Article pubs.acs.org/jced
Thermodynamic Studies of Molecular Interactions in Mixtures Containing Tetrahydropyran, 1,4-Dioxane, and Cyclic Ketones Vinod Kumar Sharma,* Sunita Malik, and Subhash Solanki Department of Chemistry, M. D. University, Rohtak, Haryana, India S Supporting Information *
ABSTRACT: The densities ρ, speeds of sound u, and molar heat capacities CP of tetrahydropyran or 1,4-dioxane (1) + cyclohexanone or cycloheptanone (2) mixtures at 293.15, 298.15, 303.15, and 308.15 K, and excess molar enthalpies, HE at 308.15 K and atmospheric pressure 0.1 MPa have been measured over the entire composition range. The excess molar volumes VE, excess isentropic compressibilities κES , and excess heat capacities, CEP of the studied mixtures have been determined using the measured experimental data. The observed VE, κES , HE, and CEP data have been tested in terms of graph theory. The analyses of VE data by graph theory suggest that while tetrahydropyran or 1,4-dioxane exists as a mixture of monomer and dimer; cyclohexanone or cycloheptanone exists as a mixture of open and cyclic dimer. Further, (1 + 2) mixtures are characterized by interactions between oxygen atom/s and hydrogen atom of tetrahydropyran or 1,4-dioxane with hydrogen atom/s and oxygen atom of cyclohexanone or cycloheptanone. The quantum mechanical calculations and analysis of IR spectral data of (1 + 2) mixtures also support this viewpoint. It has been observed that graph theory correctly predicts the VE, κES , HE, and CEp data of the present mixtures.
1. INTRODUCTION The thermodynamic properties of liquid mixtures are important for the convenient design of industrial processes involving chemical separation, mass transfer, heat transfer, and fluid flow.1−5 Such properties provide insight about the state of liquids in pure as well as the mixed state along with the interactions operating among the constituent molecules and can also be used for the development or testing of theories/ models describing the thermodynamic behavior of mixtures.6−8 Cyclic ethers have attracted interest as a model substance for biosystems, separation techniques, chemical reactions such as in synthetic and natural resin, extraction of animal and vegetable oil; as a cosolvent in printing inks; and as dispersing agent in textile chemistry.9−11 Tetrahydropyran is a liquid for next generation heterocyclic oxygenated fuels.12 It is widely used in petrochemical and pharmaceutical industries and also for the synthesis of biologically active compounds with analgesic, antiinflammatory, or cytotoxic activity.13−17 1,4-Dioxane is a model molecule to correlate its physicochemical properties with polyethers possessing an OCCO unit.18 1,4-Dioxane has also been used as a model cosolvent for solubility studies, as it acts as a hydrogen acceptor due to its two cyclic ether groups.19−21 Cyclic ketones are a class of chemical compounds containing a carbonyl group which in turn is part of several biologically important molecules such as proteins, lipids, and hormones. These liquids have a variety of applications such as insecticides, fungicides, lacquers, oils, resins, flavors, and fragrances.22−24 Cyclohexanone is used as a solvent for vinyl resins, crude rubber, waxes, fats, and shellac. It is also used as raw materials © 2017 American Chemical Society
for adipic acid synthesis, as well as precursors of nylon-6 polymers.25,26 This paper is a part of an ongoing project to measure and characterize the properties of mixtures containing cyclic ethers, ketones, and cyclic ketones. In continuation of our work on thermodynamic properties of multicomponent liquid mixtures containing cyclic ether as one of the component,27−29 we report here densities, ρ, speeds of sound, u, and heat capacities, CP, at 293.15, 298.15, 303.15, and 308.15 K and excess molar enthalpies, HE of the tetrahydropyran 1,4-dioxane or (1) + cyclohexanone or cycloheptanone (2) mixtures at 308.15 K.
