Calorimetric determination of enthalpies for the proton ionization of N,N-bis[2-hydroxyethyl]-2-aminoethanesulfonic acid (BES) and N-tris[hydroxymethyl]methyl-2-aminoethanesulfonic acid (TES) in water-methanol mixtures

The enthalpies of proton ionization of the biochemical buffers N,N-bis[2-hydroxyethyl]-2-aminoethanesulfonic acid (BES) and N-tris[hydroxymethyl]methyl-2-aminoethanesulfonic acid (TES) were obtained in water-methanol mixtures in which the methanol mole fraction (X_m) varied in the range 0-0.36. For both buffers, ionization enthalpy for the first proton (ΔH₁) was small in all solvent media. However, upon addition of methanol, ΔH₂ increased steadily from 22.2 to a maximum of 27.2 kJ mol⁻¹ for BES, whereas for TES it varied from 30.0 to 32.4, with a minimum of 28.6 kJ mol⁻¹ at X_m=0.123. It is noteworthy that this solvent composition lies within the region of maximum structure enhancement of water by methanol. The results were interpreted in terms of methanol-water interactions.     

Calorimetric determination of enthalpy changes for the proton ionization of glycine, N,N-bis(2-hyroxyethyl)glycine (“bicine”) and N-tris(hydroxymethyl)methylglycine (“tricine”) in water-methanol mixtures

Enthalpies for the two proton ionizations of glycine, N,N-bis(2-hyroxyethyl)glycine (“bicine”) and N-tris(hydroxymethyl)methylglycine (“tricine”) were obtained in water-methanol mixtures with methanol mole fraction (X_m) from 0 to 0.360. With increasing methanol the ionization enthalpy for the first proton (ΔH₁) of glycine increased from 4.4 to 9.4 kJ mol⁻¹ with a minimum of 4.1 kJ mol⁻¹ at X_m = 0.059. The ionization enthalpy of the second proton (ΔH₂) for glycine decreased from 46.3 to 38.1 kJ mol⁻¹. ΔH₁ of bicine increased from 3.5 to 7.6 kJ mol⁻¹ at X_m = 0.273 before dropping to 4.1 kJ mol⁻¹ at X_m = 0.360. ΔH₂ of bicine increased from 24.9 to 29.4 kJ mol⁻¹. For tricine, ΔH₁ increased from 6.7 to 9.8 kJ mol⁻¹ at X_m = 0.194 then dropped to 7.4 kJ mol⁻¹ at X_m = 0.360. ΔH₂ for tricine first dropped from 30.8 to 28.5 kJ mol⁻¹ at X_m = 0.059 before increasing to 33.3 kJ mol⁻¹ at X_m = 0.273. The solvent composition was selected so as to include the region of maximum structure enhancement of water by methanol. The results were interpreted in terms of solvent-solvent and solvent-solute interactions.     

Calorimetric determination of enthalpy changes for proton ionization of N-[2-hydroxyethyl]piperazine-N′-[2-ethane sulfonic acid] (HEPES) and N-[2-hydroxyethyl]piperazine-N′-[2-hydroxypropane sulfonic acid] (HEPPSO) in water-methanol mixtures

Enthalpies for the two proton ionizations of the biochemical buffers N-[2-hydroxyethyl]piperazine-N′-[2-ethane sulfonic acid] (HEPES) and N-[2-hydroxyethyl]piperazine-N′-[2-hydroxypropane sulfonic acid] (HEPPSO) were obtained in water-methanol mixtures with methanol mole fraction (X_m) from 0 to 0.360. With increasing methanol, the ionization enthalpy for the first proton (ΔH₁) of HEPES increased steadily from 8.4 to 15.3 kJ mol⁻¹ whereas that for HEPPSO rose to a maximum of 21.0 kJ mol⁻¹ at X_m = 0.123 before dropping to 18.4 kJ mol⁻¹ at X_m = 0.360. The ionization enthalpy for the second proton (ΔH₂) of HEPES varied from 20.8 kJ mol⁻¹ in water to 13.6 kJ mol⁻¹ at X_m = 0.360 with a maximum of 24.8 kJ mol⁻¹ at X_m = 0.194. For HEPPSO, ΔH₂ increased steadily from 23.4 to 29.2 kJ mol⁻¹. The solvent composition was selected so as to include the region of maximum structure enhancement of water by methanol. The results were interpreted in terms of solvent-solvent and solvent-solute interactions.     

