Spectroscopic and Thermodynamic Evidence of Dimer and Trimer

Article pubs.acs.org/JPCB

Spectroscopic and Thermodynamic Evidence of Dimer and Trimer Hydrogen Bonded Complex Formation between Chloroform and 2‑Butanone. Excess Molar Enthalpy for the Chloroform + 2‑Butanone Binary System at 303 K Ana C. Gómez Marigliano,*,† Viviana del Valle Campos,† Lis Fernández,‡ M. L. Roldán,§ and Horacio N. Sólimo† †

Departamento de Física, Facultad de Ciencias Exactas y Tecnología, Universidad Nacional de Tucumán, Avenida Independencia 1800, 4000-San Miguel de Tucumán, Argentina ‡ Departamento de Química Física, Facultad de Bioquímica, Química y Farmacia, Universidad Nacional de Tucumán, San Lorenzo 456, 4000-San Miguel de Tucumán, Argentina § Instituto de Estructura de la Materia, CSIC, Serrano 121, 28006 Madrid, Spain S Supporting Information *

ABSTRACT: FT-Raman and FT-infrared spectra of pure chloroform (A) and 2-butanone (B), as well as of the binary system chloroform + 2-butanone, were recorded to investigate the type and nature of the intermolecular complexes formed when both chemicals are mixed. The optimized structures and vibrational frequencies for 2-butanone, chloroform, and their 1:1 and 1:2 complexes were calculated by means of density functional theory (DFT) techniques using the B3LYP functional combined with the 6-31G(d,p) and 6-311++G(d,p) basis set. The recorded FTIR and Raman spectra confirm the existence of these types of hydrogen-bonded complexes, making it possible, furthermore, to calculate the heteroassociation constants. Heat of mixing at 303 K over the whole mole fraction range at atmospheric pressure was also measured. The excess molar enthalpy was fitted to a Redlich−Kister-type equation, using least-squares to obtain its dependence on concentration. The ideal associated solution model was also used to calculate these equilibrium constants among the chemical species in solution, which compare well with that calculated with the spectral determinations and the enthalpy of hydrogen bond formation. Furthermore, the McGlashan−Rastogi linearization test was also used to provide thermodynamic evidence about the stoichiometry of the formed complexes.

1. INTRODUCTION Several works are found in the literature, which deals with the study of complex association between chloroform and several compounds, such as ketones, esters, hydrocarbons, dimethyl sulfoxide, 1,4-dioxane, etc.1−8 In these works, it has been shown that the thermodynamic behavior could be interpreted in terms of the formation of hydrogen-bonded complexes. However, there is some discrepancy about type and nature of the formed complexes, which arises from the lack of spectroscopic evidence to carry out the correct assignment. For example, for the chloroform (A) + 2-butanone (B) binary system, it sometimes has been indicated that there are only 1:1 H-bonded complexes (AB) and sometimes that the 2:1 complexes (A2B) are also present.6,9 This discrepancy is also observed for the chloroform + acetone binary system.10−12 Although all these works ensure that the intermolecular complexes exist, there is no irrefutable evidence about their nature. It is important to point out that both types of complexes (AB and A2B) are potentially feasible since the carbonyl group has © 2013 American Chemical Society

an oxygen atom with two lone electron pairs, which both would be able to form hydrogen bonds with one or two molecules of chloroform, as shown in Figure 1. Furthermore, the polar character of the chloroform would facilitate its self-association,13 and then this dimer could be H-bonded with a molecule of 2-butanone through one of its lone electron pairs, as postulated.2 Keeping in mind these considerations, we take into account that: (a) A computational method is at present widely used for simulating IR and Raman spectra. Such simulations have proved to be an essential tool for interpreting and predicting the vibrational spectra. Then, the optimized structures and vibrational frequencies for 2-butanone, chloroform, and their 1:1 and 1:2 complexes were calculated by means of density Received: December 28, 2012 Revised: February 19, 2013 Published: March 22, 2013 5121

dx.doi.org/10.1021/jp3128109 | J. Phys. Chem. B 2013, 117, 5121−5128

The Journal of Physical Chemistry B

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Figure 1. B3LYP/6-31G(d,p) optimized geometry for 2-butanone−chloroform complexes: (a) dimer with a single C−H···O hydrogen bond; (b) trimer with a bifurcated C−H···O hydrogen bond. Selected C−O, C−H, and C−H···O bond distances are displayed on the figure, and bond distances of monomers are given in parentheses.

