390 resultados para thermodynamic function
em Indian Institute of Science - Bangalore - Índia
Resumo:
A ternary thermodynamic function has been developed based on statistico-thermodynamic considerations, with a particular emphasis on the higher-order terms indicating the effects of truncation at the various stages of the treatment. Although the truncation of a series involved in the equation introduces inconsistency, the latter may be removed by imposing various thermodynamic boundary conditions. These conditions are discussed in the paper. The present equation with higher-order terms shows that the α function of a component reduces to a quadratic function of composition at constant compositional paths involving the other two components in the system. The form of the function has been found to be representative of various experimental observations.
Calciothermic reduction of TiO2: A diagrammatic assessment of the thermodynamic limit of deoxidation
Resumo:
Calciothermic reduction of TiO2 provides a potentially low-cost route to titanium production. Presented in this article is a suitably designed diagram, useful for assessing the degree of reduction of TiO2 and residual oxygen contamination in metal as a function of reduction temperature and other process parameters. The oxygen chemical potential diagram à la Ellingham-Richardson-Jeffes is useful for visualization of the thermodynamics of reduction reactions at high temperatures. Although traditionally the diagram depicts oxygen potentials corresponding to the oxidation of different metals to their corresponding oxides or of lower oxides to higher oxides, oxygen potentials associated with solution phases at constant composition can be readily superimposed. The usefulness of the diagram for an insightful analysis of calciothermic reduction, either direct or through an electrochemical process, is discussed. Identified are possible process variations, modeling and optimization strategies.
Resumo:
The applicability of a formalism involving an exponential function of composition x1 in interpreting the thermodynamic properties of alloys has been studied. The excess integral and partial molar free energies of mixing are expressed as: $$\begin{gathered} \Delta F^{xs} = a_o x_1 (1 - x_1 )e^{bx_1 } \hfill \\ RTln\gamma _1 = a_o (1 - x_1 )^2 (1 + bx_1 )e^{bx_1 } \hfill \\ RTln\gamma _2 = a_o x_1^2 (1 - b + bx_1 )e^{bx_1 } \hfill \\ \end{gathered} $$ The equations are used in interpreting experimental data for several relatively weakly interacting binary systems. For the purpose of comparison, activity coefficients obtained by the subregular model and Krupkowski’s formalism have also been computed. The present equations may be considered to be convenient in describing the thermodynamic behavior of metallic solutions.
Resumo:
The compounds Pb2PtO4 and PbPt2O4 were synthesized from an intimate mixture of yellow PbO and Pt metal powders by heating under pure oxygen gas at 973 K for periods up to 600 ks with intermediate grinding and recompacting. Both compounds were found to decompose on heating in pure oxygen to PbO and Pt, apparently in conflict with the requirements for equilibrium phase relations in the ternary system Pb–Pt–O. The oxygen chemical potential corresponding to the three-phase mixtures, Pb2PtO4 + PbO + Pt and PbPt2O4 + PbO + Pt were measured as a function of temperature using solid-state electrochemical cells incorporating yttria-stabilized zirconia as the solid electrolyte and pure oxygen gas at 0.1 MPa pressure as the reference electrode. The standard Gibbs free energies of formation of the ternary oxides were derived from the measurements. Analysis of the results indicated that the equilibrium involving three condensed phases Pb2PtO4 + PbO + Pt is metastable. Under equilibrium conditions, Pb2PtO4 should have decomposed to a mixture of PbO and PbPt2O4. Measurement of the oxygen potential corresponding to this equilibrium decomposition as a function of temperature indicated that decomposition temperature in pure oxygen is 1014(±2) K. This was further confirmed by direct determination of phase relations in the ternary Pb–Pt–O by equilibrating several compositions at 1023 K for periods up to 850 ks and phase identification of quenched samples using X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDS). Only one ternary oxide PbPt2O4 was stable at 1023 K under equilibrium conditions. Alloys and intermetallic compounds along the Pb–Pt binary were in equilibrium with PbO.
Resumo:
The exact expressions for the partition function (Q) and the coefficient of specific heat at constant volume (Cv) for a rotating-anharmonic oscillator molecule, including coupling and rotational cut-off, have been formulated and values of Q and Cv have been computed in the temperature range of 100 to 100,000 K for O2, N2 and H2 gases. The exact Q and Cv values are also compared with the corresponding rigid-rotator harmonic-oscillator (infinite rotational and vibrational levels) and rigid-rotator anharmonic-oscillator (infinite rotational levels) values. The rigid-rotator harmonic-oscillator approximation can be accepted for temperatures up to about 5000 K for O2 and N2. Beyond these temperatures the error in Cv will be significant, because of anharmonicity and rotational cut-off effects. For H2, the rigid-rotator harmonic-oscillator approximation becomes unacceptable even for temperatures as low as 2000 K.
