Dependence of the density of solutions of alkali metal halides on the composition of methylpyrrolidone-water mixed solvents

The densities of solutions of alkali metal halides in methylpyrrolidone (MP)-water mixtures were measured at 298.15 K over the entire range of mixed solvent compositions. The standard partial molar volumes of the electrolytes \(\overline {V_2^ \circ } \) were calculated. The \(\overline {V_2^ \circ } \) values of alkali metal halides in MP-H₂O mixtures were related linearly to the \(\overline {V_2^ \circ } \) values in aqueous solutions. These dependences were used to determine the standard partial molar volumes of ions \(\overline {V_i^ \circ } \) in the mixtures studied. The standard partial molar volumes of transfer of the ions from water into MP-water mixtures were calculated.     

The thermodynamic properties and solvation of ammonium bromide,iodide, and nitrate in methylpyrrolidone at 298.15 K

The heat capacity and density of solutions of ammonium bromide, iodide, and nitrate in methylpyrrolidone (MP) were studied calorimetrically and densimetrically at 298.15 K. The standard partial molar heat capacities and volumes (\(\overline {C_{p_2 }^O } \) and \(\overline {V_2^O } \)) of the electrolytes in MP were calculated. The standard heat capacities \(\overline {C_{p_i }^O } \) and volumes \(\overline {V_i^O } \) of the nitrate and ammonium ions in MP were determined. The mean coordination numbers of the NH ₄ ⁺ and NO ₃ ^? ions in a solution in MP at 298.15 K were calculated.     

Thermodynamic Properties of Ternary Ionic Liquid Mixture Containing a Common Ion: Excess Molar Volumes,Excess Isentropic Compressibilities,Excess Molar Enthalpies and Excess Heat Capacities

In the present investigations, the excess molar volumes, \( V_{ijk}^{\text{E}} \), excess isentropic compressibilities, \( \left( {\kappa_{S}^{\text{E}} } \right)_{ijk} \), and excess heat capacities, \( \left( {C_{p}^{\text{E}} } \right)_{ijk} \), for ternary 1-butyl-2,3-dimethylimidazolium tetrafluoroborate (i) + 1-butyl-3-methylimidazolium tetrafluoroborate (j) + 1-ethyl-3-methylimidazolium tetrafluoroborate (k) mixture at (293.15, 298.15, 303.15 and 308.15) K and excess molar enthalpies, \( \left( {H^{\text{E}} } \right)_{ijk} \), of the same mixture at 298.15 K have been determined over entire composition range of x _i and x _j . Satisfactorily corrections for the excess properties \( V_{ijk}^{\text{E}} \), \( \left( {\kappa_{S}^{\text{E}} } \right)_{ijk} \), \( \left( {H^{\text{E}} } \right)_{ijk} \) and \( \left( {C_{p}^{\text{E}} } \right)_{ijk} \) have been obtained by fitting with the Redlich–Kister equation, and ternary adjustable parameters along with standard errors have also been estimated. The \( V_{ijk}^{\text{E}} \), \( \left( {\kappa_{S}^{\text{E}} } \right)_{ijk} \), \( \left( {H^{\text{E}} } \right)_{ijk} \) and \( \left( {C_{p}^{\text{E}} } \right)_{ijk} \) data have been further analyzed in terms of Graph Theory that deals with the topology of the molecules. It has also been observed that Graph Theory describes well \( V_{ijk}^{\text{E}} \), \( \left( {\kappa_{S}^{\text{E}} } \right)_{ijk} \), \( \left( {H^{\text{E}} } \right)_{ijk} \) and \( \left( {C_{p}^{\text{E}} } \right)_{ijk} \) values of the ternary mixture comprised of ionic liquids.     