2. EXPERIMENTAL SECTION Tetrahydropyran (THP) (Fluka, mass fraction, 0.987, GC), 1,4dioxane (D) (Fluka, mass fraction, 0.983, GC), cyclohexanone (CHO) (Fluka, mass fraction, 0.99, GC), cycloheptanone (CHPO) (Fluka, mass fraction, 0.98, GC) were purified by standard methods.30,31 Details of the chemical source along with their purification method, initial and final purity are presented in Table 1. The densities ρ and speeds of sounds u of the purified liquids were measured by using a density and sound analyzer (Anton Paar DSA-5000) in the manner as described elsewhere.32,33 The measurements were based on measuring the period of oscillation of a vibrating U-shaped hollow tube filled with Received: July 8, 2016 Accepted: January 16, 2017 Published: January 30, 2017 623
DOI: 10.1021/acs.jced.6b00606 J. Chem. Eng. Data 2017, 62, 623−632
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Table 1. Details of Studied Chemicals, CAS Number, Source, Purification Method, Initial Purity, Final Purity, and Analysis Method
a
chemical name
CAS number
source
initial mass fraction purity
purification method
final mass fraction purity
analysis method
tetrahydropyran 1,4-dioxane cyclohexanone cycloheptanone
142-68-7 123-91-1 108-94-1 502-42-1
Fluka Fluka Fluka Fluka
0.987 0.983 0.99 0.98
vacuum distillation fractional distillation fractional distillation fractional distillation
0.993 0.991 0.994 0.989
GCa GC GC GC
Gas chromatography.
Table 2. Comparison of Experimental Densities ρ, Speeds of Sound u, and Heat Capacities CP of Pure Components with Their Literature Values at Temperature from T = 293.15, 298.15, 303.15, and 308.15 K and Atmospheric Pressure (p = 0.1 MPa)a ρ/kg·m−3 components
T/K
exp
lit.
expt
tetrahydropyran
293.15 298.15
884.23 879.09
1293.0 1269.7
303.15
873.91
308.15
868.75
293.15
1033.59
298.15
1027.94
303.15
1022.28
883.7934 879.1635 879.2036 873.9534 874.2036 869.2036 868.8039 1033.5010 1033.6140 1027.8510 1027.9241 1027.9256 1022.1910
308.15
1016.59
293.15
947.38
298.15
942.92
303.15
938.07
1016.5210 1016.5941 947.3945 946.4446 942.9045 942.7647 942.0456 938.0545 940.339 933.1845 933.847 951.86948 947.63348 943.38048 939.13448
1,4-dioxane
cyclohexanone
cycloheptanone
a
u/m·s−1
308.15
933.19
293.15 298.15 303.15 308.15
951.85 947.62 943.38 939.14
CP/J·K−1·mol−1 lit. 1269.3035 1270.0037
expt 148.03 149.68
lit.
1246.7
151.18
149.8035 149.6038 150.234
1224.3
153.01
152.634
1367.8
1367.1510
151.62
1346.0
152.76
152.7744 150.7556
153.92
154.0244
1302.5
1345.0410 1345.5042 1344.7356 1324.0043 1325.0037 1301.0910
1431.2
1431.945
176.17
176.1945
1415.5
1414.845 1407.6056
178.27
178.3745 177.9722 177.9756
1324.4
1395.1
155.09
180.38
1375.1
1395.645 1375.845
182.46
1477.3 1455.0 1432.4 1409.6
1477.2948 1455.0248 1432.4648 1409.7348
201.11 202.01 203.21 204.51
180.4645 182.3945
202.0849
Standard uncertainties u are u(T) (DSA) = 0.01 K; u(ρ) = 0.5 kg·m−3; u(u) = 0.5 m·s−1, ur(CP) = 0.008; u(T) (DSC) = 0.02 K; u(p) = 0.01 MPa.
