Influence of Solvent Nature on the Solubility of Halogenated Alkanes

Article pubs.acs.org/jced

Influence of Solvent Nature on the Solubility of Halogenated Alkanes Marina Prezhdo,† Valentina Zubkova,‡ and Victor Prezhdo*,‡ †

Department of Chemistry, University of Rochester, Rochester, New York 14627, United States Institute of Chemistry, Jan Kochanowski University, 15G Swietokrzyska Str., 25-406 Kielce, Poland

‡

ABSTRACT: The solubility of 19 halogenated alkanes was measured in polar and nonpolar organic solvents using a dynamic method that produces more precise measurements than static methods. The solutions were analyzed with gas chromatography. A discrete-continuum solvation model was applied to investigate the influence of the solvent nature on the solubility of the compounds studied. It was shown that universal interactions between the solvent and the solute molecules, including the dispersive, inductive, and dipole−dipole interactions, dominate the solvation process. The dependences ln x298 ∼ φα and ln x298 ∼ φμ were obtained between the solubility logarithms at 298 K (ln x298) and the parameters that determine the solute− solvent interactions for nonpolar (φα) and polar (φμ) solvents, respectively. The role of the cavity formation energy in the solvation process was demonstrated. Finally, the correlation ln x298 = f(V2) was suggested, where V2 is the volume of a solute molecule in the solution.

1. INTRODUCTION One of the most important chemical phenomena, solubility, continues to present theoretical challenges. Solubility theory has a long history, dating back to the 19th century. Notable milestones include the Henry law for solubility of gases, the Alekseev rules for liquid−liquid systems, including the laws governing the distribution of a substance between two liquids in equilibrium, and the Schroeder equation for solubility of a solid. The theory of regular solutions1,2 was developed in the 1950s and 60s. A number of scientists attempted to decompose the Hildebrand solubility parameter (δ) into several terms. Various decomposition schemes presented different viewpoints on the energy of mixing. Prausnitz and coauthors3,4 separated the solubility parameter into two components, and defined the nonpolar solubility parameter (δλ) and the polar solubility parameter (δτ). The polar and nonpolar parameters relate to the Hildebrand total solubility parameter (δ) as δ 2 = δλ 2 + δτ 2

scheme provides an improvement over the Hildebrand scheme. Still, both approaches are not completely accurate for predicting the solution thermodynamics for arbitrary systems. The expanded solubility parameters describing and correlating the solvating ability of liquids are based on a variety of chemical and physical properties. Although these parameters agree in their general trends, the specific order, for example, of solvent basicity depends on the system from which the scale is derived.6 The necessity of experimental determination of the majority of the proposed parameters, as well as their reference to ideal systems only, resulted in a large divergence of the theoretical and experimental data. The solubility of gases that do not interact with the solvent by a specific interaction, such as hydrogen bonding, decreases with growth in the solvent dielectric permittivity (ε). In many cases, this dependence is a straight line. For example, the solubility of a series of gases in aliphatic alcohols C1 to C8 with a normal structure may be described with the following equation:

(1)

ln x = A + B /ε

Here, δλ can be identified as a dispersive term, and δτ is interpreted as a polar orientation term. Hansen5 proposed a practical extension of the Hildebrand parameter method to polar and hydrogen-bonding systems. He assumed that the dispersion, polar, and hydrogen-bonding parameters could be used simultaneously and can be related by eq 2. δt 2 = δd 2 + δp2 + δ h 2

where x is the molar fraction of gas in solution. In ref 7, the following expression was proposed, allowing one to calculate the solubility of gases on the basis of the fiveparameter Koppel−Palm equation.8 ln x = A 0 + A1

n2 − 1 ε−1 + A2 + A3δ 2 + A4 B 2 ε + 2 1 n +2

+ A5ET

(2)

where δt is Hansen's total solubility parameter, δd is the dispersive term, δp is the polar term, and δh is the hydrogen-bonding term. The values of each component were determined empirically on the basis of many experimental observations. The Hansen © 2012 American Chemical Society

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Received: January 28, 2012 Accepted: May 30, 2012 Published: June 14, 2012 1945

dx.doi.org/10.1021/je300127e | J. Chem. Eng. Data 2012, 57, 1945−1952

Journal of Chemical & Engineering Data

Article

The expression takes into account polarizability f(n), polarity ψ(ε), and cohesion energy of a solvent δ2 = (ΔHvap − RT)/v, as well as the nucleophilicity parameter B and the electrophilicity parameter ET. The analysis of eq 4 shows that the expendable energy of cavity formation, related to the density of cohesion energy of a solvent, determines the gas solubility. The A3δ2 value has a positive contribution to ln x. This means that the closer the association of a solvent is, the more energy is needed for the cavity formation, and the smaller value of gas solubility one obtains. Therefore, for example, nonpolar gases are soluble in water or alcohols worse than in hydrocarbons, CCl4, and so forth. The use of linear solvation energy relationships (LSERs) to understand the types and relative strength of the intermolecular interactions that control retention and selectivity in various modes of chromatography was described in ref 9. The recent widely accepted symbolic representation of the LSER model, as proposed by Abraham et al.,10 is shown by the following equation: SP = c + eE + sS + aA + bB + vV

solubility.15 Hansen suggested that the cohesion energy (E) should be considered as a sum of the energies of the dispersive (Ed) and polar (Ep) interactions along with the energy of H-bond (Eh): E = Ed + Ep + E h

The analysis of the solvent−solute interactions is carried out based on classification according to the scheme:16 ΔE = ΔEi + ΔEij + ΔEjj

(8)

where i is used for a solute and j is for a solvent. The influence of dispersion forces on the solute−solvent interactions was analyzed in ref 17. The solution model based on dispersive, polar, acidic, and basic interactions was used to correlate the solubility of fullerene at 298 K in 55 solvents.18 A simple method was presented for the evaluation of the second cross-virial coefficients for the interactions.19 The general structure of the obtained semiempirical equation arose from a theoretical relationship valid for interactions between spherical nonpolar molecules. 1.2.1. Discrete-Continuum Model. In dilute solutions, every molecule of a solute in the first coordination sphere is surrounded by solvent molecules only; therefore, the energy of interaction between the molecules of a solute is very small (Figure 1).