Thermodynamic analysis of the structure of aqueous solutions of C<Subscript>12</Subscript>–C<Subscript>18</Subscript> hydrocarbons

Thermodynamic cycles including the increments \(\Delta G_{CH_2 }^0 , \Delta H_{CH_2 }^0 \), and \(T\Delta S_{CH_2 }^0 \) were constructed for dissolution, evaporation, hydrophobic hydration of C₅–C₉ hydrocarbons, and transfer from vapor (\(\Delta G_{CH_2 }^0 \) = ?0.7 kJ·mol^?1, \(\Delta H_{CH_2 }^0 \) = 2.9 kJ·mol^?1, \(T\Delta S_{CH_2 }^0 \) = 3.6 kJ·mol^?1) and water (\(\Delta G_{CH_2 }^0 \) = ?1.4 kJ·mol^?1, \(\Delta H_{CH_2 }^0 \) = 5.8 kJ·mol^?1, \(T\Delta S_{CH_2 }^0 \) = 7.2 kJ·mol^?1) to micelles of C₁₂–C₁₈ hydrocarbons. The formation of bistable hydrated micelles of C₁₂–C₁₈ is explained by a transition between the order-disorder states in an assembly of small (nano) systems of water. The extensive parameters of small systems and critical phenomena predicted by fluctuation theory are discussed.     

Thermo Physical and Spectroscopic Properties of Binary Liquid Systems: Ethanoic Acid/Propanoic Acid/Butanoic Acid with 2-Methylaniline

Densities (ρ), speeds of sound (u), and viscosities (η) are reported for binary mixtures of 2-methylaniline with carboxylic acids (ethanoic acid, propanoic acid and butanoic acid) over the entire composition range of mole fraction at T?=?(303.15–318.15) K and at atmospheric pressure (0.1 MPa). The excess properties such as excess molar volume (V _m ^E ), excess isentropic compressibility (κ _S ^E ) and excess Gibbs energy of activation of viscous flow (G^*E) are calculated from the experimental densities, speeds of sound and viscosities. Excess properties are correlated using the Redlich–Kister polynomial equation. The partial molar volumes, \( \bar{V}_{\text{m,1}} \) and \( \bar{V}_{\text{m,2}} \), partial molar isentropic compressibilities, \( \bar{K}_{\text{s,m,1}} \) and \( \bar{K}_{\text{s,m,2}} \), excess partial molar volumes, \( \bar{V}_{\text{m,1}}^{\text{E}} \) and \( \bar{V}_{\text{m,2}}^{\text{E}} \), and excess partial molar isentropic compressibilities, \( \bar{K}_{\text{s,m,1}}^{\text{E}} \) and \( \bar{K}_{\text{s,m,2}}^{\text{E}} \), over whole composition range, partial molar volumes, \( \bar{V}_{\text{m,1}}^{ \circ } \) and \( \bar{V}_{\text{m,2}}^{ \circ } \), partial molar isentropic compressibilities, \( \bar{K}_{\text{s,m,1}}^{ \circ } \) and \( \bar{K}_{\text{s,m,2}}^{ \circ } \), excess partial molar volumes, \( \bar{V}_{\text{m,1}}^{{ \circ {\text{E}}}} \) and \( \bar{V}_{{{\text{m}},2}}^{{ \circ {\text{E}}}} \), and excess partial molar isentropic compressibilities, \( \bar{K}_{\text{s,m,1}}^{{ \circ {\text{E}}}} \) and \( \bar{K}_{\text{s,m,2}}^{{ \circ {\text{E}}}} \), of the components at infinite dilution have also been calculated from the analytically obtained Redlich–Kister polynomials. The excess molar volume V^E results are analyzed using the Prigogine–Flory–Patterson theory. Analysis of each of the three contributions viz. interactional V^E(int.), free volume V^E(fv.) and characteristic pressure p* to V^E showed that the interactional contributions are positive for all systems while the free volume and characteristic pressure p* contributions are negative for all the binary mixtures. The results are analyzed in terms of attractive forces between 2-methylaniline and carboxylic acids molecules. Good agreement is obtained between excess quantities and spectroscopic data.     

Thermochemical Properties of Dissolution of Nicotinic Acid C<Subscript>6</Subscript>H<Subscript>5</Subscript>NO<Subscript>2</Subscript>(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 \( {\Delta_{\text{f}}^{} H}_{\text{m}}^{\text{o}} ({\text{C}}_{ 6} {\text{H}}_{ 4} {\text{NO}}_{2}^{-} \text{,aq}) = - \left( {603.2 \pm 1.2} \right)\;{\text{kJ}}{\cdot}{\text{mol}}^{-1} \).     

