A Monte Carlo computer simulation of the thermodynamic properties of solid N2

Selected thermodynamic properties of solid N₂ are investigated by carrying out classical Monte Carlo calculations for a system of 108 rigid linear molecules initially disposed in the cubic Pa3 structure and interacting via Mie—Lennard-Jones pair potentials between their ends. One run was carried out at (T = 96.4 K, V = 23.6 cm³ mole^?I) using a (12-6) potential, the other at T = 192.8 K and the same volume using a (9-6) potential. Only the latter potential appears to correlate well with recent experimental pVT data. In both runs the molecules were found to be orientationally disordered.     

Theory of phase diagrams described by thermodynamic potentials with T d symmetry

Phase diagrams of crystals induced by irreducible representations with symmetry group \(L = \bar 43m\) (T _d ) are constructed within the phenomenological theory of second-order phase transitions. A model of the Landau thermodynamic potential is studied, state equations of all symmetry-conditioned phases are obtained, and general conditions for their thermodynamic stability are formulated. Equations for the boundaries of phase areas and lines of phase transitions are obtained for the fourth order of expansion of the potential via components of the order parameter. Some types of the collapse of the multicritical point of the phase diagram for the eighth order of potential expansion are studied using computer calculations. The possible existence of phase diagrams that contain one or more triple points and areas of existence of three and four phases is shown for the first time for the potentials with the above symmetry. Examples are given of crystals that undergo phase transitions in the considered symmetry of the order parameter.     

Standard potentials of silver-silver bromide electrode and related thermodynamic quantities in (5, 10 and 15 wt-%) 2-butanol-water mixtures

The standard potentials of silver-silver bromide electrode in 5, 10 and 15 wt.-% 2-butanol have been determined from e.m.f. measurements of a cell of the type: Pt(or Pd), H₂(g)|HBr(m), 2-butanol-water mixtures| AgBr, Ag at temperatures 15°, 25° and 35°C and in the molality range of HBr from 0.003 to 0.1 mol kg^?1. Standard potentials were utilized to calculate: (1) the standard thermodynamic quantities for the cell reaction and for the reaction of HBr formation, (2) the mean activity coefficients of HBr, and (3) the standard thermodynamic quantities for transfer of HBr from water to 2-butanol-water mixtures. The thermodynamic functions for the transfer process have been interpreted in regard to the acid-base properties and structure of the solvents.     

Experimental study and modeling of the thermodynamic properties of magnesium silicates

The thermodynamic properties of all MgO-SiO₂ system phases were studied by Knudsen mass spectrometry over a wide temperature range (1571–1873 K) and the whole range of compositions. An approach based on the generation of volatile interaction products formed in the reduction of oxide components was used. The reducing agents were Nb, Ta, and Mo. The observed ion current intensity ratios I(Mg⁺)/I(SiO⁺) were used to calculate the activities and partial thermodynamic functions of the components in liquid and crystalline MgO-SiO₂ mixtures and the integral thermodynamic functions of formation of magnesium ortho-and metasilicates. For the first time, direct and reliable information about the thermodynamic properties of all system phases at high temperatures was obtained. These results in combination with all the available data on the thermodynamic properties and phase equilibria in the MgO-SiO₂ system were used to develop a statistical-thermodynamic model of liquid magnesium silicates based on treating them as associated liquids. Simultaneously, the problem of obtaining self-consistent data on the thermodynamic functions of all phases and conditions of equilibria between them was solved. In addition to polymeric silicon-oxygen structures of arbitrary sizes and spatial configurations, heteromolecular complexes such as MS, M₂S, and M₃S (S=SiO₂ and M=MgO) were found to exist in liquid MgO-SiO₂ mixtures. The correctness of the results obtained was substantiated by the virtually complete coincidence of the calculated thermodynamic properties and phase equilibrium conditions with experimental data and their conformity to the general patterns characteristic of binary silicate systems.     

