Molar Gibbs Energy Of Formation Research Articles

Thermodynamic insights of ternary compounds of NiO - V2O5 system

We present the first experimental investigation on thermochemical stability of three ternary nickel vanadates, namely, NiV2O6(s), Ni2V2O7(s) and Ni3V2O8(s) in the NiO-V2O5 system. The standard molar entropies of formation of the compounds were determined by low temperature heat capacity measurements from 2 to 300 K using relaxation calorimetry. The standard molar enthalpy of formation and molar heat capacities were determined employing high temperature oxide melt solution calorimetry in conjunction with differential scanning calorimetry. Using the experimentally obtained thermochemical data, the standard molar Gibbs energy of formation of these compounds were derived and the corresponding expressions are given as follows:∆Gf,m°<NiV2O6>±1.4kJmol−1=−1839.4+0.5132(T/K)(T:298.15−1000K)∆Gf,m°<Ni2V2O7>±1.4kJmol−1=−2101.8+0.5971(T/K)(T:298.15−1000K)∆Gf,m°<Ni3V2O8>±3.2kJmol−1=−2360.5+0.6538(T/K)(T:298.15−1000K)

Electrode potentials involving atoms and ions of metals in intermediate oxidation states in aqueous solutions

The electrode potentials of metal atoms (M+/M0 and M2+/M0 couples) were calculated from their standard electrode potentials in water minus the standard molar Gibbs energy of formation of the atoms in the gas phase, ΔfG0(Mgas0), and the Gibbs energy of hydration in solution, ΔhydG°. Electrode potentials are appreciably shifted (by 2.0–2.5 V) toward negative values relative to the potentials of the solid metals. For the univalent metals Cu0, Ag0, and Au0 (d10s1 electronic configuration), the electrode potentials of M+/M0 couples are –2.73, –1.90, and –1.82 V; for Ga0, In0, and Tl0 (d10s2p1 electronic configuration), they are –3.14, –2.45, and –1.99 V, respectively. For bivalent transition metals of period IV with the d5+ns2 configuration, the potentials of M2+/M0 couples are –2.50 V for Mn0, –2.45 V for Fe0, –2.33 V for Co0, –2.34 for Ni0, –1.29 V for Cu0, and –1.34 V for Zn0. For Cd0 and Hg0 (d10s2 configuration), the potentials are –0.87 and + 0.42 V. Estimation of the electrode potentials of bivalent metals in the intermediate and unstable oxidation states (M2+/M+ and M+/M0 couples) revealed their significant difference. In the case of Zn, Cd, and Hg, this difference is particularly noticeable, as large as 2–3 V, because of different configurations of the M+ (d10s1) and M0 (d10s2) electronic shells. Regular trends in variations of the electrode potentials in the periods and groups of the periodic table were revealed. In going from the atomic-molecular to the solid state, the chemical activity of the metals decreases. The metal surface catalyzes the reactions that are thermodynamically unfavorable in the solution volume.

Estimation of the reduction potential of transition metal atoms in aqueous solutions

The reduction potentials of the M2+/M0 couples of transition metals Mn, Fe, Co, Ni, Cu, and Zn were calculated by subtracting from their standard electrode potentials in liquid water the standard molar Gibbs energy of formation of atoms in the gas phase ΔfG0(Mgas0) and the Gibbs energy of their hydration in solution ΔfG0(Maq0). The potentials are –2.503 V for Mn0, –2.454 V for Fe0, –2.333 V for Co0, –2.335 V for Ni0, –1.291 V for Cu0, and –1.335 V for Zn0. The disproportionation of ions in the intermediate oxidation state M+ with the formation of the M0 atom is thermodynamically favorable in the solution volume only for zinc.