2. EXPERIMENTAL SECTION

functional theory (DFT) techniques using the B3LYP functional combined with the 6-31G(d,p) and 6-311++G(d,p) basis set. (b) FT-Raman spectroscopy is a useful tool that allows us to obtain experimental evidence to elucidate type and nature of the formed complex because it does not need use any “inert” solvent to obtain the spectra. Therefore, no solvent effect is present. Consequently, the spectra of both pure components and their binary system at three different concentrations were recorded to analyze the dependence of the intensity of some target bands on concentration. (c) FT-infrared spectroscopic studies were carried out for the chloroform + 2-butanone binary system, to elucidate this discrepancy and to calculate the equilibrium constants. (d) Heat of mixing measurements in the whole concentration range at 303 K and at atmospheric pressure were also made. From these last experimental results, we interpret the excess molar enthalpy in terms of the simplest and more convenient thermodynamic model: the “ideal associated solution model”, calculating the association constants for the intermolecular complexes and the enthalpy of hydrogen bond formation. Furthermore, these association constants are compared with that calculated from infrared spectroscopy. On the other hand, the McGlashan−Rastogi linearization test7 was used as an additional tool to thermodynamically decide if this binary mixture has only 1:1 complexes or if 2:1 complexes are also present. As far as we know, there is only an old infrared spectroscopic study14 for this binary system, which reports a band in the region of 4 μm (= 2500 cm−1) that the author says is not characteristic of either component of the mixture, which was attributed to the complex. However, this wavenumber does not correspond at any important region of the infrared spectrum for this binary system. On the other hand, to the best of our knowledge, there is no reference in the literature to either Raman or recent infrared studies or quantum calculations for this binary system.

2.1. Materials. Chloroform (analytical reagent) and 2butanone (analytical reagent) were supplied by Sintorgan (Argentina), and CCl4 (analytical reagent) was supplied by Uvasol, Merck. They were used as received because no impurity was found in the infrared spectrum of the pure compound and nor was detected by gas chromatography using an HP 6890 gas chromatograph with an FID detector, showing that their mole fractions were higher than 0.999. The pure components were stored over 0.3 nm molecular sieves to prevent water absorption, and their water content was periodically checked by Karl Fischer titration using an automatic Mettler DL18 Karl Fischer titrator. 2.2. Experimental Procedure. 2.2.1. FT-Raman Spectra. Raman absorption spectra at a resolution of 4 cm−1 were recorded using a Bruker IFS 66 spectrometer both for pure components and three different chloroform + 2-butanone binary mixtures (5.6 and 6.2 M; 6.1 and 5.6 M, and 8.4 and 3.1 M in 2-butanone and chloroform, respectively, where M denotes concentrations in mol·L−1). 2.2.2. FT-Infrared Spectra. Infrared spectra of pure components and their binary solutions were recorded on a Perkin-Elmer FT-IR Spectrometer − Spectrum RXI, using a KBr-sealed cell with 0.500 mm of path, provided for PerkinElmer. For this purpose, several highly diluted ternary mixtures were prepared mixing dissimilar masses of both pure and diluted in CCl4. The concentrations of these ternary solutions were in the range 0.027−0.20 M for both solutes. The infrared spectra of pure components and their binary mixtures were recorded against pure CCl4 as a reference, to eliminate the absorption bands of the solvent. 2.2.3. Heat of Mixing Measurements. Heat of mixing measurements at atmospheric pressure were performed using an adiabatic calorimeter described previously.15 Pure liquids were weighed inside the calorimeter using an electronic top loading balance (Mettler Toledo PB 1502-S) with an uncertainty of 0.01 g. The uncertainty in the mole fractions is estimated to be lower than ±0.001, while for heat of mixing 5122



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Table 1. Physical Properties of Pure Components at 303.15 Ka density/kg·m−3 chemicals chloroform 2-butanone

exp. 1469.4 795.1

refractive index lit.

exp. b

1470.60 794.6b 794.83d 794.38f

1.43987 1.37530

viscosity/mPa·s lit. c

1.43987 1.37383c

exp.

lit.