Temperature dependence vapour pressure measurements of Mg(tmhd)2(tmeda) [(tmhd = 2,2,6,6-tetramethyl-3,5-heptanedione, tmeda = N,N,N′,N′-tetramethylethylenediamine]

The reaction between the magnesium β-diketonate complex Mg(tmhd)₂(H₂O)₂ and 1 equiv. of N,N,N′,N′-tetramethylethylenediamine (tmeda = Me₂NCH₂CH₂NMe₂) in hexane at room temperature yielded Mg(tmhd)₂(tmeda). The standard enthalpy of sublimation (83.2 ± 2.3 kJ mol⁻¹) and entropy of sublimation (263 ± 6.3 J mol⁻¹ K⁻¹) of Mg(tmhd)₂(tmeda) were obtained from the temperature dependence vapour pressure, determined by adopting a horizontal dual arm single furnace thermogravimetric analyser as a transpiration apparatus. From the observed melting point depression DTA, the standard enthalpy of fusion (58.3 ± 5.2 kJ mol⁻¹) was evaluated, using the ideal eutectic behaviour of Mg(tmhd)₂(tmeda) as a solvent with bis(2,4-pentanedionato)magnesium(II), Mg(acac)₂ as a non-volatile solute.     

New Insights into Buffer-Ionic Salt Interactions: Solubilities,Transfer Gibbs Energies,and Transfer Molar Volumes of TAPS and TAPSO from Water to Aqueous Electrolyte Solutions

The solubilities of N-[tris(hydroxymethyl)methyl]-3-aminopropanesulfonic acid (TAPS) or N-[tris(hydroxymethyl)methyl]-3-amino-2-hydroxypropanesulfonic acid (TAPSO) in water and in aqueous solutions of CH₃COOK (KAc), KBr, KCl, or NaCl were determined from density measurements at 298.15 K. The solubilities of TAPS in aqueous solution decrease with increasing concentration of the salts (salting-out effect), whereas those of TAPSO increase with increasing concentration of the salts (salting-in effect). The solubility and density data were further used to calculate the apparent transfer Gibbs energies, Δ_tr G, and transfer molar volumes, D_trV_f^o\Delta_{\mathrm{tr}}V_{\phi}^{\mathrm{o}}, of these buffers from water to aqueous electrolyte solutions at 298.15 K. The contributions of various functional groups of TAPS, TAPSO, and the related buffers (tris(hydroxymethyl)aminomethane, TRIS, and N-tris[hydroxymethyl]-4-amino-butanesulfonic acid, TABS) to the transfer properties were systematically estimated from the calculated Δ_tr G and D_trV_f^o\Delta_{\mathrm{tr}}V_{\phi}^{\mathrm{o}}.     

Dinitrogen and carbon monoxide hydrogen bonding in protonic zeolites: Studies from variable-temperature infrared spectroscopy

Adsorption (at a low temperature) of nitrogen on the protonic zeolite H-Y results in hydrogen bonding of the adsorbed N₂ molecules with the zeolite Si(OH)Al Brønsted-acid groups. This hydrogen-bonding interaction leads to activation, in the infrared, of the fundamental N–N stretching mode, which appears at 2334 cm⁻¹. From infrared spectra taken over a temperature range, the standard enthalpy of formation of the OH···N₂ complex was found to be ΔH⁰ = −15.7(±1) kJ mol⁻¹. Similarly, variable-temperature infrared spectroscopy was used to determine the standard enthalpy change involved in formation of H-bonded CO complexes for CO adsorbed on the zeolites H-ZSM-5 and H-FER; the corresponding values of ΔH⁰ were found to be −29.4(±1) and −28.4(±1) kJ mol⁻¹, respectively. The whole set of results was analysed in the context of other relevant data available in the literature.     

