Standard Heat Capacity Research Articles

Aqueous nonelectrolyte solutions. Part XVIII. Equilibrium pressures of two methane hydrates with water. Formulae and dissociation thermo -dynamic functions for the structures I and II methane hydrates

Literature data for the saturation pressure P(hl1g) of methane hydrate with water, at 102 temperatures between –0.29 and 46.87°C, are properly represented by two distinct equations, with a quadruple point Q(h1h2l1g) transition temperature at 26.7°C with standard error (SE) 0.9°C and 55.5 MPa with SE 5.3 MPa. The structure I type methane hydrate phase h1 is stable below 26.7°C and the structure II type methane hydrate phase h2 is stable above 26.7°C. Between –0.29 and 25.54°C, 85 equilibrium pressures of methane hydrate with water are best represented, with SE 1.33% on a single pressure measurement, by a four-parameter thermodynamic equation. The corresponding equilibrium methane fugacities are represented, with SE 0.94% on a fugacity determination, by a five-parameter equation. Between 26.98 and 46.87°C, 17 equilibrium methane hydrate pressures with water are best represented, with SE 2.22% on a pressure measurement, by a three-parameter equation. Composition of the equilibrium aqueous phase is evaluated using methane fugacity with the solubility equation including a Poynting correction. Literature data between –2.22 and –14.10°C, for the saturation pressure P(h1s1g) of structure I methane hydrate with ice, are properly represented by a two-parameter equation, with SE 1.1% on a single pressure measurement. Standard enthalpy change for structure I methane hydrate dissociation into ice and methane gas is found to be ΔHot(h1[Formula: see text] s1g) = 18058 J mol–1 with SE 608 J mol–1 at -8.28°C. The quadruple point Q(h1s1l1g) is estimated at –0.290°C with SE 0.0064°C and at 2.527 MPa with SE 0.053 MPa. Using the classical thermodynamic method, as described for deuterium sulfide D-hydrate, methane hydrate equilibrium fugacities define 85 equilibrium constants Kp(h1[Formula: see text]l1g) between –0.29 and 25.54°C for dissociation of structure I hydrate h1 into liquid water l1 and methane gas. Temperature dependence of ln Kp(h1[Formula: see text]l1g) is well-represented by a three-parameter thermodynamic equation that gives both estimates and their standard errors for (i) ΔHot(h1[Formula: see text]l1g) and ΔCpot(h1[Formula: see text]l1g), the standard enthalpy and heat capacity changes, respectively, for hydrate h1 dissociation, and for (ii) n = r, the approximate formula number of the hydrate CH4·nH2O at each experimental temperature. The formula CH4·6.205H2O with SE 0.066H2O is found for the structure I methane hydrate h1 with water at quadruple point Q(h1s1l1g) –0.29°C; an approximate formula CH4·5.759H2O with SE 0.077H2O is found at quadruple point Q(h1h2l1g) 26.7°C. Between 26.98 and 46.87°C, the 17-equilibrium constants Kp(h2[Formula: see text]l1g) for dissociation of structure II methane hydrate h2 into liquid water l1 and methane gas are represented by a constrained three-parameter thermodynamic equation. For structure II methane hydrate the formula CH4·5.822H2O with SE 0.064H2O is found at quadruple point Q(h1h2l1g) 26.7°C and the formula CH4·5.699H2O with SE 0.064H2O at 46.87°C. Molar volumes and cohesive energy densities of the methane hydrates are compared with equilibrium compressed water.Key words: clathrate hydrates of methane, two methane gas hydrates, formula of structure I methane hydrate, thermodynamics of clathrate hydrate dissociation, dissociation equilibrium constants of structure I methane hydrate, standard enthalpy and heat capacity changes for dissociation of structure I methane hydrate, methane hydrates' transition temperature, formula of structure II methane hydrate, dissociation equilibrium constants of structure II methane hydrate, standard enthalpy change for dissociation of structure II methane hydrate, methane hydrates' cohesive energy density.