Imidazolium-Based Ionic Liquids Containing the Trifluoroacetate Anion: Thermodynamic Study

New experimental vapor pressures and vaporization enthalpies of the ionic liquids \( [ {\text{C}}_{2} {\text{mim][CF}}_{3} {\text{CO}}_{2} ] \) and \( [ {\text{C}}_{4} {\text{mim][CF}}_{3} {\text{CO}}_{2} ] \) have been measured by the QCM method. The solution enthalpies of these ionic liquids were measured by using high-precision solution calorimetry and were used for calculation the aqueous enthalpy of formation \( \Delta_{\text{f}} H_{\text{m}}^{ \circ } ({\text{CF}}_{ 3} {\text{CO}}_{2}^{ - } ,_{{}} {\text{aq}}) \) of the anion for combination with quantum-chemical results. The solubility parameters of the ILs under study have been derived from experimental \( \Delta_{\text{l}}^{\text{g}} H_{\text{m}}^{ \circ } \)(298.15 K) values and were used for estimation of miscibility of some common solutes with \( [ {\text{C}}_{n} {\text{mim][CF}}_{3} {\text{CO}}_{2} ] \).     

Heat capacity and density of potassium iodide solutions in mixed N-methylpyrrolidone-water solvent at 298.15 K

The heat capacity and density of potassium iodide solutions in a mixed N-methylpyrrolidone (MP)-water solvent with a low content of the organic component are measured via calorimetry and densimetry at 298.15 K. Standard partial molal heat capacities \(\bar C_{p,2}^ \circ \) and volumes \(\bar V_2^ \circ \) of potassium iodide in MP-water mixtures are calculated. Standard heat capacities \(\bar C_{p,i}^ \circ \) and volumes \(\bar V_i^ \circ \) of potassium and iodide ions are determined. The character of the changes in heat capacity and volume are discussed on the basis of calculating additivity coefficients δ _c and δ _v upon the mixing of isomolal binary solutions KI-MP and KI-water, depending on the composition of the MP-H₂O mixture and the concentration of the electrolyte.     

Thermodynamic analysis of the dynamic structure of micellar solutions of sodium alkyl sulfates

The results of previous studies of the increments \(\Delta G_{CH_2 }^0 \), \(\Delta H_{CH_2 }^0 \), and \(T\Delta S_{CH_2 }^0 \) in hydrocarbon solution processes in water, evaporation, hydration, and transfer from vapor and water to surfactant micelles are summarized. The corresponding thermodynamic cycles were constructed. A micelle was shown to be a bistable structure formed by the contact and water-separated hydrophobic interactions of the alkyl groups of surfactants. The fraction in \(\Delta G_{CH_2 (M)}^0 \) is ?2.3 kJ·mol^?1 for the contact associate and ?0.7 kJ·mol^?1 for the hydrated one. Water is involved in the hydrophobic interaction of each associate. In a dualist micelle, however, \(\Delta G_{CH_2 }^0 \) = ?3.0 kJ mol^?1 equals that of the dispersion interaction after condensation from vapor. The dual nature of the dynamic properties of micelles is discussed.     

The Study of Solute–Solvent Interactions in 1-Butyl-3-Methylimidazolium Hexafluorophosphate + 2-Pyrrolidone from Volumetric,Acoustic, Optical and Spectral Properties

The density (ρ), speed of sound (u) and refractive index (n_D) of [Bmim][PF₆], 2-pyrrolidone and their binary mixtures were measured over the whole composition range as a function of temperature between (303.15 and 323.15)?K at atmospheric pressure. Experimental values were used to calculate the excess molar volumes \( \left( {V_{m}^{\text{E}} } \right) \), excess partial molar volumes \( \left( {\overline{V}_{m}^{\text{E}} } \right) \), partial molar volumes at infinite dilution \( \left( {\overline{V}_{m}^{{{\text{E}},\infty }} } \right) \), excess values of isentropic compressibility \( \left( {\kappa_{S}^{\text{E}} } \right) \), free length \( \left( {L_{\text{f}}^{\text{E}} } \right) \) and speeds of sound \( \left( {u^{\text{E}} } \right) \) for the binary mixtures. The calculated properties are discussed in terms of molecular interactions between the components of the mixtures. The results reveal that interactions between unlike molecules take place, particularly through intermolecular hydrogen bond formation between the C₂–H of [Bmim][PF₆] and the carbonyl group of pyrrolidin-2-one. An excellent correlation between thermodynamic and IR spectroscopic measurements was observed. The observations were further supported by the Prigogine–Flory–Patterson (PFP) theory of excess molar volume.     