0.516 0.382

0.514b 0.366b 0.379e 0.382c 0.372f

a

Density, refractive index for the sodium D-line, and viscosity were measured with a vibrating-tube densimeter KEM DA-300, a Leica AR600 refractometer, and an Anton Paar Stabinger viscometer (SVM 3000/G2), respectively. The uncertainties were: ±0.1 kg·m−3 for density, ±0.00005 for refractive index, and ±0.35% of the measured value for viscosity. bRiddick, J. A., Bunger, W. B., Sakano, T. K. Organic Solvents, 4th ed.; John Wiley: New York, 1986. cClará, R. A.; Gómez Marigliano, A. C.; Sólimo, H.; Morales, D. Density, Viscosity,Vapor−Liquid Equilibrium, and Excess Molar Enthalpy of [Chloroform + Methyl tert-Butyl Ether]. J. Chem. Eng. Data 2006, 51, 1473−1478 dTRC Thermodynamic Tables, NonHydrocarbons; Thermodynamic Research Center: The Texas A&M University System, College Station, TX, 1991; p d-5870. eInterpolated from ref 26. fFrom ref 27.

these Raman spectra, it is possible to visualize the CH, CO, and CCl stretching bands and the CCl bending ones necessary for the purpose of this work. Figure 2 shows that the spectrum of the binary system presents important differences compared with those of pure components. 3.1.1. FT-Raman CH Stretching Region. Figure 3 shows the CH stretching region around 3000 cm−1 for both pure

measurements it is estimated to be lower than 3% of the measured value. The temperature inside the Dewar flask was measured with a Hart Scientific 1502A platinum resistance thermometer (certified by the National Institute of Standards and Technology-NIST) with an accuracy of ±0.007 K. Temperatures are reported in terms of ITS-90. The excess enthalpy curves at 303 K were established a point at a time, performing two separate runs to cover the entire mole fraction range at atmospheric pressure. Each run usually consists of six or seven separate additions. The self-consistency of the technique may be judged by the overlap of the data from the two runs.

3. RESULTS AND DISCUSSION Experimental density, refractive index, and viscosity at 303.15 K of the pure chemicals used in this work are compared with available literature values in Table 1. 3.1. FT-Raman Spectra. Figure 2 shows the Raman spectra at T = 293 K of pure chloroform and 2-butanone, together with one binary mixture with a concentration of 6.1 and 5.6 M in 2butanone and chloroform, respectively, to qualitatively represent the whole Raman spectroscopic behavior of the binary system compared with those of pure components. In

Figure 3. FT-Raman spectra of the CH stretching region. Dash dot line, pure chloroform; continuous line, pure 2-butanone; ●, ○, and ····, chloroform + 2-butanone binary mixtures whose concentrations are: 6.1 and 5.6; 8.4 and 3.1; and 8.5 and 3.0 M in 2-butanone and chloroform, respectively.

components and three binary mixtures. From the inspection of this region we conclude that: (i) pure chloroform has a very intense band at 3018 cm−1 assigned to the CH stretching vibrational mode of free molecules (monomers), which remarkably decreases when this chemical is mixed with 2butanone; (ii) although the CH stretching band of free chloroform molecules diminishes in intensity, it does not disappear completely; (iii) three new weak bands in the stretching band region at 3001, 2980, and 2937 cm−1 appear which are attributed to the hydrogen-bonded species; (iv) pure 2-butanone presents several bands around 2900 cm−1, which are assigned to symmetric and asymmetric stretching modes of the methyl and methylene groups; and (v) the shape of the 2butanone CH stretching bands is not appreciably affected by the mixture with chloroform, while their intensities diminish as a consequence of the dilution.