Stability Constants for the Equilibrium Models of Iron(III) with Several Biological Buffers in Aqueous Solutions

The complexation equilibria of Fe(III) with two buffer families, which are ubiquitous in biological system studies, were studied by potentiometric measurements at a constant ionic strength of I = 0.1 mol·dm^?3 NaNO₃ in aqueous solutions at 298.15 K. The members of TRIS family are tris(hydroxymethyl)aminomethane (TRIS), N-[tris(hydroxymethyl)methyl]-2-aminoethanesulfonic acid (TES), N-[tris(hydroxymethyl)methyl]-3-aminopropanesulfonic acid (TAPS), N-[tris(hydroxymethyl)methyl]-3-amino-2-hydroxypropanesulfonic acid (TAPSO), and N-tris(hydroxymethyl)methyl-4-aminobutanesulfonic acid (TABS) buffers. The members of morpholine family are 4-morpholineethanesulfonic acid (MES), 4-morpholinepropanesulfonic acid (MOPS), 3-morpholino-2-hydroxypropanesulfonic acid (MOPSO), and 4-(N-morpholino) butanesulfonic acid (MOBS) buffers. The overall stability constants were determined from pH-metric data using the least-squares curve-fitting program HYPERQUAD 2008. Based on the best-fit results, the species formed at equilibrium are ML, ML₂, ML₂H_?1, and ML₃ in the systems with TRIS family buffers. The complex species ML, ML₂, ML₂H_?1, and MLH_?1 are formed in the MOPSO-containing system, while ML, ML₂, and ML₂H_?1 are formed in the systems with MES, MOPS, and MOBS. The stabilities of the complexes fall in the order TABS > TRIS > TAPS > TAPSO > TES and MOBS > MOPS > MOPSO > MES for the TRIS family and morpholine families, respectively.     

Energetics of copper diphosphates – Cu2P2O7 and Cu3(P2O6OH)2

Differential scanning calorimetry and high temperature oxide melt solution calorimetry are used to study enthalpy of phase transition and enthalpies of formation of Cu₂P₂O₇ and Cu₃(P₂O₆OH)₂. α-Cu₂P₂O₇ is reversibly transformed to β-Cu₂P₂O₇ at 338–363 K with an enthalpy of phase transition of 0.15 ± 0.03 kJ mol⁻¹. Enthalpies of formation from oxides of α-Cu₂P₂O₇ and Cu₃(P₂O₆OH)₂ are −279.0 ± 1.4 kJ mol⁻¹ and −538.8 ± 2.7 kJ mol⁻¹, and their standard enthalpies of formation (enthalpy of formation from elements) are −2096.1 ± 4.3 kJ mol⁻¹ and −4302.7 ± 6.7 kJ mol⁻¹, respectively. The presence of hydrogen in diphosphate groups changes the geometry of Cu(II) and decreases acid–base interaction between oxide components in Cu₃(P₂O₆OH)₂, thus decreasing its thermodynamic stability.     

Study on dynamic interfacial tension of 3-dodecyloxy-2-hydroxypropyl trimethyl ammonium bromide at liquid/liquid interface

Dynamic interfacial tension between aqueous solutions of 3-dodecyloxy-2-hydroxypropyl trimethyl ammonium bromide (R₁₂HTAB) and n-hexane were measured using the spinning drop method. The effects of the R₁₂HTAB concentration (the concentration below the CMC) and temperature on the dynamic interfacial tension have been investigated; the reason of the change of dynamic interfacial tension with time has been discussed. The effective diffusion coefficient, D_a, and the adsorption barrier, _a, have been obtained from the experimental data using the extended Word–Tordai equation. The results show that the dynamic interfacial tension becomes smaller while _a becomes higher with increasing R₁₂HTAB concentration in the bulk aqueous phase. D_a decreases from 5.56 × 10⁻¹² m⁻² s⁻¹ to 0.87 × 10⁻¹² m⁻² s⁻¹ while _a increases from 5.41 kJ mol⁻¹ to 7.74 kJ mol⁻¹ with the increase of concentration in the bulk solution of R₁₂HTAB from 0.5 × 10⁻³ mol dm⁻³ to 4 × 10⁻³ mol dm⁻³. Change of temperature affects the adsorption rate through altering D_a and _a. The value of D_a increases from 5.56 × 10⁻¹² m⁻² s⁻¹ to 13.98 × 10⁻¹² m⁻² s⁻¹ while that of _a decreases from 5.41 kJ mol⁻¹ to 5.07 kJ mol⁻¹ with temperature ascending from 303 K to 323 K. The adsorption of surfactant from the bulk phase into the interface follows a mixed diffusion–activation mechanism, which has been discussed in the light of interaction between surfactant molecules, diffusion and thermo-motion of molecules.     