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in which SP can be any free energy-related property. In studies on solubility, SP is often taken as ln x, where x is the molar fraction of a solute. The E, S, A, B, and V terms entering the above equation represent the effects of solute's polarizability, polarity, hydrogenbond donating ability, hydrogen-bond accepting ability, and molecular size, respectively, on the SP value. The e-, s-, a-, b-, and v-coefficients, along with the constant c, are determined via multiparameter linear least-squares regression analysis of a data set comprised of solutes with known E, S, A, B, and V values, spanning a sufficiently wide range in interaction strengths. The thermodynamic relationships connecting many phenomena of solubility were described in ref 11. The paper12 discusses how calorimetric information, including enthalpy and heat capacity changes in solution, can be derived from the solubility data of gases in liquids as a function of temperature. 1.1. Solubility of Liquids. The critical highest and lowest temperatures of mixing and the geometry of solvation shells were discussed in many works on the mutual solubility of liquids.13 The separation of a solution into two nonmixing phases depends on the physical-chemical properties of a solvent. The equilibrium constant describing the distribution of a substance between the two phases can be calculated with an equation similar to eq 4 and containing solvent properties:

Figure 1. Discrete-continuum model of interaction of a solute molecule (i) with solvent molecules (j) in a medium with dielectric permittivity ε.

The energy of universal interaction20 of any two molecules i and j in solution consists of the energies of dispersive interaction 3IiIj αiαj Edisp = 2 2(4πε) (Ii + Ij) R6 (9) dipole−dipole interaction

n2 − 1 ε−1 + a2 + a3δ 2 + a4B log K = a0 + a1 2 2ε + 1 n +2 + a5ET

(7)

Ed − d

μi2 μj2 2 = 3 (4πε)2 kTR6

and dipole−induced dipole interaction 1 Ed − id = (αiμj2 + αjμi2 ) (4πε)2 R6

(6)

1.2. Solubility of Solids. The processes taking place during the formation of liquid solutions of the electrolytes and nonelectrolytes have significantly different natures; therefore, the solubility of these two classes of solid compounds should be taken into consideration individually. Most quantitative dependences of solubility nonelectrolytes on solvent properties are derived using macroscopic characteristics of the solvent. The equations derived from the theory of regular solutions1,2 run into the difficulty of quantifying the solubility parameter δA2. Typically, this approach allows one to predict the character of changes in the solubility of nonelectrolytes in a range of solvents. The solubility of polymers in different solvents was studied14 from the practical point of view. The multiparameter form of the Hansen equation is often used to analyze the data on polymer

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where I is the ionization potential, α is polarizability, μ is the molecular dipole moment, ε is the dielectric permittivity of the solution, and R is the distance between the interacting molecules. Then, the energy of interaction of a solute molecule with solvent molecules can be expressed by eq 12 2 2 ⎡ 1 ⎛⎜ Z ⎞⎟ ⎢ 3 IiIj 2 μi μj ΔE = ⎜ 6 ⎟ ⎢φdisp 2 I + I αiαj + φd − d 3 kT (4πε)2 ⎝ R1,2 ⎠⎣ i j 1

⎤ + ϕd − id(μi2 αj + μj2 αi)⎥ ⎥⎦ 1946

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Article

The number of solvent molecules surrounding the solute molecule in the first coordination sphere Z is expressed as Z = 1/(V1)[4/3πR31,2 − V2], where 4/3πR31,2 is the volume of the first coordination sphere, V2 is the volume of one solute molecule, V1 is the volume of one solvent molecule, and R1,2 is the radius of the first coordination sphere. The latter can be expressed as the sum of the radii the solvent and solute molecules, R1,2 = R1 + R2. The volumes of solvent and solute molecules can be obtained by dividing molar volumes Vm by the Avogadro number NA, for instance, for the solute V2 = V2m/NA, where V2m is the molar volume of the solute. The coefficients φi in the above equation are corrections for the nonadditivity of pairwise interactions. During investigations of the same solute in a series of solvents the corrections can be assumed constant, leading to

Table 1. Source and Purity of Compounds

Solute dichloromethane trichloromethane tetrachloromethane

1-ClPr 2-ClPr 1-ClBu 1-Cl-2-MetPr

1-bromopropane 2-bromopropane 1-bromobutane

1-BrPr 2-BrPr 1-BrBu

1-bromo-2methylpropane 1-bromopentane 1-bromoheptane 1-bromoheptadecane iodoethane