temperature control peltiercooler and works between 228.15 to 393.15 K. A constant sweeping of nitrogen gas for about 4 h (0.3−0.4 MPa pressure) was supplied to avoid steam condensation in the calorimetric walls, and 0.08 MPa pressure of nitrogen gas was maintained after this period. The calibration of equipment was done by the Joule effect method which in turn is controlled by SETARAM software and checked by measuring the heat capacity of naphthalene. The measured heat of fusion for naphthalene (148.39 J·g−1) was comparable to its literature value (148.7 J·g−1).52 The heat of fusion of naphthalene has been measured at 298 K and atmospheric pressure and the uncertainty of heat of fusion of naphthalene is within the range 0.001−0.002.52 For the measurement of HE of (1 + 2) binary mixtures, a known amount of liquids 1 and 2 was taken in the lower and upper chamber of the mixing batch cell. The information regarding (i) mixture temperature at which investigations are carried out and (2) time of isothermal level at
liquid sample. The equipment was calibrated with double distilled, freshly degassed water at T = 293.15 K. The desired temperature of the cell was set in the temperature setting range which was controlled by built-in Peltier thermostat. The standard uncertainties in densities and speeds of sound measurements are 0.5 kg·m−3 and 0.5 m·s−1, respectively. The working frequency for density and sound analyzer is 3 MHz.33 The standard uncertainty in temperature measurement is 0.01 K. The measured densities ρ, speeds of sound u, and heat capacities CP, of purified liquids at studied temperatures are listed in Table 2 and also compared with the literature values.34−49,56 The excess molar enthalpies, HE, heat capacities, CP of (1 + 2) mixtures and molar heat capacities of pure liquids were measured as a function of composition in a microdifferential scanning calorimeter [model-μ DSC 7 EVO] that has been described elsewhere.50,51 The calorimeter uses a double624
DOI: 10.1021/acs.jced.6b00606 J. Chem. Eng. Data 2017, 62, 623−632
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thermal expansion coefficient respectively of pure component (i) (i = 1 or 2). The α values for liquids were predicted by utilizing their density values at various temperatures in the manner described elsewhere.54 The excess molar enthalpies HE were directly provided by microdifferential scanning calorimeter. The excess properties XE (X = V, κS, or H or CP) for the present (1 + 2) mixtures (reported in Tables S1−S3 and presented graphically in Figures 1−4 respectively) were fitted to Redlich−Kister equation55
the desired temperature on the experimental setup screen (desired by the software suggested by M/S SETARAM) was then filled. The stability in the calorimetric signal was indicated by consistent heat flow and temperature line. The temperature and isothermal level was maintained by software. After attaining the stability, the knob of the upper cell of the mixing batch cell was pressed for mixing the liquids. After the isothermal level time, the data were automatically transferred to the experimental result tab and a graph was obtained of heat flow vs time. The relative standard uncertainty in the measured HE is 0.01. The heat capacity of a liquid was measured in a standard batch cell (Hastalloy C276) composed of a cylinder of 6.4 mm of internal diameter and 19.5 mm height and had a capacity of containing 1 cm3 of a liquid. The reference experimental cell was filled with water (equivalent to the mass of liquid in a standard batch cell). For a scanning sequence the initial and final temperatures were supplied along with heating rate of 0.4 K·min−1. The reliability of the calorimeter was checked by measuring heat capacities (listed in Table 2) for purified liquids. The mole fractions for the mixtures were obtained with uncertainty of 1× 10−4 from the measured apparent masses of the components. All the mass measurements were made on an electric balance (Mettler AX-205 Delta Range) with an uncertainty of 10−5 g. The relative standard uncertainty in the measured CP value is 0.008. The samples of binary mixtures for the IR studies were prepared by mixing components in 1:1 (w/w) and their IR spectra were recorded on NICOLET iS50 FT-IR spectrometer supplied by Thermo Fisher (U.S.A).
