Changes In Thermodynamic Functions Research Articles

Study on the fractions of thermodynamic function changes for both adsorption and desorption from a liquid-solid system

On the basis of the thermodynamics of the stoichiometric displacement model for adsorption of a solute, two equations to calculate separately two fractions of the Gibbs free energy for the solute adsorption and the solvent desorption to be the functions of temperature and the solute activity in bulk solution, were deduced. It was found that ΔG ( βa) (the affinity Gibbs free energy change between an adsorbate and adsorbent) in any equilibrium activity of the solute, α PDm, and another fraction ΔG ( q Z,PDm ) (the desorption Gibbs free energy of a solvent from an adsorbent) under the same α PDm, are linear functions of temperature. When temperature is fixed, ΔG ( βa) is a constant while ΔG ( q Z,PDm ) is proportional to log α PDm. The changes in enthalpy and entropy corresponding to the solute adsorption and the solvent desorption can also be derived from the plot of the foregoing calculations of ΔG ( βa) and ΔG ( q Z,PDm ) vs. thermodynamic temperatures T, respectively. Experimental data on isotherms from the literature are used to test all of the fractions of thermodynamic function changes computed quantitatively with the equations presented in this study, and a satisfactory result was obtained.

Thermodynamics of the tautomeric, hydration and hemiacetalization of 5-deoxypyridoxal and pyridoxal in water-dioxane mixtures

The resolution of electronic spectra using log-normal curves has permitted a quantitative description of the equilibria of pyridoxal, one of the vitamin B6 molecules, and of the related 5-deoxypyridoxal in solution. Tautomeric, hydration and hemiacetalization equilibrium constants for water-dioxane mixtures of these compounds are reported (0–70% weight fraction in dioxane) at temperatures ranging from 10°C to 50°C. These results provide the standard thermodynamic function changes for the indicated processes in the different mixtures studied. The aldehyde content in the two compounds increases concomitantly with the dioxane content of the solution and also when it changes from the cationic to the anionic species. 5-deoxypyridoxal becomes significantly more hydrated in its more protonated form, K h (+a)/K h (±a)≈7–8, as do other aldehydes. Hemiacetalization in pyridoxal follow a similar pattern, K he (±a)/K he (−a)≈20–30, due principally to differences in the enthalpy contribution. Hemiacetalization is favored over hydration by ∼20.6 kJ-mol−1 in water solution.

Solubility of gases in butanols. I. Solubilities of nonpolar gases in 1-butanol from 263.15 to 303.15 K at 101.33 kPa partial pressure of gas

Solubility measurements of 15 nonpolar gases (He, Ne, Ar, Kr, Xe, H 2, D 2, N 2, O 2, CH 4, C 2H 4, C 2H 6, CF 4, SF 6 and CO 2) in 1-butanol were carried out at 263.15, 273.15, 283.15, 293.15, and 303.15 K and partial pressure of gas of 101.33 kPa. Standard changes in thermodynamic functions for the solution process at 298.15 K (Gibbs energy, enthalpy and entropy) are derived from the experimental values of the solubility of gases and its variation with temperature. Lennard-Jones 6,12 pair potential parameters and the dependence of the effective hard-sphere diameter with respect to the temperature for 1-butanol have been estimated using the equations of scaled particle theory (SPT). Making use of SPT in the reverse direction, i.e., starting from the potential parameters found through it, theoretical solubilities and thermodynamic functions for the solution process have been calculated and compared with the experimental values.

