Relative Apparent Molar Enthalpies Research Articles

Thermodynamically Traceable Calorimetric Results for Aqueous Sodium Chloride Solutions from T = (273.15 to 373.15) K up to the Saturated Solutions: Part 1—The Quantities Associated with the Partial Molar Enthalpy

The three-parameter extended Hückel equations with parameters B, b1, and b2 have recently been successfully tested against existing vapor pressure, electrochemical, and solubility data for aqueous NaCl solutions at temperatures from (273 to 373) K (Partanen and Partanen in J. Chem. Eng. Data 65:5226–5239, 2020). In the present study, we extend this model to the apparent and partial molar enthalpy data of these solutions. The enthalpy equations were determined using a new calculation method that gives practically the same results as that used in another previous study (Partanen et al. in J. Chem. Eng. Data 62:2617–2632, 2017), but the new method is much simpler. In the previous enthalpy study, dilute NaCl solutions up to m = 0.2 mol⋅kg−1 were considered in the range from T = 273 to 353 K. Following the success of the three-parameter extended Hückel model within the whole concentration range at various temperatures, we tabulate new values for relative apparent and partial molar enthalpies for NaCl solutions at rounded molalities. The resulting values are extensively tested against the literature ones. The best agreement is obtained for temperatures below 288 K and between 313 and 353 K. Elsewhere, at least a reasonable agreement is obtained. As no enthalpy or heat capacity data were used in the estimation of our model’s parameters and as the model has excelled in explaining other high-precision thermodynamic data, we argue that the recommended enthalpy values should be preferred even for the temperatures where the agreement is only reasonable due to potential problems associated with the literature values. These problems are also considered in the study.Graphical

Thermodynamic properties of aqueous lanthanum sulfate solutions taking into account the association

Thermodynamic properties (the mean activity coefficients, γ±, and the relative apparent molar enthalpies, φL) of lanthanum sulfate aqueous solutions, strongly deviating from the Debye-Hückel limiting law even at lowest experimentally accessible concentrations, can easily and quantitatively be reproduced assuming the formation of two sulfate complexes, LaSO4+ and LaSO42-, whose existence was established in numerous complex formation studies. The analysis was carried out using a simple SIT model for the activity coefficients of ions with only the electrostatic Debye-Hückel terms. Excellent agreement between measured values of γ± and φL and the values of equilibrium constants was obtained by using the following values of equilibrium constants and enthalpy changes of reactions of formation of LaSO4+ (La3++SO42-⇄ LaSO4+) and La(SO4)2- (La3++2SO42-⇄ La(SO4)2-): log10K1o = 3.65 ± 0.05; log10K2o = 5.63 ± 0.2, ΔrH1o = 17.6 ± 1.0 kJ mol−1; ΔrH20 = 28.1 ± 4.0 kJ mol−1. The agreement with literature data is excellent for log10K1o and ΔrH1o and satisfactory for log10K2o and ΔrH2o. With these log10K1o, log10K2o, ΔrH1o and ΔrH2o results the experimental γ± and φL values are reproduced quantitatively.

Study on the dissolution behaviors of CL-20/TNT co-crystal in N,N-dimethylformamide (DMF) and dimethyl sulfoxide (DMSO)

2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (CL-20)/2,4,6-trinitrotoluene (TNT) co-crystal in 1:1 molar ratio was prepared by a solvent evaporation method, and the structural characterizations of CL-20/TNT co-crystal were systematically investigated by powder X-ray diffraction, Raman and differential scanning calorimeter. The dissolution behaviors of CL-20/TNT co-crystal in N,N-dimethylformamide (DMF) and dimethyl sulfoxide (DMSO) were investigated by a DC08-1 Calvet microcalorimeter at 298.15 K, showing that the dissolution processes were all exothermic. The heat effects (Q) of CL-20/TNT co-crystal dissolved in DMF and DMSO both increased with the increase of the amount of co-crystal. Empirical formulas for the calculation of the enthalpies of dissolution ( $$\Delta _{\text{diss}} H$$ ), relative apparent molar enthalpies ( $$\Delta _{\text{diss}} H_{\text{apparent}}$$ ), relative partial molar enthalpies ( $$\Delta _{\text{diss}} H_{\text{partial}}$$ ) were obtained from the experimental data of CL-20/TNT co-crystal dissolved in DMF and DMSO. It was found that the values of $$\Delta _{\text{diss}} H$$ , $$\Delta _{\text{diss}} H_{\text{apparent}}$$ and $$\Delta _{\text{diss}} H_{\text{partial}}$$ were affected by the molality of co-crystal (b). The kinetic equations describing the dissolution of CL-20/TNT co-crystal in DMF and DMSO at 298.15 K are $${\text{d}}\alpha / {\text{d}}t = 10^{ - 2.39} \left( {1 - \alpha } \right)^{0.89}$$ and $${\text{d}}\alpha / {\text{d}}t = 10^{ - 2.47} \left( {1 - \alpha } \right)^{0.62}$$ , respectively.