A comprehensive investigation on CdO-SnO2 system: Structure, thermal expansion and energetics

An extensive investigation into the thermochemical stability of two ternary oxides, ilmenite-type CdSnO3(s) and orthorhombic Cd2SnO4(s), in the Cd-Sn-O system was reported for the first time using high temperature oxide melt solution calorimetry in conjunction with differential scanning calorimetry and thermal relaxation calorimetry. The values of standard molar enthalpy of formation (∆fH298.15°), standard molar entropy (S298.15°), molar heat capacity and Debye temperature (θD) for ilmenite-type CdSnO3(s) and orthorhombic Cd2SnO4(s) were determined. Using the experimentally obtained thermochemical data, the standard molar Gibbs energy of formation of these compounds were derived and the corresponding expressions are given as follows:∆fGm°<CdSnO3>±1.3kJmol−1=−847.9+0.2781(T/K)(T:298.15−1000K)∆fGm°<Cd2SnO4>±3.6kJmol−1=−1138.1+0.3831(T/K)(T:298.15−1000K)Moreover, high temperature XRD experiments were conducted to evaluate their thermal expansion behaviour as well as for the in-situ identification of phase evolution resulting from decomposition of cadmium stannates.

Experimental and Theoretical Investigation on the Thermochemistry of 3-Methyl-2-benzoxazolinone and 6-Nitro-2-benzoxazolinone.

The determination of the reliable thermodynamic properties of 2-benzoxazolinone derivatives is the main goal of this work. Some correlations are established between the energetic properties determined and the structural characteristics of the title compounds, and the reactivity of this class of compounds is also evaluated. Static-bomb combustion calorimetry and high-temperature Calvet microcalorimetry were used to determine, respectively, the standard molar enthalpies of formation in the solid state and the standard molar enthalpies of sublimation, both at T = 298.15 K. Using the results obtained for each compound, the respective gas-phase standard molar enthalpy of formation was derived. High-level quantum chemical calculations were performed to estimate the same property and the results evidence good accordance. Moreover, the gas-phase relative thermodynamic stability of 2-benzoxazolinone derivatives was also evaluated using the respective gas-phase standard molar Gibbs energy of formation. In addition, the relationship between the energetic and structural characteristics of the benzoxazolinones is presented, evidencing the enthalpic increments associated with the presence of a methyl and a nitro groups in the molecule, and this effect is compared with similar ones in other structurally related compounds.

Calorimetric investigations on lithium based ceramics

Lithium based ceramics namely lithium titanate, lithium zirconate, and lithium aluminate are proposed materials for tritium breeding in a D-T based fusion reactor. Thermodynamic stability of these materials is important for their use under extreme conditions. In this paper, the thermodynamic stability analysis of lithium titanate, lithium zirconate, and lithium aluminate ceramics is reported. The standard molar enthalpy of formation Li2TiO3(s), Li2ZrO3(s), and LiAlO2(s) compounds have been determined for the first time employing an isoperibol room temperature solution calorimeter. The standard molar enthalpy of formation of Li2TiO3(s), Li2ZrO3(s), and LiAlO2(s) at 298.15 K are found to be – (1632.4 ± 9.7), – (1776.7 ± 6.7), and – (1188.2 ± 5.2) kJ·mol−1, respectively. The isobaric heat capacity of these compounds has been measured over the temperature range 300 K to 770 K employing Differential Scanning Calorimeter (DSC). Using the above experimental results the standard molar Gibbs energy of formation and other thermodynamic functions for these compounds have been derived and compared with the literature values.

Thermodynamic properties over two phase region of Gd–Al system: Knudsen effusion mass spectrometric study

Vaporisation behaviour of <GdAl2(cr)+GdAl(cr)> two phase region of Gd-Al system was investigated by employing Knudsen Effusion Mass Spectrometry (KEMS) in the temperature range 1158–1323 K. Al(g) was the neutral species observed in the equilibrium vapour and partial pressure-Temperature (p-T) relation over this two phase region was deduced as log (pAl/Pa) = (−20282 ± 260)/T + (13.06 ± 0.21). The standard enthalpy change, at 298.15 K, of the reaction (GdAl2(cr) = GdAl(cr) + Al(g)) was evaluated by second law method. ΔfHm,GdAlcr,298.15Ko was deduced to be − 83.8 ± 11.8 kJ mol−1. The expression for standard molar Gibbs energy of formation of GdAl(s) derived is given as, ΔfGm,GdAlcr,To = (−101.7 ± 6.6) + (0.00667 ± 0.00560)T kJ mol−1. These data are being reported for the first time.