Vibratio nal assig nme nts,co nformatio nal a nalysis,a nd molecular structures of $$\left[ {\text{C}_{\text{ n}} \text{mim}} \right]\left[ {\text{NTF}_{\text{2}} } \right]$$C nmimNTF2 ( n = 2, 4, 6, a nd 8) imidazolium-based io nic liquids: a combi ned experime ntal a nd qua ntum chemical approach

This work is aimed at providing physical insights about the interactions of cations, anion, and ion pairs of four imidazolium-based ionic liquids of \(\left[ {{\text{C}}_{\text{n}} {\text{mim}}} \right]\left[ {{\text{NTF}}_{2} } \right]\) with varying alkyl chain lengths (n = 2, 4, 6, and 8) using both DFT calculations and vibrational spectroscopic measurements (IR absorption and Raman scattering) in the mid- and far regions. The calculated Mulliken charge distributions of \(\left[ {{\text{C}}_{\text{n}} {\text{mim}}} \right]\left[ {{\text{NTF}}_{2} } \right]\) ion pairs indicate that hydrogen-bonding interactions between oxygen and nitrogen atoms (more negative charge) on \(\left[ {{\text{NTF}}_{2} } \right]^{ - }\) anion and the hydrogen atoms (more positive charge) on the imidazolium ring play a dominating role in the formation of ion pair. Thirteen stable conformers of \(\left[ {{\text{C}}_{2} {\text{mim}}} \right]\left[ {{\text{NTF}}_{2} } \right]\) were optimized. According to our results, the strongest and weakest hydrogen bonds were existing in \(\left[ {{\text{C}}_{2} {\text{mim}}} \right]\left[ {{\text{NTF}}_{2} } \right]\) and \(\left[ {{\text{C}}_{8} {\text{mim}}} \right]\left[ {{\text{NTF}}_{2} } \right]\), respectively. A redshift of 290, 262, 258, and 257 cm^?1 has been observed for cations involving \(\left[ {{\text{C}}_{2} {\text{mim}}} \right]^{ + }\), \(\left[ {{\text{C}}_{4} {\text{mim}}} \right]^{ + }\),\(\left[ {{\text{C}}_{6} {\text{mim}}} \right]^{ + }\), and stretching vibrations of \({\text{C}}12{-}{\text{H}}3\), respectively. By increasing the chain length, the strength of hydrogen bonds decreases as a result of \({\text{C}}12{-}{\text{H}}3\) bond elongation and less changes are observed in stretching vibrations of \({\text{C}}12{-}{\text{H}}3\) compared to the free cations. To the best of our knowledge, this research is the first work which reports the far-IR of \(\left[ {{\text{C}}_{4} {\text{mim}}} \right]\left[ {{\text{NTF}}_{2} } \right]\), \(\left[ {{\text{C}}_{6} {\text{mim}}} \right]\left[ {{\text{NTF}}_{2} } \right]\), and \(\left[ {{\text{C}}_{8} {\text{mim}}} \right]\left[ {{\text{NTF}}_{2} } \right]\) and the mid-IR of \(\left[ {{\text{C}}_{8} {\text{mim}}} \right]\left[ {{\text{NTF}}_{2} } \right]\).     