Investigation on the dissolution behavior of 2HNIW·HMX co-crystal prepared by a solvent/non-solvent method in N,N-dimethylformamide at T = (298.15–318.15) K

2,4,6,8,10,12-Hexanitro-2,4,6,8,10,12-hexazisowurtzitane (HNIW)·1,3,5,7-tetranitro-1,3,5,7-tetrazocane (HMX) co-crystal in a 2:1 molar ratio was prepared by a solvent/non-solvent method, and the co-crystal has been characterized by several methods. The enthalpies of dissolution of 2HNIW·HMX co-crystal in N,N-dimethylformamide at different temperatures were measured by a DC08-1 Calvet microcalorimeter under standard atmospheric pressure, and it is indicated that the dissolutions are exothermic process. The empirical formulae for the calculation of the molar enthalpy ( $$\Delta_{\text{diss}} H$$ ) of dissolution, relative partial molar enthalpy ( $$\Delta_{\text{diss}} H_{\text{partial}}$$ ), relative apparent molar enthalpy ( $$\Delta_{\text{diss}} H_{\text{apparent}}$$ ), and enthalpy of dilution ( $$\Delta_{\text{dil}} H_{1,2}$$ ) at 298.15 K are obtained. The differential enthalpies ( $$\Delta_{\text{dif}} H$$ ) and kinetic equations describing the dissolution process at different temperatures are deduced. Furthermore, the apparent activation energy E = 10.54 ± 0.22 kJ mol-1 and pre-exponential constant A = 0.34 ± 0.03 s−1 of 2HNIW·HMX co-crystal are obtained. The standard molar Gibbs free energy of activation ( $$\Delta G_{ \ne }^{\theta }$$ ) at different temperatures is 86.44 ± 0.02 kJ mol−1 (298.15 K), 88.02 ± 0.03 kJ mol−1 (303.15 K), 89.61 ± 0.01 kJ mol−1 (308.15 K), 91.18 ± 0.01 kJ mol−1 (313.15 K), and 92.75 ± 0.02 kJ mol−1 (318.15 K), respectively. The standard molar entropy of activation ( $$\Delta S_{ \ne }^{\theta }$$ ) and standard molar enthalpy of activation ( $$\Delta H_{ \ne }^{\theta }$$ ) are − 262.55 ± 0.72 J mol−1 K−1 and 7.98 ± 0.22 kJ mol−1, respectively.

Structural Elucidation of the Binary Mixtures of [EMIM][BF4] and [BMIM][BF4] in Ethyl‐Substituted Solvents by Isothermal Titration Calorimeter

AbstractIn order to address the issue whether both ionic liquids and solvents influence the enthalpy of their solutions, highly accurate excess partial molar enthalpy, values have been measured using Isothermal Titration Calorimeter (ITC). Therefore, thermodynamic behavior has been observed in the mixtures containing ionic liquids. It essentially depends on the molecular structure of the constituents of the mixture. The hydrogen bonding between ionic liquids and ethyl‐substituted solvents (2‐ethoxyethanol, ethylene glycol, diethylamine, ethyl acetate and N,N‐ diethylacetamide) may lead to strong ion‐solvent interactions. In the present study, an effort has been made to quantify various interactions between ionic liquid and solvent, based on the values. Linear solvation free relation shows dependence of limiting excess partial molar enthalpies, upon the solvent properties. Structural orientation of solvent molecules and ionic liquids also described by the values. The ion‐ion, ion‐solvent interactions have also been investigated in terms of the enthalpic interaction parameters, and relative apparent molar enthalpy, φL of ionic liquid‐ethyl‐substituted solvent systems.