X E(X = V orκSorH orC P) = x1(1 − x1)[X (0) + X (1)(2x1 − 1) + X (2)(2x1 − 1)2 ]
3. RESULTS The experimental results of the densities,ρ, speeds of sounds u, heat capacities CP, and excess molar enthalpies HE of THP or D (1) + CHO or CHPO (2) mixtures at the temperatures under investigation are reported in Tables S1−S3. The excess molar volume VE, isentropic compressiblities κS, excess isentropic compressiblities κSE, and excess heat capacities CPE were calculated from the experimental data as follows:
Figure 1. Excess molar volumes V E at 308.15 K for (I) tetrahydropyran (1) + cyclohexanone (2) expt (red ■); graph (red ); (II) tetrahydropyran (1) + cycloheptanone (2) expt (green ●); graph (green ); (III) 1,4-dioxane (1) + cyclohexanone (2) expt (blue ▲); graph (blue ); (IV) 1,4-dioxane (1) + cycloheptanone (2) expt (pink ★); graph (pink ). VE at 298.15 K for (V) 1,4dioxane (1) + cyclohexanone (2) expt (aqua ); (VI) 1,4-dioxane (1) + cyclohexanone (2) expt (maroon ).56
2
VE =
∑ xiM i(ρ−1 − ρi−1) i=1
(1)
1 ρu 2
(2)
κSE = κS − κSid
(3)
κS =
The adjustable binary parameters Xn (n=0−2) (X = V or κS or H or CP) were determined by fitting eq 6 to the experimental results using a least-squares regression method. The standard deviations σ(XE) in XE(X = V, κS, H, or CP) were calculated by using E E 2 ⎫0.5 ⎧ ⎪ ∑ (X(expt) − X {calcequation(6)}) ⎪ ⎬ σ (X ) = ⎨ ⎪ ⎪ (m − n) ⎩ ⎭ E
2
C PE = C P −
∑ xi(CP)i i=1
(4)
(7)
where m is the number of data points and n is the number of adjustable parameter. The fitted values of adjustable parameters along with standard deviations are summarized in Table 3.
κidS
The values were obtained by using the Benson and Kiyohara equation53 2 2 ⎡ (∑i = 1 φiαi)2 Tviαi2 ⎤ ⎢ ⎥ φ κ + − T ( x v ) ∑ i⎢ S,i ∑ ii 2 C P,i ⎥⎦ (∑i = 1 x iC P,i) ⎣ i=1 i=1
4. DISCUSSION The VE and κES data of D (1) + CHO (2) mixtures at 298.15 K are available in the literature.56 The general shapes of VE and κES curves of this mixture are similar to those at 298.15 K. Our VE and κES values at equimolar composition differ than values reported in the literature by a maxima of 0.008 cm3·mol−1 and 0.31 TPa−1, respectively. The measured CEP values for D (1) + CHO (2) mixtures at 298.15 K differ by 0.049 J·mol−1 than literature values.56 Further, the HE values of tetrahydropyran or
2
κSid =
(6)
(5)
where x1, x2 are mole fractions; M1, M2 are molar masses; ρ1, ρ2 are densities, (C P) 1,(C P) 2 are heat capacities of pure components and ρ, u, and CP are densities, speeds of sound, and heat capacities of the mixtures. The φi, κS,i, ν1, and α1 are volume fraction, isentropic compressibility, molar volume, and 625
DOI: 10.1021/acs.jced.6b00606 J. Chem. Eng. Data 2017, 62, 623−632
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Figure 2. Excess isentropic compressibilities, κES , at 308.15 K for (I) tetrahydropyran (1) + cyclohexanone (2) expt (red ■); graph (red ); (II) tetrahydropyran (1) + cycloheptanone (2) expt (green ●); graph (green ); (III) 1,4-dioxane (1) + cyclohexanone (2) expt (blue ▲); graph (blue ); (IV) 1,4-dioxane (1) + cycloheptanone (2) expt (pink ★); graph (pink ). κES at 298.15 for (V) 1,4-dioxane (1) + cyclohexanone (2) expt (aqua ) ;(VI) 1,4-dioxane (1) + cyclohexanone (2) expt (maroon ).56
