Topological investigations of the molecular species and molecular interactions that characterize pyrrolidin-2-one + lower alkanol mixtures

Molar excess volumes, V^E, molar excess enthalpies, H^E, and speeds of sound data, u, of pyrrolidin-2-one (i) + ethanol or propan-1-ol or propan-2-ol or butan-1-ol (j) binary mixtures have been determined over entire composition range at 308.15 K. The observed speeds of sound data have been utilized to predict excess isentropic compressibilities, of the investigated binary mixtures. The observed excess thermodynamic properties V^E, H^E and have been analyzed in terms of Graph theory. The analysis of V^E data by the Graph theory suggests that pyrrolidin-2-one exists mainly as a mixture of cyclic and open dimer; ethanol as a mixture of dimer and trimer; butan-1-ol and propan-2-ol as mixture of monomer and dimer and propan-1-ol as a dimer in the pure state, and their mixtures contain 1:1 molecular complex. The IR studies lend additional credence to the nature and extent of interactions for the proposed molecular entities in the mixtures. Also, it has been observed that V^E, H^E and values predicted by the Graph theory compare well to with their corresponding experimental values.     

Topological and thermodynamic investigations of molecular interactions of aniline and o-toluidine with chloroform

Molar excess volumes, V^E, molar excess enthalpies, H^E, and speeds of sound data, u, of chloroform (i) + aniline or o-toluidine (j) binary mixtures have been measured as a function of composition at 308.15 K. Isentropic compressibility changes of mixing, have been determined by employing speed of sound data. Topological investigations of V^E data reveals that aniline, chloroform and o-toluidine are associated entities and these (i + j) mixtures contain a 1:1 molecular complex. The IR studies lend further support to the nature and extent of interaction for the proposed molecular entity in the mixtures. H^E and values have also been calculated by employing Moelwyn-Huggins concept [Polymer 12 (1971) 387] taking topology of the constituents of the mixtures. It has been observed that calculated H^E and values compare well with their corresponding experimental values. The observed V^E, H^E and data have also been analyzed in terms of Flory theory.     

Excess Isentropic Compressibilities for 1,3-Dioxolane or 1,4-Dioxane <Emphasis Type="Italic">+</Emphasis> Water <Emphasis Type="Italic">+</Emphasis> Formamide or N,N-Dimethylformamide Ternary Mixtures at 308.15 K

Speeds of sound, u_ijk, of 1,3-dioxolane or 1,4-dioxane (i) + water (j) + formamide or dimethylformamide (k) ternary mixtures and of their binary subsystems, u_ij, of 1,3-dioxolane or 1,4-dioxane (i) + formamide or dimethylformamide (j), and water (i) + formamide or dimethylformamide (j) have been measured over the entire composition range at 308.15 K. The experimental data have been used to evaluate the excess isentropic compressibilities of binary (κ_s^E)_ij and ternary (κ_s^E)_ijk mixtures using their densities calculated from molar excess volume data. The Moelwyn-Huggins concept [M. L. Huggins, Polymer 12, 389 (1971)] of interaction between the surfaces of components of a binary mixture has been employed to evaluate the excess isentropic compressibilities (using the concept of connectivity parameter of third degree of a molecule, ³ξ, which in turn depends on its topology) of binary mixtures, and this method has been extended to predict excess compressibilities of ternary mixtures. Values of (κ_s^E)_ij and (κ_s^E)_ijk have also been calculated by the Flory theory. It was observed that (κ_s^E)_ij and (κ_s^E)_ijk predicted by the Moelwyn-Huggins approach compare well with calculated and experimental values.     

Topological and thermodynamic investigations of binary mixtures: Molar excess volumes, molar excess enthalpies and isentropic compressibility changes of mixing

Molar excess volumes, V^E, molar excess enthalpies, H^E, and speeds of sound, u, of o-toluidine (i) + cyclohexane or n-hexane or n-heptane (j) binary mixtures have been determined over entire range of composition at 308.15 K. Speeds of sound data have been utilized to predict isentropic compressibility changes of mixing, of (i + j) mixtures. The observed V^E, H^E and data have been analyzed in terms of Graph theory. The analysis of V^E data by Graph theory reveals that o-toluidine exists as an associated molecular entity and (i + j) mixtures contain 1:1 molecular complex. It has been observed that V^E, H^E and values calculated by Graph theory compare well with their corresponding experimental values. The observed data have also been analyzed in term of Flory theory.     

