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  • 1.
    Driver, Gordon W.
    et al.
    Umeå University, Faculty of Science and Technology, Department of Chemistry.
    Johnson, Keith E.
    Interpretation of Fusion and Vaporisation Entropies for Various Classes of Substances, with a Focus on Salts2014In: Journal of Chemical Thermodynamics, ISSN 0021-9614, E-ISSN 1096-3626, Vol. 70, no March 2014, p. 207-2013Article in journal (Refereed)
    Abstract [en]

    Entropies of fusion and vaporisation of a variety of elements and compounds have been derived from literature data. Fusion entropies range from low values for metals and certain cyclic hydrocarbons (e.g. cyclopentane) through modest values for salts to high values for materials undergoing drastic rearrangement or disentanglement such as aluminium chloride and n-alkanes. Entropies of vaporisation for most substances are close to the Trouton’s Law value of ∼100 J deg.-1 mol.-1, with low values for species which associate on boiling (e.g. acetic acid) and higher values signifying simple dissociation (e.g. nitrogen tetroxide) or total decomposition (e.g. some ionic liquids). The nature of inorganic and semi-organic salts in all 3 phases is discussed.

  • 2. Lindberg, Daniel
    et al.
    Backman, Rainer
    Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics, Energy Technology and Thermal Process Chemistry.
    Chartrand, Patrice
    Thermodynamic evaluation and optimization of the (Na2CO3+Na2SO4+Na2S+K2CO3+K2SO4+K2S) system2007In: Journal of Chemical Thermodynamics, ISSN 0021-9614, E-ISSN 1096-3626, Vol. 39, no 6, p. 942-960Article in journal (Refereed)
    Abstract [en]

    A critical evaluation of all phase diagram and thermodynamic data were performed for the solid and liquid phases of the (Na2CO3 + Na2SO4 + Na2S + K2CO3 + K2SO4 + K2S) system and optimized model parameters were obtained. The Modified Quasichemical Model in the Quadruplet Approximation was used for modelling the liquid phase. The model evaluates first- and second-nearest-neighbour short-range ordering, where the cations (Na+ and K+) are assumed to mix on a cationic sublattice, while anions are (CO32- ,SO42-, and S2-) are assumed to mix on an anionic sublattice. The Compound Energy Formalism was used for modelling the solid solutions of (Na, K)(2)(CO3, SO4, S). The models can be used to predict the thermodynamic properties and phase equilibria in multicomponent heterogeneous systems. The experimental data from the literature were reproduced within experimental error limits.

  • 3. Lindberg, Daniel
    et al.
    Backman, Rainer
    Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics, Energy Technology and Thermal Process Chemistry. Åbo Akademi Process Chemistry Centre, Åbo Akademi University, Biskopsgatan 8, FI-20500 Turku, Finland.
    Chartrand, Patrice
    Thermodynamic evaluation and optimization of the (Na2SO4+K2SO4+Na2S2O7+K2S2O7) system2006In: Journal of Chemical Thermodynamics, ISSN 0021-9614, E-ISSN 1096-3626, Vol. 38, no 12, p. 1568-1583Article in journal (Refereed)
    Abstract [en]

    A complete, critical evaluation of all phase diagram and thermodynamic data was performed for all phases of the (Na2SO4 + K2SO4 + Na2S2O7 + K2S2O7) system and optimized model parameters were obtained. The Modified Quasichemical Model in the Quadruplet Approximation was used for modelling the liquid phase. The model evaluates first- and second-nearest-neighbour short-range ordering, where the cations (Na+ and K+) are assumed to mix on a cationic sublattice. The Compound Energy Formalism was used for modelling the solid Solutions of (Na,K)(2)SO4 and (Na,K)(2)S2O7. The models can be used to predict the thermodynamic properties and phase equilibria in multicomponent heterogeneous systems. The experimental data from the literature were reproduced within experimental error limits.

  • 4. Lindberg, Daniel
    et al.
    Backman, Rainer
    Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics, Energy Technology and Thermal Process Chemistry. Åbo Akademi Process Chemistry Centre, Åbo Akademi University, Biskopsgatan 8, FI-20500 Turku, Finland.
    Chartrand, Patrice
    Thermodynamic evaluation and optimization of the (NaCl + Na2SO4+Na2CO3+KCl+K2SO4+K2CO3) system2007In: Journal of Chemical Thermodynamics, ISSN 0021-9614, E-ISSN 1096-3626, Vol. 39, no 7, p. 1001-1021Article in journal (Refereed)
    Abstract [en]