Ideal gas state thermodynamic functions for monohalogenated cyclo-alkanes

The thermodynamic functions, C°_p, S°, ?(F°?H°^O)/T and (H°?H°_O)/T, have been calculated in the ideal gas state at 1 atm for the following monohalogenated cycloalkanes: bromocyclopropane, bromocyclobutane, chlorocyclobutane, fluorocyclobutane, bromocyclopentane. The effect of pseudorotation of the cyclobutanes and bromocyclopentane on the thermodynamic function values was considered to be negligible.     

Heat capacity and thermodynamic functions of ferrocenemethanol

The heat capacity (C _{p, m}) of ferrocenemethanol (FM) C₅H₅FeC₅H₄CH₂OH have been measured by the low-temperature adiabatic calorimetry method in the range 6–371 K. The triple point temperature, the enthalpy of fusion, and the purity of the substance under consideration have been determined. The ideal gas thermodynamic functions of FM—absolute entropy S _m(g) ⁰ and change in the enthalpy Δ ₀ ^T H _m at 298.15 K—have been derived from the heat capacity data and the known values of the saturation vapor pressure and enthalpy of sublimation. The ideal gas thermodynamic functions C _{p, m} ⁰ and S _m(g) ⁰ and the enthalpy of formation of FM have been calculated by the empirical difference method at T = 298.15 K. The experimental and calculated values of the thermodynamic functions are consistent within error limits, which proves their reliability.     

Normal coordinate analysis and thermodynamic functions of niobium and tantalum pentahalides

Normal coordinate treatment of NbX₅ and TaX₅ (X = F, Cl, Br) in the Urey-Bradley force fields was performed using published vibrational frequencies. The analysis was carried out with Wilson's FG formalism and the force constants were evaluated by a computer program based on the least-squares-fit method. Normal coordinates, potential energy distributions and thermodynamic functions were also determined. The results support the reported assignments of the fundamental frequencies of the pentachlorides and the pentabromides, and suggest that the pentafluoride assignments are incorrect.     

The thermodynamic properties of star-shaped fullerene-containing poly-N-vinylpyrrolidone

The temperature dependence of the heat capacity of star-shaped fullerene-containing poly-N-vinylpyrrolidone was studied over the temperature range 6–390 K by precision adiabatic vacuum and dynamic scanning calorimetry. The temperature intervals and thermodynamic characteristics of phase transitions were determined. The low-temperature dependence of the heat capacity of the substance was analyzed according to the Debye theory of the heat capacity of solids and its multifractal generalization. The data obtained were used to calculate the standard thermodynamic functions C _p ^o (T),H ^o(T)-H ^o(0), S ^o(T), and G ^o(T)-H ^o(0) of fullerene-containing poly-N-vinylpyrrolidone from T → 0 to 390 K. The standard entropy of formation of the polymer from simple substances and the entropy of its synthesis from poly-N-vinylpyrrolidone and fullerite C₆₀ at 298.15 K were calculated. The thermodynamic characteristics of fullerene-containing poly-N-vinylpyrrolidone are compared with those of the polymer-analogue without C₆₀.     

Corresponding states theory and thermodynamic properties of liquid alkali metals

According to phenomenological scaling and the law of corresponding states, reduced coordinates F ^*-T ^*, where F* represents the reduced thermodynamic properties (enthalpy of vaporization, speed of sound, surface tension, saturated liquid density) and T ^* is the reduced temperature, are introduced for the prediction of the thermodynamic properties of alkali metals. Values of the thermodynamic properties from the melting point up to boiling point are correlated. It has been shown that the correlation between reduced thermodynamic properties, as well as with the reduced temperature, can be expressed as a unique straight-line plot with a linear correlation coefficient of 0.9998. The proposed correlation has a simple form for easy calculation, requires only the melting and boiling point parameters, which are usually easy to acquire, and can predict the thermodynamic properties from the melting temperature up to the boiling temperature accurately.     

Standard thermodynamic properties of nitrobenzene in the ideal gas state

The standard enthalpy of formation of gaseous nitrobenzene was calculated by the G3X nonempirical quantum-mechanical method. The value obtained (56 kJ/mol) was noticeably lower than the experimental enthalpy, which casts doubt on the accuracy of measurements. The thermodynamic functions (C° _p , S°, ?[G° ? H°(0)]/T, H° ? H°(0), Δ_f H°, and Δ_f G°) of nitrobenzene in the ideal gas state were calculated by the statistical thermodynamics method over the temperature range 150–1500 K (the molecular constants, including the structural parameters, vibrational frequencies, and internal rotation potential used in the calculations were taken from the literature or estimated by the quantum-mechanical method).     