Topological Investigations of Some Cyclic Ether-Water-Alkanol Ternary Mixtures: Molar Excess Volumes

Molar excess volumes, V_ijk^E, of 1,3-dioxolane or 1,4-dioxane (i) + water (j) + propan-1-ol or + propan-2-ol (k) ternary mixtures have been determined dilatometrically over the entire composition range at 308.15 K. The resulting data have been analyzed in terms of (1) the graph theoretical approach (which involves the topology of the mixture constituents), (2) the Sanchez and Locombe theory and (3) the Flory theory. It was observed that V_ijk^Evalues predicted by the graph theory compare reasonably well with their corresponding experimental values. However, although V_ijk^E values calculated by the Sanchez and Lacombe and Flory theories are of same sign and magnitude, the qualitative agreement is poor.     

Isentropic Compressibility Changes of Mixing for 1,3-Dioxolane or 1,4-Dioxane + Water + Propanol Ternary Mixtures

Speed of sound data, u_ijk, of 1,3-dioxolane or 1,4-dioxane(i) + water(j) + propan-1-ol or propan-2-ol(k) ternary mixtures and their sub-binary mixtures, u_ij, of 1,3-dioxolane or 1,4-dioxane(i) + water or propan-1-ol or propan-2-ol(j) and water(i) + propan-1-ol or propan-2-ol(j) mixtures have been measured over the entire composition range at 308.15 K. Isentropic compressibility changes of mixing, (κ_s^E)_ij and (κ_s^E) _ijk, for the binary and ternary mixtures have been determined by employing the observed speeds of sound data and densities (calculated from their molar excess volumes data). The (κ_s^E) _ij and (κ_s^E) _ijk values have also been predicated by the graph theoretical approach and the Flory theory. It has been observed that (κ_s^E) _ij and (κ_s^E) _ijk predicted by the graph theoretical approach compare well with their corresponding experimental values.     

Excess Molar Volumes of Ternary Mixtures of a Cyclic Ether with Aromatic Hydrocarbons at 308.15 K

Excess molar volumes, V_ijk^EV_{ijk}^{E}, are reported for ternary mixtures of tetrahydropyran (i)+benzene (j)+toluene or o- or p-xylenes (k) and tetrahydropyran (i)+toluene (j)+o- or p-xylenes (k) as a function of composition at 308.15 K. These V_ijk^EV_{ijk}^{E} values have been fitted to the Redlich–Kister equation to predict ternary adjustable parameters and standard deviations. The measured V_ijk^EV_{ijk}^{E} data have been analyzed in terms of Graph theory (which involves the topology of the constituents of mixtures). It has been observed that V_ijk^EV_{ijk}^{E} values predicted by Graph theory compare well with their corresponding experimental values.     

Excess Molar Volumes,Viscosities and Speeds of Sound of the Ternary Mixture 1-Heptanol (1) + Tetrachloroethylene (2) + Methylcyclohexane (3) at 298.15 K

Densities (ρ), viscosities (η) and speeds of sound (u) of the ternary mixture (1-heptanol + tetrachloroethylene + methylcyclohexane) and the corresponding binary mixtures (1-heptanol + tetrachloroethylene), (1-heptanol + methylcyclohexane) and (tetrachloroethylene + methylcyclohexane) at 298.15 K were measured over the whole composition range. The data obtained are used to calculate the excess molar volumes (V ^E), excess isobaric thermal expansivities (α ^E), viscosity deviations (Δη), excess Gibbs energies of activation of viscous flow (ΔG ^*E) and excess isentropic compressibilities (κ _S ^E) of the binary and ternary mixtures. The data from the binary systems were fitted by the Redlich–Kister equation whereas the best correlation method for the ternary system was found using the Nagata equation. Viscosities, speeds of sound and isentropic compressibilities of the binary and ternary mixtures have been correlated by means of several empirical and semi-empirical equations. The best correlation method for viscosities of binary systems is found using the Iulan et al. equation and for the ternary system using the Heric and McAllister equations. The best correlation method for the speeds of sound and isentropic compressibilities of the binary system (1-heptanol + methylcyclohexane) is found using IMR (Van Deal ideal mixing relation) and for the binary system (tetrachloroethylene + methylcyclohexane) it is found using the NR (Nomoto relation) and for the binary system (1-heptanol + tetrachloroethylene) and the ternary system (1-heptanol + trichloroethylene + methylcyclohexane) it is obtained from the FLT (Jacobson free length theory).     

