailed nature of a hydrophobic acetonitrile (AN) by NIR spectroscopy, the 5020 cm1 solid-like chromophore within its Mixing Scheme I region should be targeted, while for nonhydrophobic acetone (AC) the 5230 cm1 liquid-like chromophore must be studied within its Mixing Scheme I. Further spectroscopic studies certainly add important information about the molecular arrangement of the system. To fulfill such purpose, the proper mole fraction range must be studied. Without recognizing the importance of the concentration specific mixing scheme, as we have been pointing out throughout this book, any investigation would not result in fruitful conclusions.

[X-4] SPECTRA OF EXCESS MOLAR ABSORPTIVITY, εE, AND EXCESS PARTIAL MOLAR ABSORPTIVITY OF SALT, εES , IN AQUEOUS SOLUTIONS OF NA-HALIDES We applied the same analysis methodology described in the foregoing section to the NIR spectra of aqueous solutions of Na-halides (Sebe et al., 2012). As we concluded in Sections [VIII-2] and [VIII-3], Na+, F, and Cl ions belong to the class of “hydration centers” that are hydrated by a number, nH, given in Table VIII-3 (p. 303) and Table VIII-4 (p. 304) and more importantly leave the bulk H2O away from hydration shells unperturbed. Br and I are “hydrophilic ions” that form hydrogen bonds directly to the hydrogen bond network of H2O and retard the S-V cross fluctuation inherent in liquid H2O. Here we seek any additional knowledge by the present analysis methodology about the difference between Cl, a hydration center, and (Br, I) pair, hydrophilic ions with the counter cation fixed at Na+. The calculated values of εE by Eq. (X-3) are plotted in Fig. X-7A–C for aqueous NaCl, NaBr, and NaI. The spectra of ε0S for pure salt were assumed to be constant at zero. As is evident from these figures, there are three bands

365

200 NaCl

e E (cm2 mol−1)

100

0

−100

(A)

4600

Arrow indicates xNaCl from 0 to 0.09

4800

5000 5200 n (cm−1)

5400

400

300

NaBr

e E (cm2 mol−1)

200

100

0

−100

−200 4600

(B)

Arrow indicates xNaBr from 0 to 0.13

4800

5000 5200 n (cm−1)

5400

Fig. X-7 (A) Excess molar absorptivity, εE, for NaCl-H2O at room temperature. (B) Excess molar absorptivity, εE, for NaBr-H2O at room temperature. (Continued)

in the εE spectra: a negative band at 4873 cm1, a positive one at 5123 cm1, and a negative one at 5263 cm1, and the three are at the same wavenumbers regardless of the identity of anions. In comparison with those for AN-H2O and AC-H2O shown in Fig. X-3, we suggest that the negative εE band that

Fig. X-7(C) to X-8(B)

366

800

600 NaI

e E (cm2 mol−1)

400

200

0

−200

−400 4600

(C)

Arrow indicates xNal from 0 to 0.17

4800

5000

5200

5400

n (cm−1)

Fig. X-7, cont’d (C) Excess molar absorptivity, εE, for NaI-H2O at room temperature. (Reproduced with permission from Sebe et al. (2012). Copyright (2012), the Royal Society of Chemistry).

we assigned as the solid-like chromophore red-shifted by 120 cm1, the positive liquid-like band red-shifted by 80 cm1, and the new negative one appeared at 5263 cm1. The value of 100 cm1 corresponds to 1.2 kJ mol1 and is only about 5% of the hydrogen bond energy (Wendler et al., 2010); hence such red-shifts may not be entirely unreasonable. What is this new negative chromophore at 5263 cm1? We tentatively assign it to a gas-like (without hydrogen bonding to adjacent H2O molecules) chromophore. The findings by Fornes and Cahussidon (1978) that the ν2 + ν3 band of pure H2O blue shifts on temperature increase and that at 50°C the peak top was at about 5020 cm1 provides some support for the above assignment. There is a Raman and Monte Carlo work on the effects of halides on the symmetric stretch (ν1) band of H2O (Smith et al., 2007). Similar studies for the ν2 + ν3 combination band of H2O are awaited. To investigate the effect of salt on εE spectra further, we calculate the average value of εE at 5263 cm1, 5123 cm1, and 4873 cm1 in the same

367

e E (ave) (103 cm2 mol−1)

0.02

5263 cm−1

0.00

NaCl NaBr NaI

−0.02

−0.04

−0.06 0.00

(A)

Error

0.02 0.04 0.06 0.08 xsalt (salt = NaCl, NaBr, or NaI)

0.10

e E (ave) (103 cm2 mol–1)