Calculation of the standard molal thermodynamic properties as a function of temperature and pressure of some geochemically important organic sulfur compounds

The standard molal thermodynamic properties and heat capacity power function coefficients of more than 100 organic sulfur compounds in the crystalline, liquid, and/or gas state have been calculated by combining regressions of experimental data reported in the literature together with carbon number systematics and group additivity algorithms. The compounds for which these calculations have been made include carbon disulfide, branched thiols, cyclic thiols, aromatic thiols, n-alkyl sulfides, branched sulfides, cyclic sulfides (including long-chain n-alkylthiolanes and n-alkylthianes), aromatic sulfides, n-alkyl disulfides, alkylthiophenes, methylated benzothiophenes and dibenzothiophenes, and thianthrene. In addition, the corresponding properties and coefficients for 12 sulfur-containing groups in the crystalline, liquid, and/or gas states have been retrieved, which can be used to estimate the standard molal thermodynamic properties and heat capacity power function coefficients of sulfur-rich kerogens or other high molecular weight organic sulfur compounds of geochemical interest.

Geological constraints on the thermodynamic properties of the stilbite—stellerite solid solution in low-grade metabasalts

Standard state thermodynamic data for stilbite (Ca2NaAl5Si13O36∗16H2O) and stellerite (Ca2Al4Si14O36∗14H2O), together with mixing properties of the stilbite -stellerite solid solution (stilbite SS) are derived through assessment of geological observations of stilbite SS compositions in metabasalts, experimental phase equilibria, and calorimetric observations. Measured compositions of stilbite SS in Tertiary metabasalts in Iceland and Icelandic geothermal systems change systematically towards the stellerite endmember with increasing stratigraphic depth and temperature. Standard molal volumes, heat capacities, and entropies for the endmembers of the solid solution are derived through critical review of published crystallographic and calorimetric data for natural stilbite SS. Standard molal Gibbs energies of formation at 298.15 K and 1 bar for stilbite (−4,946,475cal mol−1) and stellerite (−4,762,036 cal mol−1) and the mixing properties of the solid solution are retrieved from observed phase- and compositional-relations in metabasalts at Berufjördur, Iceland, measured temperatures of zeolite mineral distribution in active geothermal systems, and published observations of reversed phase equilibria. Mixing in stilbite SS can be described with an athermal solid solution model. Thermodynamic data resulting from our analysis provide close correlation between compositions of stilbite SS in Icelandic geothermal systems predicted from compositions of geothermal solutions and observed compositions of these minerals in low-grade metabasalts of Iceland, as well as the observed temperature of the stilbite SS to laumontite (leonhardite) transition in Icelandic geothermal systems. Stilbite SS composition in metabasalts is a sensitive function of temperature, fluid composition, coexisting minerals (especially silica polymorphs) and geothermal gradient.

Carbohydrates in thermophile metabolism: calculation of the standard molal thermodynamic properties of aqueous pentoses and hexoses at elevated temperatures and pressures

Experimental thermodynamic data for aqueous organic compounds can be combined with the revised Helgeson-Kirkham-Flowers (HKF) equations of state to generate parameters that can be used to estimate standard molal properties as functions of temperature and pressure. In this study, we regressed thermodynamic data for aqueous carbohydrates at temperatures up to 393 K reported in the literature to permit the calculation of the apparent standard molal Gibbs free energies and enthalpies of formation (ΔGo and ΔHo, respectively) and the standard molal entropies (S2o), heat capacities (CP,2o), and volumes (V2o) to 423 K and several hundred MPa of aqueous C5 aldoses (ribose, arabinose, xylose, lyxose) and C5 ketoses (ribulose, xylulose) as well as C6 aldoses (glucose, mannose, galactose) and C6 ketoses (fructose, sorbose). Values of ΔGo for these 11 aqueous carbohydrates are given as a function of temperature at the saturated water vapor pressure (PSAT) and at 50 MPa. Values of ΔGo for aqueous glucose are then combined with those of other aqueous organic and inorganic compounds to calculate values of the standard molal Gibbs free energies of 13 fermentation and respiration reactions (ΔGro) known or likely to be carried out by thermophilic microorganisms. Finally, values of the overall Gibbs free energies of these reactions (ΔGr) are calculated at the temperature, pressure, and chemical composition that obtain in the hydrothermal fluids of Vulcano Island, southern Italy, a site that is widely known for its tremendous diversity of organisms able to live at high temperatures. At likely activities of aqueous glucose, it is shown that thermophiles in the hot springs of Vulcano at 373 K and ∼0.1 MPa can gain between 400 and 3000 kJ per mole of glucose fermented or respired.