Influence of the molecular weight of polystyrene on its thermodynamic properties

The thermodynamic properties of a series of polystyrene samples with different molecular weights (M _w was varied from 2.5·10³ to 6.57·10⁴) were studied by precision adiabatic vacuum, high-accuracy dynamic, and combustion calorimetry: temperature dependences of the heat capacity in a wide temperature range, thermodynamic characteristics of glass transition and glassy state under standard pressure, and energy of combustion. The thermodynamic functions C ^○ _p (T), H ^○(T) - H ^○(0), S ^○(T) - S ^○(0), and G ^○(T) - H ^○(0) of polystyrene with different molecular weights, enthalpies of combustion Δ_c H ^○, thermodynamic parameters of formation from simple substances Δ_f H ^○, Δ_f S ^○, and Δ_f G ^○ at T = 298.15 K, and parameters of their synthesis from monomers were calculated from the experimental data. The temperature dependences of the heat capacity for a region of 0–380 K, glass transition temperatures, and thermodynamic characteristics of formation and synthesis of polystyrene depending on its molecular weight were examined.     

The low-temperature heat capacity and ideal gas thermodynamic properties of isobutyl tert-butyl ether

The heat capacities of isobutyl tert-butyl ether in crystalline, liquid, supercooled liquid, and glassy states were measured by vacuum adiabatic calorimetry over the temperature range from (7.68 to 353.42) K. The purity of the substance, the glass-transition temperature, the triple point and fusion temperatures, and the enthalpy and entropy of fusion were determined. Based on the experimental data, the thermodynamic functions (absolute entropy and changes of the enthalpy and Gibbs free energy) were calculated for the solid and liquid states over the temperature range studied and for the ideal gas state at T = 298.15 K. The ideal gas heat capacity and other thermodynamic functions in wide temperature range were calculated by statistical thermodynamics method using molecular parameters determined from density-functional theory. Empirical correction for coupling of rotating groups was used to calculate the internal rotational contributions to thermodynamic functions. This correction was found by fitting to the calorimetric entropy values.     

Heat capacity and thermodynamic functions of 4,4′-dimethylbiphenyl and 4,4′-di-tert-butylbiphenyl

The heat capacity (C _{p m} ) of 4,4′-dimethylbiphenyl and 4,4′-di-tert-butylbiphenyl in the temperature range of 8—373 K was measured by low-temperat ure adiabatic calorimetry, and thermodynamic characteristics of the solid-phase transitions of 4,4′-d i-tert-butylbiphenyl were determined. Temperatures, enthalpies, entropies of melting, and the purity of the samples of the tested substances were determined by means of differential scanning calorimetry. The main thermodynamic functions of the substances in the condensed state at 298 K were calculated.     

Excess thermodynamic functions and complex formation in binary liquid mixtures containing acetonitrile

Nagata, I. and Kawamura, Y., 1979. Excess thermodynamic functions and complex formation in binary liquid mixtures containing acetonitrile. Fluid Phase Equilibria, 3: 1–11.Molar excess enthalpy and isothermal vapor-liquid equilibrium data of acetonitrile-chloroform have been obtained at 298.15 and 328.15 K, respectively. Excess thermodynamic functions for the former system and for acetonitrile-carbon tetrachloride have been discussed in terms of a thermodynamic association theory for complex binary liquid mixtures containing self-associating species and a binary complex.     