Thermochemical Properties of the Dissolution of Rubidium d-Gluconate Rb[d-C6H11O7]2(s) in Aqueous Solutions

A novel coordination compound rubidium d-gluconate Rb[d-C6H11O7](s) has been synthesized and characterized by chemical analysis, elemental analysis, and X-ray diffraction. Single-crystal X-ray analysis reveals that the crystal is monoclinic with space group P21 and Z = 2. Also, the d-gluconate anion in Rb[d-C6H11O7](s) has a bent-chain conformation, in which the carbon atoms of the anion form two approximate planes. The compound exhibits an obvious chelation of the d-gluconate anions to the rubidum(I) cation and the cation is seven-coordinated to all seven oxygen atoms. The lattice potential energy and ionic volume of the anion d-\( {\text{C}}_{ 6} {\text{H}}_{ 1 1} {\text{O}}_{7}^{ - } \) were obtained to be UPOT = 484.23 kJ·mol−1 and V− = 0.2004 nm3 from crystallographic data. Molar enthalpies of dissolution of Rb[d-C6H11O7](s) in double-distilled water at various molalities were measured by use of an isoperibol solution–reaction calorimeter at T = 298.15 K. According to Pitzer’s electrolyte solution model, the molar enthalpy of dissolution of the title compound at infinite dilution was determined to be \( \Delta_{\text{s}} H_{\text{m}}^{\infty } = (29.76 \pm 0.72){\text{ kJ}}{\cdot}{\text{mol}}^{ - 1} \). The values of the apparent relative molar enthalpies (\( ^{\phi } L_{{}} \)) of the title compound and relative partial molar enthalpies (\( \bar{L}_{2} \) and \( \bar{L}_{1} \)) of the solute and the solvent at different concentrations were derived from the experimental enthalpies of dissolution of the compound. Furthermore, the molar enthalpy of hydration of the anion d-\( {\text{C}}_{ 6} {\text{H}}_{ 1 1} {\text{O}}_{7}^{ - } \) was calculated to be ΔH− = − (166.4 ± 2.7) kJ·mol−1 by use of a thermochemical cycle.

Phase diagrams and thermochemical modeling of salt lake brine systems. III. Li2SO4+H2O, Na2SO4+H2O, K2SO4+H2O, MgSO4+H2O and CaSO4+H2O systems

This paper is part of a series of studies on the development of a multi-temperature thermodynamically consistent model for salt lake brine systems. Under the comprehensive thermodynamic framework proposed in our previous study, the thermodynamic and phase equilibria properties of the sulfate binary systems (i.e., Li2SO4 + H2O, Na2SO4 + H2O, K2SO4 + H2O, MgSO4 + H2O and CaSO4 + H2O) were simulated using the Pitzer-Simonson-Clegg (PSC) model. Various type of thermodynamic properties (i.e., water activity, osmotic coefficient, mean ionic activity coefficient, enthalpy of dilution and solution, relative apparent molar enthalpy, heat capacity of aqueous phase and solid phases) were collected and fitted to the model equations. The thermodynamic properties of these systems can be well reproduced or predicted using the obtained model parameters. Comparisons with the experimental or model values in literature indicate that the model parameters determined in this study can describe all of the thermodynamic and phase equilibria properties of these binary sulfate systems from infinite dilution to saturation and freezing point temperature to approx. 500K.

Enthalpic interactions in aqueous strong electrolytes upon addition of ionic liquids.

The present study deals with the inter-ionic interactions between strong electrolytes and ionic liquids based on the thermodynamic properties such as excess partial molar enthalpy, HEIL, relative apparent molar enthalpy, φL, and the enthalpic interaction parameters. The thermodynamic properties of the systems are the key indicators to understand the interionic interactions. We have conducted a systematic investigation of the enthalpic behavior of aqueous solution of salts and ionic liquids and their mixtures. The present study also emphasizes how the HEIL values for the mixture of aqueous solution of ionic liquids and salts deviate from linearity as compared to those of the constituent aqueous ionic liquid or salt. This deviation from linearity for the HEIL values has been discussed here.