    A complete, critical evaluation of all phase diagrams and thermodynamic data was performed for all condensed phases of the (NaCl + Na2SO4 + Na2CO3 + KCl + K2SO4 + K2CO3) system, and optimized parameters for the thermodynamic solution models were obtained. The Modified Quasichemical Model in the Quadruplet Approximation was used for modelling the liquid phase. The model evaluates first- and second-nearest-neighbour short-range order, where the cations (Na+ and K+) were assumed to mix on a cationic sublattice, while anions (CO32-, SO42-, and Cl-) were assumed to mix on an anionic sublattice. The thermodynamic properties of the solid solutions of (Na,K)(2)(SO4,CO3) were modelled using the Compound Energy Formalism, and (Na,K)CI was modelled using a substitutional model in previous studies. Phase transitions in the common-cation ternary systems (NaCl + Na2SO4 + Na2CO3) and (KCl + K2SO4 + K2CO3) were studied experimentally using d.s.c./t.g.a. The experimental results were used as input for evaluating the phase equilibrium in the common-cation ternary systems. The models can be used to predict the thermodynamic properties and phase equilibria in multicomponent heterogeneous systems. The experimental data from the literature are reproduced within experimental error limits.

  • 5. Lindberg, Daniel
    et al.
    Backman, Rainer
    Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics, Energy Technology and Thermal Process Chemistry.
    Hupa, Mikko
    Chartrand, Patrice
    Thermodynamic evaluation and optimization of the (Na+K+S) system2006In: Journal of Chemical Thermodynamics, ISSN 0021-9614, E-ISSN 1096-3626, Vol. 38, no 7, p. 900-915Article in journal (Refereed)
    Abstract [en]

    The (Na + K + S) system is of primary importance for the combustion of black liquor in the kraft recovery boilers in pulp and paper mills. A thermodynamic evaluation and optimization for the (Na + K + S) system has been made. All available data for the system have been critically evaluated to obtain optimized parameters of thermodynamic models for all phases. The liquid model is the quasichemical model in the quadruplet approximation, which evaluates 1st- and 2nd-nearest-neighbour short-range-order. In this model, cations (Na+ and K+) are assumed to mix on a cationic sublattice, while anions (S2-, S-2(2-), S-3(2-), S-4(2-), S-5(2-), S-6(2-), S-7(2-), S-8(2-), Va(-)) are assumed to mix on an anionic sublattice. The thermodynamic data of the liquid polysulphide components M2S1+n (M = Na, K and n = 1-7) are fitted to Delta G = A(n) + B(n) . T for the reaction M2S(1) + nS(1) = M2Sn+1 (1). The solid phases are the alkali alloys, alkali sulphides, several different alkali polysulphides and sulphur. The solid solutions (Na, K), (Na, K)(2)S and (Na, K)(2)S-2 are modelled using the compound energy formalism. The models can be used to predict the thermodynamic properties and phase equilibria in the multicomponent heterogeneous system. The experimental data are reproduced within experimental error limits for equilibria between solid, liquid and gas. The ternary phase diagram of the system (Na2S + K2S + S) has been predicted as no experimental determinations of the phase diagram have been made previously.

  • 6.
    Lindberg, Gustav
    et al.
    Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics, Energy Technology and Thermal Process Chemistry.
    Larsson, Anders
    Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics, Energy Technology and Thermal Process Chemistry.
    Råberg, Mathias
    Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics, Energy Technology and Thermal Process Chemistry.
    Boström, Dan
    Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics, Energy Technology and Thermal Process Chemistry.
    Backman, Rainer
    Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics, Energy Technology and Thermal Process Chemistry.
    Nordin, Anders
    Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics, Energy Technology and Thermal Process Chemistry.
    Determination of thermodynamic properties of Na2S using solid-state EMF measurements2007In: Journal of Chemical Thermodynamics, ISSN 0021-9614, E-ISSN 1096-3626, Vol. 39, no 1, p. 44-48Article in journal (Refereed)
    Abstract [en]

    To obtain reliable thermodynamic data for Na2S(s), solid-state EMF measurements of the cell Pd(s)|O2(g)|Na2S(s), Na2SO4(s)|YSZ| Fe(s), FeO(s)|O2(g)ref| Pd(s) were carried out in the temperature range 870 < T/K < 1000 with yttria stabilized zirconia as the solid electrolyte. The measured EMF values were fitted according to the equation Efit/V (±0.00047) = 0.63650 − 0.00584732(T/K) + 0.00073190(T/K) ln (T/K). From the experimental results and the available literature data on Na2SO4(s), the equilibrium constant of formation for Na2S(s) was determined to be lg Kf(Na2S(s)) (±0.05) = 216.28 − 4750(T/K)−1 − 28.28878 ln (T/K). Gibbs energy of formation for Na2S(s) was obtained as ΔfG(Na2S(s))/(kJ · mol−1) (±1.0) = 90.9 − 4.1407(T/K) + 0.5415849(T/K) ln (T/K). By applying third law analysis of the experimental data, the standard enthalpy of formation of Na2S(s) was evaluated to be ΔfH(Na2S(s), 298.15 K)/(kJ · mol−1) (±1.0) = −369.0. Using the literature data for Cp and the calculated ΔfH, the standard entropy was evaluated to S(Na2S(s), 298.15 K)/(J · mol−1 · K−1) (±2.0) = 97.0.