Equation of state for lambda transition in quartz

An equation of state has been developed for quartz, a substance with a lambda‐type phase transition. It has the properties of the Murnaghan equation of state in the normal region and reflects the fundamental behavior of thermodynamic functions in the anomalous region. The term jT/(i‐T)1/2 has been introduced in the temperature dependent equations of isobaric heat capacity and the volume coefficient of thermal expansion, where i and j are fitting coefficients. The i coefficient is numerically close to the temperature of the phase transition Tc and is usually in the 0.1<|i‐Tc|<20 K interval. The range of applicability of the Murnaghan equation is delineated in the PT stability field of quartz. In the lambda range, the derivative of thermal expansion with respect to temperature is pressure dependent according to rules that allow integration of the thermal expansion and molar volume for calculation of the change in thermodynamic functions from room pressure to any given pressure. Available phase equilibria and thermochemical data have been used with the proposed equation of state to calculate the standard thermodynamic properties for coesite and the SiO2 phase diagram including alpha quartz, beta quartz, and coesite.

Dipole polarizability and bond dissociation energy

The change of thermodynamic equilibrium-state functions, such as the change in enthalpy ΔH or free enthalpy ΔG, in bond dissociation processes is well known in general. On the other hand, the systematic investigation of the change in electrical and electro-optical properties, such as the dipole polarizability α, seems to be a rather unexplored field in physical chemistry. In this Communication we report on a remarkable correlation between the change in dipole polarizability Δα and the bond dissociation energy D0298 for various dissociation processes.

Glassy state in 2-amino-2-methyl-1,3 propanediol plastic crystal

Heat capacity measurements between 293 K and 363 K have been carried out in order to elucidate the different states appearing in 2-amino-2-methyl-1,3 propanediol (AMP) plastic crystal. The results allowed one of them to be identified as a glassy crystal.The changes of enthalpy, entropy and Gibbs free energy thermodynamic functions with temperature have been calculated from the experimental heat capacity values.

Dehydration of lanthanide aquations in the course of their extraction in the tributylphosphate (TBP)-isothiocyanate system

Extraction coefficients for all lanthanides have been determined in two systems: 0.2M TBP-3M NaNCS, and 3.6M TBP-0.2M NaNCS. The data have been used for the calculation of relative changes in thermodynamic functions accompanying the investigated extraction process. The compensation of enthalpy and entropy changes is found as a result of dehydration of the lanthanide aquaions.

Solubility of 13 non-polar gases (He, Ne, Ar, Kr, Xe, H 2, D 2, N 2, CH 4, C 2H 4, C 2H 6, CF 4 and SF 6) in 2-methyltetrahydrofuran at 273.15 to 303.15 K and 101.33 kPa partial pressure of gas

Gibanel, F., López, M.C., Royo, F.M., Pardo, J. and Urieta, J.S., 1993. Solubility of 13 non-polar gases (He, Ne, Ar, Kr, Xe, H 2, D 2, N 2, CH 4, C 2H 4, C 2H 6, CF 4 and SF 6) in 2-methyltetrahydrofuran at 273.15 to 303.15 K and 101.33 kPa partial pressure of gas. Fluid Phase Equilibria, 87: 285-294. Solubility measurements of several non-polar gases (He, Ne, Ar, Kr, Xe, H 2, D 2, N 2, CH 4, C 2H 4, C 2H 6, CF 4 and SF 6) in 2-methyltetrahydrofuran in the temperature range 273.15–303.15 K and at 101.33 kPa partial pressure of gas are reported. Standard changes in thermodynamic functions for the solution process (Gibbs energies, enthalpies and entropies) at 298.15 K are evaluated from experimental solubilities and their variation with temperature. Lennard-Jones 6,12 pair potential parameters and the temperature dependence on effective hard-sphere diameter for 2-methyltetrahydrofuran are estimated using the scaled particle theory applied to gas-liquid solubility. Experimental solubilities as mole fractions are compared with calculated values using this theory.

The thermodynamics of the ionization of 3-hydroxypyridine and pyridoxine in water–dioxane mixtures

A potentiometric method has been used to determine the thermodynamic equilibrium constants for the macroscopic ionization processes of 3-hydroxypyridine and pyridoxine in water–dioxane mixtures (0–70% weight fraction in dioxane) at temperatures from 10 to 50 °C. From these data the reaction standard thermodynamic function changes were obtained for the processes in various water–dioxane mixtures at 25 °C. It was found, in both molecules, that during the first ionization process the contributions of entropy and enthalpy to free energy are similar but that during the second ionization the main contribution comes from entropy, especially in mixtures with a high dioxane content. The effect of the solvent on the tautomeric equilibrium in the net zero charge specie could explain this behaviour.