0.4

0.3

5123 cm–1

0.2

Error

0.1

0.0

NaCl NaBr NaI

–0.1 0.00

(B)

0.02 0.04 0.06 0.08 xsalt (salt = NaCl, NaBr, NaI)

0.10

Fig. X-8 (A) The average excess molar absorptivity, εE(ave), at 5263 cm1 for aqueous NaCl, NaBr, and NaI. (B) The average excess molar absorptivity, εE(ave), at 5123 cm1 for aqueous NaCl, NaBr, and NaI. (Continued)

manner as the previous section, except that the strip width is increased to 30 cm1. The resulting average excess molar absorptivity, εE(ave), is shown in Fig. X-8A–C. The values of εE(ave) for all cases tend to zero at xS ¼ 0 (S ¼ NaCl, NaBr, or NaI), as they should. We then draw smooth

Fig. X-8(C) to X-9(B)

368

e E (ave) (10 3 cm 2 mol–1)

0.00

NaCl NaBr NaI

–0.02

–0.04

–0.06 0.00

(C)

4873 cm

–1

Error

0.02 0.04 0.06 0.08 xsalt (salt = NaCl, NaBr or NaI)

0.10

Fig. X-8, cont’d (C) The average excess molar absorptivity, εE(ave), at 4873 cm1 for aqueous NaCl, NaBr, and NaI. (Reproduced with permission from Sebe et al. (2012). Copyright (2012), the Royal Society of Chemistry).

curves as shown in the figures, read the εE(ave) values off the smooth curves drawn and calculated εEsalt (salt ¼ NaCl, NaBr, or NaI) by Eq. (X-5). The results are plotted in Fig. X-9A–C. In the gas-like chromophore at 5263 cm1, Fig. X-9A suggests that effects of halides on εE of the ν2 + ν3 band of H2O are only quantitatively different. The values of εEsalt start at xsalt ¼ 0 with about 0, 450, and 900 cm2 mol1for Cl, Br, and I, respectively, with the counter cation fixed at Na+. This quantitative difference in εEsalt among halides is apparently in the reverse order of charge density. Furthermore, all values of εEsalt decrease with about the same slope as xsalt increases irrespective of the identity of halides. Thus, the qualitative difference between “hydration center” and “hydrophilic halides” that we seek is not apparent in this 5263 cm1 chromophore. Another important point to note in Fig. X-9A is that the slope of decrease of εEsalt on increasing xsalt changes suddenly to a mutually similar but much smaller value at xsalt ¼ 0.032, 0.036, and 0.040 for Cl, Br, and I, respectively (along the dotted line in Fig. X-9A). Namely, the effect of each salt on εE slows down suddenly at the respective threshold mole fractions. This hints some form of ion association, perhaps H2O-mediated ion pairing of the kind suggested by Buchner and Hefter (2009). However, we did not

369

1.0 NaCl NaBr 5263 cm–1

3 2 –1 eE salt (10 cm mol )

0.5

NaI

0.0

–0.5

–1.0

0.00

(A)

0.02

0.04 0.06 0.08 xsalt (salt = NaCl, NaBr or NaI)

0.10

5 NaCl 5123 cm–1

NaI

4

3 2 –1 eE salt (10 cm mol )

NaBr

3

2

1

0 0.00

(B)

0.02

0.04 0.06 0.08 xsalt (salt = NaCl, NaBr or NaI)

0.10

Fig. X-9 (A) Excess partial molar absorptivity of salt, εEsalt, at 5263 cm1 for aqueous NaCl, NaBr, and NaI. (B) Excess partial molar absorptivity of salt, εEsalt, at 5123 cm1 for aqueous NaCl, NaBr, and NaI. The dotted line shows a smooth extension of the trend seen from I to Br, for a guide to eyes. (Continued)

Fig. X-9(C)

370

0.0 NaCl NaBr

3 2 –1 eE salt (10 cm mol )

–0.2

NaI

4873 cm–1

–0.4

–0.6

–0.8

–1.0 0.00

(C)

0.02

0.04

0.06

0.08

0.10

xsalt (salt = NaCl, NaBr or NaI)

Fig. X-9, cont’d (C) Excess partial molar absorptivity of salt, εEsalt, at 4873 cm1 for aqueous NaCl, NaBr, and NaI. (Reproduced with permission from Sebe et al. (2012). Copyright (2012), the Royal Society of Chemistry).