Thermodynamic investigation of Cr2TeO6 and Cr2Te4O11

Knowledge on thermodynamic stability of the compounds formed by the interaction of volatile fission products with the components of structural materials during reactor operation is important to predict life time of the nuclear fuel pin inside a nuclear reactor. In the present study, thermodynamic properties of two compounds viz., Cr2TeO6(cr) and Cr2Te4O11(cr) in Cr-Te-O system are reported. The standard molar Gibbs energy of formation of Cr2TeO6(cr) and Cr2Te4O11(cr) have been determined by EMF measurement technique employing galvanic cells: (-) Pt, C, Cr2O3(cr), Te(cr or l), Cr2TeO6(cr)│CSZ│O2(g) (pO2 = 0.21 atm), Pt (+) and (-) Pt, C, Cr2TeO6(cr), TeO2(cr), Cr2Te4O11(cr)│CSZ│O2(g) (pO2 = 0.21 atm), Pt (+), in the temperature range 685 ≤ T/K≤877 and 705 ≤ T/K≤843, respectively. The standard Gibbs energy of formation of Cr2TeO6(cr) and Cr2Te4O11(cr) derived from the measured EMF data could be expressed as: ΔfGº (Cr2TeO6, cr) (±5.6 kJ.mol−1) = -1644.2 + 0.5606 T (725 ≤ T/K≤877) and ΔfGº (Cr2Te4O11, cr) (±6.3 kJ.mol−1) = -2458.2 + 1.013 T (705 ≤ T/K≤843), respectively. The values of ‘third-law’ enthalpy of formation ΔHf,298Ko of Cr2TeO6(cr) and Cr2Te4O11(cr) are found to be -1632.2 ± 0.8 kJ mol-1 and -2432.4 ± 0.5 kJ mol−1, respectively.

Fluoride electrolyte based galvanic cell: Stability of the hollandite BaRu6O12(s)

BaRu6O12(s), a quasi one dimensional hollandite with a tetragonal crystal structure, exhibits interesting electronic properties. The solid state reaction route was used for the synthesis of BaRu6O12(s), and was identified by X-ray diffraction analysis, its structural parameters determined and its hollandite structure illustrated. A fluoride ion conducting solid electrolyte based Galvanic cell was constructed and the standard molar Gibbs energy of formation of BaRu6O12(s) was determined. This cell was standardized using phase mixtures of {Ni(s) + NiF2(s)} and {Fe(s) + FeF2(s)} as the two electrodes and CaF2 as the solid electrolyte prior to the measurement of the cell electromotive force, given by:-Pt/O2(g),{CaO(s)+CaF2(s)}//CaF2//{BaF2(s)+RuO2(s)+Ru(s)+BaRu6O12(s)},O2(g)/Pt+.The measured electromotive cell measurements for the above cell along with known Gibbs energy values from literature were used to calculate the standard molar Gibbs energy of formation of BaRu6O12(s) from elements in their standard state and the equation of ΔfGo(T) for BaRu6O12(s) can be given by: ΔfGo(BaRu6O12(s))/kJ⋅ mol−1(±2.94) = - 2447.7 + 1.165 ⋅ (T/K).The slope and intercept of the above equation gives the standard molar entropy and enthalpy of formation respectively, at the average experimental temperature. Thermodynamic stability was determined of this important one dimensional hollandite BaRu6O12(s) from these studies for the first time.

Thermodynamic stability of Li3ThF7(cr) and LiTh4F17(cr)

For the successful operation of high temperature Molten Salt reactors (MSR), comprehensive information on the thermodynamic properties of multi-component fluoride fuel salt systems is required. In this paper, thermodynamic properties of compounds of LiF–ThF4 system are reported. The standard molar Gibbs energy of formation for Li3ThF7(cr) and LiTh4F17(cr) has been determined by measuring the vapour pressure of HF(g) over the equilibrium reactions: Li3ThF7(cr)+2H2O(g)=3LiF(cr)+ThO2(cr)+4HF(g) and LiTh4F17(cr)+8H2O(g)=LiF(cr)+4ThO2(cr)+16HF(g) respectively. The standard molar heat capacity Cpmo(T) of these compounds has been measured in the temperature range 2–303 K. From the heat capacity data, the Debye constant and standard molar entropies at 298 K (S298°) of Li3ThF7(cr) and LiTh4F17(cr) were derived. Based on the experimental results, the thermodynamic functions for these compounds have been generated.