Figure 2. FT-Raman spectra. Solid line, pure chloroform; dashed line, pure 2-butanone; ●, chloroform + 2-butanone binary mixture with a concentration of 6.1 and 5.6 M in 2-butanone and chloroform, respectively. 5123



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and chloroform), which were assigned to the CO stretching the monomer, dimer, and trimer, respectively. 3.1.3. FT-Raman CCl Stretching Region. Figure 6 shows the CCl stretching and CCl bending regions for pure chloroform and the three binary mixtures. As shown, the band at 759 cm−1 also contains a shoulder.

From the above observations, we conclude that the CH group of the chloroform molecule is directly involved in the formation of a hydrogen-bonded complex when this is mixed with 2-butanone, while those of 2-butanone do not participate in any way. 3.1.2. FT-Raman CO Stretching Region. Figure 4 shows the CO stretching region around 1710 cm−1 for pure 2-butanone

Figure 6. FT-Raman spectra of the CCl stretching and CCl bending regions. Dashed dot line, pure chloroform; ●, ○, and ····, chloroform + 2-butanone binary mixtures whose concentrations are: 6.1 and 5.6; 8.4 and 3.1; and 8.5 and 3.0 M in 2-butanone and chloroform, respectively.

Figure 4. FT-Raman spectra of the CO stretching region. Continuous line, pure 2-butanone; ●, ○, and ---, chloroform + 2-butanone binary mixtures whose concentrations are: 6.1 and 5.6; 8.4 and 3.1; and 8.5 and 3.0 M in 2-butanone and chloroform, respectively.

The curve fitting of this band (see Figure 7) shows that two bands fit adequately the original spectrum whose maxima are

and the three binary mixtures. From the inspection of this region we conclude that: (i) the shape of the CO stretching band is significantly modified when 2-butanone is mixed with chloroform, and this modification is influenced by the concentration of the mixture. As can be seen, the band at 1714 cm−1 contains a shoulder suggesting the presence of bands underneath it; (ii) the curve fitting of this band (see Figure 5) shows that three bands fit adequately the original spectrum whose maxima are located at 1720, 1710, and 1702 cm−1 (for 8.5 and 3.0 M in 2-butanone

Figure 7. Curve fitting of the FT-Raman CCl stretching region. ■, experimental band; continuous line, sum of the two fitted bands; ○ and □, bands obtained in the fitting process: 754 and 767 cm−1 corresponding to the symmetric and asymmetric CCl stretching vibrational modes, respectively. ---, baseline that is practically coincident with the residual of the fitting process.

located at 767 and 754 cm−1, which were assigned to the asymmetric and symmetric CCl stretching vibrational modes, respectively. Also, Figure 6 shows that there are three bands located at 667, 365, and 260 cm−1 which are assigned to the CCl bending vibrational modes. The analysis of the spectra shown in Figure 6 is important to determine if another type of complex could have been formed in addition to those between the CH and CO groups in this

Figure 5. Curve fitting of the FT-Raman CO stretching region. ■, experimental band; □, Δ, and ○, bands obtained in the fitting process: 1720, 1710, and 1702 cm−1 corresponding to the monomer, dimer, and trimer CO stretching vibrational modes, respectively. , baseline that is practically coincident with the residual of the fitting process. 5124



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Table 2. Interaction Energies for Monomers and Complexes Calculated with the B3LYP Functional and Different Basis Sets E (Hartree)a

B3LYP 6-31G(d,p)

2-butanone

chloroform

dimer

trimer

−232.48189

−1419.28034

−232.54306

−1419.37970

−1651.76882 4.1 −1651.92948 4.2

−3071.05193 5.9 −3071.31228 6.2

ΔEintb 6-311++G(d,p) ΔEintb a

BSSE-corrected energies for complexes. bDifference in energies between the monomers and the complexes in kcal mol−1.

Table 3. Experimental and Calculated Frequencies (in cm−1) for 2-Butanone, Chloroform, and Their Complexes 2-butanone

chloroform

exp. modea ν C−H ν CO

exp.

IRb

Ramanc

calc.d

1720 (vs)

1713 (17)

1746

ν CH3 antisym.

ν CH3 sym. ν ν ρ ν

CH2 antisym. CH2 sym. CCl3 CCl3 antisym.