Crystal structure and chemical thermodynamic properties of potassium d-gluconate K(d-C6H11O7)(s)

An important coordination compound potassium d-gluconate K[d-C6H11O7](s) has been synthesized by liquid phase method. The chemical component and crystal structure of the important compound are characterized by chemical analysis, elemental analysis, and X-ray crystallography. Single-crystal X-ray analysis reveals that the compound exhibits the chelate property of d-gluconate anions to K+ cations, a six-membered chelate ring is formed by the coordination of K+ with O2 of carboxylate and O4 of hydroxyl in a d-gluconate, and one cation is coordinated to six d-gluconate anions. The lattice potential energy and ionic volume of the anion [d-C6H11O7]− are obtained from crystallographic data. In accordance with Hess’ law, a reasonable thermochemical cycle is designed according to the practical synthesis reaction of the compound and the standard molar enthalpy of formation of the compound is calculated to be −(1754.17 ± 0.19) kJ mol−1 as an important physical quantity in chemical thermodynamics by an isoperibol solution–reaction calorimeter. Molar enthalpies of dissolution of the compound at various molalities are measured at T = 298.15 K in the double-distilled water. According to Pitzer’s electrolyte solution theory, molar enthalpy of dissolution of the title compound at infinite dilution is calculated to be \(\Delta_{\text{s}} H_{\text{m}}^{\infty }\) = (27.92 ± 0.21) kJ mol−1. In terms of the above value, the standard molar enthalpy of formation of the anion [d-C6H11O7]− in the aqueous solution is determined to be = −(1473.87 ± 0.28) kJ mol−1. The values of relative apparent molar enthalpies (Φ L) and relative partial molar enthalpies of the solvent (\(\bar{L}_{1}\)) and the compound (\(\bar{L}_{2}\)) at different concentrations m/(mol kg−1) are derived from the experimental values of the enthalpies of dissolution of the compound.

Thermochemical Properties of Dissolution of Nicotinic Acid C6H5NO2(s) in Aqueous Solution

Nicotinic acid (also known as niacin) was recrystallized from anhydrous ethanol. X-ray crystallography was applied to characterize its crystal structure. The crystal belongs to the monoclinic system, space group P2(1)/c. The crystal cell parameters are a = 0.71401(4) nm, b = 1.16195(7) nm, c = 0.71974(6) nm, α = 90°, β = 113.514(3)°, γ = 90° and Z = 4. Molar enthalpies of dissolution of the compound, at different molalities m/(mol·kg−1) were measured with an isoperibol solution–reaction calorimeter at T = 298.15 K. The molar enthalpy of solution at infinite dilution was calculated, according to Pitzer’s electrolyte solution model and found to be \( \Delta_{\text{sol}} H_{m}^{\infty } = ( 2 7. 3 \pm 0. 2) \) kJ·mol−1 and Pitzer’s parameters (\( \beta_{{\text{MX}}}^{{\text{(0)}L}} \), \( \beta_{{\text{MX}}}^{{\text{(1)}L}} \) and \( C_{{\text{MX}}}^{\phi L} \)) were obtained. The values of apparent relative molar enthalpies (\( {}^{\phi }L \)) and relative partial molar enthalpies (\( \overline{{L_{2} }} \) and \( \overline{{L_{1} }} \)) of the solute and the solvent at different molalities were derived from the experimental enthalpy of dissolution values of the compound. Also, the standard molar enthalpy of formation of the anion \( {\text{C}}_{ 6} {\text{H}}_{ 4} \text{NO}_{2}^{-} \) in aqueous solution was calculated to be \( {\Delta_{\text{f}}^{} H}_{\text{m}}^{\text{o}} ({\text{C}}_{ 6} {\text{H}}_{ 4} {\text{NO}}_{2}^{-} \text{,aq}) = - \left( {603.2 \pm 1.2} \right)\;{\text{kJ}}{\cdot}{\text{mol}}^{-1} \).