The interaction of various types of microcrystalline cellulose and starch with water

Sorption isotherms of water onto/into potato, wheat and maize starch and Avicels PH-101, RC-581 and CL-611 have been prepared. In previous publications, a vacuum microbalance and a sorption microcalorimeter have been used to study interactions between water vapour and crystalline solids. In an attempt to extend the application of these techniques, the thermodynamic functions for sorption of water have been calculated for solids where water sorbs in the amorphous regions (i.e. maize and potato starch and Avicel PH-101 and CL-611). Microcalorimetric methods were also used to study the kinetics of the sorption process. As was expected the potato starch sorbed more water than the other two starches, and the Avicel grades sorbed water in proportion to their sodium carboxymethylcellulose content. The numerical values for the thermodynamic functions were lower than those obtained previously from similar studies on crystalline pharmaceutical powders. For starches and celluloses, it is proposed that water binds to anhydroglucose units within the amorphous regions of the solid. It has been suggested that over the sorption process water initially binds as one molecule between two anhydroglucose units, but that these bonds are then broken to form a 1 : 1 stoichiometry. This process of forming and breaking bonds could explain the low values for the net change in thermodynamic functions. The kinetic interpretation demonstrated that the sorption process was split into three discrete regions. The results from vapour sorption microcalorimetry, in combination with a vacuum microbalance, are valuable in probing interactions between water and crystalline or semi-amorphous solids.

Solubility of non polar gases in formaldehyde diethyl acetal between-10 and 30�C, and 1 Atm partial pressure of gas

Solubility measurements of the gases He, Ne, Ar, Kr, Xe, H2, D2, N2, CH4, C2H4, C2H6, CF4, SF6, and CO2 in formaldehyde diethyl acetal in the range of −10 to 30°C, and a gas partial pressure of 1 atmosphere (101.32 kPa) are reported. Standard changes of thermodynamic functions for the solution process are evaluated. The scaled particle theory is used to obtain the effective Lennard-Jones 6, 12 pair potential parameters for formaldehyde diethyl acetal. Experimental solubilities values are compared with those obtained from the application of the scaled particle theory to gas liquid solubility.

The solubility and isotopic fractionation of gases in dilute aqueous solution. IIa. solubilities of the noble gases

A method for the analysis of precise gas solubility data is presented and applied to new determinations of the Henry constant, k2, for He, Ne, Ar, Kr, and Xe. The values of k2 are fitted to the same sets of temperature functions which we have tried for oxygen. Our previously proposed power series in 1/T, ln(k2/P )=a0+a1/T+a2/T2 (Mark I), gives the best 3-term fit within the temperature range 0–60°C. For use over the full range to the critical temperature of water, we have discovered a new function given by (T*)2ln(k2/P )=A0(T*)2+A1(1-T*)1/3+A2(1-T*)2/3(Mark II), where T*≡T/T c1 . It fits our data from 0–60°C nearly as well as Mark I; it fits high temperature data from other sources; and at the critical temperature of water it satisfies theoretical requirements. Expansion of Mark II reveals the relationship between Mark II and Mark I and leads to a 4-term smoothing function, ln(k2/P )=a−2(T*)−2+a−1(T*)−1+a0+a1T* (Mark III), which we believe gives the best values only for the 0–60°C range. Mark III is used to calculate values for $$\Delta \bar G^\theta ,\Delta \bar H^\theta ,\Delta \bar S^\theta $$ , and $$\Delta \bar C^\theta $$ , 0–60°C, and a procedure is empolyed to estimate the errors. Agreement is excellent between these results and those obtained from precise microcalorimetric measurements made by others. With the inclusion of pressure correction terms, Mark II yields the four thermodynamic function changes for use at high temperatures. With increasing temperature, these changes suddenly turn upward toward plus infinity as T c1 is approached. Essentially direct determinations of $$\Delta \bar C^\theta $$ for argon by other workers are in excellent agreement with our results. The symmetrical activity coefficient at infinite dilution, γ 2 ° is examined and the hypothetical properties of k2 are explored below 0°C. Mark II can be expressed in the reduced form (T*)2ln(k 2 * )=A1(1-T*)1/3+A2(1-T*)2/3, where k 2 * ≋k 2/(p c1φ2c1). A2 is a very good linear fit to A1, which suggests a characteristic temperature for water at 287.3 K.