Figure 4. Excess heat capacities, C PE at 308.15 K for (I) tetrahydropyran (1) + cyclohexanone (2) expt (red ■); graph (red ); (II) tetrahydropyran (1) + cycloheptanone (2) expt (green ●); graph (green ); (III) 1,4-dioxane (1) + cyclohexanone (2) expt (blue ▲); graph (blue ); (IV) 1,4-dioxane (1) + cycloheptanone (2) expt (pink ★; graph (pink ). CEP at 298.15 for (V) 1,4-dioxane (1) + cyclohexanone (2) expt (aqua ); (VI) 1,4-dioxane (1) + cyclohexanone (2) expt (maroon ).56
The VE,κES data of THP (1) + CHO or CHPO (2) are negative over the entire range of mole fraction. However, VE and κES values for D (1) + CHO or CHPO (2) mixtures are positive over the entire range of composition, and for an equimolar mixture they vary as CHPO > CHO. The HE values of THP or D (1) + CHO or CHPO (2) mixtures are positive over the entire composition, and for an equimolar composition of THP (1) + CHO or CHPO (2), and D (1) + CHO or CHPO (2) they follow the order CHPO > CHO and CHO > CHPO, respectively. The CEP values of THP (1) + CHO or CHPO (2) mixtures are positive across the full range of composition and for an equimolar mixture vary in the order CHO > CHPO. While CEP data for D (1) + CHPO (2) mixtures are positive, those for D (1) + CHO (2) are negative over the entire mole fraction range and for an equimolar composition follow the sequence CHPO > CHO. The HE values are due to the cumulative effect of two opposite effects, namely, (i) break down of dipole−diploe interactions in cyclic ethers and cyclic ketones and (ii) molecular interactions among the constituent molecules. The HE data of THP or D (1) + CHO or CHPO (2) mixtures may be rationalized if it is assumed that the (1 + 2) mixtures formation comprises the following processes: (i) THP or D or CHO or CHPO are characterized by dipole−dipole interactions; (ii) interaction between 1 and 2 weakens 1−1 and 2−2 interactions to form their respective molecules; and (iii) there is interaction between hydrogen and oxygen atoms of THP or D with oxygen and hydrogen atoms of CHO or CHPO to yield a 1:2 molecular complex. Since HE is a cumulative effect of factors (i)−(iii), the positive HE values for the investigated mixtures suggest that the contribution due to factor (ii) dominates over the contributions due to factors (i) and (iii). The HE values of the THP (1) + CHO (2) mixture are less than that of the THP (1) + CHPO (2) mixture. This may occur because CHO is more basic in nature and possesses the chair form with almost no strain, which in turn leads to strong interactions between THP (1) + CHO (2) in comparison to the THP (1) + CHPO (2) mixture. However, HE values of the D (1) + CHO (2) mixture are higher than those of the D (1) +
Figure 3. Excess molar enthalpies, HE at 308.15 K for (I) tetrahydropyran (1) + cyclohexanone (2) expt (red ■); graph (red ); (II) tetrahydropyran (1) + cycloheptanone (2) expt (green ●); graph (green ); (III) 1,4-dioxane (1) + cyclohexanone (2) expt (blue ▲); graph (blue ); (IV) 1,4-dioxane (1) + cycloheptanone (2) expt (pink ★); graph (pink line);HE at 298.15 K (V) tetrahydropyran (1) + cyclohexanone (2) expt (yellow );57 (VI) 1,4-dioxane (1) + cyclohexanone (2) expt (aqua );56 (VII) 1,4dioxane (1) + cyclohexanone (2) expt (maroon ).58