Dissolution properties of 5,5′-bistetrazole-1, 1′-dihydroxy and disodium 5,5′-bistetrazole-1, 1′-diolate in dimethyl sulfoxide

The enthalpies of dissolution for 5,5′-Bistetrazole-1, 1′-dihydroxy ((H2O)2BTO) and disodium 5,5′-Bistetrazole-1,1′-diolate ([Na2(H2O)4]BTO) in dimethyl sulfoxide (DMSO) at 298.15 K were studied by using a C-80 Calvet microcalorimeter. Empirical formulae for the calculation of the molar enthalpies of dissolution (Δdiss H), relative partial molar enthalpies (Δdiss H partial), and relative apparent molar enthalpies (Δdiss H apparent) were deduced by the experimental results of the dissolution processes of (H2O)2BTO and [Na2(H2O)4]BTO in DMSO. Finally, the corresponding kinetic equations describing the dissolution processes were dα/dt = 10−2.60(1−α)0.61 for the dissolution of (H2O)2BTO in DMSO, and dα/dt = 10−2.69(1−α)0.62 for the dissolution of [Na2(H2O)4]BTO in DMSO.

A safety way to measure the thermal properties of nitroglycerin dissolved in ethyl acetate and ethanol

The enthalpies of dissolution for nitroglycerin in ethanol and ethyl acetate were measured successfully at 298.15 K under atmospheric pressure by designing a special mixing device and using microcalorimetry technology. Empirical formulae for the calculation of the molar enthalpies of dissolution (∆dissH), relative partial molar enthalpies (∆dissHpartial), and relative apparent molar enthalpies (∆dissHapparent) were obtained by experimental data analysis and theoretical calculation. Furthermore, the corresponding kinetic equations describing the two dissolution processes are dα/dt = 10−3.21 (1 − α)1.01 in ethyl acetate and dα/dt = 10−3.43 (1 − α)1.02 in ethanol, respectively.

Thermochemical properties of 2,6-diamino-3,5-dinitropyrazine-1-oxide in dimethyl sulfoxide and N-methyl pyrrolidone

The molar enthalpies of dissolution for 2,6-diamino-3,5-dinitropyrazine-1-oxide (LLM-105) in dimethyl sulfoxide (DMSO) and N-methyl-2-pyrrolidone (NMP) were measured using a RD496-2000 Calvet microcalorimeter at 298.15 K under atmospheric pressure. Empirical formulae for the calculation of the molar enthalpies of dissolution (ΔdissH), relative partial molar enthalpies (ΔdissHpartial) and relative apparent molar enthalpies (ΔdissHapparent) were obtained from the experimental data of the dissolution processes of LLM-105 in DMSO or NMP. Furthermore, the corresponding kinetic equations describing the two dissolution processes were dα/dt = 10−2.37(1 − α)0.47 for the dissolution of LLM-105 in DMSO, and dα/dt = 10−2.38(1 − α)0.42 for the dissolution of LLM-105 in NMP.

Crystal structure and thermochemical properties of potassium pyruvate C3H3O3K(s)

One important compound potassium pyruvate C3H3O3K(s) is synthesized and characterized by chemical analysis, elemental analysis, and X-ray crystallography. X-ray single-crystal structural analysis reveals that the compound is formed by one CH3COCOO− anion and one metal cation K+. An obvious feature of the crystal structure of the compound is the formation of the five-membered chelate ring, and it is good for the stability of the compound in structure. The lattice potential energy of the compound and ionic volume of the anion CH3COCOO− are obtained from crystallographic data. The lattice potential energy is determined to be: UPOT[C3H3O3K(s)] = 567.7 kJ mol−1. The V− (the volume of the anion CH3COCOO−) is estimated to be 0.088 nm3. Molar enthalpies of dissolution of the compound at various molalities in the double-distilled water are measured by use of an isoperibol solution-reaction calorimeter at 298.15 K. According to Pitzer’s electrolyte solution theory, molar enthalpy of dissolution of C3H3O3K(s) at infinite dilution is derived to be 22.9 kJ mol−1. The values of relative apparent molar enthalpies (ΦL), relative partial molar enthalpies (\( \bar{L}_{2} \)) of the compound, and relative partial molar enthalpies (\( \bar{L}_{1} \)) of the solvent (water) at different concentrations m/(mol kg−1) are derived from the experimental values of the enthalpies of dissolution of the compound. Finally, the molar enthalpy of hydration of the anion CH3COCOO−(g) is calculated to be −227.8 kJ mol−1 by the design of the thermochemical cycle.

