Standard Thermodynamic Quantities Research Articles

Thermodynamics of divalent-metal fluorides VI. Heat capacity and thermodynamic properties of the fast-ion conductor CaSn2F6 at temperatures from 6 K to 310 K

The molar heat capacity Cp. m of calcium hexafluorostannate CaSn2F6 was measured at temperatures T from 6 K to 310 K by adiabatic calorimetry. Reproducible heat capacities were obtained only after cooling the sample twice to T < 150 K. The curve of heat capacity against temperature is continuous and rises smoothly to T ≈ 140 K, where a small anomaly appears. Above T ≈ 150 K, the curve resumes its smooth path. The anomaly, whose source is unknown, is centred at T ≈ 143 K. The greatest difference of the curve from that defined by the curve of the lattice vibrations is 0.01·Cp. m, which lies outside the error in the measurements. The excess molar enthalpy associated with the anomaly amounts to Δ150 K135 KHom = (1.3±0.3)·R·K (R = 8.31451 J·K-1·mol-3), while the excess entropy is zero within the experimental error of the measurements. Smoothed values of the standard thermodynamic quantities for pure CaSn2F6 are tabulated up to T = 310 K and Som(298.15 K) = (33.16±0.03)·R.

Thermodynamics of Ammonium Halopallidates II. Heat Capacity and Thermodynamic Properties of (ND4)2PdCl6 at Temperatures from 5 K to 325 K

AbstractThe heat capacity of deuterated ammonium hexachloropallidate (ND4)2pDCl6 was measured from 5 K to 325 K by adiabatic calorimetry. One λ‐shaped phase transition, absent in the protonated salt, was found in the curve for heat capacity against temperature. This transition reaches its maximum Cp.m ≃ 150 · R at (30.2 ± 0.1) K with ΔtrsSm0 = (2.005 ± 0.009) · R (R = 8.31451 J · K−1 · mol−1) and marks the change from the high temperature cubic structure to the low temperature tetragonal structure. The Debye temperature at 0 K equals (96.5 ± 2.4) K and below 10 K, only lattice vibrations make significant contributions to the heat capacity. Smoothed values of the standard thermodynamic quantities for pure (ND4)2PdCl6 are tabulated up to 320 K and the Sm0(273.15 K) = (49.80 ± 0.05) · R.

Thermodynamics of ammonium halogenated tellurides I. Heat capacity and thermodynamic properties of (NH 4) 2 TeCl 6 at temperatures from 5 K to 350 K

The heat capacity of ammonium hexachlorotellurate (NH 4 ) 2 TeCl 6 was measured at temperatures from 5 K to 350 K. The heat-capacity curve shows a small anomaly around 86 K and a broad peak extending from 100 K to 280 K. The small anomaly reaches its greatest divergence from the lattice curve at 86.5 K and is coincident with the known transition from cubic Fm3m structure to trigonal R3. The low values of enthalpy and entropy of transition are consistent with the subtle change in orientation of the anions involved in the rotational displacive transition: Δ trs H o m = (5.97 ± 1.74) R · K and Δ trs S o m = (0.071 ± 0.028) R , where R = 8.31452 J · K −1 · mol −1 . Smoothed values of the standard thermodynamic quantities are tabulated up to 350 K.

Thermodynamics of ammonium halogenated tellurides II. Heat capacity, phase transitions, and thermodynamic properties of (ND 4) 2TeCl 6 at temperatures from 5 K to 325 K

The heat capacity of deuterated ammonium hexachlorotellurate (ND4)2TeCl6 was measured at temperatures T from 5 K to 325 K by adiabatic calorimetry. A small anomaly in the curve of heat capacity against temperature was found at T=(89.5±0.3)K with a maximum Cp,m = 23.84·R, ΔtrsS°m = (0.234±0.006)·R. The discovery of this anomaly supports the presence of a rotative displacive transition similar to that involving TeCl2−6 in the undeuterated salt. In addition, two λ-shaped transitions were discovered at T = (31.4±0.1) K, with a maximum Cp,m = 34.7·R, ΔtrsS°m = (0.861±0.007) R, and at T = (47.6±0.1)K, with a maximum Cp,m = 18.6 R, ΔtrsS°m = (0.247±0.006) R. Smoothed values of the standard thermodynamic quantities for pure (ND4)2TeCl6 are tabulated up to T = 320 K.