2981 (s)

2979 (23)

2939 (m)

2939 2923 2899 2885

2906 (m) 2880 (m)

butanone + chloroform

(69) (100) (54) (44)

exp.

IR

Raman

calc.d

IR

3018 (s)

3018 (22)

3064 (A1)

3018 (s) 1719 (sh) 1715 (vs)

3040 3018 3012 2986 2942 2927 2933 2907

2961 (w)

2922 (w)

1215 (7) 761 (10)

ν CCl3 sym. δ CCl3 sym. δ CCl3

667 (100) 366 (85) 262 (56)

Raman 3020 1721 1711 2995 2981 2971

(17) (3) (15) (16) (24) (24)

2940 2923 (100) 2899 (55) 2885 (46)

1202 (E) 708 (E)

762 (50)

640 (A1) 353 (A1) 251 (E)

667 (54) 366 (49) 262 (36)

dimer calc.d

trimer calc.d

3033

3052, 3040

1727 3042 3020 3014 2991 2944 2930 2936 2908

1710 3040 3020 3015 3000 2945 2933 2934 2907

706 695 634 333

714, 698, 636, 354,

706 693 632 353

ν, stretching; δ, deformation; ρ rocking. bv, very; s, strong; m, medium; w, weak; sh, shoulder. cRelative Raman intensities in parentheses. dFrom B3LYP/6-31G(d,p) calculation and multiplied by the factor 0.9613. a

binary mixture. Comparing the CCl stretching band at 759 cm−1 of pure chloroform with those at the same wavenumber for the binary mixtures, it is evident that the binary spectra have similar shapes, and no modification is observed in this band. Furthermore, the same is concluded for the other three CCl bending bands. Thus, no hydrogen bond of the C−H···Cl type is detected, which is clear evidence that the postulated selfassociation of two molecules of chloroform to form a dimer, which is bounded through a hydrogen bond to a molecule of 2butanone,6,9 does not exist in this binary system. Additionally, although the CH and CO stretching bands diminish in intensity, they do not disappear completely when both chemicals are mixed. This is interpreted in terms that there are free molecules of both components without associating in the solution. This gives sustainability to the chemical equilibrium (expressed by reaction 1, see below). That is, equilibrium exists among free molecules of both chemicals and the complexes. To ensure the existence and proportion of each species, a simulation process was perfomed, whose results are then compared with experimental IR and Raman.

method is preferred over the B3LYP one with regard to binding energies, the same trend can be observed with B3LYP calculations with the advantage of lowering the computational cost.19 For all calculations, zero-point energies were corrected. In addition, binding energies for complexes were corrected for the basis set superposition error (BSSE) using the counterpoise (CP) method proposed by Boys and Bernardi. 20 All calculations were made for the isolated species using the Gaussian 03 set of programs.21 For both levels of theory, the geometry was fully optimized with C3v symmetry for chloroform and without symmetry constraints for 2-butanone and their two complexes. The frequency calculation confirmed that all the structures are global minima on the potential surface. The energies of the monomers and the complexes corrected by BSSE are listed in Table 2. The structures of the complexes are shows in Figure 1 along with some relevant geometrical parameters calculated at the B3LYP/6-31G(d,p) level of theory. The distances and angles obtained with both basis sets do not differ in more than 0.005 Å and 3.8°, respectively. However, the high-level theoretical calculation predicts the hydrogen bond distances notably larger, these differences being equal to 0.017 Å and 0.010−0.025 Å for the O···H distances in the dimer and the trimer, respectively. Theoretical frequencies, infrared intensities, and Raman scattering were used to simulate the experimental spectra. The vibrational frequencies of 2-butanone, chloroform, and their complexes calculated with the B3LYP/6-31G (d,p) combination were multiplied by the factor 0.961322 to better

4. THEORETICAL CALCULATIONS The optimized structures and vibrational frequencies for 2butanone, chloroform, and their 1:1 and 1:2 complexes were calculated by means of density functional theory (DFT) techniques using the B3LYP functional16,17 combined with the 6-31G(d,p) and 6-311++G(d,p) basis set. Although the MP218 5125



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On the other hand, KD and KTr are related to K, in terms of mole fractions, by

reproduce the experimental data. No anharmonicity corrections of these frequencies were made because of a lack of necessary experimental data. These calculated values appear in Table 3 along with the frequencies observed in the infrared and Raman spectra.