Thermal and volumetric properties of complex aqueous electrolyte solutions using the Pitzer formalism – The PhreeSCALE code

The thermal and volumetric properties of complex aqueous solutions are described according to the Pitzer equation, explicitly taking into account the speciation in the aqueous solutions. The thermal properties are the apparent relative molar enthalpy (Lϕ) and the apparent molar heat capacity (Cp,ϕ). The volumetric property is the apparent molar volume (Vϕ). Equations describing these properties are obtained from the temperature or pressure derivatives of the excess Gibbs energy and make it possible to calculate the dilution enthalpy (∆HD), the heat capacity (cp) and the density (ρ) of aqueous solutions up to high concentrations. Their implementation in PHREEQC V.3 (Parkhurst and Appelo, 2013) is described and has led to a new numerical tool, called PhreeSCALE. It was tested first, using a set of parameters (specific interaction parameters and standard properties) from the literature for two binary systems (Na2SO4–H2O and MgSO4–H2O), for the quaternary K–Na–Cl–SO4 system (heat capacity only) and for the Na–K–Ca–Mg–Cl–SO4–HCO3 system (density only). The results obtained with PhreeSCALE are in agreement with the literature data when the same standard solution heat capacity (Cp0) and volume (V0) values are used. For further applications of this improved computation tool, these standard solution properties were calculated independently, using the Helgeson–Kirkham–Flowers (HKF) equations. By using this kind of approach, most of the Pitzer interaction parameters coming from literature become obsolete since they are not coherent with the standard properties calculated according to the HKF formalism. Consequently a new set of interaction parameters must be determined. This approach was successfully applied to the Na2SO4–H2O and MgSO4–H2O binary systems, providing a new set of optimized interaction parameters, consistent with the standard solution properties derived from the HKF equations.

Phase diagrams and thermochemical modeling of salt lake brine systems. II. NaCl+H2O, KCl+H2O, MgCl2+H2O and CaCl2+H2O systems

This study is part of a series of studies on the development of a multi-temperature thermodynamically consistent model for salt lake brine systems. Under the comprehensive thermodynamic framework proposed in our previous study, the thermodynamic properties of the binary systems (i.e., NaCl+H2O, KCl+H2O, MgCl2+H2O and CaCl2+H2O) are simulated by the Pitzer–Simonson–Clegg (PSC) model. Various thermodynamic properties (i.e., water activity, osmotic coefficient, mean ionic activity coefficient, enthalpy of dilution and solution, relative apparent molar enthalpy, heat capacity of aqueous phase and solid phases) are collected and fitted to the model equations. The thermodynamic properties of these systems are reproduced or predicted by the obtained model parameters. Comparison to the experimental or model values in the literature suggests that the model parameters determined in this study can describe all of the thermodynamic and phase equilibria properties over wide temperature and concentration ranges. This modeling study of binary systems provides a solid basis for property predictions of salt lake brines under complicated conditions.

Dissolution Properties of Dihydroxylammonium 5,5ʹ-Bistetrazole-1,1ʹ-diolate and Disodium 5,5ʹ-Bistetrazole-1,1ʹ-diolate in Water

The dissolution and thermochemical properties of dihydroxylammonium 5,5ʹ-bistetrazole-1,1ʹ-diolate (TKX-50) and its intermedium disodium 5,5ʹ-bistetrazole-1,1ʹ-diolate ([Na2(H2O)4]BTO) in water at 298.15 K were studied using a C-80 Calvet microcalorimeter. Empirical formulae for the calculation of the molar enthalpies of dissolution (ΔdissH), relative partial molar enthalpies (ΔdissHpartial), and relative apparent molar enthalpies (ΔdissHapparent) were deduced by the experimental results of the dissolution processes of TKX-50 and [Na2(H2O)4]BTO in water. Finally, the corresponding kinetic equations describing the dissolution processes were dα/dt = 10−2.95(1 − α)0.64 for the dissolution of TKX-50 in water and dα/dt = 10−2.76(1 − α)1.07 for the dissolution of [Na2(H2O)4]BTO in water.