Molar excess volumes of ternary mixtures of nonelectrolytes

Molar excess volumes V^E_ijk of methylenebromide i + pyridine j + β-picoline (k, cyclohexane (i) + pyridine (j) + β-picoline(K), benzene(i)+toluene(j)+1,2-dichloroethane(k), benzene(i) + 0-xylene(j) + 1,2-dichloroethane(k) and benzene(i) + p-xylene(j) + 1,2-dichloroethane(k) mixtures have been determined dilatometrically at 298.15 K. The data have been examined in terms of Sanchez and Lacombe theory and the graph-theoretical approach, and it is found that they are described well by the latter. Self- and cross-volume interaction coefficients V_jk, V_jjk and V_jkk, etc., have also been evaluated and the values utilised to study molecular interactions between the jth and kth molecular species in the presence of the ith in these i + j + k mixtures.     

Molar Excess Volumes of Ternary Mixtures Containing a Cyclic Ether

Molar excess volumes, V_ijk^E, of 1,3-dioxolane or 1,4-dioxane (i) + water (j) + formamide or dimethylformamide (k) ternary mixtures have been determined dilatometrically over the entire composition range at 308.15 K. The measured data have been analyzed in terms of (a) the graph theoretical approach, (b) the Lacombe and Sanchez theory, and (c) the Flory theory. It was observed that V_ijk^E values predicted by graph theory compare well with their corresponding experimental values. However, V_ijk^E values evaluated by the Lacombe and Sanchez as well as the Flory theory are of same sign and order.     

Molar excess enthalpies of ternary mixtures of non-electrolytes

Molar excess enthalpies, H^E_ijk(T₁, x_i, x_j), for methylenebromide (i)+pyridine (j)+β-picoline (k); pyridine (i)+β-picoline (j)+cyclohexane (k); benzene (i)+toluene (j)+1,2-dichloroethane (k); benzene (i)+o-xylene (j)+1,2-dichloroethane (k); and benzene (i)+p-xylene (j)+1,2-dichloroethane (k) mixtures have been measured calorimetrically as a function of temperature and composition. The data have been analysed in terms of the Sanchez and Lacombe theory and using an approach employing the “graph theoretical” concept of connectivity parameters to characterize its pure components. It has been observed that the H^E_ijk (T, x_i, x_j) data calculated from the “graph theoretical” approach using ³ξ values based on δ^v considerations (that take into consideration the valency of individual atoms of the molecular graph constituent components) best reproduces the corresponding experimental H^E_ijk data.     

Modeling of the three-phase equilibrium in systems of the type water + nonionic surfactant + alkane

Liquid–liquid equilibria of systems water (A) + C_iE_j surfactant (B) + n-alkane (C) have been modeled by a mass-action law model previously developed and so far successfully applied to a series of binary water + C_iE_j systems and to the ternary system water + C₄E₁ + n-dodecane. These calculations provide the basis for the presented modeling. The aqueous systems give information about the association constants and the χ_AB-parameter of the Flory–Huggins theory and the ternary C₄E₁-system provides universal temperature functions for the χ_AC- and the χ_BC-parameter. The three-phase equilibrium for seven ternary C_iE_j systems (i = 6–12, j = 3–6) has been calculated by fitting one additional parameter for each of both temperature functions to the characteristic “fish-tail” point. The agreement with the experimental data is reasonably well. For systems with very small three-phase areas the results can considerably be improved by individual temperature functions that incorporate the experimental temperature maximum of the “fish” into the parameter fit. Based on the parameters of the system water + C₈E₄ + n-C₈H₁₈ the “fish-shaped” phase diagram of the system water + C₈E₄ + n-C₁₄H₃₀ was predicted reasonably well.     

The Hydrolysis of AuCl<Stack><Subscript>4</Subscript><Superscript>−</Superscript></Stack> and the Stability of Aquachlorohydroxocomplexes of Gold(III) in Aqueous Solution

The equilibria AuCl₄⁻+jOH⁻+kH₂O⇌AuCl_4−j−k (OH) _j (H₂O) _k ^k−1+(j+k)Cl⁻, β _jk (0≤j,k≤4) have been studied spectrophotometrically at 20 °C in aqueous solution. For I=2 mol⋅dm⁻³(HClO₄) the conventional constants, β _i ^*, of the equilibria, Au^*+iCl⁻ ⇌AuCl _i ^*, are equal to log ₁₀ β ₁^*=(6.98±0.08); log ₁₀ β ₂^*=(13.42±0.05); log ₁₀ β ₃^*=(19.19±0.09); and log ₁₀ β ₄^*=(24.49±0.07), where [AuCl _i ^*]=∑[AuCl _i (OH) _j (H₂O)_4−i−j ] at i=const. The hydrolysis and other transformations of AuCl₄⁻ in aqueous solution are discussed. On the basis of new and known data, a full set of equilibrium constants, β _jk , or their estimates has been obtained.     