K C/L·mol−1 = K (P /RT )Δn

where P, R, and T are the normal pressure (1 atm), universal gas constant (= 0.08206 L·atm·mol−1·K−1), and absolute temperature (= 293 K), respectively, while Δn = −1 for dimer formation and Δn= −2 for trimer, which leads to

5. FT-INFRARED SPECTRA Infrared spectra were recorded at high dilution of both components and the different mixtures, using CCl4 as solvent. Figure SI.I (Supporting Information) shows an important change in the shape of the CO stretching band toward lower frequency for the ternary mixture with respect to that of the binary mixture of 2-butanone in CCl4, together with a band broadening, which is compatible with a new band attributed to the complexes between both chemical solutes. A similar effect is observed for the CH stretching band, although it is less evident (see Figure SI.II, Supporting Information). This is in agreement with our conclusions obtained from Raman spectra. From these spectra, and using the same curve fitting procedure previously applied, the association constants for the reactions 1 were calculated and compared with that arisen from the ideal associated solution model. Since the Raman spectra and DFT calculations showed that there is conclusive evidence of AB complex formation between unlike molecules in this binary system, we consider that chloroform (A) and 2-butanone (B) are in chemical equilibrium with the complex (AB and A2B), represented by reactions 1, and then, the equilibrium constants for these reactions in terms of molar concentrations KD and KTr may be written as c ⎫ A + B ↔ AB ⇒ KD = AB ⎪ c BcA ⎪ ⎬ c A 2B ⎪ AB + A ↔ A 2B ⇒ KTr = c c ⎪ ⎭ AB A

(3)

KD = (1.96 ± 0.4) and KTr = (0.66 ± 0.2)

6. EXCESS MOLAR ENTHALPY The excess molar enthalpy in the whole mole fraction range at T = 303 K and atmospheric pressure is listed in Table 4, while Table 4. Heat of Mixing of the Binary System {x1 Chloroform + (1 − x1) 2-Butanone} at 303 K x1

−HE/J·mol−1

x1

−HE/J·mol−1

0.000 0.043 0.092 0.208 0.487

0 251 529 990 1398

0.591 0.666 0.898 0.945 1.000

1272 1178 663 504 0

Figure 8 shows this excess property against the mole fraction of chloroform, together with literature values and calculated ones using the ideal associated solution model for comparison.

(1)

where c B0 = c B + cD + c Tr = c B + KDc BcA + KTrcABcA ⎫ ⎪ ⎪ ⎬ 0 cA = cA + c D + 2c Tr ⎪ ⎪ = cA + KDc BcA + 2KTrcABcA ⎭

c0B

(2)

c0A

and are the macroscopic molar concentrations of 2butanone and chloroform, respectively, in each highly diluted ternary mixture, and cAB, cA, and cB are the molar equilibrium concentrations of the complex, chloroform, and 2-butanone, respectively. The molar equilibrium concentrations of both monomer species (cA and cB) for eq 2 were calculated with Beer’s law from the absorbance values of the CH (3018 cm−1) and CO (1719 cm−1) stretching bands of the two monomer species in the infrared spectrum. The absorptivity for each solute was calculated from the absorbance values of the CH and CO stretching bands of highly diluted solutions of chloroform or 2-butanone in CCl4 whose concentrations are well-known and applying the Beer’s law again. The absorptivity values are (650 ± 10) dm2·mol−1 and (126 000 ± 1000) dm2·mol−1 for chloroform and 2-butanone, respectively. The KD and KTr values at T = 293.15 K, evaluated through eq 2, are (5 ± 1) × 10 L mol−1 and (4 ± 1) × 102 L mol−1, respectively

Figure 8. Excess molar enthalpy HE against the mole fraction of chloroform x1 of the chloroform + 2-butanone binary system at T = 303 K. ■, Experimental values; ○, from ref 6 at 308.15 K. Continuous line is the least-squares representation by means of eq 4. Dashed line is calculated values by means of eq 12. I, Error bars.