Resumo:
The folding and stability of maltose binding protein (MBP) have been investigated as a function of pH and temperature by intrinsic tryptophan fluorescence, far- and near-UV circular dichroism, and high-sensitivity differential scanning calorimetric measurements. MBP is a monomeric, two-domain protein containing 370 amino acids. The protein is stable in the pH range of 4-10.5 at 25 degrees C. The protein exhibits reversible, two-state, thermal and guanidine hydrochloride-mediated denaturation at neutral pH. The thermostability of MBP is maximal at pH 6, with a Tm of 64.9 degrees C and a deltaHm of 259.7 kcal mol(-1). The linear dependence of deltaHm on Tm was used to estimate a value of deltaCp of 7.9 kcal mol(-1) K(-1) or 21.3 cal (mol of residue)(-1) K(-1). These values are higher than the corresponding deltaCp's for most globular proteins studied to date. However, the extrapolated values of deltaH and deltaS (per mole of residue) at 110 degrees C are similar to those of other globular proteins. These data have been used to show that the temperature at which a protein undergoes cold denaturation depends primarily on the deltaCp (per mol of residue) and that this temperature increases with an increase in deltaCp. The predicted decrease in stability of MBP at low temperatures was experimentally confirmed by carrying out denaturant-mediated unfolding studies at neutral pH at 2 and 28 degrees C.
Resumo:
Sequence specific interaction between DNA and protein molecules has been a subject of active investigation for decades now. Here, we have chosen single promoter containing bacteriophage Delta D-III T7 DNA and Escherichia coli RNA polymerase and followed their recognition at the air-water interface by using the surface plasmon resonance (SPR) technique, where the movement of one of the reacting species is restricted by way of arraying them on an immobilized support. For the Langmuir monolayer studies, we used a RNA polymerase with a histidine tag attached to one of its subunits, thus making it an xcellent substrate for Ni(II) ions, while the SPR Studies were done using biotin-labeled DNA immobilized on a streptavidin-coated chip. Detailed analysis of the thermodynamic parameters as a function of concentration and temperature revealed that the interaction of RNA polymerase with T7 DNA is largely entropy driven (83 (+/- 12) kcal mol(-1)) with a positive enthalpy of 13.6 (+/- 3.6) kcal mol(-1), The free energy of reaction determined by SPR and Langmuir-Blodgett technique was -11 (+/- 2) and -15.6 kcal mol(-1), respectively. The ability of these methods to retain the specificity of the recognition process was also established.
Resumo:
The standard free energy of formation of titanium boride (TiB2) Was measured by the Electro Motive Force (EMF) method (by using yttria doped thoria (YDT) as the solid electrolyte). Two galvanic cells viz. Cell (I): Pt, TiB2 (s), TiO2 (s), B (s) vertical bar YDT vertical bar NiO (s), Ni (s), Pt and cell (II): Pt, TiB2 (s), TiO2 (s), B (s) vertical bar YDT vertical bar FeO (s). Fe (s), Pt were constructed in order to determine the Delta(f)G degrees, of TiB2. Enthalpy increments on TiB2 were measured by using inverse drop calorimetry over the temperature range 583-1769 K. The heat capacity, entropy and the free energy function have been derived from these experimental data in the temperature range 298-1800 K. The mean value of the standard enthalpy of formation of TiB2 (Delta H-f(298)degrees (TiB2)) was obtained by combining these Delta(f)G degrees, values and the free energy functions of TiB2 derived from the drop calorimetry data. The mean values of Delta H-f(298)degrees (TiB2) derived from the Delta(f)G degrees, data obtained from cell I and II were -322 +/- 1.2 kJ mol(-1) and -323.3 +/- 2.1 kJ mol(-1), respectively. These values were found to be in very good agreement with the assessed data. (C) 2009 Elsevier B.V. All rights reserved.
Resumo:
The activity of molybdenum dioxide (MoO2) in the MoO2–TiO2 solid solutions was measured at 1600 K using a solid-state cell incorporating yttria-doped thoria as the electrolyte. For two compositions, the emf was also measured as a function of temperature. The cell was designed such that the emf is directly related to the activity of MoO2 in the solid solution. The results show monotonic variation of activity with composition, suggesting a complete range of solid solutions between the end members and the occurrence of MoO2 with a tetragonal structure at 1600 K. A large positive deviation from Raoult's law was found. Excess Gibbs energy of mixing is an asymmetric function of composition and can be represented by the subregular solution model of Hardy as follows.The temperature dependence of the emf for two compositions is reasonably consistent with ideal entropy of mixing. A miscibility gap is indicated at a lower temperature with the critical point characterized by Tc (K)=1560 and . Recent studies indicate that MoO2 undergoes a transition from a monoclinic to tetragonal structure at 1533 K with a transition entropy of 9.91 J·(mol·K)−1. The solid solubility of TiO2 with rutile structure in MoO2 with a monoclinic structure is negligible. These features give rise to a eutectoid reaction at 1412 K. The topology of the computed phase diagram differs significantly from that suggested by Pejryd.