1,4-dioxane (1) + cyclohexanone (2) mixtures have been reported in the literature56−58 at 298.15 K. The experimental HE value of THP (1) + cyclohexanone (2) mixture at 308.15 K and equimolar composition are higher (28.9 J·mol−1) than the literature value57 reported at 298.15 K. However, the measured HE values for 1,4-dioxane (1) + cyclohexanone (2) mixture at 308.15 K and equimolar composition are higher (12.6, 4.56 and J·mol−1) than literature values56−58 reported at 298.15 K. The comparison between experimental and literature values of VE, κES , HE, and CEP has been shown in Figures 1−4, respectively. We have found no references on VE, κES , HE, and CEP of the remaining mixtures for comparison with measured results. 626
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Table 3. Binary Adjustable Parameters, Xn (X = V or κS or H or CP) (n = 0 to 2) of eq 6 with Their Standard Deviations, σ(XE) (X = V or κS or H or CP) of VE, κES , HE, and CEP at T = 293.15, 298.15, 303.15, and 308.15 K parameter
T/K = 293.15
T/K = 298.15
T/K = 303.15
Tetrahydropyran (1) + Cyclohexanone (2) −1.676 −1.814 −1.993 V(0) V(1) −0.406 −0.434 −0.487 V(2) −0.132 −0.118 −0.182 σ(VE)/cm3·mol−1 0.001 0.001 0.001 κ(0) −9.39 −9.91 −10.42 S κ(1) 1.37 1.68 1.83 S κ(2) −2.27 −3.67 −4.54 S σ(κES )/TPa−1 0.01 0.01 0.01 H(0) H(1) H(2) σ(HE)/J·mol−1 C(0) 40.44 42.62 45.16 P C(1) 4.08 4.25 4.24 P C(2) −15.24 −10.16 −5.67 P σ(CEP)/J·K−1·mol−1 0.02 0.02 0.03 Tetrahydropyran (1) + Cycloheptanone (2) V(0) −1.844 −2.526 −2.267 V(1) −0.429 −0.548 −0.615 V(2) −0.085 −0.281 −0.241 σ(VE)/cm3·mol−1 0.001 0.001 0.001 κ(0) −12.353 −13.122 −13.947 S κ(1) 1.017 1.109 0.545 S κ(2) −2.436 −4.039 −5.391 S σ(κES )/TPa−1 0.01 0.01 0.01 H(0) H(1) H(2) σ(HE)/J·mol−1 C(0) 18.53 19.59 20.81 P C(1) 7.73 8.68 8.92 P C(2) −1.86 0.05 2.74 P σ(CEP)/J·K−1·mol−1 0.01 0.01 0.01
T/K = 308.15
parameter
T/K = 293.15
T/K = 298.15
T/K = 303.15
1,4-Dioxane (1) + Cyclohexanone (2) 1.101 1.059 1.021 V(0) V(1) −0.005 −0.009 −0.015 V(2) 0.014 −0.033 0.040 σ(VE)/cm3·mol−1 0.001 0.001 0.001 κ(0) 25.85 24.30 22.83 S κ(1) 4.54 4.52 4.19 S κ(2) 3.36 2.49 0.58 S σ(κES )/TPa−1 0.01 0.01 0.01 H(0) H(1) H(2) σ(HE)/J·mol−1 C(0) −6.39 −6.19 −6.01 P C(1) 1.08 1.05 1.01 P C(2) −1.20 −1.13 −0.93 P σ(CEP)/J·K−1·mol−1 0.01 0.01 0.01 1,4-Dioxane (1) + Cycloheptanone (2) V(0) 1.242 1.283 1.361 V(1) 0.393 0.392 0.381 V(2) −0.134 0.153 0.298 σ(VE)/cm3·mol−1 0.001 0.001 0.001 κ(0) 13.49 12.62 11.74 S κ(1) −1.36 −1.42 −1.52 S κ(2) −1.30 −2.01 −2.75 S σ(κES )/TPa−1 0.01 0.01 0.01 H(0) H(1) H(2) σ(HE)/J·mol−1 C(0) 40.64 43.89 48.06 P C(1) 3.05 3.27 3.46 P C(2) −6.27 −3.86 −4.04 P σ(CEP)/J·K−1·mol−1 0.03 0.03 0.03
−2.061 −0.547 −0.232 0.001 −11.01 2.26 −5.19 0.01 457.1 −45.8 −59.9 0.9 47.58 4.72 −1.79 0.03 −2.439 −0.719 −0.383 0.001 −14.804 0.172 −6.616 0.01 492.6 −46.1 200.0 1.1 22.03 9.25 5.08 0.01
T/K = 308.15 0.979 −0.016 −0.062 0.001 21.07 4.13 −0.34 0.01 1152.3 215.9 195.5 2.5 −5.82 1.00 −0.70 0.01 1.416 0.378 0.491 0.001 10.97 −1.61 −3.37 0.01 492.6 −46.1 200.0 1.1 51.14 4.38 0.36 0.03
viewpoint.64 The positive CEP values for THP (1) + CHO or CHPO (2) or D (1) + CHPO (2) mixtures suggest that the contribution to CEP due to formation of molecular complexes possessing nonrandom structure dominates over the contribution to CEP due to the breaking of associated entities. However, the opposite is the viewpoint for the D (1) + CHO (2) mixture. The CEP values for THP (1) + CHPO (2) mixtures are lower than those for D (1) + CHPO (2) mixtures. This may be due to strong dipole−dipole interaction in THP as compared to that in D which results in less mixing and hence the least nonrandomness. The HE data for these mixtures also support this viewpoint. Further, higher CEP data for THP (1) + CHO (2) in comparison to the D (1) + CHO (2) mixture suggests a strong interaction between THP and CHO which in turn leads to form a nonrandom structure in the mixed state. The (∂CEP/ ∂T) for THP (1) + CHO or CHPO (2) is positive which may be due to the destruction of the dipole−dipole interaction of THP or CHO or CHPO, which makes the interaction between like molecules more difficult than between unlike molecules and makes a more compact structure. However, the (∂CEP/∂T) for D (1) + CHO or CHPO (2) mixture is negative. The decrease in CEP values with increase in temperature may be associated with a decrease of molecular interactions between
CHPO (2) mixture. This can be explained by arguing that on average somewhat less mixing occurs in the THP (1) + CHO (2) mixture, because of strong dipole−dipole interactions with themselves in CHO. The HE values of THP (1) + CHO (2) mixtures are less than those for D (1) + CHO (2). This may be due to the high dipole moment and dielectric constant of THP59,60 (μ= 1.87 D, ε = 5.38) as compared to those of D (μ= 0.45 D, ε = 2.21)61−63 which in turn results in strong interactions between THP and CHO. However, HE values for the THP (1) + CHPO (2) mixtures are higher than those for the D (1) + CHPO (2) mixture. This may be due to strong dipole−dipole interactions in THP as compared to D in the pure state, and thus contribution to HE due to factor (ii) will be higher in the THP (1) + CHPO (2) in comparison to the THP (1) + CHO (2) mixture. The CEP data reflect the variation of the mixture entropy against that of the ideal mixture, which is due to the cumulative effect of the rupture of associated entities to yield an increase in randomness and interactions among the components of the mixtures to form molecular complexes possessing nonrandom structure. The HE values for THP (1) + CHO or CHPO (2) or D (1) + CHPO (2) mixtures at equimolar composition lie in the range of 107−288 J·mol−1 which in turn supports our 627
DOI: 10.1021/acs.jced.6b00606 J. Chem. Eng. Data 2017, 62, 623−632
Journal of Chemical & Engineering Data
Article
To extract information about the state of CHO or CHPO in THP or D mixtures, we assumed that these mixtures may have molecular entities XI-XII, XII-XIV, respectively, and their (3ξ2′ )m values were estimated. In evaluating (3ξ2′ )m values for these molecular entities, it was next assumed that (i) molecular entities XI−XII are characterized by interactions between the oxygen and hydrogen atom of THP with the hydrogen and oxygen atom of CHO or CHPO; and (ii) XIII−XIV are characterized by interactions between oxygen and hydrogen atoms of D with the hydrogen and oxygen atoms of CHO or CHPO. The (3ξ2′ )m values for such molecular entities were then calculated to be 1.606, 1.606, 1.928, and 1.928, respectively. The (3ξ2)m values of 1.897, 2.056, 1.897, and 2.056 for CHO or CHPO in (1 + 2) mixtures (Table S5) support the presence of molecular entities XI−XII and XIII−XIV. The postulation of molecular entities XI−XIV then suggests that there must be a change in (C−O); (C−H) vibrations of THP or D and (C O); (C−H) vibrations of CHO, CHPO on the addition of (1) to (2) in (1 + 2) mixtures. It was observed that THP, D, CHO, and CHPO in their pure state showed characteristic vibrations70 at 1091, 1083 cm−1 (C−O vibration in THP and D); 2753, 2754 cm−1 (C−H vibrations in THP and D);71,72 1714, 1694 cm−1 (CO vibrations in CHO and CHPO); 2938, 2948 cm−1 (C−H vibrations of CHO and