1-Br-2-MetPr

1-iodopropane

1-IPr

2-iodopropane

2-IPr

1-iodobutane

1-IBu

1-iodo-2methylpropane Solvent octane heptane cyclohexane

1-I-2-MetPr

hexane tetrachloromethane

CH3(CH2)4CH3 CCl4

⎤

benzene

C6H6

⎦

1,4-dioxane

C4H8O2

methylbenzene

C6H5CH3

1,2-dimethylbenzene 1,3-dimethylbenzene ethyl acetate

1,2-(CH3)2C6H4 1,3-(CH3)2C6H4 EtAc

chloroform chlorobenzene

CHCl3 C6H5Cl

etanol

C2H5OH

1-butanol

1-OH-Bu

2-methyl-1-propanol

2-OH-Bu

2-propanone

(CH3)2CO

nitrobenzene

C6H5NO2

⎤ 2 2 + (μi αj + μj αi)⎥ ⎥ ⎦

(13)

In a series of nonpolar solvents (μj = 0) for the same solute (Ii = const, μi = const, αi = const), the energy of interaction can be expressed as ⎡ ⎤ 1 ⎛⎜ Z ⎞⎟ ⎢ 3 IiIj 2 ⎥ ΔEn = + ≡ φα α α μ α ⎜ 6 ⎟ ⎢2 I + I i j i j⎥ (4πε)2 ⎝ R1,2 ⎠⎣ i j ⎦ 1

2 2 ⎡ 1 ⎛⎜ Z ⎞⎟ ⎢ 3 IiIj 2 μi μj ΔEp = ⎜ 6 ⎟ ⎢ 2 I + I αiαj + 3 kT (4πε)2 ⎝ R1,2 ⎠⎣ i j 1

μj2 αi)⎥ ⎥

≡ φμ

(15)

defining the solubility parameter φμ in a polar solvent. Thus, if the universal interactions determine the solute− solvent interaction, then the solubility (ln x) in a range of nonpolar solvents will be directly proportional to the φα parameter value

ln x ∼ φα

(16)

Similarly, for polar solvents

ln x ∼ φμ

TriBrMet

1-BrPe 1-BrHe 1-BrHeD IEt

(14)

This equation defines the solubility parameter φα in a nonpolar solvent. In a series of polar solvents (μj ≠ 0) for the same solute (Ii = const, μi = const, αi = const) the energy of interaction is

+ (μi αj +

DClMet TriClMet TetClMet

1-chloropropane 2-chloropropane 1-chlorobutane 1-chloro-2-methylpropane tribromomethane

⎡ μ 2μ2 1 ⎛⎜ Z ⎞⎟ ⎢ 3 IiIj α α + 2 i j const ΔE = ⎜ 6 ⎟ ⎢ 2 Ii + Ij i j 3 kT (4πε)2 ⎝ R1,2 ⎠1 ⎣

2

abbreviation, formula

chemical name

(17)

The investigations of solubility of halogen derivatives of aliphatic hydrocarbons in a series of nonpolar and polar solvents were carried out to test the suggested eqs 16 and 17.

2. EXPERIMENTAL SECTION 2.1. Chemicals. The suppliers and the purities of compounds are reported in Table 1. The properties of the halogenalkanes studied are given in Table 2 and the properties of the solvents

CH3(CH2)6CH3 CH3(CH2)5CH3 C6H12

source Merck Lachem Polish Chem. Reagents Merck Fluka Merck Fluka

mass fraction purity > 0.99 0.999 0.99 0.98 > 0.99 > 0.98 0.98

Polish Chem. Reagents Aldrich Aldrich Polish Chem. Reagents Aldrich

> 0.97

Fluka Fluka Fluka Polish Chem. Reagents Polish Chem. Reagents Polish Chem. Reagents Polish Chem. Reagents Polish Chem. Reagents

> 0.995 0.99 0.99 > 0.98

Roskhimexport Roskhimexport Polish Chem. Reagents Roskhimexport Polish Chem. Reagents Polish Chem. Reagents Polish Chem. Reagents Polish Chem. Reagents Roskhimexport Roskhimexport ́ s̨ kie Piekary Sla (Poland) Lachem Polish Chem. Reagents Polish Chem. Reagents Polish Chem. Reagents Polish Chem. Reagents Polish Chem. Reagents Reactival Bucuresti

> 0.99 > 0.98 0.975 0.99

> 0.99 > 0.98 0.99 > 0.99

0.995 > 0.995 0.99 0.999 0.99 > 0.99 0.99 > 0.99 0.996 0.995 0.99 0.98 > 0.99 > 0.99 > 0.99 0.995 > 0.99 > 0.99

used in Table 3. These compounds were used without further purification. Prior to the measurements, all chemicals were dried with activated molecular sieves (type 4 A molecular sieve) and 1947



Article

Table 2. Solute Molecular and Macroscopic Characteristicsa α2

μ2·1030

3

solute

formula

Å (ref 21)

DClMet TriClMet TetClMet 1-ClPr 2-ClPr 1-ClBu 1-Cl-2-MetPr

CH2Cl2 CHCl3 CCl4 CH3(CH2)2Cl CH3CH(Cl)CH3 CH3(CH2)3Cl CH3CH(CH3)CH2Cl

5.76 8.41 10.33 8.26 8.27 9.56 9.54

TriBrMet 1-BrPr 2-BrPr 1-BrBu 1-Br-2-MetPr 1-BrPe 1-BrHe 1-BrHeD

CHBr3 CH3(CH2)2Br CH3CH(Br)CH3 CH3(CH2)3Br CH3CH(CH3)CH2Br CH3(CH2)4Br CH3(CH2)6Br CH3(CH2)16Br

11.84 9.98 10.02 11.25 11.33 13.09 16.78 35.21

IEt 1-IPr 2-IPr 1-iodobutane 1-I-2-MetPr

C2H5I CH3(CH2)2I CH3CH(I)CH3 CH3(CH2)3I CH3CH(CH3)CH2I

9.61 11.45 11.45 13.29 13.29

C·m (ref 22) Chlorinated Alkanes 5.24 4.07 0.00 6.57 6.84 6.40 6.80 Brominated Alkanes 3.30 6.54 6.80 6.60 6.57 6.54 6.50 6.50 Iodized Alkanes 5.84 6.20 6.94 6.67 6.40