Vapor pressure, kinetics and enthalpy of sublimation of bis(2,2,6,6-tetramethyl-3,5-heptanedionato)copper(II)

The kinetics of sublimation of bis(2,2,6,6-tetramethyl-3,5-heptanedionato)copper(II), [Cu(tmhd)₂] was studied by non-isothermal and isothermal thermogravimetric (TG) methods. The non-isothermal sublimation activation energy values determined following the procedures of Friedman, Kissinger, and Flynn–Wall methods yielded 93 ± 5, 67 ± 2, and 73 ± 4 kJ mol⁻¹, respectively and the isothermal sublimation activation energy was found to be 97 ± 3 kJ mol⁻¹ over the temperature range of 375–435 K. The dynamic TG run proved the complex to be completely volatile and the equilibrium vapor pressure (p_e)_T of the complex over the temperature range of 375–435 K determined by a TG-based transpiration technique, yielded a value of 96 ± 2 kJ mol⁻¹ for its standard enthalpy of sublimation (Δ_subH°).     

Interaction of biological buffers with electrolytes: Densities of aqueous solutions of two substituted aminosulfonic acids and ionic salts from T = (298.15 to 328.15) K

Biological buffers are of utmost importance for research in biological and clinical chemistry and in oceanography, but they may not be inert enough, thus interfering with the system under study. The N-[Tris(hydroxymethyl)methyl]-3-aminopropanesulfonic acid (TAPS) and N-[Tris(hydroxymethyl)methyl]-3-amino-2-hydroxypropanesulfonic acid (TAPSO) are useful zwitterionic buffers for pH control as standard buffers in the physiological region of pH 7.7 to 9.1 for TAPS and 7.0 to 8.2 for TAPSO, respectively. In this work, interaction between these zwitterionic compounds and electrolytes of potassium acetate (KAc), potassium bromide (KBr), potassium chloride (KCl), and sodium chloride (NaCl) were investigated through measuring the densities of these buffers in aqueous and in aqueous electrolyte solutions by a high precision vibrating tube digital densitometer from T = (298.15 to 328.15) K under atmospheric pressure. In this series of measurements, the aqueous samples were prepared with various concentrations of the zwitterionic buffers, up to saturated conditions, and over salt concentrations from (1 to 4) mol · dm^?3. The measured densities served to evaluate the cubic expansion coefficients, α(m, T) and the apparent molar volumes, V_?(m, T). An empirical equation was used to correlate quantitatively the experimental densities over the entire concentration ranges.     

Diffusion of Sr and Zr in BaTiO3 single crystals

The diffusion of strontium and zirconium in single crystal BaTiO₃ was investigated in air at temperatures between 1000 °C and 1250 °C. Thin films of SrTiO₃, deposited by spin coating a precursor solution and thin films of zirconium, deposited onto the sample surfaces by sputtering, were used as diffusion sources. The diffusion profiles were measured by SIMS depth profiling on a time-of-flight secondary ion mass spectrometer (ToF-SIMS). The diffusion coefficients of strontium and zirconium were given by D_Sr = 3.6 × 10^2.0±4.4 exp[−(543 ± 117) kJ mol⁻¹/(RT)] cm² s⁻¹ and D_Zr = 1.1 × 10^1.0±2.1 exp[−(489 ± 56) kJ mol⁻¹/(RT)] cm² s⁻¹. The results are discussed in terms of different diffusion mechanisms in the perovskite structure of BaTiO₃.     

Standard molar enthalpies of formation of 2-, 3- and 4-cyanobenzoic acids

The standard (p = 0.1 MPa) molar enthalpies of formation of 2-, 3- and 4-cyanobenzoic acids were derived from their standard molar energies of combustion, in oxygen, at T = 298.15 K, measured by static bomb combustion calorimetry. The Calvet high temperature vacuum sublimation technique was used to measure the enthalpies of sublimation of 2- and 3-cyanobenzoic acids. The standard molar enthalpies of formation of the three compounds, in the gaseous phase, at T = 298.15 K, have been derived from the corresponding standard molar enthalpies of formation in the condensed phase and standard molar enthalpies for phase transition. The results obtained are −(150.7 ± 2.0) kJ · mol⁻¹, −(153.6 ± 1.7) kJ · mol⁻¹ and −(157.1 ± 1.4) kJ · mol⁻¹ for 2-cyano, 3-cyano and 4-cyanobenzoic acids, respectively. Standard molar enthalpies of formation were also estimated by employing two different methodologies: one based on the Cox scheme and the other one based on several different computational approaches. The calculated values show a good agreement with the experimental values obtained in this work.     