Dissolution properties of potassium salt of bis(dinitromethyl)difurazanyl ether in N-methyl pyrrolidone and water

The molar enthalpies of dissolution for potassium salt of bis(dinitromethyl)difurazanyl ether [K2(BDFE)] in N-methyl-2-pyrrolidone (NMP) and water were measured using a RD496-2000 Calvet microcalorimeter at 298.15 K under atmospheric pressure. Empirical formulae for the calculation of the molar enthalpies of dissolution (ΔdissH), relative partial molar enthalpies (ΔdissHpartial), and relative apparent molar enthalpies (ΔdissHapparent) were obtained from the experimental data of the dissolution processes of K2(BDFE) in NMP or water. Furthermore, the corresponding kinetic equations describing the two dissolution processes were dα/dt = 10−4.11(1 − α)1.12 for the dissolution of K2(BDFE) in NMP and dα/dt = 10−3.76(1 − α)0.88 for the dissolution of K2(BDFE) in water.

Comparison of the Pitzer and Hückel Equation Frameworks for Activity Coefficients, Osmotic Coefficients, and Apparent Molar Relative Enthalpies, Heat Capacities, and Volumes of Binary Aqueous Strong Electrolyte Solutions at 25 °C

Detailed numerical analysis of literature data for five key thermodynamic properties (activity coefficients, osmotic coefficients, apparent molar relative enthalpies, heat capacities, and volumes) of well-characterized aqueous strong electrolyte solutions shows that equally good fits are generally obtained from the Pitzer and Huckel equations when both frameworks have the same number of adjustable parameters. Fifty-seven strong electrolyte systems with published values at 25 °C have been examined: the differences found between the two frameworks are never large and are only significant with the activity and osmotic coefficients of eight systems. Most of these eight exceptions involve a lanthanide salt that has been characterized by just one research group. For describing the solution thermodynamics of binary (single) strong electrolytes, the Pitzer equations are found to possess no fundamental theoretical advantage over an extended Huckel framework. On the other hand, slight additional flexibility inherent in the Pitzer formalism makes it more susceptible than the Huckel equations to the numerical effects of experimental error. Comparing the fits achieved by the Pitzer and Huckel equation frameworks can help to identify (a) the simple behavior characteristic of strong electrolytes even at high concentration and (b) signs of error in experimental data sets lacking confirmation by independent measurement.

Molar heat capacities and solution thermochemistry of n-undecylammonium bromide monohydrate C11H28BrNO(s)

Crystal structure of n-undecylammonium bromide monohydrate was determined by X-ray crystallography. Molar enthalpies of dissolution of the compound at different concentrations (m/mol kg−1) were measured by an isoperibol solution reaction calorimeter at T = 298.15 K. According to the Pitzer electrolyte solution theory, molar enthalpy of dissolution of the compound at infinite dilution was determined as $$ \Delta _{\text{s}} H_{\text{m}}^{\infty } ({\text{C}}_{11} {\text{H}}_{28} {\text{BrNO}}) $$ = 32.40 kJ mol−1 and Pitzer’s parameters ( $$ \beta_{\text {MX}}^{(0)\text {L}} $$ and $$ \beta_{\text {MX}}^{(1)\text {L}} $$ ) were obtained. The values of apparent relative molar enthalpies ( $$ {}^{\varPhi}L $$ ) of the title compound and relative partial molar enthalpies ( $$ \overline{{L_{2} }} $$ and $$ \overline{{L_{1} }} $$ ) of the solute and the solvent at different concentrations were derived from experimental values of enthalpies of dissolution of the compound. Low-temperature heat capacities of the compound were measured by a precision automated adiabatic calorimeter over the temperature range from 78 to 390 K. Two solid–solid phase transitions were observed for the title compound. The temperatures, molar enthalpies and entropies of the phase transitions were determined as T trs,1 = (314.42 ± 0.229) K, T trs,2 = (338.66 ± 0.228) K, Δtrs H m,1 = (15.542 ± 0.059) kJ mol−1, Δtrs H m,2 = (6.431 ± 0.209) kJ mol−1, Δtrs S m,1 = (49.803 ± 0.079) J K−1 mol−1 and Δtrs S m,2 = (17.658 ± 0.072) J K−1 mol−1, respectively, based on the analysis of heat capacity curve. Two polynomial equations of heat capacities as a function of temperature were fitted by least squares method. Based on the two polynomial equations, smoothed heat capacities and thermodynamic functions of the compound relative to the standard reference temperature 298.15 K were calculated and tabulated at 5-K intervals.