I2·102 kJ·mol

−1

V2m

V2·1024

R2

cm3

Å

−1

cm ·mol 3

(ref 23)

11.25 ± 0.01 11.40 ± 0.02 11.45 ± 0.01 10.80 ± 0.03 10.76 ± 0.02 10.64 ± 0.03 10.65 ± 0.03

63.57 80.50 96.44 88.04 91.43 104.48 104.55

105.5 133.5 159.9 146.2 151.8 173.5 175.2

2.932 3.173 3.368 3.263 3.31 3.46 3.472

10.49 ± 0.02 10.16 ± 0.01 10.06 ± 0.01 10.11 ± 0.01 10.07 ± 0.02 10.08 ± 0.02 10.08 10.08

87.45 90.83 93.88 107.42 108.78 124.00 157.10 305.64

145.2 150.8 155.9 178.3 180.6 205.8 260.8 507.4

3.261 3.302 3.339 3.492 3.507 3.663 3.964 4.949

9.328 ± 0.005 9.24 ± 0.01 9.15 ± 0.02 9.19 ± 0.01 9.16 ± 0.02

79.98 97.53 99.82 113.83 115.20

132.8 161.9 165.7 188.9 191.2

3.165 3.382 3.408 3.560 3.574

a α2 is the polarizability of the solute molecule, Å3; μ2 is the dipole moment of the solute molecule, C·m; I2 is the first ionization potential of the solute molecule, kJ·mol−1; V2m is the solute molar volume, cm3·mol−1; V2 is the volume occupied by one solute molecule in a liquid, cm3; R2 is radius of the cavity created by one solute molecule in a liquid, Å.

Table 3. Solvent Molecular and Macroscopic Characteristicsa α1

MR solvent code 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

solvent Nonpolar octane heptane cyclohexane hexane tetrachloromethane benzene 1,4-dioxane Polar methylbenzene 1,2-dimethylbenzene 1,3-dimethylbenzene ethyl acetate chloroform chlorobenzene ethanol 1-butanol 2-methyl-1-propanol 2-propanone nitrobenzene

ε20 (ref 24)

−1

cm ·mol 3

(ref 25)

3

μ1·1030

I1·102

Å (ref 21)

C·m (ref 22)

−1

kJ·mol

(ref 23)

V1·1024

R1

cm ·mol

cm3

Å

V1m 3

−1

1.948 1.924 2.023 1.890 2.238 2.284 2.235

39.27 34.62 26.61 29.97 26.12 26.48 23.16

15.58 13.74 10.56 11.89 10.36 10.51 9.19

0.0 0.0 0.0 0.0 0.0 0.0 0.0

10.01 9.88 9.86 10.13 11.44 9.23 9.08

162.23 146.24 107.82 100.42 103.36 88.74 85.13

269.3 242.8 179.0 216.5 171.6 147.3 141.3

3.384 3.269 2.953 3.146 2.912 2.767 2.729

2.379 2.568 2.374 6.110 4.806 5.710 4.806 17.80 24.30 20.74 34.82

30.68 34.04 34.31 25.00 20.77 31.14 12.85 22.14 22.14 15.96 30.91

12.17 13.50 13.61 9.91 8.24 12.35 5.10 8.78 8.78 6.33 12.26

1.23 1.17 1.80 3.30 3.84 5.37 5.27 5.50 5.67 9.50 13.01

8.80 8.56 8.54 9.48 11.26 9.06 10.45 10.02 9.88 9.67 9.83

106.11 120.44 122.66 97.78 80.11 101.56 58.68 91.85 92.28 73.55 102.23

176.2 200.0 203.6 162.3 133.0 168.6 97.42 152.5 153.2 122.1 169.7

2.937 3.064 3.064 2.858 2.675 2.895 2.411 2.799 2.804 2.599 2.901

a ε20 is the dielectric permittivity; MR is molar refraction, cm3·mol−1; α1 is the polarizability of the solvent molecule, Å3; μ1 is the dipole moment of the solvent molecule, C·m; I1 is the first ionization potential of the solvent molecule, kJ·mol−1; V1m is the solvent molar volume, cm3·mol−1; V1 is the volume occupied by one solvent molecule in a liquid, cm3; R1 is the radius of the cavity created one solvent molecule in a liquid, Å.

degassed in an ultrasonic stream. The samples were stored in a drybox over P2O5. 2.2. Apparatus and Procedure. The solubility in a liquid− liquid system was studied with a special sample cell by the

addition of a solute to the solvent to obtain two visually separated layers of liquid. To confirm the moment of separation determined visually, the chromatography method26 was used. The calibration of the gas chromatograph N502 was carried out 1948



Article

Table 4. Solubility Parameters of Some Chlorinated Alkanes in Polar and Nonpolar Organic Solventsa (a) dichloromethane solvent code

Z

φα·1020

1 2 3 4 5 6 7 8 9 10 11 12 13 15 16 17 18

5.57 5.98 6.42 5.34 5.84 5.75 5.72 5.85 5.48 5.47 6.53 6.81 5.68 6.30 6.31 6.51 5.94