observe any hint of ion-pairing behaviors for Cl, Br, and I in Chapter VIII up to 0.035, 0.06, and 0.07 mole fractions, respectively. See the upper limits of the applicability of the 1P-probing methodology listed in Table VIII-4 (p. 304). At 5123 cm1, Fig. X-9B clearly indicates a qualitative difference in E εsalt between Cl and (Br, I) pair. While the values of εEsalt at xsalt ¼ 0 decrease in the reverse order of charge density of halides, there is a large gap between (Br, I) pair and Cl. Furthermore, εEsalt remains constant independent of xsalt for Cl, but those for Br and I decrease on increasing xsalt. The slope for I appears steeper than that of Br. As discussed in Chapter VIII, Cl is a hydration center that is hydrated by 2.3  0.6 molecules of H2O and more importantly leaves the bulk H2O away from hydration shells unperturbed. Br and I, on the other hand, are “hydrophilic anions” that form hydrogen bonds directly to the hydrogen bond network of H2O and retard the fluctuation inherent in liquid H2O, with a stronger

371

effect by I than Br. The observation in Fig. X-9B above therefore is related to the aforementioned findings by the 1P-probing methodology described in Chapter VIII. Or rather, the qualitative difference between Cl and (Br, I) pair manifests itself in the 5123 cm1 liquid-like chromophore. Thus, further elucidation on this difference may be facilitated by targeting further investigation to the transition moment of vibrational excitation of this liquid-like chromophore. At the solid-like 4873 cm1 chromophore, the order of the values of εEsalt is now swapped from the other two chromophores. Otherwise, the difference appears only in the values of εEsalt. There may be a slight curvature difference between Cl and (Br, I) pair. But it is premature to discuss this issue due to possible uncertainties in εEsalt.

[X-5] SPECTRA OF EXCESS MOLAR ABSORPTIVITY, εE, IN AQUEOUS SOLUTIONS OF SOME OTHER SALTS We applied the same analysis methodology to NIR spectra of aqueous solutions of (CH3)4NCl (TMACl) and (C2H5)4NCl (TEACl) (Koga et al., 2013) and KCl, KBr, CsCl, and CsBr (Sebe et al., 2015). TMA+ and TEA+ are both hydrophilic cations, and K+ and Cs+ are hydration centers. See Section [VIII-4] and Table VIII-3 (p. 303). The spectra of εE calculated by Eq. (X-3) are plotted in Figs. X-10 and X-11. As is evident from these figures, there are generally the same three chromophores: a negative band at 4873 cm1, a positive one at 5123 cm1, and a negative chromophore at 5263 cm1. For TMACl (Fig. X-10A) and TEACl (Fig. X-10B), however, the 4873 cm1 bands are almost zero, and for TMACl, Fig. X-10A, this band may be weakly positive, if not zero. In calculating εE the same assumption that ε0S for pure salt is constant at zero was made. Perhaps such assumption may not give quantitatively correct εE spectra, judging from those in Fig. X-10. Tetraalkyl group may have a spill over spectra that must have been properly subtracted. With this in mind, there seem to be small negative bands at 4873 cm1 for TMACl- and TEACl-H2O systems also. Here we leave the values of εE as calculated assuming that ε0S for these tertraalkylammonium salts to be constant at zero, and the data for these salts will be used for qualitative discussion. For other inorganic salts, the εE spectra shown in Fig. X-11 indicate that the base lines in the low wavenumber region are acceptable, while those in the region above 5300 cm1 could be questionable. We investigated the total of nine salts and two nonelectrolytes. While further investigation on many more nonelectrolyte and electrolyte solutes

Fig. X-10 to X-11(B)

372

5123 cm–1 0.3

e E (103 cm2 mol–1)

TMAC 0.2

0.1

5236 cm–1

4873 cm–1

0.0

–0.1 4600

4800

(A)

5000

0.3

0.2

e E (103 cm2 mol–1)

5200

5400

n (cm–1) 5123 cm–1

TEAC

5263 cm–1

0.1 4873 cm–1 0.0

–0.1

–0.2 4600

(B)

4800

5000

5200

5400

n (cm–1)

Fig. X-10 (A) Spectra of the excess molar absorptivity, εE, in aqueous tetramethylammonium chloride (TMAC). The arrows indicate the mole fraction xS (S ¼ TMAC) from 0 to 0.1. See text about the band at 4873 cm1. (B) Spectra of the excess molar absorptivity, εE, in aqueous tetraethylammonium chloride (TEAC). The arrows in the figure indicate the mole fraction xS (S ¼ TMAC) from 0 to 0.1, with no xS dependence at 4873 cm1. See text about the band at 4873 cm1. (Reproduced with permission from Koga Y, Sebe F, Nishikawa K. J Phys Chem B 2013;117:877. Copyright (2013), American Chemical Society).