The excess molar enthalpy was fitted by means of a Redlich− Kister-type equation23 of the form HE/J·mol−1 = x1(1 − x1)[− 5400 − 1300(1 − 2x1) − 2200(1 − 2x1)2 + 3600(1 − 2x1)3 ] (4)

Here x1 is the mole fraction of chloroform. Numerical values of the coefficients were obtained from a least-squares analysis of the data. The number of coefficients was determined as the minimum number needed to adequately represent the data. 5126



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Equation 7 can be expressed

The significant digits were determined taking into account the error of each parameter. The standard deviation, σ, between the experimental and calculated values was defined as E E 2 1/2 σ = [∑ (Hexp . − Hcalc.) /(N − p)]

(1 − aA − aB)/(aBaA ) = KD + KTaA

If 2:1 complexes are also present, FA2B(aA) must be a straight line with KD intercept and slope KT. Figure 9 shows a straight line, and from this we obtained

(5)

where N and p are the numbers of experimental points and parameters, respectively. Calculated average standard deviation for eq 4 leads to σ = 40 J·mol−1. Figure 8 also shows that this binary system exhibits exothermic behavior with a minimum close to x1 = 0.5. This is in agreement with the inferences reported in a previous work for the same system,6 indicating that the interactions among different molecules are stronger than among those in the pure liquids. The presence of a minimum in the isotherm of HE close to equimolar concentration, together with a maximum in the viscosity deviation at the same concentration,4 is macroscopically consistent with a 1:1 intermolecular complex formation for this binary system. However, the isotherms for the excess molar volume4 show minima at a mole fraction of chloroform approximately equal to 0.66. This evidences that each excess property contributes different factors, and these excess macroscopic properties do not always provide a single way to infer the microscopic behavior of the mixture. 6.1. Ideal Associated Solution Model. The ideal associated solution model assumes that all deviations from ideality of the properties of solution are due to complex formation, with all activity coefficients equal to unity at all temperatures, pressures, and compositions. Therefore, in the chemical equilibrium represented by reactions 1 there are four distinct chemical species (A, B, AB, and A2B), which mix ideally. To confirm our conclusion, we use the McGlashan−Rastogi linearization test.24 In this test, two functions FAB and FA2B are defined as FAB = (1 − aA − aB)/aA

(6)

FA 2B = (1 − aA − aB)/(aA aB)

(7)

KD = (1.58 ± 0.05) = (39 ± 1) L mol−1

KT = (0.85 ± 0.09) = (53 ± 6) × 10 L mol−1

Figure 9. Plot of FA2B = (1 − aA − aB)/aA against aA.

Excess enthalpies are calculated from McGlashan−Rastogi’s theory6 HE = (1 − xA )zA(KDΔHD + KTΔHTzA ) /(1 + KDzA + KTzA2 )

aA = {(1 −

− VA )(P −

xA = [(1 + KD)zA + KTzA2(2 − z B)] /[1 + KDzA(2 − zA ) + KTzA2(3 − 2zA )]

7. CONCLUSIONS The Raman spectrum shows that two intermolecular complexes are present for this binary system, having an AB and A2B stoichiometric relationship. This conclusion was obtained by analyzing the Raman spectrum at three different concentrations of chloroform and 2-butanone, together with quantum chemical calculations with DFT procedures. Consequently with this statement, no other intermolecular complex was observed for the chloroform + 2-butanone binary mixture. This reveals that inferences done only on a macroscopic thermodynamic basis sometimes can be erroneous and require microscopic confirmation. Although no spectrum was recorded for the chloroform + acetone binary system, it is highly probable that this system also shows the same stoichiometric relationship between components for their intermolecular complexes. Furthermore, the ideal associated solution model is able to represent the experimental excess molar enthalpy, as can be

(8)

aB = (yA P /PBo)exp{(BBB − VB)(P − PBo)/RT } exp{(1 − yA )2 Pδ /RT }

(9)

Here, yA is the mole fraction in the vapor phase of chloroform. P and Poi are the total pressure and the pure component vapor pressure, respectively, and Vi is the molar volume of component i. The value of δ is given by δ = 2BAB − BAA − BBB

(13)

The enthalpies of complex formation (ΔHD and ΔHT) were evaluated from two experimental heats of mixing data.