Structures, Intramolecular Rotation Barriers, and Thermochemical Properties of Radicals Derived from H Atom Loss in Mono-, Di-, and Trichloromethanol and Parent Chloromethanols

Structures and thermochemical properties, , and Cp(T) of three (mono-, di-, and tri-) chloromethanols; three chloromethoxy and the two hydroxychloromethyl radicals are determined by ab initio and density functional calculations. The molecular structures and vibration frequencies are determined at the B3LYP/6-31G(d,p) density functional level, with single point calculations for the energy at the B3LYP/6-311+G(3df,2p), QCISD(T)/6-31G(d,p), and CBSQ//B3LYP/6-31G(d,p) levels. The vibration frequencies are scaled for zero-point energies and for thermal corrections. The enthalpies of formation ( ) are determined at each calculation level using several isodesmic reactions. Standard entropy ( ) and heat capacity (Cp(T)'s, 300 ≤ T/K ≤ 1500) from vibrational, translational, and external rotational contributions are calculated using the rigid-rotor-harmonic-oscillator approximation based on the vibration frequencies and structures obtained from the density functional study. Potential barriers for internal rotation o...

Thermodynamic properties of the MZr2(PO4)3 (M=Na, K, Rb or Cs) compounds

The enthalpies of the solution of MZr2(PO4)3(M=Na, K, Rb or Cs) compounds have been measured by the help of a differential automatic isothermal Calvet calorimeter and the standard enthalpies of formation have been derived. The temperature dependencies of the standard heat capacity of the samples of crystalline NaZr2(PO4)3 and CsZr2(PO4)3 were studied between 7 and 340 K in an automatic adiabatic vacuum calorimeter. The main thermodynamic functions H 0(T)–H 0(0), S 0(T) andG 0(T)–H 0(0) have been determined. The Gibbs energies of formation of the NaZr2(PO4)3and CsZr2(PO4)3 at 298.15 K were calculated on the basis of these experimental data and the enthalpy of formation data. Qualitative explanations for the results observed were presented.

Can thermodynamic measurements of receptor binding yield information on drug affinity and efficacy?

The present commentary surveys the methods for obtaining the thermodynamic parameters of the drug–receptor binding equilibrium, ΔG°, ΔH°, ΔS°, and ΔC°p (standard free energy, enthalpy, entropy, and heat capacity, respectively). Moreover, it reviews the available thermodynamic data for the binding of agonists and antagonists to several G-protein coupled receptors (GPCRs) and ligand-gated ion channel receptors (LGICRs). In particular, thermodynamic data for five GPCRs (β-adrenergic, adenosine A1, adenosine A2A, dopamine D2, and 5-HT1A) and four LGICRs (glycine, GABAA, 5-HT3, and nicotinic) have been collected and analyzed. Among these receptor systems, seven (three GPCRs and all LGICRs) show “thermodynamic agonist–antagonist discrimination”: when the agonist binding to a given receptor is entropy-driven, the binding of its antagonist is enthalpy-driven, or vice versa. A scatter plot of all entropy versus enthalpy values of the database gives a regression line with the equation TΔS° (kJ mol−1; T = 298.15 K) = 40.3 (± 0.7) + 1.00 (±0.01) ΔH° (kJ mol−1); N = 184; r = 0.981; P < 0.0001 – which is of the form ΔH° = β · ΔS°, revealing the presence of the “enthalpy–entropy compensation” phenomenon. This means that any decrease of binding enthalpy is compensated for by a parallel decrease of binding entropy, and vice versa, in such a manner that affinity constant values (KA) of drug–receptor equilibrium (ΔG° = −RT ln KA = ΔH° − TΔS°) cannot be greater than 1011 M−1. According to the most recent hypotheses concerning drug–receptor interaction mechanisms, these thermodynamic phenomena appear to be a consequence of the rearrangement of solvent molecules that occurs during the binding.

High Temperature Dissociation Constants of HS- and the Standard Thermodynamic Values for S2-