Thermodynamic Studies of Copper(II) Sulfate in Aqueous Mannitol from Electromotive Force Measurements

Abstract Electromotive force measurements of the cell Cu–Hg/CuSO4(m)/Hg2SO4(s)/Hg have been made at 288, 298, 308, and 318 K for mannitol composition X=5, 15, and 25% (w/w) in water. The standard emf values of the cell at different temperatures and at different composition of mannitol + water mixtures have been determined by an extrapolation method. These have been utilized to evaluate the mean activity coefficient of copper(II) sulfate. The standard free energy for the cell reaction, and the primary medium effects upon CuSO4 have been evaluated. The standard thermodynamic quantities for the process of transfer of CuSO4 from water to the mannitol solution have been calculated from the values of the standard potential. The transfer parameters have been split into the electrostatic and chemical contributions and the results have been explained in the light of ion–solvent interactions and structural contributions to solvents.

Thermodynamic properties of ammonium haloplatinates: II. Heat capacity and thermodynamic functions of deuterated ammonium hexachloroplatinate (ND 4) 2PtCl 6 at temperatures from 5 K to 350 K

The heat capacity of deuterated ammonium hexachloroplatinate (ND 4 ) 2 PtCl 6 was measured at temperatures from 5 K to 350 K by adiabatic calorimetry. One λ-shaped anomaly, absent in the undeuterated salt, was found in the curve for heat capacity against temperature. This λ-shaped transition reaches its maximum C p,m ≈ 59.3· R at (27.2±0.05) K with Δ trs S o m = (1.216±0.004)· R , characteristic of an order-disorder transition. Smoothed values of the standard thermodynamic quantities for pure (ND 4 ) 2 PtCl 6 are tabulated at temperatures up to 350 K.

Thermodynamic properties of indium triiodide in the temperature range 5 K to 360 K

The heat capacities of InI 3 (cr, II) and InI 3 (cr, I) were measured from 5.5 K to 356 K using adiabatic calorimetry. The temperature, enthalpy, and entropy of the phase transition (cr, II = cr, I) were determined. Values of the standard molar thermodynamic quantities for InI 3 are presented at temperatures up to 360 K.

Solute-solvent interactions: dissolution of sparingly soluble silver salts in aqueous-organic solvent systems

The solubilities of the salts Ag 2X (where X is sulphate, chromate, tungstate, dichromate, oxalate, malonate, succinate, glutarate or adipate) and Ag 3Y (where Y is phosphate or arsenate) have been determined in various compositions of water+dioxan (5, 10, 15 and 20 wt.%), water+urea (11.52, 20.31, 29.64 and 36.83 wt.%), water+ mannitol (5 wt.%) and water + sorbitol (5 wt%) mixtures at different temperatures. The solubility data have been discussed in the light of electrostatic as well as solute—solvent interaction effects on the dissolution processes of the silver salts. Standard transfer thermodynamic quantities derived from the change in the solubility product are also examined.

Thermodynamic properties of ammonium haloplatinates I. Heat capacity and thermodynamic functions of ammonium hexachloroplatinate (NH 4) 2PtCl 6 from 6 K to 348 K

The heat capacity of ammonium hexachloroplatinate (NH 4) 2PtCl 6 was measured from 6 K to 348 K by adiabatic calorimetry. The heat-capacity curve is sigmate without anomalies. It rises rapidly from T → 0 to 250 K where the C p, m R value is 30.1 and increases by only 7 per cent from 250 K to 350 K. Values of the standard thermodynamic quantities are tabulated to 350 K.