CHPO).73 However, characteristics vibrations for equimolar (1 + 2) mixtures were observed at 1121, 1112; 1123,1122 cm−1 (C−O vibration for THP or D in THP or D (1)+ CHO or CHPO (2) mixtures); 2755, 2757; 2749, 2752 cm−1 (C−H vibrations for THP or D in THP or D (1)+ CHO or CHPO (2) mixtures); 1712,1702; 1701, 1702 cm−1 (CO vibration or CHO or CHPO in THP or D (1) + CHO or CHPO (2) mixtures); and 2922, 2931; 2959, 2928 cm−1 (C−H vibration of CHO or CHPO in THP or D (1)+ CHO or CHPO (2) mixtures). The analysis of IR spectral data thus lends additional support to the existence of molecular entities XI−XIV in the studied mixtures. Quantum mechanical calculations using density functional theory74−76 were performed to estimate internuclear distances between the interacting atoms in molecular entities I−X in the pure states and XI−XIV in mixed states. These distances were estimated to confirm the presence of molecular entities in pure and mixed states. For this purpose, all quantum mechanical calculations were carried with the Gaussian program package 09.77 The full optimization of the structure of molecular entities I−XIV were carried out on the B3LYP/6-311++G (d, p) level of theory.77,78 The various internuclear distances among interacting atoms in the investigated molecular entities are presented in Scheme 1. The internuclear distances of 3.93 Å, 4.62 Å between carbon and oxygen atoms of THP (molecular entity II); 3.64 Å, 3.74 Å between carbon and oxygen atoms of D (molecular entity IV); 3.19 Å between carbon and oxygen atoms of CHO (molecular entities VI−VII); 3.43 Å between carbon and oxygen atoms of CHPO (molecular entities IX-X) suggest that molecular entities THP (II), D (IV) exist as dimers and CHO (molecular entities VI−VII) as well as CHPO (molecular entities IX−X) exist as a mixture of open and cyclic dimers. The internuclear distances between (i) hydrogen and oxygen atoms of THP or D with oxygen and hydrogen atoms of CHO; (ii) hydrogen and oxygen atoms of THP or D with oxygen and hydrogen atoms of CHPO were calculated to be 2.73, 3.16, 2.62, 2.38, 2.44, 2.44, 5.22, and 2.58, 2.39, 5.46 Å, respectively. These internuclear distances between interacting atoms in the molecules support the existence of molecular
unlike molecules in comparison with like molecules in the mixed state. The VE data for the investigated mixtures suggests that THP or D gives a relatively more packed structure in CHPO as compared to CHO. The VE, κES , HE, and CEP data were next tested in terms of graph theory.
5. GRAPH THEORY 5.1. Excess Molar Volumes. Graph theory deals with the topology of the constituent molecules. Topological indices are powerful tools65 for predicting physical, biological, and pharmacological properties of organic compounds (solids, liquids). These indices can be derived from molecular structure and thus provide a simple and forward method for the prediction of property. Singh et al.66,67 have advocated the use of connectivity parameters of the third degree of a molecule (3ξ) to obtain thermodynamic properties such as VE, κES , HE, CEP, and GE liquid mixtures. According to graph theory, excess molar volume VE is given by68 2
V E = α12[∑ xi(3ξ i)m i=1
−1
2
−
∑ xi(3ξi)m i=1
−1
] (8)
where x1 is the mole fraction of component (1). The (3ξi) (i = 1 or 2); (3ξi)m (i = 1 or 2) are connectivity parameters of components 1 and 2 in the pure and mixed state and are defined by 3
ξ=
∑ m