The magnitude of the dissociation constant for HS- = S2- + H+ at saturation vapor pressure, 25 °C, and infinite dilution is log K2a⊖ = −14.0 ± 0.2. The value of ΔG2a⊖ = (79.9 ± 2.3) kJ·mol-1, calculated from this log K2a⊖, was combined with the calorimetric enthalpy ΔH2a⊖ = (54.8 ± 1.7) kJ·mol-1, to obtain the entropy of dissociation, ΔS2a⊖ = (−84.2 ± 30.0) J·K-1·mol-1. Consistent standard thermodynamic values for the aqueous species S2- obtained from these data are as follows: ΔfG° = (91.9 ± 2.3) kJ·mol-1, ΔfH° = (38.7 ± 1.8) kJ·mol-1, and S° = (−16.0 ± 10.0) J·K-1·mol-1. The standard heat capacity of S2-, Cp° = (−284 ± 60) J·K-1·mol-1, was calculated from a correlation between Cp° and S°. The heat capacity of dissociation, ΔCp,2a⊖ = (−192 ± 60) J·K-1·mol-1, was calculated from Cp° for HS- and this Cp° for S2-. The change in R ln K2a with temperature was computed up to 300 °C and compared with experimental data from the literature. The standard potential for S(rhomb) + 2e → S2- at 25 °C and infinite dilution is E⊖ = (−0.476 ± 0.004) V. Published experimental data with the more negative log Km,2a = −17 were rejected because, while valid in, for example, (12 to 17) mol·L-1 NaOH solutions, they could not be calculated with confidence to the standard condition of infinite dilution.

Thermodynamic properties of surface species at the mineral–water interface under hydrothermal conditions: a Gibbs energy minimization single-site 2p KA triple-layer model of rutile in NaCl electrolyte to 250°C

Standard partial molal thermodynamic properties of surface species in a single-site 2p K A triple-layer model (TLM) for rutile in NaCl electrolyte, consistent with the SUPCRT92-98 data, were estimated at temperatures T = 0 to 250°C and saturated vapor pressure P SAT using a Gibbs energy minimization (GEM) approach (Kulik, 1999) and hydrothermal potentiometric titration data (Machesky et al., 1998a). Evaluation strategy was based on conventional setting to zero of standard state entropy and heat capacity effects of the “surface hydronium desorption” reaction >O 0.5H 2 + = >O 0.5H 0 + H aq +, with one-term temperature extrapolation appropriate. The standard state properties of the “surface water dissociation” reaction >O 0.5H 0 = >O 0.5 − + H aq + in a three-term extrapolation, with Cp ° 298(>O 0.5 −) assumed equal to Cp ° 298(OH aq −) and Δ S ° 298 estimated from enthalpy of rutile surface protonation in water Δ H ° prot,298 , yielded a very good match of predicted pristine point of zero charge (pH PPZC) and measured point of zero charge (pH PZC) on rutile to T = 250°C. Correlation of Δ H ° prot,298 for various oxides versus pH PPZC suggests that the entropy Δ S ° prot,298 = 25 ± 4 J K −1 mol −1 may be constant for all oxide surfaces, pH PPZC( T) be hence a function of pH PPZC at T 0 = 25°C only: pH PPZC,T = −29.134 + T 0/ T(pH PPZC,T0 + 3.2385) + 4.545ln T. The standard partial molal properties of Na + and Cl − outer-sphere surface complexes on rutile were estimated from GEM TLM fits of potentiometric titration data at different T and m NaCl. Adjustable parameters were: standard partial molal Gibbs energy g 0(>O 0.5 −Na +), interdependent with inner capacitance density C 1 (increasing from 1.6 F · m −2 at 25°C to 2.3 F · m −2 at 250°C), and maximum site density Γ max (>O 0.5H 2 +Cl −). No surface activity term (SAT) ln Ξ = f(Γ max ) corrections were needed for >O 0.5 −Na + species, i.e., Na + adsorption on rutile occurs in the “TLM ideal region” up to 300°C and 1 m NaCl. From the GEM fits, parameters of three-term temperature extrapolations were found for a reaction >O 0.5H 0 + Na aq + = >O 0.5 −Na + + H aq +. Directly fitted g 0 (>O 0.5H 2 +Cl −) values were less certain because the SAT with low Γ max(>O 0.5H 2 +Cl −) = 0.9 ± 0.1 sites nm −2 had to be involved. Hence, symmetric electrolyte adsorption (pH PZSE = pH PPZC) has been assumed, from which the standard partial molal properties of >O 0.5H 2 +Cl − species were found using a zero-term extrapolation of an isocoulombic reaction >O 0.5H 2 +Cl − + >O 0.5 − + Na aq + = >O 0.5 −Na + + >O 0.5H 2 + + Cl aq −. This balanced like-charge reaction can serve as a very useful constraint reducing the set of adjustable TLM parameters at given T and pH PZC to C 1, p K Na and Γ max (>O 0.5H 2 +Cl −), optimal values of which could have been found from GEM fits of the rutile potentiometric titration data at different T and m NaCl.