Stability studies and magnetic behaviour of rhodium vanadate

Rhodium vanadate an important catalytic compound was synthesized by solid state reaction route and characterized by X-ray diffraction. The standard molar Gibbs energy of formation of rhodium vanadate was determined using solid state electrochemical technique employing a calcia stabilized zirconia (CSZ) oxide ion conducting electrolyte. The Gibbs energy of formation was determined from electromotive force measurements carried out in the temperature range from 959 K to 1137 K.Magnetic measurements using a Vibration Sample Magnetometer (VSM) in the temperature range from 4 K to 300 K under the influence of a magnetic field of 1 kOe was carried out. The measurements concluded that the compound RhVO4(s) shows paramagnetic behavior. The magnetization measured at 1.8 K under a changing magnetic field shows a very narrow and symmetric loop that further reiterates the above conclusion.

Electrochemical extraction of metallic Y using solid and liquid double cathodes

To select proper electrode material for the extraction of rare earth elements and purification of salt, double cathode electrolysis cell was designed to compare the extraction of Y on solid and liquid electrodes. The electrode process kinetic and thermodynamic data of Y(III) on liquid Zn electrode and solid Cu electrode were studied employing cyclic voltammetry (CV), open-circuit chronopotentiometry (OCP) and linear polarization (LP), respectively. The thermodynamic results indicated that the reduction peak potentials of (Y–Zn)solution and Zn-rich Y–Zn compound are more positive than that of Cu-richest Y–Cu compound, and the standard molar Gibbs energy of formation for (Y–Zn)solution is smaller than those for Y–Cu compounds, which meant (Y–Zn)solution formed easily. Furthermore, the dynamic properties, such as exchange current densities and charge-transfer resistances of Y(III)/Cu7Y and Y(III)/(Y–Zn)solution couples, were determined employing LP technique. The reaction activation energies for the two couples were also estimated according to the relationship of exchange current density and temperature, which showed the reaction activation energy for Y(III)/Cu7Y couple is larger than that for Y(III)/(Y–Zn)solution couple. To compare to the extraction rate and efficiency, the electrochemical extracting Y on single cathode (solid Cu or liquid Zn) and double cathodes (solid Cu and liquid Zn) was executed by constant current electrolysis under same conditions. The results displayed that the extraction rate and efficiency of metallic Y is higher on liquid Zn electrode in the first 6 h, and only a small amount of metallic Y was deposited on solid Cu electrode in double cathode system.

In‐situ microcalorimetry study on thermodynamic functions of Cu 2 O nanocubes

Four different sizes of cuprous oxides (Cu2 O) nanocubes in the range of 40–120 nm were synthesised by liquid phase reduction method. The morphology, size, and structure of synthesised Cu2 O nanocubes were characterised by scanning electron microscopy, X-ray diffraction, and X-ray photoelectron spectroscopy. In-situ microcalorimetry was used to calculate the conventional and surface thermodynamic functions of Cu2 O nanocubes by combining thermodynamic principles and transition state theory. The effect of particle size on conventional thermodynamic functions and surface thermodynamic functions were investigated and analysed, whose results were supported by the established thermodynamic models. Results showed that both the standard molar enthalpy of formation and the standard molar entropy of formation were increased with decreasing particle size, while the standard molar Gibbs energy of formation decreased. Also, the molar surface Gibbs energy, molar surface enthalpy, and molar surface entropy grew with the reduction of particle size, which correlated well with the models. Such a property is of scientific significance for enriching and developing disciplines such as surface physics and surface thermodynamics.