Polarographic determination of stability constants and thermodynamic parameters of lead(II) propanoate and 2-hydroxypropanoate complexes with a computer-controlled system

A computer-controlled electrometric system is described. It is used for d.c. polarographic determinations of the stability constants of lead(II) propanoate and 2-hydroxypropanoate complexes at four temperatures. From the values of the monoligand complex stability constants obtained at different temperatures, standard thermodynamic functions (ΔH_j and ΔS_j) for the first and second steps of complex formation were obtained. Closed-loop interaction between the minicomputer and electrometric instrument was achieved through computer control of the potentiostat, drop-life timer, burette and valve for nitrogen purging. Computer programs are outlined for numerical and statistical evaluation of the experimental data giving E_{$\text{1}\text{2}$}i_d and slope of logarithmic presentation of polarograms, F_o functions and cumulative stability constants, β_j as well as for calculation of the standard thermodynamic functions.     

Alkali-metal-intercalated transition metal disulfides: A thermodynamic model

In the lithium-intercalated disulfides, Li_xMS₂, where M = Ti, Ta, a nearly linear compositional variation of the lithium chemical potential is observed throughout the composition range 0 < x < 1.0. For most sodium-intercalated disulfides, chemical potential plateaus are observed between regions exhibiting linear variations of sodium chemical potential. Our thermodynamic model indicates that the two most important factors which determine the compositional variation of the alkali metal chemical potential are the interaction energy between intercalated alkali-metal atoms and the compositional variation of the electron chemical potential. Although these two factors determine the compositional variation of chemical potential in single-phase regions, the existence of two-phase regions in the concentration range x = 0?0.15 are influenced by the energy required to expand the interlayer gap and the configurational entropy.     

Thermodynamic properties of the silver ion in alcohol + water solvent mixtures from electromotive force measurements and thermodynamic solubility product constants of AgX (X = Cl,Br, I or CNS) at different temperatures

The standard potentials of the silver-silver ion electrode in alcohol+water solvent mixtures containing 10 and 20 wt% methanol, ethanol, 1-propanol and 2-propanol have been determined from the electromotive force measurements of the cell Ag(s), AgCl(s), NaCl(c), NaNO₃(c)// NaNO₃(c), AgNO₃(c), Ag(s) at seven different temperatures in the range 5–35°C. The standard potentials in each solvent have been represented as a function of temperature. The standard thermodynamic functions for the electrode reaction, the primary medium effects of various solvents upon Ag⁺, and the standard thermodynamic quantities for the transfer of 1 g-ion of Ag⁺ from water to the respective alcohol + water media have been evaluated and discussed in the light of ion-solvent interactions as well as the structural changes of the solvents. From the values of the standard potentials of the Ag/Ag⁺ and Ag/AgX, X^? electrodes, the thermodynamic solubility product constants of silver chloride, silver bromide, silver iodide and silver thiocyanate have been determined in alcohol + water solvent mixtures at different temperatures.     

Statistical thermodynamic generalization of the Hellmann—Feynman and quantum mechanical curvature theorems

The statistical thermodynamic analogs and generalization of the Hellmann—Feynman theorem and the quantum mechanical curvature theorem of Silverman and van Leuven are derived for hamiltonians of the form Σ_m=1^MP_mHP_m the P's forming a complete set of mutually orthogonal and parametrically-dependent projections which maximize the associated partition functions.     

Chemical potentials,concentration fluctuations,etc., in binary metal alloys

Abstract

Relationships among transport parameters and the mean square composition fluctuations as determined by measurements of the chemical potentials are described for a variety of binary liquid metal alloys. The measurement of the chemical potential is described and the thermodynamic basis for the analysis given in terms of the concentration correlation functions as well as more traditional thermodynamic parameters. Alloys involving group III_A metals with Te are used as an example     

The standard thermodynamic properties of 4<Emphasis Type="Italic">f</Emphasis> metal trichlorides

The enthalpies of sublimation Δ_sub H ⁰(298) of 4f metal trichlorides were calculated by the second and third laws of thermodynamics from saturated vapor pressures using the thermodynamic functions of the condensed and gaseous states suggested by us. The set of the Δ_sub H ^o(298) enthalpies was analyzed to determine the most reliable values. The enthalpies of atomization found from these values were compared with those calculated from the measured equilibrium constants of gas phase reactions with the participation of the compounds under consideration and the enthalpies of atomization found from the experimental appearance potentials AP(Ln⁺/LnCl₃). Recommended Δ_at H ^o(298) values were obtained for all the 4f metal trichlorides.