Aqueous nonelectrolyte solutions. Part XVII. Formula of hydrogen sulfide hydrate and its dissociation thermodynamic functions

Literature data for the saturation vapor pressure P(hl1g) of hydrogen sulfide hydrate with water, at 43 temperatures between quadruple points Q(hs1l1g) at –0.4°C and Q(hl1l2g) at 29.484°C, are properly represented by a six-parameter equation to give a standard error (SE) of 0.13% on a hydrate pressure measurement of unit weight. Equilibrium hydrogen sulfide and water fugacities and the gas and aqueous phase compositions are derived using the Redlich–Kwong equation of state. Literature data for the saturation vapor pressure P(hs1g) of hydrogen sulfide hydrate with ice, at 15 temperatures between –1.249 and –21.083°C, are properly represented by a two-parameter equation to give a SE of 0.26% on a single hydrate pressure measurement. Quadruple point Q(hs1l1g) is evaluated at temperature –0.413° with SE 0.042°C and at pressure 94.7 with SE 0.26 kPa. Using the thermodynamic method, described for deuterium sulfide D-hydrate, the equilibrium fugacities of hydrogen sulfide are used to define 43 equilibrium constants Kp(h[Formula: see text]l1g) for hydrate dissociation into water and hydrogen sulfide gas. The temperature dependence of ln Kp(h[Formula: see text]l1g) is represented by a three-parameter thermodynamic equation which gives both values and standard errors (i) for Kp(h[Formula: see text]l1g), and for δHot(h[Formula: see text]l1g) and δCpot(h[Formula: see text]l1g), the standard enthalpy and heat capacity changes for hydrate dissociation and (ii) for n = r the approximate formula number of the hydrate H2S·nH2O at each experimental temperature. The formula H2S·6.119H2O with standard error 0.029H2O is found for hydrogen sulfide hydrate with water at lower quadruple point Q(hs1l1g) –0.413°C: an approximate formula H2S·5.869H2O with SE 0.026H2O is found at upper quadruple point Q(hl1l2g) 29.484°C. These estimates for the formula of hydrogen sulfide hydrate at its quadruple points are not significantly different from those found for the deuterium sulfide D-hydrate.Key words: clathrate hydrate of hydrogen sulfide, hydrogen sulfide hydrate, formula of hydrogen sulfide hydrate, thermodynamics of clathrate hydrate dissociation, dissociation equilibrium constant of hydrogen sulfide hydrate, standard enthalpy and heat capacity changes for dissociation of hydrogen sulfide hydrate.

Thermodynamics of half-filled Landau levels: A study of the composite fermion mass

The thermodynamics of a partially spin-polarized half-filled Landau level is examined and a thermodynamic method for determining the composite fermion (CF) mass is proposed. The present approach does not involve the measurement of activation or optical gaps and is free from disorder effects. The mechanism is complementary to the standard heat-capacity techniques and can also be used to probe the density of states of low-lying excitations of CF around the Fermi surface. The fractional quantum Hall state at $\ensuremath{\nu}=\frac{1}{2}$ is investigated.

A Titration Microcalorimetric Study of the Effects of Halide Counterions on Vesicle-Forming Aggregation in Aqueous Solution of Branched-Chain Alkylpyridinium Surfactants

Titration microcalorimetry is used to study the influences of iodide, bromide, and chloride counterions on the aggregation of vesicle-forming 1-methyl-4-(2-pentylheptyl)pyridinium halide surfactants. Formation of vesicles by these surfactants was characterised using transmission electron microscopy. When the counterion is changed at 303 K through the series iodide, bromide, to chloride, the critical vesicular concentration (cvc) increases and the enthalpy of vesicle formation changes from exo- to endothermic. With increase in temperature to 333 K, vesicle formation becomes strongly exothermic. Increasing the temperature leads to a decrease in enthalpy and entropy of vesicle formation for all three surfactants. However the standard Gibbs energy for vesicle formation is, perhaps surprisingly, largely unaffected by an increase in temperature, as a consequence of a compensating change in both standard entropy and standard enthalpy of vesicle formation. Interestingly, standard isobaric heat capacities of vesicle formation are negative, large in magnitude but not strikingly dependent on the counterion. We conclude that the driving force for vesicle formation can be understood in terms of overlap of the thermally labile hydrophobic hydration shells of the alkyl chains.