2.064 1.918 1.797 1.813 1.942 1.954 1.730

trichloromethane

φμ·108

x298

Z

φα·1020

5.62 6.15 6.53

0.028 0.055 0.023 0.211 0.322 0.551 0.613 0.628 2.091 3.392

0.316 0.181 0.125 0.334 0.419 0.155 0.051 0.233 0.194 0.172 0.034 0.060 0.188 0.135 0.212 0.216 0.146

5.96 5.91 6.07 5.93 5.65 5.63 6.75

x298

Z

φα·1020

2.113 1.954 1.813

0.267 0.324 0.291

5.84 6.27 6.67 6.07

1.971 1.952 1.741

0.282 0.252 0.272 0.197 0.355 0.214 0.221

6.03 6.08 6.00 5.76 5.78

0.029 0.058 0.024 0.222

5.75 6.43 6.46 6.55 6.00

0.573 0.631 0.640 2.185 3.515

2-chloropropane solvent code

Z

φα·1020

1 2 3 4 5 6 7 8 9 10 11 12 13 15 16 17 18

5.98 6.25 6.56 6.17 6.47 6.10 6.08 6.01 5.77 5.86 6.90 7.12 5.90 6.72 6.75 6.87 6.15

1.245 1.133 1.109 1.137 1.128 1.127 1.047

φμ·108

tetrachloromethane

0.240 0.150 0.222 0.235 0.287 (b)

φμ·108

x298

Z

φα·1020

1.803 1.654 1.572 1.561

0.116 0.095 0.098 0.104

1.667 1.528

1.041 1.114 1.107 1.108 1.142 1.018 1.182

0.025 0.051 0.019

0.101 0.117 0.133 0.174 0.108

6.06 6.33 6.75 6.12 6.51 6.23 6.17 6.09 5.88 5.95

7.02 5.83

0.283 0.485

0.072 0.165

6.48 6.66 6.09

0.577 1.823 4.128

0.090 0.111 0.111

1-chlorobutane

φμ·108

x298

Z

φα·1020

6.16 6.35 6.80 6.25 6.55 6.27 6.20 6.13 5.96 6.03 7.07 7.15 5.97 6.59 6.70 6.86 6.16

1.670 1.590 1.496 1.528 1.615 1.618 1.435

0.024 0.047 0.020 0.179 0.237 0.463 0.516 0.552 2.091 2.862

0.208 0.179 0.184 0.248 0.269 0.161 0.154 0.245 0.216 0.130 0.229 0.237 0.275 0.170 0.141 0.216 0.292

1-chloropropane

7.07 5.88 6.50 6.53 6.78 6.11

φμ·108

x298

0.025 0.049 0.021

0.353 0.318 0.317 0.319 0.320 0.353 0.306 0.186 0.191 0.183

0.285 0.211 0.544 0.575 2.167 3.018

0.256 0.211 0.202 0.225 0.213 0.218

1-chloro-2-methylpropane

φμ·108

x298

Z

φα·1020

6.09 6.27 6.72 6.2 6.51 6.22 6.18 6.11 5.91 6.01 7.00 7.11 5.89 6.52 6.66 6.84 6.13

1.667 1.579 1.480 1.517 1.609 1.613 1.427

0.028 0.049 0.023 0.185 0.249 0.477 0.532 0.570 2.113 2.959

0.272 0.230 0.301 0.311 0.430 0.301 0.201 0.211 0.228 0.160 0.217 0.220 0.110 0.142 0.180 0.170 0.172

φμ·108

x298

0.027 0.047 0.021 0.180 0.243 0.470 0.520 0.565 2.108 2.901

0.260 0.273 0.283 0.290 0.402 0.283 0.179 0.190 0.201 0.145 0.200 0.203 0.295 0.173 0.170 0.156 0.160

Z is the number of solvent molecules in the first coordinative sphere; φα is the solubility parameter in a nonpolar solvent; φμ is the solubility parameter in a polar solvent; x298 is the solute concentration (mole fraction) in solution.

a

by adding the studied compound using the standard method.27 The conditions for the chromatographic analysis were as follows. The chromatographic column was 1.5 m long and had a 0.4 cm internal radius. Helium was used as the carrier gas, and Porapak Q was the filling substance for the column. The carrier gas flow rate was 60 cm3·min−1. The temperature of the dispenser was 423 K, the temperature of the detector was 100 K, and the temperature of the columns ranged between (373 and 473) K, depending on the boiling temperature of the solvent and the compound studied. Drops of solute were added to the solvent until the intensities of both chromatographic peaks remained constant despite further addition of the solute. Every measurement was repeated several times to obtain the same results. The solubility of the solids was studied with the dynamic method,28 which is characterized by a considerably greater rate of measurement in comparison to the static method. The uncertainty of the

experimental solubility values is about 2.0 %, arising from the uncertainties in the temperature measurements, weighting procedure, and the aggregated error of the chromatographic method. The experimental data used in the study of the solubility of halogenated alkanes are shown in the following tables: Tables 4a and b for chloroalkanes, Tables 5a and b for bromoalkanes, and Table 6 for iodoalkanes.