Volumetric,Acoustic and Transport Properties of Metformin Hydrochloride Drug in Aqueous <Emphasis Type="SmallCaps">d</Emphasis>-Glucose Solutions at <Emphasis Type="Italic">T</Emphasis> = (298.15–318.15) K

Apparent molar volumes, apparent molar adiabatic compressibilities and viscosity B-coefficients for metformin hydrochloride in aqueous d-glucose solutions were determined from solution densities, sound velocities and viscosities measured at T = (298.15–318.15) K and at pressure p = 101 kPa as a function of the metformin hydrochloride concentrations. The standard partial molar volumes (\( \phi_{V}^{0} \)) and slopes (\( S_{V}^{*} \)) obtained from the Masson equation were interpreted in terms of solute–solvent and solute–solute interactions, respectively. Solution viscosities were analyzed using the Jones–Dole equation and the viscosity A and B coefficients discussed in terms of solute–solute and solute–solvent interactions, respectively. Adiabatic compressibility (\( \beta_{s} \)) and apparent molar adiabatic compressibility (\( \phi_{\kappa }^{{}} \)), limiting apparent molar adiabatic compressibility (\( \phi_{\kappa }^{0} \)) and experimental slopes (\( S_{\kappa }^{*} \)) were determined from sound velocity data. The standard volume of transfer (\( \Delta_{t} \phi_{V}^{0} \)), viscosity B-coefficients of transfer (\( \Delta_{t} B \)) and limiting apparent molar adiabatic compressibility of transfer (\( \Delta_{t} \phi_{\kappa }^{0} \)) of metformin hydrochloride from water to aqueous glucose solutions were derived to understand various interactions in the ternary solutions. The activation parameters of viscous flow for the studied solutions were calculated using transition state theory. Hepler’s coefficient \( (d\phi /dT)_{p} \) indicated the structure making ability of metformin hydrochloride in the ternary solutions.     

Heat capacity and density of solutions of calcium and cadmium nitrates in N-methylpyrrolidone at 298.15 K

The heat capacity and density of solutions of calcium and cadmium nitrates in N-methylpyrrolidone (MP) at 298.15 K are studied by calorimetry and densimetry. The obtained data are discussed in relation to certain features of solvation and complex formation in solutions of these salts. The standard partial molar heat capacities and volumes ( $\overline {C_{p^2 }^0 }$ and $\overline {V_2^0 }$ ) of the electrolytes in MP are calculated. The standard heat capacities $\overline {C_{p^i }^0 }$ and volumes $\overline {V_i^0 }$ of Ca²⁺ and Cd²⁺ ions in MP at 298.15 K were determined, along with the contribution from specific interactions to the values of $\overline {C_{p^i }^0 }$ and $\overline {V_i^0 }$ of Cd²⁺ ions in MP solution.     

Additional Aspects of Complexation of Gold(I) with Thiomalate

Some equilibria involving gold(I) thiomalate (mercaptosuccinate, TM) complexes have been studied in the aqueous solution at 25 °C and I?=?0.2 mol·L^?1 (NaCl). In the acidic region, the oxidation of TM by \( {\text{AuCl}}_{4}^{ - } \) proceeds with the formation of sulfinic acid, and gold(III) is reduced to gold(I). The interaction of gold(I) with TM at n_TM/n_Au?≤?1 leads to the formation of highly stable cyclic polymeric complexes \( {\text{Au}}_{m} \left( {\text{TM}} \right)_{m}^{*} \) with various degrees of protonation depending on pH. In general, the results agree with the tetrameric form of this complex proposed in the literature. At n_TM/n_Au?>?1, the processes of opening the cyclic structure, depolymerization and the formation of \( {\text{Au}}\left( {\text{TM}} \right)_{2}^{*} \) occur: \( {\text{Au}}_{4} ( {\text{TM)}}_{4}^{8 - } + {\text{TM}}^{3 - } \rightleftharpoons {\text{Au}}_{ 4} ( {\text{TM)}}_{5}^{11 - } \), log₁₀ K₄₅?=?10.1?±?0.5; 0.25 \( {\text{Au}}_{4} ( {\text{TM)}}_{4}^{8 - } + {\text{TM}}^{3 - } \rightleftharpoons {\text{Au(TM)}}_{2}^{5 - } \), log₁₀ K₁₂?=?4.9?±?0.2. The standard potential of \( {\text{Au(TM)}}_{2}^{5 - } \) is \( E_{1/0}^{ \circ } = -0. 2 5 5\pm 0.0 30{\text{ V}} \). The numerous protonation processes of complexes at pH?<?7 were described with the use of effective functions.     