373

140 120 100

KCl

80

e E (cm2 mol–1)

60 40 20 0 –20 –40 –60

Arrows indicate xS from 0 to 0.06

–80 4600

4800

(A)

5000 5200 Wavenumber (cm–1)

5400

300

250 KBr

e E (cm2 mol–1)

200

150

Arrows indicate xS from 0 to 0.08

100

50

0

–50

–100 4600

(B)

4800

5000 5200 Wavenumber (cm–1)

5400

Fig. X-11 (A) Spectra of excess molar absorptivity, εE, for KCl-H2O at room temperature. (B) Spectra of excess molar absorptivity, εE, for KBr-H2O at room temperature. (Continued)

Fig. X-11(C) to X-12

374

400

300 CsCl

e E (cm2 mol–1)

200

100

0

–100

–200 4600

Arrows indicate xS from 0 to 0.16

4800

5000

(C)

5200

5400

Wavenumber (cm–1) 250 200

CsBr

e E (cm2 mol–1)

150 100 50 0 –50 –100 –150 4600

(D)

Arrows indicate xS from 0 to 0.09 4800

5000

5200

5400

–1

Wavenumber (cm )

Fig. X-11, cont’d (C) Spectra of excess molar absorptivity, εE, for CsCl-H2O at room temperature. (D) Spectra of excess molar absorptivity, εE, for CsBr-H2O at room temperature. (Reproduced with permission from Sebe F, Nishikawa K, Koga Y. J Solution Chem 2015;44:1833. Copyright (2015), Springer).

375

0.2

0.0 3 2 –1 eE salt (10 cm mol )

NaCl KCl CsCl TMACl

–0.2

TEACl –0.4

–0.6

–0.8 0.00

0.01

0.02

0.03

0.04

0.05

xsalt

Fig. X-12 Excess partial molar absorptivity of salt, εEsalt, at 4873 cm1 in aqueous solutions of chlorides of some cations (salt ¼ NaCl, KCl, CsCl, TMACl, and TEACl). (Data were taken from Sebe F, Nishikawa K, Koga Y. J Solution Chem 2015;44:1833; Koga Y, Sebe F, Nishikawa K. J Phys Chem B 2013;117:877; Sebe et al., 2012. Copyright (2013), American Chemical Society).

are required, these results hint that for aqueous nonelectrolytes, there may be two universal chromophores in εE spectra of the ν2 + ν3 band of H2O: solid- and liquid-like ones. For aqueous electrolytes, there are three chromophores in the presence of ions. The first two in low-energy excitations are most likely red-shifted by about 100 cm1 from the two for aqueous nonelectrolytes, and the last one with high vibrational excitation is a gas-like chromophore. With nine salt cases studied, the latter three are more likely to be universal. Whether this observation is limited to the ν2 + ν3 band of H2O is yet to be tested. For this group of aqueous solutions of salts, TMACl, TEACl, KCl, KBr, CsCl, and CsBr, εEsalt data, the effect of a salt on εE did not reveal any qualitatively different features except for the 4873 cm1 chromophores (Koga et al., 2013; Sebe et al., 2015). Fig. X-12 shows excess partial molar absorptivity of salt, εEsalt, at 4873 cm1 for the chloride salts of all the cations we studied. According to the findings by the 1P-probing methodology in Section [VIII-4] and Tables VIII-3 (p. 303) and VIII-4 (p. 304), TMA+ and TEA+ are hydrophilic cations, and Na+, K+, and Cs+ are hydration centers. The counter anion, Cl, is a hydration

376

center, and Br and I are hydrophilic anions. Unfortunately we do not have NIR data for I salts, and the trend between Br and I could not be observed to estimate a qualitative difference between the effect of Cl and (Br, I) pair. Here we limit ourselves to chloride salts in Fig. X-12. Nonetheless, Fig. X-12 suggests that while εEsalt remains almost constant for this solid-like chromophore at 4873 cm1, the values of εEsalt for hydrophilic cations tend to be close to zero, in comparison with other hydration center cations. Namely, the hydrophilic cations have no, if not small, effects on εEsalt at 4873 cm1, while the hydration center cations show sizable negative values of εEsalt. If the universality of the presence of small number of chromophores is real, it would give us the target vibrational excitations to concentrate further attention on, in order to elucidate the nature of aqueous solutions of solutes belonging to a different class. However, our studies so far are limited to the ν2 + ν3 combination band of H2O. Whether this applies to other H2O bands or not is yet to be investigated. We stress such investigation are possible by applying the concept common in solution thermodynamic studies, resulting in the analysis of absorbance data based on Eqs. (X-3), (X-5).