3. RESULTS AND DISCUSSION The experimental data shown in Figures 2 and 3 confirm the linear character of the relationships 16 and 17. The deviations from the dependences based on the universal interactions of molecules in solutions arise from specific interactions. They can be used to compare the influence of different interactions on solubility. To describe the solubility of organic compounds in a nonaqueous solvent, one can use the molecular characteristics of 1949



Article

Table 5. Solubility Parameters of Some Brominated Alkanes in Polar and Nonpolar Organic Solventsa (a) tribromomethane solvent code

Z

φα·1020

1 2 3 4 5 6 7 8 9 10 11 12 13 15 16 17 18

5.97 6.16 6.52 6.77 6.13 6.05 6.17 6.13 5.86 5.90 6.82 7.01 6.07 6.41 6.57 6.67 6.07

2.420 2.200 1.957 1.990 2.034 2.177 1.968

1-bromopropane

φμ·108

x298

Z

φα·1020

6.20 6.22 6.77 6.30 6.69 6.33 6.27 6.29 6.01 6.07 6.68

1.762 1.634 1.447 1.567 1.620 1.615 1.510

0.040 0.073 0.034 0.280 0.373 0.607 0.720 0.745 2.341 3.645

0.254 0.301 0.240 0.247 0.289 0.230 0.201 0.212 0.240 0.165 0.210 0.137 0.214 0.119 0.218 0.201 0.217

6.15 6.48 6.56 7.11 6.26

1-bromo-2-methylpropane solvent code

Z

φα·1020

1 2 3 4 5 6 7 8 9 10 11 12 13 15 16 17 18

6.36 6.52 6.98 6.29 6.78 6.39 6.33 6.45 6.08 6.19 6.82 7.33 6.27 6.61 6.85 6.99 6.24

1.836 1.705 1.566 1.610 1.699 1.687 1.523

2-bromopropane

φμ·108

x298

Z

φα·1020

6.17 6.38 6.86 6.28

0.027 0.049 0.022 0.209

0.263 0.225 0.216 0.214 0.240 0.317 0.202 0.159 0.152 0.162 0.159

6.33 6.24 6.18 6.07 6.11

0.504 0.580 0.578 1.930 3.098

0.169 0.142 0.204 0.166 0.203 (b)

1-bromopentane φμ·108

x298

Z

φα·1020

1.754 1.630 1.430 1.578

0.187 0.152 0.202 0.227

1.598 1.507

1.830 1.735 1.592 1.615 1.711 1.703 1.520

0.024 0.047 0.019

0.228 0.118 0.240 0.205 0.143

0.290 0.499 0.552 0.570 1.875 3.007

0.161 0.240 0.147 0.121 0.167 0.170

6.39 6.57 7.01 6.33 6.88 6.45 6.34 6.36 6.09 6.14 6.72 7.36 6.29 6.67 6.78 7.04 6.27

7.30 6.17 6.59 6.66 7.01 6.15

φμ·108

1-bromobutane

1-bromoheptane

x298

0.030 0.052 0.023 0.203 0.307 0.510 0.563 0.585 1.907 3.048

0.237 0.215 0.185 0.312 0.444 0.317 0.187 0.201 0.213 0.115 0.201 0.229 0.183 0.121 0.215 0.147 0.200

1-bromoheptadecane

φμ·108

x298

Z

φα·1020

x298

Z

φα·1020

x298

Z

φα·1020

6.45 6.64 7.07

1.703 1.588 1.472

0.209 0.189 0.149

6.50 6.68 7.12

1.548 1.439 1.305

0.171 0.148 0.129

7.39 7.60 7.87

1.942 1.823 1.665

0.095 0.134 0.064

6.99 6.53 6.37 6.40 6.17 6.25 6.88 7.37 6.37 6.78 6.90 7.20 6.31

1.564 1.555 1.383

0.541 0.258 0.307 0.205 0.227 0.206 0.205 0.221 0.232 0.131 0.220 0.135 0.169

7.03 6.68 6.40 6.52 6.27 6.35 6.97 7.48 6.54 6.83 6.98 7.27 6.39

1.405 1.391 1.234

0.372 0.209 0.314 0.199 0.211 0.210 0.183 0.198 0.230 0.122 0.261 0.141 0.192

7.88 7.65 7.34 7.46 7.19 7.24 7.92 8.36 7.49 7.77 7.86 8.14 7.27

1.970 1.981 1.433

0.027 0.050 0.024 0.215 0.297 0.506 0.558 0.580 1.891 3.039

0.310 0.237 0.198 0.330 0.466 0.308 0.208 0.229 0.258 0.175 0.217 0.150 0.231 0.139 0.230 0.139 0.183

0.338 0.136 0.150 0.110 0.198 0.207 0.212 0.125 0.192 0.059 0.038 0.072 0.090

0.024 0.048 0.024 0.183 0.288 0.473 0.525 0.556 1.761 2.926

φμ·108

φμ·108

0.022 0.044 0.020 0.165 0.218 0.428 0.474 0.502 1.581 2.650

φμ·108

0.028 0.057 0.061 0.172 0.299 0.508 0.587 0.59 1.876 3.342

x298


a

the compounds studied (I, μ, α) and the solution structure parameters (Z, R) that can be obtained with X-ray diffraction and neutron scattering.29,30 The solvent reorganization energy is the most important factor to be taken into consideration in the thermodynamic analysis of solvation.31 The reorganization energy is largely determined by the size of the solute molecule. The size can be estimated by computing the volume for one solute molecule in a liquid: V2 = V2m/N. The analysis of the dependence ln x298 = f(V2) for bromoalkanes shows (Figure 4) that, as the value of V2 increases due to the growth in the number of carbon atoms in the molecule, the solubility decreases. This occurs despite the growth of polarizability of the CnH2n+1Br molecules (n = 3 to 17) from α2 = 9.98 Å3 for C3H7Br to α2 = 35.21 Å3 for C17H35Br. A similar trend of solubility decrease with increase in the alkyl chain length of 1-chloroalkanes was shown in the work.32