Theoretical kinetic and thermodynamic study on the disilene-silylsilylene isomerization

The titled isomerization has been studied at the HF/3–21G level. The changes in thermodynamic functions, equilibrium constant K(T), conversion efficiency C(T), and the rate constant k(T) for the isomerization have been calculated using our energies of the reactant (R), transition state (TS), and product (P), their harmonic vibrational frequencies, and the classical and corrected barrier (by vibrational zero-point energies). In the range of temperature, 300–1200K, ΔH < 0, ΔS > 0 and ΔG < 0; i.e., it is exothermic, increasing in the entropy, and spontaneous reaction. ΔS≠ < 0, log A is about 12.0 ±0.15 (s−1), but the k(T) is from 2.627 × 10(−33) to 6.933 × 10(8) (5−1); i.e., it passes through a tight TS, the A factor changes little, but the rate constant varies rapidly with the temperature. These results agree with the fact that the isomerization occurs readily at high temperature. Furthermore, Newman's mechanism, 2SiH2 → (H2SiSiH2)* → (HSiSiH3)* → Si2H2 + H2, is supported. Similarly, the isomerization, HDSiSiH2 → HSiSiDH2, is also studied.

Features of the structuration of oligomer solutions of surfactants

Solutions of surfactants of differing concentrations in polyoxypropylene glycol have been investigated by electron microscopy, NMR and surface tension methods. It is shown that the introduction of surfactants leads to a morphological transition in surface layers of the oligoether, and this is related to a change in their energetic and entropic states. In the interval of surfactant concentration from 0 to 0·3% it was found that a 0·03% concentration corresponds to a reorientation of sufractant molecules in surface layers, thus ensuring their stability. The formation of micelles in these solutions at a surfactant concentration of 0·15% is preceded by an extremal type of change in thermodynamic functions of surface layers of the surfactants.

Association effects in adsorption of polar substances on microporous adsorbents: Analysis of thermodynamic functions

Expressions describing the changes of fundamental thermodynamic functions resulting from the modified Polanyi-Dubinin theory have been presented. These dependences are related to equations of adsorption isotherms including parameters for both the structural heterogeneity and the association of molecules. The degree of molecule association is influenced by the adsorbent forces field in all cases examined.

Chelate effect and cooperativity effect in metal-ligand and macromolecule-ligand equilibria. I. Chemical potential changes and cooperativity-chelation parameters

Chelate and cooperativity effects both in the field of complexes formed in solution by metal ion with ligands and in the field of binding between protein and ligands were examined on the basis of thermodynamic arguments. The analysis was carried out by means of the formation function n = ∂ ln Σ M/∂ ln[A] where Σ M is a partition function having free metal or macro-molecule as basis reference level and A is a ligand. The chemical potential changes due to cooperativity and chelation are calculated from differences between areas of the diagram n = f(ln[A]). The chemical potentials are: Δμ° γ = -RT ln K γ (homotropic co-operativity), Δμ° γ′ = -RT ln K γ′ (heterotropic co-operativity), Δμ° ϵ = -RT ln K ϵ (homotropic chelation), Δμ° ϵ′ = -RT ln K ϵ′ (heterotropic chelation). The cooperativity and chelation parameters K γ, K γ′, K ϵ, K ϵ′ are related to each other by other parameters K η = K ϵ·K γ and K η′= K ϵ′·K γ′. All these dimensionless parameters are derived as ratios of experimental equilibrium constants. Therefore a corresponding consistent chemical potential scale can be obtained from experimental data for all these effects, leading to quantitative comparisons between cooperative and chelate effects, either homotropic or heterotropic. Thermodynamic function changes in metal-ligand complexes can also be compared on this same scale with the energetic changes in protein-ligand complexes.