Densities,Ultrasonic Velocities,Excess Properties and IR Spectra of Binary Liquid Mixtures of Organic Esters (Ethyl Lactate,Some Organic Carbonates)

Organic esters of carbonic acid {dimethyl carbonate (DMC)/diethyl carbonate (DEC)/propylene carbonate (PC)}, in combination with a lactate ester {ethyl lactate (EL)}, with green chemistry characteristics were chosen for the present study of molecular interactions in binary liquid mixtures. Densities (ρ) and ultrasonic velocities (U) of the pure solvents and liquid mixtures were measured experimentally over the entire composition range at temperatures (303.15, 308.15, 313.15 and 318.15) K and atmospheric pressure. The experimental data was used to calculate thermodynamic and acoustic parameters \( V_{\text{m}}^{\text{E}} \), \( \kappa_{S}^{\text{E}} \), \( L_{\text{f}}^{\text{E}} \), \( \bar{V}_{\text{m,1}}^{{}} \), \( \bar{V}_{\text{m,2}}^{{}} \), \( \bar{V}_{\text{m,1}}^{\text{E}} \), \( \bar{V}_{\text{m,2}}^{\text{E}} \), \( \bar{V}_{ 1}^{\text{E,0}} \) and \( \bar{V}_{ 2}^{\text{E,0}} \) and the excess functions were fitted with the Redlich–Kister polynomial equation to obtain the binary solution coefficients and the standard deviations. It was observed that the values of \( V_{\text{m}}^{\text{E}} \), \( \kappa_{S}^{\text{E}} \) and \( L_{\text{f}}^{\text{E}} \) are positive for the mixtures of (EL + DMC/DEC) and negative for those of (EL + PC) over the entire range of composition and temperature. The positive values of \( V_{\text{m}}^{\text{E}} \), \( \kappa_{S}^{\text{E}} \) and \( L_{\text{f}}^{\text{E}} \) indicate the action of dispersion forces between the component molecules of (EL + DMC/DEC) mixtures whereas negative values for the mixture (EL + PC) suggest the existence of strong specific interactions between the component molecules, probably resulting from chemical and structural contributions. The excess properties have also been analyzed by using the reduced (\( Y^{\text{E}} /x_{1} x_{2} \)) excess function approach and the results are found to be in agreement with those from the corresponding \( Y^{\text{E}} \)(= \( V_{\text{m}}^{\text{E}} \), \( \kappa_{S}^{\text{E}} \) and \( L_{\text{f}}^{\text{E}} \)) values. This is further supported by FTIR spectral analysis.     

Transport selectivity of carbonate and chloride ions througha strongly alkaline anion-exchange membrane before and after its modification with sodium alginate

The transport selectivity of carbonate ions relative to chloride ions \(\left( {P_{Cl^ - }^{CO_3^{2 - } } } \right)\) through an anion-exchange membrane during electrodialysis is investigated before and after the membrane was modified by the electrolytic precipitation of sodium alginate on its surface, as well as by pretreating the membrane in a solution of sodium alginate. It is established that the experimental value of \(P_{Cl^ - }^{CO_3^{2 - } } \) is appreciably smaller than the calculated value for the unmodified membrane at low values of current density. At large currents the calculated value of \(P_{Cl^ - }^{CO_3^{2 - } } \) is 0.83, and the experimental value is 0.64. During electrodialysis of the working solution, which contains sodium alginate at a concentration of 1–2 g l^?1, \(P_{Cl^ - }^{CO_3^{2 - } } \) decreases by 2–3 times in the current-density range 0.25–1 A dm^?2. Pretreatment of the membrane in a solution of sodium alginate having a concentration of 10 g l^?1 for 72 h decreases \(P_{Cl^ - }^{CO_3^{2 - } } \) from 0.50 (unmodified membrane) to 0.35.     

Contact and water-separated hydrophobic interactions in micellar solutions of surfactants

Contact and water-separated hydrophobic interactions accompanying the solution of C₆–C₈ n-alcohols in water and micellar solutions of sodium dodecyl sulfate were studied by the method of \(\Delta G_{CH_2 }^ \circ \) coupled thermodynamic cycles. The results are discussed in terms of the dualistic model of micelle formation consistent with the rigorous theory of solutions. The theoretical results were in agreement with the experimental \(\Delta G_{CH_2 }^ \circ \) values for the solubilization of alcohols and association numbers.     