Excess molar heat capacities and excess molar volumes of some mixtures of propylene carbonate with aromatic hydrocarbons

Excess molar volumes V ^E and excess molar heat capacities C _P ^E at constant pressure have been measured, at 25°C, as a function of composition for the four binary liquid mixtures propylene carbonate (4-methyl-1,3-dioxolan-2-one, C₄H₆O₃; PC) + benzene (C₆H₆;B), + toluene (C₆H₅CH₃;T), + ethylbenzene (C₆H₅C₂H₅;EB), and + p-xylene (p-C₆H₄(CH₃)₂;p-X) using a vibrating-tube densimeter and a Picker flow microcalorimeter, respectively. All the excess volumes are negative and noticeably skewed towards the hydrocarbon side: V ^E (cm³-mol^–1) at the minimum ranges from about –0.31 at x₁=0.43 for {x₁C₄H₆O₃+x₂p-C₆H₄(CH₃)₂}, to –0.45 at x₁=0.40 for {x₁C₄H₆O₃+x₂C₆H₅CH₃}. For the systems (PC+T), (PC+EB) and (PC+p-X) the C _P ^E s are all positive and even more skewed. For instance, for (PC+T) the maximum is at x _1,max =0.31 with C _P,max ^E =1.91 J-K^–1-mol^–1. Most interestingly, C _P ^E of {x₁C₄H₆O₃+x₂C₆H₆} exhibits two maxima near the ends of the composition range and a minimum at x _1,min =0.71 with C _P,min ^E =–0.23 J-K^–1-mol^–1. For this type of mixture, it is the first reported case of an M-shaped composition dependence of the excess molar heat capacity at constant pressure.Communicated at the Festsymposium celebrating Dr. Henry V. Kehiaian's 60^th birthday, Clermont-Ferrand, France, 17–18 May 1990.     

Reactivity of C<Subscript>3</Subscript>-C<Subscript>8</Subscript> alkanes with nitronium ions in sulfuric acid

We have determined the parameters of the Arrhenius equation (E, log A) for reactions between \textNO₂⁺ {\text{NO}}_2^{+} ions and C₃-C₈ alkanes in HNO₃–93 wt.% H₂SO₄ solutions at 277–353 K, and we have also estimated the activation parameters E _j , log A _j for secondary and tertiary C—H bonds of these alkanes. We show that the following compensation relations are satisfied: E = 2.3R βlog A + C with isokinetic temperature β = 360 ± 65 K, and also E _j =2.3Rβ _j log A _j  + C _j , for secondary C—H bonds, β₂ =300 ± 60, and for tertiary C—H bonds, β₃ =310 ± 50.     

Thermodynamic Investigation of Dimethyl Sulfoxide Binary Mixtures at 293.15 and 313.15 K

Densities (ρ), speeds of sound (u), and isentropic compressibilities (k _S) of binary mixtures of dimethyl sulfoxide (DMSO) with water, methanol, ethanol, 1-propanol, 2-propanol, acetone and cyclohexanone have been measured over the entire composition range at 293.15 and 313.15 K. The excess molar volumes (V ^E), the deviations in speed of sound (u ^E) and the deviations in isentropic compressibility (k _S ^E) have been determined. The V ^E, u ^E and k _S ^E values were fitted by the Redlich-Kister polynomial equation and the A _k coefficients as well as the standard deviations (d) between the calculated and experimental values have been derived. The results obtained are discussed from the viewpoint of the existence of interactions between the components of the binary mixtures.     

Determination of excess molar enthalpies for the ternary system <Emphasis Type="Italic">p</Emphasis>-xylene+octane+diethyl carbonate

Excess molar enthalpies, H ^E, for the binary mixtures {p-xylene+(1–x) octane}, {x p-xylene+(1–x) diethyl carbonate}, {x octane+(1–x) diethyl carbonate} and the corresponding ternary system {x ₁ p-xylene+x ₂ octane+(1–x ₁–x ₂) diethyl carbonate} have been measured by using a Calvet microcalorimeter at 298.15 K under atmospheric pressure. The experimental H ^E values are all positive for the binary and ternary mixtures over the entire composition range.     