The hard sphere (HS) model of a fluid33 produces a value of the HS diameter σ that provides an alternative estimate of the molecular volume V2. A comparison of the HS diameters (σ, A)34 to the diameters corresponding of the spherical volumes V2 (2R, A) shows close agreement: n-C6H14 (σ = 5.92, 2R = 6.29), n-C7H16 (σ = 6.25, 2R = 6.54), n-C8H18 (σ = 6.54, 2R = 6.76), C2H5OH (σ = 4.44, 2R = 4.82), and n-C4H9OH (σ = 5.38, 2R = 5.60). The choice depends on one's preference. We argue that molecular volumes computed from the molar volume of the solute provide more reliable estimates in general, since models such as the HS model can lead to oversimplification of the real processes. For example, it was suggested in ref 35 that “energy of solvation in liquids is considered a result of the compensation between the positive cavity formation energy and the negative stabilization energy of attraction”. This simplified description of the solvation process does not fully take into account the fact that 1950



Article

Table 6. Solubility Parameters of Some Iodized Alkanes in Polar and Nonpolar Organic Solventsa iodoethane solvent code

Z

φα·1020

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

5.25 5.47 6.19 5.72 6.30 6.71 6.83 6.22 5.91 5.87 6.43 7.01 6.34 8.03 6.61 6.60 7.27 6.32

2.006 2.106 2.294 2.238 2.091 2.404 2.220

1-iodopropane

φμ·108

x298

Z

φα·1020

5.66 5.91 6.70 6.19 6.82 7.28 7.42 6.75 6.40 6.35 6.99 7.62 6.87 8.76 6.48 7.18 7.91 6.86

2.515 2.229 2.416 2.426 2.206 2.175 2.074

0.028 0.050 0.018 0.215 0.312 0.534 0.116 0.701 0.721 2.092 3.539

0.216 0.281 0.225 0.237 0.379 0.255 0.251 0.293 0.259 0.272 0.234 0.260 0.208 0.133 0.135 0.196 0.216 0.246

2-iodopropane

φμ·108

x298

Z

φα·1020

5.72 5.97 6.77 6.25 6.90 7.36 7.50 6.82 6.46 6.42 7.06 7.70 6.95 8.85 7.25 7.24 8.00 6.92

2.141 2.240 2.424 2.406 2.208 2.423 2.333

0.031 0.054 0.020 0.233 0.355 0.699 0.122 0.712 0.730 2.124 3.617

0.293 0.202 0.291 0.371 0.218 0.212 0.192 0.129 0.110 0.134 0.135 0.127 0.136 0.105 0.130 0.122 0.146 0.182

φμ·108

0.031 0.063 0.023 0.245 0.384 0.792 0.124 0.722 0.737 2.225 3.791

1-iodo-2-methylpropane x298

Z

φα·1020

0.165 0.112 0.109 0.204

6.06 6.32 7.19 6.63 7.33 7.83 7.98 7.24 6.86 6.81 7.50 8.20 7.38 9.45 7.71 7.70 8.52 7.36

2.276 2.381 2.564 2.552 2.332 2.554 2.456

0.111 0.105 0.233 0.194 0.108 0.200 0.124 0.205 0.188 0.104 0.099 0.211 0.220

φμ·108

x298

0.033 0.068 0.029 0.309 0.427 0.890 0.131 0.760 0.769 2.365 4.002

0.169 0.211 0.234 0.230 0.329 0.209 0.155 0.108 0.119 0.103 0.165 0.156 0.205 0.115 0.108 0.103 0.109 0.097


a

Figure 2. Dependence of ln x298 on the molecular interaction parameter in nonpolar solvents φα for ○, propyl chloride; ×, propyl bromide and ●, propyl iodide. The values of ln x298 and φα corresponding to the specific solvent are given in Tables 4a, 5a, and 6. Figure 4. Dependence of ln x298 on the value of V2 (volume of one solute molecule in solution) for 1-BrPr, 2-BrPr, 1-BrBu, 1-Br-2-MetPr, 1-BrPe, 1-BrHe, and 1-BrHeD in ●, benzene; ×, nitrobenzene; ○, acetone. The V2·1024/cm3 values are given in Table 2, and ln x298 values are given in Table 5a and b.

Figure 3. Dependence of ln x298 on the molecular interaction parameter in polar solvents φμ for ○, propyl chloride; ×, propyl bromide and ●, propyl iodide. The values of ln x298 and φμ corresponding to the specific solvent are given in Tables 4a, 5a, and 6.

CHCl3, and CCl4 (4.57 < 5. 76 < 8.41 < 10.33) implies an increase in solubility. However, the opposite phenomenon is observed37 because of the rise in V2·1024 (cm3) (79.6 < 105.5 < 133.5 < 159.9). In the series of compounds CnH2n+1X, where X = Cl, Br, and I, with the same alkyl radical and in the same solvent, the solubility, too, decreases as a rule with an increase in the size of the halogen atom, Cl < Br < I. For example, in case of n-C3H7X dissolved in CCl4, the ln x298 values decrease, −1.142 > −1.425 > −1.523.

under real conditions the solutions are formed by mixing up components. That is why the cavity formation energy is only partly compensated by the energy spent on mixing. The molecules in solution not only attract toward each other but also repulse, even though the contribution of the attraction energy is dominant, up to 90 %.36 The two processes mentioned in the work35 are very important without any doubt. For example, the comparison of the changes in polarizability of molecules α (Å3) in the series CH3Cl, CH2Cl2,