Heat capacity and thermodynamic properties of deuterated ammonium hexafluorophosphate ND 4PF 6 from 5.8 K to 347 K

The heat capacity of deuterated ammonium hexafluorophosphate ND 4PF 6 was measured from 5.8 K to 347 K by adiabatic calorimetry. Two λ-shaped anomalies were found in the curve for heat capacity against temperature. The upper anomaly reached a peak C p,m ≈ 600· R at (194.4 ± 0.05) K with Δ trs S m o = (1.013 ± 0.016)· R ( R = 8.3145J·K −1·mol −1). The lower anomaly is also λ-shaped but is gradual, continuous, and reaches its maximum C p,m = 19.2· R at (137.5 ± 1.0) K with Δ trs S m o = (0.562 ± 0.011)· R. Both anomalies are characteristic of order-disorder transitions. Smoothed values of the standard thermodynamic quantities are tabulated up to 350 K.

Heat capacity of deuterated ammonium tetrafluoroborate ND 4BF 4 from 7 K to 348 K

The heat capacity of deuterated ammonium tetrafluoroborate ND 4BF 4 was measured from 7 K to 348 K by adiabatic calorimetry. The curve for heat capacity against temperature is smooth with a broad maximum between 120 K and 165 K, and the peak value in C p, m ≈ 14.9· R occurs between 145 K to 155 K. The shape of the broad maximum is similar to that found in other anisotropic salts and is believed to be a result of contributions both from the rotation of the ND 4 + ion and from a larger than usual dilation of the unit cell. Values of the standard thermodynamic quantities are tabulated up to 350 K.

Heat capacity of deuterated cubic ammonium hexafluorosilicate (ND 4) 2SiF 6 from 6 K to 343 K

The heat capacity of deuterated cubic ammonium hexafluorosilicate (ND 4) 2SiF 6 was measured from 6 K to 343 K by adiabatic calorimetry. The curve of heat capacity against temperature is smooth and without anomalies. Values of the standard thermodynamic quantities are tabulated below 350 K. Analysis of our heat-capacity results yielded a librational wavenumber of the ND 4 + ion of about 122 cm −1 and a maximum in the rotational heat capacity lying between 220 K and 230 K.

Thermodynamic properties of ammonium halogen stannates I. Heat capacity and thermodynamic functions of deuterated ammonium hexachlorostannate (ND 4) 2SnCl 6 from 5.9 to 347 K

The heat capacity of deuterated ammonium hexachlorostannate (ND 4) 2SnCl 6 was measured from 5.9 to 347 K by adiabatic calorimetry. The heat capacity is characterized by a λ-shaped anomaly that reaches its maximum C p,m ≈ 53· R ( R = 8.31451 J·K −1·mol −1) at approximately 244 K. The value of ΔS m o for the anomaly is 0.48· R. Values of the standard thermodynamic quantities are tabulated to 350 K.

The thermodynamics of perchlorates. I. Heat capacity of ND4ClO4 from 7 to 345 K and the analysis of heat capacities and related data of NH4ClO4 and ND4ClO4

The heat capacity of the orthorhombic salt: deuterated ammonium perchlorate, ND4 ClO4 , was measured from 7 to 345 K using adiabatic calorimetry. The heat capacity against temperature curve is smooth, continuous and without anomaly. Values of the standard molar thermodynamic quantities are presented up to 340 K. The heat capacities of ND4 ClO4 and NH4 ClO4 have been analyzed. The contributions to the vibrational heat capacity from the external optical modes of NH+4 or ND+4, ClO−4 and libration from the external modes of ClO−4 along with those of vibration from the internal optical modes of NH+4 or ND+4 and ClO−4, and the acoustic lattice modes for these ions have been calculated. The difference between the experimental and calculated heat capacity, called the residual heat capacity, equals the contribution from ammonium ion rotation and the thermal expansion of the lattice. With recent thermal expansion data, the correction from constant stress to constant strain has been applied and the derived rotational heat capacities of the NH+4 and ND+4 are determined to be in qualitative agreement with those derived from various rotational models.