Aqueous nonelectrolyte solutions. Part XVI. Formula of deuterium sulfide D-hydrate and its dissociation thermodynamic functions

A method has been devised to approximate both the hydrate formula number n and the standard thermodynamic functions for hydrate dissociation from the temperature change of the hydrate former fugacity along a univariant three-phase (hl1g) equilibrium line. Thermodynamic equations are derived, their validity discussed, and an iterative method for their solution is described. The univariant (hl1g) equilibrium dissociation of deuterium sulfide D-hydrate (D2S·nD2O phase h) into gaseous deuterium sulfide (g) and liquid deuterium oxide (l1) has been treated to give approximate formulae and dissociation constants at 58 temperatures from 2.798 to 30.666°C. Dissociation equilibrium constants Kp(h–&gt; l1g) have been represented as a function of temperature by a four-parameter equation which yields both values and standard errors (i) for ΔHot(h–&gt; l1g) and ΔCpot(h–&gt; l1g) the standard enthalpy and heat capacity changes for D-hydrate dissociation and (ii) for n = r the approximate formula number of the D-hydrate at each experimental temperature. The formula D2S·6.115D2O with standard error 0.018D2O is found for deuterium sulfide D-hydrate at lower quadruple point Q(hs1l1g) 3.392°C; an approximate formula D2S·5.840D2O with SE 0.019D2O is found at upper quadruple point Q(hs1l2g) 30.770°C. Key words: clathrate D-hydrate of deuterium sulfide, deuterium sulfide D-hyfrate, formula of deuterium sulfide D-hydrate, thermodynamics of clathrate hydrate dissociation, dissociation equilibrium constant of deuterium sulfide D-hydrate, standard enthalpy, and heat capacity changes for dissociation of deuterium sulfide D-hydrate.

Standard ferric–ferrous potential and stability of FeCl 2+ to 90°C. Thermodynamic properties of Fe (aq)3+ and ferric-chloride species

Standard electrode potentials ( E T 0) for the reaction Fe 3+ (aq)+0.5H 2(g)=Fe 2+ (aq)+H + (aq) were derived from electrochemical measurements in a non-isothermal cell at temperatures from 20.8° to 90°C in HClO 4 solutions with ionic strength of 0.11–1.31 m. A value of E 298 0=0.770±0.002 V was obtained. An equation E T 0=0.6000–3.0961×10 −3 T+6.4351×10 −4 T×ln T, where T is temperature in K, based on the assumption of a constant heat capacity for the above reaction, Δ r C p 0=14.84 cal/mol K [Hovey, J.K., 1988. Thermodynamics of aqueous solutions. PhD Thesis, Univ. Alberta, Edmonton, USA.], fits experimental values of E T 0 from the present study together with data from Whittemore and Langmuir [Whittemore, D.O., Langmuir, D., 1972. Standard electrode potential of Fe 3++e −=Fe 2+ from 5–35°C. J. Chem. Eng. Data 17, 288–290.] (5°–35°C) with an uncertainty better than ±0.002 V. The standard thermodynamic properties of ferric–ferrous reaction at 25°C were calculated: Δ r G 0=−17.75±0.04 kcal/mol, Δ r H 0=−9.4±0.5 kcal/mol, Δ r S 0=28.0±1.5 cal/mol K. Using these values and thermodynamic data for Fe (aq) 2+ and H 2(g) from SUPCRT92 [Johnson, J.M., Oelkers, E.H., Helgeson, H.C., 1992. SUPCRT92: a software package for calculating the standard molal thermodynamic properties of minerals, gases, aqueous species and reactions from 1 to 5000 bars and 0° to 1000°C. Computers and Geosciences 18, 899–947.], the standard thermodynamic properties for Fe (aq) 3+ ion at 25°C, 1 bar were generated: Δ f G 0=−4.12 kcal/mol, Δ f H 0=−12.65 kcal/mol, S 0=−68.9 cal/mol K. The equilibrium stability constants for the reaction Fe 3++Cl −=FeCl 2+ were generated from the comparison of ferric–ferrous electrode potentials in a non-complexing medium (HClO 4) with those in HCl solutions from 25° to 90°C. A value of log β 0=1.52±0.10 was obtained at 25°C, 1 bar. Experimental results were combined with the reaction enthalpies measured by Vasil'ev and Lobanov [Vasil'ev, V.P., Lobanov, G.A., 1967. Effect of temperature and ionic strength on heat of formation of hydrated FeCl 2+ in aqueous solution. Russ. J. Phys. Chem. 41, 1969–1973 [in Russian].] from 10° to 55°C, to describe the temperature dependence of the stability constant, enthalpy and heat capacity for this reaction: log β 1 0=0.018 T+420.12/ T−5.23; Δ r H 0 (cal/mol)=−1918+0.082 T 2; Δ r C P 0 (cal/mol K)=0.163 T. This data allows calculation of the standard Gibbs energy (−37.61 kcal/mol), enthalpy (−47.21 kcal/mol), entropy (−30.2 cal/mol K) and heat capacity (−5.7 cal/mol K) for FeCl 2+ using thermodynamic properties for Fe 3+ and Cl − aqueous ions from this study and SUPCRT92, respectively. Thermodynamic properties of Fe 3+ and FeCl 2+ generated in this study together with data for FeCl 2 + complex derived from the literature data (Δ f G 0=−71.27 kcal/mol, Δ f H 0=−81.84 kcal/mol, S 0=−5.9 cal/mol K, C p 0=7.0 cal/mol K at 25°C, 1 bar) allowed calculation of hematite solubility in HCl solutions from 25° to 200°C.