The standard partial molar volumes of ions in N-methylpyrrolidone at 298.15 K

The standard partial molar volumes of electrolytes and ions in N-methylpyrrolidone (MP) at 298.15 K are presented. Separate components of ionic volumes in solutions in MP at infinite dilution, \(\overline {V_i^0 } \), are considered. The influence of various volume effects on ion-solvent interactions is analyzed.     

Compatibility of activity coefficients estimated experimentally and by Pitzer equations for the assessment of seawater pH

Calibration of pH meters is usually performed with reference pH buffer solutions of low ionic strength, I ≤ 0.1 mol kg^?1. For seawater pH measurements (I ≈ 0.7 mol kg^?1), calibration buffers in high ionic strength matrix are required. The Harned cell, in association with the Nernst equation and a model for estimating the chloride ion activity coefficient, \(\gamma_{{{\text{Cl}}^{ - } }} ,\) is the basis of the primary method for pH assignment to reference pH buffers. The semi-empirical Pitzer model is, in principle, adequate to estimate \(\gamma_{{{\text{Cl}}^{ - } }}\) of complex solutions, namely seawater. Nevertheless, no assessment of the validity of the model for this matrix is known to the authors. This work aims at estimating the adequacy of the Pitzer model by assessing the metrological compatibility of mean activity coefficients, in this case \(\gamma_{ \pm } = \sqrt {\gamma_{{{\text{H}}^{ + } }} \gamma_{{{\text{Cl}}^{ - } }} }\) estimated experimentally with the Harned cell, \(\gamma_{ \pm }^{\text{Exp}} ,\) and using the Pitzer model, \(\gamma_{ \pm }^{\text{Ptz}}\). The measurement uncertainty considered in the compatibility test was estimated using the bottom-up approach, where components were combined by the numerical Kragten method after checking its adequacy. The compatibility of the estimated \(\gamma_{ \pm }\) was assessed for solutions with increasing complexity and an ionic strength of 0.67 mol kg^–1. \(\gamma_{ \pm }^{\text{Exp}}\) and \(\gamma_{ \pm }^{Ptz}\) are metrologically compatible for a confidence level of 95 % where the relative standard uncertainty of their difference ranged from 1.1 % to 3.1 % in all chloride solutions to approximately 6.3 % when sodium sulfate was also present. This led to assume the validity of the Pitzer model equations to estimate \(\gamma_{{{\text{Cl}}^{ - } }} ,\) required to define reference pH values of buffer solutions with high ionic strength.     

On the structure of discrete spectrum of a non-selfadjoint system of differential equations with integral boundary condition

In this paper, we investigated the spectrum of the operator \(L(\lambda )\) generated in Hilbert Space of vector-valued functions \(L_{2}(\mathbb {R}_{+},C_{2})\) by the system

$$\begin{aligned} iy_{1}^{'}(x,\lambda )+q_{1}(x)y_{2}(x,\lambda )&=\lambda y_{1}(x,\lambda )\\ -iy_{2}^{'}(x,\lambda )+q_{2}(x)y_{1}(x,\lambda )&=\lambda y_{2}(x,\lambda ),x\in \mathbb {R}_{+}:=(0,\infty ), \end{aligned}$$

and the integral boundary condition of the type

$$\begin{aligned} \int _{0}^{\infty }K(x,t)y(t,\lambda ){\mathrm {dt}}+\alpha y_{2}(0,\lambda )-\beta y_{1}(0,\lambda )=0 \end{aligned}$$

where \(\lambda \) is a complex parameter, \(q_{i},\,i=1,2\) are complex-valued functions and \(\alpha ,\beta \in \mathbb {C}\). K(x, t) is vector fuction such that \(K(x,t)=(K_{1}(x,t),K_{2}(x,t)),\,K_{i}(x,t)\in L_{1}(0,\infty )\cap L_{2}(0,\lambda ),\,i=1,2\). Under the condition

$$\begin{aligned} \left| q_{i}(x)\right| \le ce^{-\varepsilon \sqrt{x}},c>0,\varepsilon >0,i=1,2 \end{aligned}$$

we proved that \(L(\lambda )\) has a finite number of eigenvalues and spectral singularities with finite multiplicities.