Thermodynamics of silver-silver ion electrode in acetonitrile-water mixtures

From the electromotive force (e.m.f.) measurements of cells with liquid-junction potentials, the standard potentials of the silver electrode were obtained in 5%, 10% and 15% (w/w) acetonitrile-water mixtures at five different temperatures ranging from 15 to 35 °C. Standard thermodynamic quantities for the cell reaction were estimated. Thermodynamic solubility product constants of silver halides were computed. The results are discussed in terms of ion solvation.

Thermodynamics of individual ions in various solvent systems from electromotive force measurements

Standard e.m.f. values for the cells Pt,H 2(g, 1 atm)¦HX( m), solvent¦AgX,Ag and M(Hg)¦MX 2( m), solvent¦AgX,Ag in water and in mixtures of water with methanol, 2-propanol, acetone or dioxane were used to determine standard absolute electrode potentials of the hydrogen, Ag,AgX (X = Cl, Br and I) and M(Hg)¦M 2+ (M = Zn and Cd) electrodes in these solvents. The data at different temperatures were utilized to compute the standard thermodynamic quantities both for the electrode reaction and for the transfer of individual ions from water into water + cosolvent mixtures. Cation solvation in various solvents as well as the influence of the solvent on the thermodynamic properties of individual ions are discussed. The results provide further evidence of the adequacy of the new method (M.M. Elsemongy, Thermochim. Acta, 80 (1984) 239; 103 (1986) 387; 108 (1986) 133) of determination of the thermodynamics of individual ions and of its general applicability to different cells containing different 1:1 or 2:1 electrolytes in various solvent systems.

Thermodynamics of the cell: Cd(s) + Hg|CdCl 2(aq, m)|AgCl|Ag

The e.m.f. of the cell: Cd(s)+Hg|CdCl 2(aq, m)|AgCl|Ag was measured in the temperature range 293.15 to 313.15 K at 5 K intervals and in the range of molality m of CdCl 2 from 0.002 to 0.022 mol·kg −1. From the results and literature values of the stability constants of the Cd-complexes the standard e.m.f. of the cell was obtained at each temperature. These values made it possible to calculate also both the standard thermodynamic quantities for the cell reaction and the mean activity coefficients of CdCl 2. The obtained values were compared and discussed in relation to the corresponding values from the literature.

Importance of considerations of mixing properties in establishing an internally consistent thermodynamic database: thermochemistry of minerals in the system Mg2SiO4-Fe2SiO4-SiO2