The vapour pressure and enthalpy of sublimation of ferrocene

The vapour pressure of ferrocene was measured in the temperature range 277 to 360 K. A static method (diaphragm manometer) and dynamic methods (torsion and mass-loss effusion) were used. The results are represented by the equation: {R/(·K −1·mol −1}1n(p/p°) =-(4817±26)(K/θ)+(74.29±0.14)x10 3(K/θ-K/T)-(71±){(θ/T)-1+1n(T/θ)} , where R is the gas constant, p o is a standard pressure of 1 Pa, and θ = 317.20 K (mean experimental temperature). The numerical values with their root-mean-square-error ranges represent the thermodynamic function changes on sublimation: Δ s g G m o, Δ s g H m o, and Δ s g C p, m o respectively at 317.20 K.

Phase transitions in adsorped layers IV: Thermodynamics of monolayer adsorption

The effects of dimensional incompatibility and of potential barriers for surface diffusion on the phase transitions in a monolayer are discussed in terms of the partially mobile adsorption layer model presented in a previous publication. It is pointed out that the formation of a two-dimensional solid phase in registry with the adsorbent can be either discontinuous (first order) or continuous depending on the properties of the adsorption system. In particular, the first-order transition from the liquid to the solid phase can occur only when the system exhibits small dimensional incompatibility. The changes in various thermodynamic functions for the monolayer ( e.g. the isosteric heat of adsorption, the differential entropy and the heat capacity) due to phase transitions are discussed.

Voltammetric study of complexing sodium cation with dibenzo-18-crown-6 in nitrobenzene phase of two-phase water-nitrobenzene extraction system

The facilitated transfer of the Na + cation through the water (w)/nitrobenzene (nb) interface affected by dibenzo-18-crown-6 dissolved in the organic phase was studied by the cyclic voltammetry in the temperature range of 5–65°C. The transfer was found to be a very fast process at each studied temperature (5, 20, 35, 50, and 65°C); the process is controlled by diffusion of the electroneutral crown ionophore from the volume of the nitrobenzene phase to the interface. Changes of thermodynamic functions characterising the studied equilibrium reaction Na + (nb) + L(nb) ⇌ NaL + (nb), where L = dibenzo-18-crown-6, were determined for a temperature of 25°C: Δ G = −36.0 kJ mol −1, Δ H = 38.9 kJ mol −1, and Δ S = −9.7 J mol −1 K −1. Further, the change of the standard Gibbs energy of the transfer of the NaL + complex from the aqueous phase into the nitrobenzene one, Δ G 0,w → nb tr, NaL + = −20.1 kJ mol −1, was calculated together with the value of the standard Galvani potential difference of the NaL + cation between the nitrobenzene and the aqueous phases, Δ nb wφ 0 NaL + = 0.208 V, and the value of Briggs' logarithm of individual extraction constant, log K i Nal + = 3.5 (L = dibenzo-18-crown-6), for the two-phase water-nitrobenzene system.

Hydration of the surface of pure sulphur covered with n-alkanes

This paper presents the results of an investigation of the kinetics of adsorption and desorption of water on the surface of pure sulphur covered with n-alkanes. Changes of thermodynamic functions depending on adsorption values, as well as activation energy of water molecules were determined. On the basis of these results the effect of n-alkanes on the thickness of water layers formed on modified sulphur samples was shown. The mechanism of water adsorption here gives much information on the mode of molecule bonding on the sulphur surface.