PAo )/RT }

exp{yA2 Pδ /RT }

(12)

where the stoichiometric mole fraction xA is related to the true mole fraction of chemical species A, zA, by

where a1 and a2 are the activities of components A (chloroform) and B (2-butanone) forming the binary mixture, respectively. Following McGlashan and Rastogi,7 these activities were calculated from yA )P /PAo }exp{(BAA

(11)

(10)

where BAA and BBB are the second virial coefficients of pure components, and BAB is the cross second virial coefficient. These virial coefficients at 303.15 K were estimated by the method of Hayden and O’Connell25 and the Gómez Marigliano et al.4 data. They are: BAA, −1141.176 cm3 mol−1; BBB, −2222.731 cm3 mol−1; and BAB, −2264.939 cm3 mol−1. 5127



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seen in Figure 8, and leads to equilibrium constant values which compare well with that calculated from infrared spectroscopy. The reported values of HE calculated in this work are less exothermic than those for the chloroform + acetone binary system,10,11 probably due to a greater steric hindrance for 2butanone compared with acetone. Figure 8 also shows a serious discrepancy between our results and those reported by Nagata et al.6 for the chloroform + 2butanone binary system at 308.15 K, not justified by the small temperature difference between their results and ours. However, taking into account the previous paragraph, we conclude that the results of Nagata et al.6 are not correct because they are sensibly more negative than those for the chloroform + acetone binary system, whereas ours are only a little less exothermic, as expected.

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ASSOCIATED CONTENT

S Supporting Information *

Figure SI-1 shows the curve FT-Infrared spectrum of the CO stretching region of chloroform and butanone in CCl4, together with a given ternary mixture. Figures SI-2 shows the FTInfrared spectrum of the CH stretching region of chloroform and butanone in CCl4, together with a given ternary mixture. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are grateful for the support provided by Consejo de Investigaciones de la Universidad Nacional de Tucumán of Argentina (Project n° 26/E417). We thank Dr. Eduardo L. Varetti (CEQUINOR, Universidad Nacional de La Plata of Argentina) for infrared and Raman laboratory facilities. M.L. Roldán. also acknowledges a MAEC-AECID postdoctoral fellowship from the Ministerio de Asuntos Exteriores.

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REFERENCES

(1) Sólimo, H. N.; Gómez Marigliano, A. C. Excess Properties and Vapor−Liquid Equilibrium Data for the Chloroform + Tetrahydrofuran Binary System at 30 °C. A. C. J. Solution Chem. 1993, 22, 951−961. (2) Savchenko, V. V.; Levin, V. V.; Shakhparonov, M. I. Dielectric Properties of Methyl Ethyl Ketone−Chloroform Solutions. J. Struct. Chem. 1972, 12, 999−1002. Translated from: Zh. Strukturnoi Khim. 1971, 12, 1086−1091. (3) Barta, L.; Kooner, Z. S.; Hepler, L. G. Thermodynamics of Complex Formation in Chloroform and 1,4-Dioxane. Can. J. Chem. 1989, 67, 1225−1229. (4) Clará, R. A.; Gómez Marigliano, A. C.; Sólimo, H. N. Density, Viscosity, Vapour−Liquid Equilibrium, Excess Molar Volume, Viscosity Deviation, and Their Correlations for Chloroform + 2Butanone Binary System. J. Chem. Eng. Data 2006, 51, 1473−1478. (5) Grolier, J. P. E.; Roux - Desgranges, G.; Kooner, Z. C.; Smith, J. F.; Hepler, L. G. Thermal and Volumetric Properties of Chloroform + Benzene Mixtures and the Ideal Associated Solution Model of Complex Formation. J. Solution Chem. 1987, 16, 745−752. (6) Ohta, T.; Asano, H.; Nagata, I. Thermodynamic Study of Complex Formation in Four Binary Liquid Mixtures Containing Chloroform. Fluid Phase Equilib. 1980, 4, 105−114. 5128


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