Thermodynamic properties of the nickel silicide NiSi between 8 and 400 K

The molar heat capacities of NiSi have been determined by low-temperature adiabatic calorimetry at temperatures between 8 and 400 K. From the heat capacity data the derived thermodynamic functions Δ 0 T H 0 and S 0 were calculated. At T = 298.15 K a molar standard heat capacity of 45.55 ± 0.05 J K −1 mol −1 and a molar standard entropy of 47.58 ± 0.04 J K −1 mol −1 have been found. The entropy of formation for NiSi was calculated to be −1.11 ± 0.08 J K −1 mol −1.

Ab initio studies on the conformations, thermodynamic properties and rotational isomerization of diphenylamine (DPA)

Molecular orbital ab initio calculations were performed at the MP2/6-31G* and HF/6-31G* levels to investigate the conformations and properties of diphenylamine (DPA). According to the MP2/6-31G* results, DPA has two rotational optical isomers which differ only in the direction of rotation of the phenyl rings. Two rings in each conformer are essentially planar. One is distorted around the C–N bond by 9.6° and another by 46.8°, and the angle between them is 52.4°. Inclusion of electron correlation shrinks the C–N bonds and the ∠C–N–C angle, stretches the C–C bonds and increases the H⋯H non-bonded distance between the two rings. The standard thermodynamic properties, enthalpy( H 0), entropy( S 0) and heat capacity( C p 0), as well as the kinetic rate constant for rotational conversion between the isomers of DPA at various temperatures were also derived using the scaled HF/6-31G* IR frequencies. The low internal rotational barrier (7.76 kJ mol −1) and high rate coefficient (about 10 14 l mol −1 s −1) imply that rotational conversion between the two isomers are very easy.

A Calorimetric Determination of the Standard Enthalpy and Heat Capacity Changes that Accompany Micelle Formation for Four Long Chain Alkyldimethylphosphine Oxides in H2O and D2O Solution from 15 to 79 °C

Relative partial molar enthalpy data were obtained at five degree intervals between 15 and 79 °C for n-C8-, C9-, and C10-dimethylphosphine oxides and between 15 and 60 °C for n-C11-dimethylphosphine oxide in H2O and D2O. The results were used to calculate the standard molar enthalpy and heat capacity changes for micelle formation for comparison with the data previously reported for the C12 homologue. These values were then used to calculate the temperature dependence of the cmc, which was always lower in D2O than in H2O solutions. A small temperature dependence of the heat capacity change for micelle formation was observed in both solvents. Changes in thermodynamic parameters that accompany the transfer of the surfactant from H2O to D2O solution were also determined. It is interesting that differences in heat capacity noted for micelle formation or transfer of monomeric surfactant between the two solvents exhibited a greater dependence on the molecular weight of the surfactants than the corresponding enth...