Excess molar enthalpies of the ternary system <Emphasis Type="Italic">p</Emphasis>-xylene+decane+diethyl carbonate

Excess molar enthalpies of the ternary system {x ₁ p-xylene+x ₂decane+(1–x ₁–x ₂)diethyl carbonate} and the involved binary mixtures {p-xylene+(1–x)decane}, {xp-xylene+(1–x)diethyl carbonate} and {xdecane+(1–x)diethyl carbonate} have been determined at the temperature of 298.15 K and atmospheric pressure, over the whole composition range, using a Calvet microcalorimeter. The experimental excess molar enthalpies H _m ^E are positive for all the binary systems studied over the whole composition range. Excess molar enthalpy for the ternary system is positive as well, showing maximum values at x ₁=0, x ₂=0.4920, x ₃=0.5080, H _m,123 ^E=1524 J mol^–1.     

Chromium(III) Hydroxide Solubility in the Aqueous K+-H+-OH?-CO2-HCO 3? -CO 32? -H2O System: A?Thermodynamic Model

Chromium(III)-carbonate reactions are expected to be important in managing high-level radioactive wastes. Extensive studies on the solubility of amorphous Cr(III) hydroxide solid in a wide range of pH (3–13) at two different fixed partial pressures of CO₂(g) (0.003 or 0.03 atm.), and as functions of K₂CO₃ concentrations (0.01 to 5.8 mol⋅kg⁻¹) in the presence of 0.01 mol⋅dm⁻³ KOH and KHCO₃ concentrations (0.001 to 0.826 mol⋅kg⁻¹) at room temperature (22±2 °C) were carried out to obtain reliable thermodynamic data for important Cr(III)-carbonate reactions. A combination of techniques (XRD, XANES, EXAFS, UV-Vis-NIR spectroscopy, thermodynamic analyses of solubility data, and quantum mechanical calculations) was used to characterize the solid and aqueous species. The Pitzer ion-interaction approach was used to interpret the solubility data. Only two aqueous species [Cr(OH)(CO₃)₂²⁻ and Cr(OH)₄CO₃³⁻] are required to explain Cr(III)-carbonate reactions in a wide range of pH, CO₂(g) partial pressures, and bicarbonate and carbonate concentrations. Calculations based on density functional theory support the existence of these species. The log ₁₀ K° values of reactions involving these species [{Cr(OH)₃(am) + 2CO₂(g)⇌Cr(OH)(CO₃)₂²⁻+2H⁺} and {Cr(OH)₃(am) + OH⁻+CO₃²⁻ ⇌Cr(OH)₄CO₃³⁻}] were found to be −(19.07±0.41) and −(4.19±0.19), respectively. No other data on any Cr(III)-carbonato complexes are available for comparisons.     

High-Pressure Densities and Derived Volumetric Properties (Excess,Apparent and Partial Molar Volumes) of Binary Mixtures of Methanol + [BMIM][PF<Subscript>6</Subscript>]

The density of five (0.02297, 0.08317, 0.26147, 0.49343, 0.75255 mole fraction BMIMPF₆) binary methanol + BMIMPF₆ (1-n-butyl-3-methylimidazolium hexafluorophospate) mixtures have been measured with a vibrating-tube densimeter. Measurements were performed at temperatures from 298 to 398 K and at pressures up to 40 MPa. The total uncertainties of the density, temperature, pressure, and concentration (mole fractions) measurements were estimated to be less than 0.1 kg⋅m⁻³, 15 mK, 5 kPa, and 10⁻⁴, respectively. The uncertainties reported in this paper are expanded uncertainties at the 95% confidence level with a coverage factor of k=2. The measured densities were used to study of the effect of temperature, pressure, and concentration on the derived volumetric properties such as excess, apparent and partial molar volumes. It is shown that the values of excess molar volume for methanol + BMIMPF₆ mixtures are negative at all measured temperatures and pressures in the whole concentration range. The measured densities were used to develop Tait-type equations of state for pure components and the mixtures. The structural properties such as direct and total correlation function integrals were calculated using the derived partial molar volumes at infinite dilution.