A thermodynamic solution model is developed for minerals whose compositions lie in the two binary systems Mg2SiO4-Fe2SiO4 and Mg2Si2O6-Fe2Si2O6. The formulation makes explicit provision for nonconvergent ordering of Fe2+ and Mg2+ between M1 and M2 sites in orthopyroxenes and non-zero Gibbs energies of reciprocal ordering reactions in both olivine and orthopyroxene. The calibration is consistent with (1) constraints provided by available experimental and natural data on the Fe-Mg exchange reaction between olivine and orthopyroxene ± quartz, (2) site occupancy data on orthopyroxenes including both crystallographic refinements and Mossbauer spectroscopy, (3) enthalpy of solution data on olivines and orthopyroxenes and enthalpy of disordering data on orthopyroxene, (4) available data on the temperature and ordering dependence of the excess volume of orthopyroxene solid solutions, and (5) direct activity-composition determinations of orthopyroxene and olivine solid solutions at elevated temperatures. Our analysis suggests that the entropies of the exchange [Mg(M2)Fe(M1)⇔Fe(M2)Mg(M1)] and reciprocal ordering reactions [Mg(M2)Mg(M1)+ Fe(M2)Fe(M1)⇔Fe(M2)Mg(M1)+Mg(M2)Fe(M1)] cannot differ significantly (± 1 cal/K) from zero over the temperature range of calibration (400°–1300° C). Consideration of the mixing properties of olivine-orthopyroxene solid solutions places tight constraints on the standard state thermodynamic quantities describing Fe-Mg exchange reactions involving olivine, orthopyroxene, pyralspite garnets, aluminate spinels, ferrite spinels and biotite. These constraints are entirely consistent with the standard state properties for the phasesα-quartz,β-quartz, orthoenstatite, clinoenstatite, protoenstatite, fayalite, ferrosilite and forsterite which were deduced by Berman (1988) from an independent analysis of phase equilibria and calorimetric data. In conjunction with these standard state properties, the solution model presented in this paper provides a means of evaluating an internally consistent set of Gibbs energies of mineral solid solutions in the system Mg2SiO4-Fe2SiO4-SiO2 over the temperature range 0–1300° C and pressure interval 0.001–50 kbars. As a consequence of our analysis, we find that the excess Gibbs energies associated with mixing of Fe and Mg in (Fe, Mg)2SiO4 olivines, (Fe, Mg)3Al2Si3O12 garnets, (Fe, Mg)Al2O4 and (Fe, Mg)Fe2O4 spinels, and K(Mg, Fe)3AlSi3O10(OH)2 biotites may be satisfactory described, on a macroscopic basis, with symmetric regular solution type parameters having values of 4.86±0.12 (olivine), 3.85±0.09 (garnet), 1.96±0.13 (spinel), and 3.21±0.29 kcals/gfw (biotite). Applications of the proposed solution model demonstrate the sensitivity of petrologic modeling to activity-composition relations of olivine-orthopyroxene solutions. We explore the consequences of estimating the activity of silica in melts forming in the mantle and we develop a graphical geothermometer/geobarometer for metamorphic assemblages of olivine+orthopyroxene+quartz. Quantitative evaluation of these results suggests that accurate and realistic estimates of silica activity in melts derived from mantle source regions,P-T paths of metamorphism and other intensive variables of petrologic interest await further refinements involving the addition of “trace” elements (Al3+ and Fe3+) to the thermodynamic formulation for orthopyroxenes.

A model for the computer simulation of chemical reactions in the condensed phase

Molecular dynamics calculations have been performed on small numbers of atoms (4-64), contained within a deformable boundary, with a view to developing a model suitable for simulating chemical reactions in the condensed phase. To determine how realistic the model is, a series of standard thermodynamic quantities have been evaluated. Velocity distributions have been determined during the course of individual simulations as a function of temperature and number of atoms. For 16 atoms or more, these distributions compare very favourably with a Maxwellian distribution. An effective pressure has been calculated by two methods, one using a virial of the internal forces and another in which the forces exerted by an external container have been calculated. In the case of the latter there is a lengthy induction period before the pressure stabilizes. For 64 argon atoms at 100 K, a calculated PV curve shows evidence of condensation. For the same number of atoms at 200 K, the PV curve fits a van der Waals expression w...

Thermodynamics of transfer of some nitroalkanes from aqueous to dodecyltrimethylammonium bromide micellar phases

The enthalpies of mixing of some aqueous n-nitroalkane solutions with dodecyltrimethylammonium bromide micellar solutions were determined. The experimental data were treated by using a previously reported approach giving the enthalpies of transfer of solute from the aqueous to the micellar phases and the distribution constant of solute between the two phases at the same time. From these, the standard thermodynamic quantities of transfer (Δ trfG°, Δ trfH° and Δ trfS°) are derived. In order to study the effect of the nature of both the solvent and the head group of solute, these properties are compared with those from water to octane and with those of alcohols and nitriles from aqueous to dodecyltrimethylammonium bromide micellar phase.