Standard thermodynamic properties and heat capacity equations of rare earth hydroxides:: II. Ce(III)-, Pr-, Sm-, Eu(III)-, Gd-, Tb-, Dy-, Ho-, Er-, Tm-, Yb-, and Y-hydroxides. Comparison of thermochemical and solubility data

Standard thermodynamic properties at 298.15 K, 1 bar for the solid hydroxides of Y, Ce(III), Pr, Sm, Eu(III), Gd, Tb, Dy, Ho, Er, Tm and Yb were calculated from thermochemical data available in the literature. `3 Rn' heat capacity equations [Fei, Y., Saxena, S.K., 1987. An equation for the heat capacity of solids. Geochim. Cosmochim. Acta 51, 251–254.] were generated for Y-, Pr-, Eu(III)-, Gd-, Tb-, and Ho-hydroxides from low-temperature heat capacity measurements. Standard entropy and enthalpy of formation were calculated using literature data and correlations developed by Bratsch and Lagowski [Bratsch, S.G., Lagowski, J.J., 1985. Lanthanide thermodynamic predictions: 6. Thermodynamics of gas-phase ions and revised enthalpy for solids at 298.15 K. J. Phys. Chem. 89, 3310–3316]. Critically assessed literature data on solubility products for freshly precipitated and slightly aged, and aged-precipitated and well-crystalline Ln-hydroxides (data for the La- and Nd-hydroxides from Diakonov et al. [Diakonov, I.I., Tagirov, B., Ragnarsdottir, K.V., 1997. Standard thermodynamic properties and heat capacity equations of rare earth hydroxides: I. La(OH) 3(s) and Nd(OH) 3(s). Comparison of thermochemical and solubility data. Radiochim. Acta, in press.]) showed that (a) the former are approximately two orders of magnitude more soluble, and (b) the solubility products ( K s10 b) for aged-precipitated and well-crystalline Ln-hydroxides decrease sharply from 10 −22.29 for La-hydroxide to 10 −25.98 for Nd-hydroxide and then changes gradually to 10 −26.99 for Lu-hydroxide. Experimental solubility products for aged (well-crystalline) Pr-, Nd-, Sm-, Eu-hydroxides at 298.15 K, 1 bar were found to be up to three orders of magnitude less compared to those calculated from thermodynamic data for hydroxides from this study and for aqueous lanthanide ions accepted in the literature [Morss, L.R., 1994. Comparative thermochemical and oxidation–reduction properties of lanthanides and actinides. In: Gschneider, K.A., Jr., Eyring, L., Choppin, G.R., Lander, G.H. (Eds.), Handbook of Physics and Chemistry of Rare Earths. Elsevier, 18, 239–291.]. Consequently, these REE are less mobile in natural and technological aqueous fluids than previously predicted.

Ab Initio Calculations and Internal Rotor: Contribution for Thermodynamic Properties S°298 and Cp(T)'s (300 &lt; T/K &lt; 1500): Group Additivity for Fluoroethanes

Ab initio calculations are performed on nine fluorinated ethane compounds and thermodynamic properties (S°298 and Cp(T)'s 300 < T/K < 1500) are calculated. Geometries of stable rotational conformers and transition states for internal rotation are optimized at the RHF/6-31G* (6-31G(d)) and MP2/6-31G* levels of theory. Harmonic vibrational frequencies are computed at the RHF/6-31G* level of theory. Potential barriers for internal rotations are calculated at the MP2/6-31G*//MP2/6-31G* level. Parameters of the Fourier expansion of the hindrance potential are tabulated. Standard entropies (S°298) and heat capacities (Cp(T)'s, 300 < T/K < 1500) are calculated using the rigid-rotor-harmonic-oscillator approximation with direct integration over energy levels of the intramolecular rotation potential energy curve. Heats of formation are adopted from literature evaluation and BAC-MP4 ab initio calculations. Thermodynamic properties for fluorinated carbon groups C/C/F/H2, C/C/F2/H, and C/C/F3 are determined by existing thermodynamic group parameter of C/C/H3 and data on CH2FCH3, CHF2CH3, and CF3CH3, respectively: no fluorine or other halogen is on the methyl carbon adjacent to the carbon bonded to the fluorine(s). Six interaction terms in addition to the above groups are developed to account for repulsion and steric effects. Interaction terms are required to accurately estimate ΔHf°298, S°298, and Cp(T)'s (300 < T/K < 1500) for fluoroethanes where fluorine(s) are on carbons adjacent to a carbon bonded to fluorine(s).

Standard Thermodynamic Properties and Heat Capacity Equations for Rare Earth Element Hydroxides

Standard Thermodynamic Properties and Heat Capacity Equations for Rare Earth Element Hydroxides