  • 7.
    Sandström, Malin
    et al.
    Umeå University, Faculty of Science and Technology, Applied Physics and Electronics. Umeå University, Faculty of Science and Technology, Applied Physics and Electronics, Energy Technology and Thermal Process Chemistry.
    Boström, Dan
    Umeå University, Faculty of Science and Technology, Applied Physics and Electronics. Umeå University, Faculty of Science and Technology, Applied Physics and Electronics, Energy Technology and Thermal Process Chemistry.
    Determination of standard Gibbs energy of formation for CaKPO4, CaK4(PO4)2, CaK2P2O7 and Ca10K(PO4)7 from solid state EMF measurements using yttria stabilised zirconia as solid electrolyte2008In: Journal of Chemical Thermodynamics, ISSN 0021-9614, E-ISSN 1096-3626, Vol. 40, no 1, p. 40-46Article in journal (Refereed)
    Abstract [en]

    The equilibrium reactions: 4CaKPO4(s) + 6Ni(s)  CaK4(PO4)2(s) + 3CaO + 2Ni3P(s) + 5/2O2(g), 4CaKPO4(s) + 3K4P2O7(s) + 6Ni(s)  4CaK4(PO4)2(s) + 2Ni3P(s) + 5/2O2(g), 4CaK2P2O7(s) + 6Ni(s)  4CaKPO4(s) + K4P2O7(s) + 2Ni3P(s) + 5/2O2(g) and Ca10K(PO4)7(s) + 9CaK2P2O7(s) + 18Ni(s)  19CaKPO4(s) + 6Ni3P(s) + 15/2O2(g) were studied in the temperature range from 880 to 1125 K. The oxygen equilibrium pressures were determined using galvanic cells incorporating yttria stabilised zirconia as solid electrolyte. From the measured data and using literature values of standard Gibbs free energy of formation for CaO, Ni3P and K4P2O7, the following relationship of the standard Gibbs free energy of formation for CaKPO4, CaK4(PO4)2, CaK2P2O7, and Ca10K(PO4)7 were calculated:

    ΔfG(CaKPO4) ± 5.2/(kJ · mol−1) = −1506.6 − 3.2933(T/K) + 0.4603(T/K) · ln(T/K) 890 < (T/K) < 1125

     

    ΔfG(CaK4(PO4)2) ± 8.9/(kJ · mol−1) = −3498.2 − 2.1339(T/K) + 0.3661(T/K) · ln(T/K) 930 < (T/K) < 1125

    ΔfG(CaK2P2O7) ± 7.2/(kJ · mol−1) = −2690.0 − 3.7820(T/K) + 0.5599(T/K) · ln(T/K) 940 < (T/K) < 1100

    ΔfG(Ca10K(PO4)7) ± 133/(kJ · mol−1) = −5988.3 − 57.063(T/K) + 7.4407(T/K) · ln(T/K) 880 < (T/K) < 1015.

  • 8.
    Sandström, Malin Hannah
    et al.
    Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics, Energy Technology and Thermal Process Chemistry.
    Boström, Dan
    Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics, Energy Technology and Thermal Process Chemistry.
    Rosén, Erik
    Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics, Energy Technology and Thermal Process Chemistry.
    Determination of standard Gibbs free energy of formation for Ca2P2O7 and Ca(PO3)2 from solid state EMF measurements using yttria stabilised zirconia as solid electrolyte2006In: Journal of Chemical Thermodynamics, ISSN 0021-9614, E-ISSN 1096-3626, Vol. 38, no 11, p. 1371-1376Article in journal (Refereed)
    Abstract [en]

    The equilibrium reactions: 3Ca2P2O7(s) + 6Ni(s) reversible arrow 2Ca3(PO4)2(s) + 2Ni3P(s) + 5/O-2(g) and 2Ca(PO3)2(s) + 6Ni(s) reversible arrow Ca2P2O7(s) + 2Ni3P(s) +/- 5/2O2(g) were studied in the temperature range 890 K to 1140 K. The oxygen equilibrium pressures were determined using galvanic cells incorporating yttria stabilized zirconia as solid electrolyte. From the measured data and using the literature values of standard Gibbs free energy of formation for Ca3(PO4)2 and Ni3P, the following relationship of the standard Gibbs free energy of formation for Ca2P2O7 and Ca(PO3)(2) were calculated:

    ΔfG° (Ca2P2O7) +/- 11/(kJ · mol-1)=-3475.9 + 1.5441 (T/K) -0.1051 (T/K) · 1n(T/K) and

    ΔfG° (Ca(PO3)2) +/- 12/(kJ · mol-1)= -3334.8 + 6.1561 (T/K) -0.6950(T/K) · 1n(T/K).

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