The oxidation mechanisms of Cu54Ni45Mn1 (Constantan) tapes: Kinetic analysis

The kinetic parameters, namely the triplet activation energy E_A, model function f(α) or g(α) and pre-exponential factor A of the oxidation of Constantan tapes in 1 atm of oxygen have been determined from both isothermal and non-isothermal thermogravimetry. For isothermal experiments, with temperatures ranging from 650 °C to 900 °C, the results from direct conversion of the weight increase as a function of the time and curve fitting, are compared with the isoconversion method. For the non-isothermal experiments, with heating rates from 1 °C/min to 20 °C/min, comparison is made between the Friedman differential method and the integral methods of Kissinger, Ozawa and Li and Tang. All methods give apparent activation energies with relative standard deviations as low as 3%. The results converge to the identification of three stages in the oxidation behaviour. A parabolic law for reaction extents α below 15% with E_A = 246 ± 7 kJ mol⁻¹, ln A = 14.3, is followed by two linear stages with E_A = 244 ± 4 kJ mol⁻¹ and ln A = 15.3 for 0.18 < α < 0.35 and E_A = 228 ± 15 kJ mol⁻¹, ln A ≈ 13 for α > 45%, respectively.     

Thermophysical characterization of aqueous ternary system containing n-tris-[hydroxymethyl]methyl-3-amino propanesulfonic acid and glycol (PG or DPG or TPG)

In this present work, a thermophysical property characterization of aqueous ternary system containing n-tris-[hydroxymethyl]methyl-3-aminopropanesulfonic acid (TAPS) and glycol was done. Thermophysical properties, including refractive index, density, and electrolytic conductivity, measurements were considered. The glycols considered are propylene glycol (PG), dipropylene glycol (DPG), and tripropylene glycol (TPG). The measurements were done over a temperature range of 298.15 K to 343.15 K and at normal atmospheric pressure. Different concentrations (4% to 16% by weight TAPS or 56% to 44% water, in a fixed amount of glycol – 40%) were used. The effects of temperature and compositions on the measured properties were discussed and then correlated based on the equation proposed for aqueous salt–glycol systems. Calculation results show that the applied model was satisfactory in representing the measured properties in the aqueous ternary systems containing TAPS and considered glycols.     

Solvatochromic studies of interactions between surfactants and poly(N-substituted acrylamide)s

Interactions between poly(N-substituted acrylamide)s and surfactants, such as sodium dodecyl sulfate (SDoS) and sodium decyl sulfate (SDeS), in aqueous solutions were investigated using a solvatochromic probe. The polymers used were poly(N,N-dimethylacrylamide) (PDMA), poly(N-isopropylacrylamide) (PIPA), poly(N-acryloylpyrrolidine) (PAPR), and poly(vinylpyrrolidone) (PVPy) for comparison. They were labeled with pyridinium dicyanomethylide chromophore as a solvatochromic probe, and the changes in the microenvironment polarity of the polymer upon association with surfactant micelles were investigated by monitoring the λ_max in the absorption spectra of the probe molecule. It was found that the Gibbs free energy of micelle stabilization by polymer complexation for SDoS is 7.6, 4.1, and 2.2 kJ mol⁻¹, and for SDeS 5.1, 2.9, and 0.8 kJ mol⁻¹ with PIPA, PAPR, and PDMA, respectively. These results indicate that the complexation between polymer and surfactant is influenced not only by the alkyl-chain length of the surfactant, but also by the polymer side groups.     

Formation of a rhodium(II) monohydrido complex derived from wilkinson's complex RhCl(PPh3)3 in the interlamellar spaces of montmorillonite and catalytic hydrogenation of cyclohexene

The interaction of molecular hydrogen with [Rh(PPh₃)₃]⁺ (1a) “immobilized” in the interlamellar spaces of montmorillonite resulted in the formation of a monohydrido complex, [Rh^IIH(PPh₃)₃] (2a), characterized by electrochemical data of the clay-loaded electrode, IR, EPR and hydrogen absorption studies. Heterogenized homogeneous catalytic hydrogenation of cyclohexene catalysed by 1a was investigated in the temperature range 283–313 K. The order of reaction with respect to cyclohexene and hydrogen concentration is fractional and first order with respect to catalyst concentration. Thermodynamic parameters ΔH⁰ and ΔS⁰ corresponding to the formation of the monohydrido species were found to be 18 kcal mol⁻¹ and 61 e.u., respectively. The activation enthalpy, ΔH^‡, and entropy, ΔS^‡, for the hydrogenation of cyclohexene by the Rh^II—H complex in clay are more negative by about 2 kcal mol⁻¹ and 7 e.u. compared to Wilkinson's catalyst, RhCl(PPh₃)₃ (1), in homogeneous solution.     