4. CONCLUSIONS Considering solutions of organic compounds in nonaqueous solvents, we show that universal interactions between solvent and solute molecules play the most important role. This fact is corroborated by the analysis of the solubility of alkanes in a variety of polar and nonpolar solvents. In the cases where solute and solvent molecules form intermolecular H-bonds or charge transfer complexes, the solubility, as a rule, increases due to the additional specific interaction. 1951



Article

(17) Goralski, P.; Wasiak, M. Influence of van der Waals interactions on volumetric properties of cholesterol in solvents of linear structure. J. Chem. Thermodyn. 2003, 35, 1623−1634. (18) Huang, J. C. Multiparameter solubility model of fullerene C60. Fluid Phase Equilib. 2005, 237, 186−192. (19) Plyasunov, A. V.; Shock, E. L.; Wood, R. H. Second virial coefficient for interactions involving water. Correlations and group contribution values. J. Chem. Eng. Data 2003, 48, 1463−1470. (20) Silla, E.; Arnau, A.; Tunon, I. Fundamental Principles in Solvents Use. In Handbook of Solvents; Wypych, G., Ed.; ChemTec Publications, William Andrew Publications: Toronto, 2001; pp 7−36. (21) Vereshchagin, A. N. The Characteristics of Anisotropy of Molecular Polarizability (in Russian); Nauka: Moscow, 1982. (22) McClellan, A. L. Table of Experimental Dipole Moments; Rahara Enterprises: New York, 1974 (Vol. 2); 1989 (Vol. 3). (23) Energy of Chemical Bonds Breaking. Ionization Potentials and Electron Affinity (in Russian);Kondratiev, V. N., Ed.; Nauka: Moscow, 1974. (24) Solvents Database; Chemtech Publishing: Toronto, 2000. (25) Poling, B. E.; Prausnitz, J. M.; O;Connell, J. P. The Properties of Gases and Liquids, 5th ed.; McGraw-Hill: New York, 2001. (26) Domańska, U.; Pobudkowska, A. Solubility of imidazoles, benzimidazoles, and phenylimidazoles in dichloromethane, 1-chloropropane, toluene, and 2-nitrotoluene. J. Chem. Eng. Data 2004, 49, 1082−1090. (27) Witkiewicz, Z. Podstawy chromatografii; Wydawnictwa NaukowoTechniczne: Warszawa, 2005; pp 163−164. (28) The dissolubility of solid in liquids. Laboratory practice; Domańska, U., Ed.; Warszawska Politechnika, Wydział Chemii: Warsaw, 1990. (29) Prezhdo, V. V.; Melnik, I. I.; Jagiello, M.; Zubkova, V. V.; Prezhdo, M. V.; Bezak-Mazur, E. Correlation of distribution of organic solutes in organic solvent-water systems with molecular properties and solution structure parameters. Indian J. Chem. 2000, 39A, 802−808. (30) Prezhdo, V. V.; Jagielo, M.; Mel'nik, I. I.; Prezhdo, M. V. Solvent Effects in Extraction of Carboxylic Acids. Sep. Sci. Technol. 2002, 37, 2875−2896. (31) Matyushov, D. V.; Schmidt, R. A thermodynamic analysis of solvation in dipolar liquids. J. Chem. Phys. 1996, 105, 4729−4741. (32) Deen, G. R.; Pedersen, J. S. Phase behavior and microstructure of C12E5 nonionic microemulsions with chlorinated oils. Langmuir 2008, 24, 3111−3117. (33) Matyushov, D. V.; Ladany, B. M. Cavity formation energy in hard sphere fluids: An asymptotically correct expression. J. Chem. Phys. 1997, 107, 5815−5820. (34) Graziano, G. On the cavity size distribution in water and n-hexane. Biophys. Chem. 2003, 104, 371−382. (35) Nasehzadeh, A.; Azizi, K. The heat of vaporization and hard sphere diameters from cavity formation energies. J. Mol. Struct.: THEOCHEM 2003, 638, 197−207. (36) Bulychev, V. P.; Sokolov, N. D. Quantum Chemical Theory of Hydrogen Bond. In Hydrogen Bond; Sokolov, N. D., Ed.; Nauka: Moscow, 1980; pp 10−29. (37) Wakita, K.; Yoshimoto, M.; Miyamoto, S.; Watanabe, H. A Method for Calculation of the Aqueous Solubility of Organic Compounds by Using New Fragment Solubility Constants. Chem. Pharm. Bull. 1986, 34, 4663−4681.

The solubility of halogenated alkanes is influenced both by the type of the halogen atom and by the size of the alkyl radical bound to this atom. Noting that the changes in the molecular dipole moment are insubstantial, this influence can be attributed to the following two competing factors. On the one side, molecular polarizability increases with a rise in the size of the alkyl radical and with the transition from Cl to Br and I. As the polarizability grows, the solubility should increase as well, because of the growing energy of solute−solvent interaction. On the other side, an increase in the molecular size leads to an increase in the volume occupied by one solute molecule in solution. As a result, the cavity formation energy grows, and solubility decreases. In most cases, the second factor dominates the first.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +48 41 3497025. Fax: +48 41 3497062. E-mail: victor@ ujk.edu.pl. Notes

The authors declare no competing financial interest.

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REFERENCES

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Influence of Solvent Nature on the Solubility of Halogenated Alkanes

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