Electrochemical behavior and extraction of zirconium on Sn-coated W electrode in LiCl-KCl melts

To recover metallic Zr from LiCl-KCl melts, the electroreduction of Zr(IV) ion was studied employing a variety of electrochemical methods on W and Sn-coated W electrodes. Zr(IV) ion was reduced to metallic Zr through two consecutive steps on W electrode: Zr(IV) + 2e− → Zr(II) and Zr(II) + 2e− → Zr, whereas one-step four-electron transfer on Sn-coated W electrode, i.e, xSn + 4e− + Zr(IV) = SnxZr. The formation of different Sn-Zr intermetallic compounds SnxZr resulted in three reduction peaks occurring at more positive potential than that of Zr(IV) on the W electrode, which was detected using cyclic voltammetry (CV) and square wave voltammetry (SWV). Meanwhile, the thermodynamic data, such as partial molar Gibbs energy and activity of Zr in Sn-Zr alloys and standard molar Gibbs energy of formation for Sn-Zr compound, were evaluated by open circuit chronopotentiometry (OCP). Furthermore, galvanostatic electrolysis (GE) at 0.1 A and potentiostatic electrolysis (PE) at −0.85 V were performed on liquid Sn electrode, and electrolytic products were analyzed by X-ray diffraction (XRD) and scanning electron microscopy (SEM) coupled with energy dispersive spectroscopy (EDS). Experimental results indicated that metallic Zr was recovered and Sn2Zr was prepared on liquid Sn electrode in LiCl-KCl-K2ZrF6 melts.

Determination of thermodynamic properties of Bi2Mo3O12 (s), Bi2MoO6 (s) and Bi6Mo2O15 (s)

The standard molar Gibbs energy of formation of monoclinic phase of Bi2MoO6 (s) was determined by measuring the equilibrium oxygen partial pressures in the Bi (l) - MoO2 (s) -Bi2MoO6 (s) phase field using solid electrolyte based emf cells and it is given by the following expression: ΔfGm°<Bi2MoO6>±0.9/kJmol-1=-1382.3+0.5064(T/K)(T:773-1023K) The molar heat capacities of Bi2Mo3O12 (s), Bi6Mo2O15 (s) and Bi2MoO6 (s) were experimentally measured employing a differential scanning calorimeter. The heat capacities measured over a temperature range is given by: CP<Bi2Mo3O12>(JK-1mol-1)±16.4=416.7-7.1×10-3T-8.8×106T-2(T:328-818K)CP<Bi6Mo2O15>(JK-1mol-1)±23.4=529.8+67.9×10-3T-6.3×106T-2(T:318-808K)CP<Bi2MoO6>(JK-1mol-1)±8.8=221.4-1.5×10-3T-3.9×106T-2(T:318-818K)The internal consistency of the measured thermodynamic data of Bi2MoO6 (s) has been verified.

Investigation in the variation of Gibbs energy of formation of RE6UO12 (RE = La, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Tm, Yb, Lu) along the 4f series

The RE6UO12 (s) (RE = La, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Tm, Yb, Lu) compounds were synthesized by citrate nitrate combustion method and characterized by X-Ray Diffraction (XRD) technique. Standard molar Gibbs energy of formation of RE6UO12(s) (RE = La, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Tm, Yb, Lu) was determined from the equilibrium electromotive force (e.m.f) data obtained from solid-state Galvanic cell with oxide ion conducting yttria-stabilized-zirconia (YSZ) electrolyte. The cells were operated under high pure argon atmosphere. E.m.f. measurements were carried out in the temperature range of 850–1150 K. Phase transition in Sm6UO12(s) and Yb6UO12(s) were detected at 1125 K and 1065 K, respectively. The transition temperatures were confirmed from high temperature XRD technique. The standard enthalpy of formation and entropy at temperature of 298.15 K for RE6UO12 (s) was calculated from the Gibbs energy data using second and third law analysis and the data were compared with the corresponding data reported for RE2O3(s). Similar trend in enthalpy as well as entropy was observed for RE6UO12 (s) and RE2O3 (s) along the series of 4f elements.

Standard molar Gibbs energy of formation of ‘Bi22Cr18O60’ and ‘Bi38CrO60’

The standard molar Gibbs energies of formation of ‘Bi22Cr18O60’ and ‘Bi38CrO60’ have been determined by emf technique using solid oxide electrolyte based emf cells and are given by:ΔfGmo ‘Bi22Cr18O60’s± 9.9kJ= -15314.4 + 4.1864T / KT: 929– 1025 KΔfGmo ‘Bi38CrO60’s± 5.6kJ= -11109.7+ 4.8582T / KT: 833 - 890 KThe temperatures of appearance of these compounds as stable phases in liquid bismuth in Bi-Cr-O system were deduced from the emf measurements. Confirmation experiments were also carried out by long term equilibration studies.