Real-time monitoring of metal deposition and segregation phenomena during preparation of PdCu membranes

The N₂ and H₂ evolution, respectively, were monitored during deposition of Pd and Cu from electroless plating baths to obtain in-process control of the composition during preparation of 3–7 μm thick PdCu membranes on tubular ceramic substrates. Compositions estimated by gas evolution compare favorably to those measured in post-mortem XRD and EDS analyses, mostly differing by not more than 1 at.%. This result suggests that use of gas evolution measurements to enable in-process control of composition to within 1 at.% is feasible. Annealing experiments in an H₂ atmosphere demonstrated that, at 893 K, only 48 h are needed to form a stoichiometrically homogeneous, 9.5 μm thick, face centered cubic (fcc) Pd₆₃Cu₃₇ membrane from sequentially deposited layers; at 723 K, the same transformation requires over 2 weeks. The appearance of transient body centered cubic (bcc) and fcc phases with lower Pd contents signaled compositional segregation in the initial stages of alloy formation at 723 and 773 K and could be a source of persistent stoichiometric heterogeneity particularly in bcc PdCu membranes. The H₂ fluxes of fcc Pd₅₈Cu₄₂ and Pd₇₀Cu₃₀ membranes were J_H2=(1.6±1.1) mol m⁻² s⁻¹ exp[(−24.8±0.4)kJ mol⁻¹/RT] and J_H2=(3.7±0.6) mol m⁻² s⁻¹ exp[(−21.3±1.0)kJ mol⁻¹/RT], respectively, at 100 kPa H₂ pressure difference.     

Voltammetric determination of N-acetylcysteine using a carbon paste electrode modified with copper(II) hexacyanoferrate(III)

The preparation and electrochemical characterization of a carbon paste electrode modified with copper(II) hexacyanoferrate(III) (CuHCF) as well as its behavior as electrocatalyst toward the oxidation of N-acetylcysteine were investigated. The electrochemical behavior of the modified electrode and the electrooxidation of N-acetylcysteine were explored using sweep linear voltammetry. The best voltammetric response was observed for a paste composition of 20% (w/w) copper(II) hexacyanoferrate(III) complex, acetate buffer solution at pH of 6.0 as the electrolyte and scan rate of 10 mV s^− 1. A linear voltammetric response for N-acetylcysteine was obtained in the concentration range from 1.2 × 10^− 4 to 8.3 × 10^− 4 mol L^− 1, with a detection limit of 6.3 × 10^− 5 mol L^− 1. The proposed electrode is useful for the quality control and routine analysis of N-acetylcysteine in pharmaceutical formulations.     

The standard partial molar entropy of the aqueous tetra-n-butylammonium cation

The standard partial molar entropy of the aqueous tetrabutylammonium cation, not known previously, has now been obtained, based on the molar entropy of two of its crystalline salts, the iodide and the tetraphenylborate, recently determined experimentally for this purpose. The calculation required also published molar enthalpies of solution and solubilities of these two salts as well as of the perchlorate. The choice of the anions depended mainly on the limited solubilities of the examined salts in water, facilitating the estimation of the relevant activity coefficients. The result is S^∞(Bu₄N⁺, aq) = (380 ± 20) J · K⁻¹ · mol⁻¹ at T = 298.15 K, on the mol · dm⁻³ scale and based on S^∞(H⁺, aq) = (−22.2 ± 1.2) J · K⁻¹ · mol⁻¹ (yielding the ‘absolute’ value). The molar entropy of this cation in the ideal gas standard state, S(Bu₄N⁺, g) = (798 ± 8) J · K⁻¹ · mol⁻¹ then yielded the molar entropy of hydration Δ_hydS^∞ (Bu₄N⁺) = (−418 ± 23) J · K⁻¹ · mol⁻¹.