Determination of thermodynamic properties of the ternary oxides in the Y-Ru-O system by electromotive force measurements and differential scanning calorimetric measurements

In this study, the standard molar Gibbs energy of formation of Y2Ru2O7(s) and Y3RuO7(s) was determined using calcia-stabilized zirconia (CSZ) as an electrolyte and air as a reference electrode. The cells can be represented by: (−)Pt/{Y2O3(s) + Y2Ru2O7(s) + Ru(s)}//CSZ//O2(p(O2) = 21.21 kPa)/Pt(+), (−)Pt/{Y3RuO7(s) + Y2Ru2O7(s) + Y2O3(s)}//CSZ//O2(p(O2) = 21.21kPa)/Pt(+). The electromotive force was measured in the temperature range from 981 to 1155 K and 932 to 1186 K, respectively. The standard molar Gibbs energy of formation of Y2Ru2O7(s) and Y3RuO7(s) from elements in their standard state was calculated by the least squares regression analysis of the data obtained in the present study and can be given, respectively, by: {ΔfG(Y2Ru2O7, s)/(kJmol−1) ± 2.22} = − 2554.1 + 0.625 ⋅ (T/K) and {ΔfG(Y3RuO7, s)/(kJmol−1) ± 2.45} = − 3249.5 + 0.635 ⋅ (T/K). The standard molar heat capacity Cop,m(T) of Y2Ru2O7(s) was measured using a heat flux–type differential scanning calorimeter (DSC) in the temperature range, from 307 to 780 K. The heat capacity was fitted into a mathematical expression and can be represented by: Cp, m(Y2Ru2O7, s, T)(JK−1mol−1) = 256.1 + 5.88 ∙ 10−2T(K) − 34.75 ∙ 105/T2(K). (307 ≤ T (K) ≤ 780). The heat capacity of Y2Ru2O7(s) was used along with the data obtained from the electrochemical cell to determine its decomposition temperature and stability in air and to calculate other thermodynamic parameters.

Thermodynamic properties of Pr7O12

To explore the potential of Pr7O12 in a biphasic oxygen buffer in automobile exhaust control systems, thermodynamic data for Pr7O12 are required. Since there is no information on Pr7O12 in thermodynamic data compilations, its Gibbs energy of formation has been determined relative to that of Pr2O3 as a function of temperature in the range from 850 to 1200 K using a solid-state electrochemical technique. The standard molar Gibbs energy of formation of Pr7O12 from elements can be represented by two equations. In the range from 850 to 1068 K, ΔGf°Jmol-1=-6454317+1085.52T/K. From 1068 to 1204 K, ΔGf°Jmol-1=-6467695+1097.77T/K.

Thermodynamic stability of CaThF6(cr) by transpiration and e.m.f. techniques

In the present paper, we report the standard molar Gibbs energy of formation for CaThF6 measured by gas equilibration and e.m.f. methods. The HF(g) vapour pressure over the equilibrium reaction: $${\text{CaThF}}_{6} \left( {\text{cr}} \right) + 2 {\text{H}}_{ 2} {\text{O}}\left( {\text{g}} \right) = {\text{CaF}}_{2} \left( {\text{cr}} \right) + {\text{ThO}}_{2} \left( {\text{cr}} \right) + 4{\text{HF}}\left( {\text{g}} \right)$$ has been measured using transpiration technique. The above reaction mechanism has been established employing TG and XRD techniques. A fluoride e.m.f. cell: (−)Pt, CaF2(cr) + ThOF2(cr) + CaThF6(cr) |CaF2(cr)| NiO(cr) + NiF2(cr), Pt(+) has been constructed to measure Gibbs energy of formation of CaThF6 (cr) using CaF2 (cr) as a solid electrolyte. The isobaric heat capacity $${\text{Cp}}_{\text{m}}^{{\circ }} \left( T \right)$$ of the compound has been measured using differential scanning calorimetric technique. Based on the experimental results, thermodynamic functions for CaThF6 have been generated.