Resumo:
The process cascade leading to the final accommodation of the carbohydrate ligand in the lectin’s binding site comprises enthalpic and entropic contributions of the binding partners and solvent molecules. With emphasis on lactose, N-acetyllactosamine, and thiodigalactoside as potent inhibitors of binding of galactoside-specific lectins, the question was addressed to what extent these parameters are affected as a function of the protein. The microcalorimetric study of carbohydrate association to the galectin from chicken liver (CG-16) and the agglutinin from Viscum album (VAA) revealed enthalpy–entropy compensation with evident protein type-dependent changes for N-acetyllactosamine. Reduction of the entropic penalty by differential flexibility of loops or side chains and/or solvation properties of the protein will have to be reckoned with to assign a molecular cause to protein type-dependent changes in thermodynamic parameters for lectins sharing the same monosaccharide specificity.
Resumo:
A thermodynamic study of the Ti-O system at 1573 K has been conducted using a combination of thermogravimetric and emf techniques. The results indicate that the variation of oxygen potential with the nonstoichiometric parameter delta in stability domain of TiO2-delta with rutile structure can be represented by the relation, Delta mu o(2) = -6RT In delta - 711970(+/-1600) J/mol. The corresponding relation between non-stoichiometric parameter delta and partial pressure of oxygen across the whole stability range of TiO2-delta at 1573 K is delta proportional to P-O2(-1/6). It is therefore evident that the oxygen deficient behavior of nonstoichiometric TiO2-delta is dominated by the presence of doubly charged oxygen vacancies and free electrons. The high-precision measurements enabled the resolution of oxygen potential steps corresponding to the different Magneli phases (Ti-n O2n-1) up to n = 15. Beyond this value of n, the oxygen potential steps were too small to be resolved. Based on composition of the Magneli phase in equilibrium with TiO2-delta, the maximum value of n is estimated to be 28. The chemical potential of titanium was derived as a function of composition using the Gibbs-Duhem relation. Gibbs energies of formation of the Magneli phases were derived from the chemical potentials of oxygen and titanium. The values of -2441.8(+/-5.8) kJ/mol for Ti4O7 and -1775.4(+/-4.3) kJ/mol for Ti3O5 Obtained in this study refine values of -2436.2(+/-26.1) kJ/mol and-1771.3(+/-6.9) kJ/mol, respectively, given in the JANAF thermochemical tables.
Resumo:
A solid-state electrochemical cell, with yttria-stabilized zirconia as the electrolyte and pure O-2 gas at 0.1 MPa as the reference electrode, has been used to measure the oxygen chemical potential corresponding to the equilibrium between beta-Rh2O3 and RhO2 in the temperature range from 850 to 1050K. Using standard Gibbs energy of formation of beta-Rh2O3 available in the literature and the measured oxygen potential, the standard Gibbs free energy of formation of RhO2 is derived as a function of temperature: Delta G(f)degrees(RhO2)(+/- 71)/J mol(-1) = 238,418 + 179.89T Using an estimated value of Delta C-p degrees; for the formation reaction of RhO2 from its elements, the standard enthalpy of formation, standard entropy and isobaric heat capacity of RhO2 at 298.15 K are evaluated: Delta H-f degrees (298.15 K)(+/- 164)/kJ mol(-1) = -244.94, S degrees (298.15 K)(+/- 3.00)/J mol(-1) K-1 = 45.11 and C-p degrees(298.15 K)(+/- 2.6)1mol(-1) K-1 =64.28. (C) 2010 Elsevier B.V. All rights reserved.
Resumo:
A first comprehensive investigation on the deflagration of ammonium perchlorate (AP) in the subcritical regime, below the low pressure deflagration limit (LPL, 2.03 MPa) christened as regime I$^{\prime}$, is discussed by using an elegant thermodynamic approach. In this regime, deflagration was effected by augmenting the initial temperature (T$_{0}$) of the AP strand and by adding fuels like aliphatic dicarboxylic acids or polymers like carboxy terminated polybutadiene (CTPB). From this thermodynamic model, considering the dependence of burning rate ($\dot{r}$) on pressure (P) and T$_{0}$, the true condensed (E$_{\text{s,c}}$) and gas phase (E$_{\text{s,g}}$) activation energies, just below and above the surface respectively, have been obtained and the data clearly distinguishes the deflagration mechanisms in regime I$^{\prime}$ and I (2.03-6.08 MPa). Substantial reduction in the E$_{\text{s,c}}$ of regime I$^{\prime}$, compared to that of regime I, is attributed to HClO$_{4}$ catalysed decomposition of AP. HClO$_{4}$ formation, which occurs only in regime I$^{\prime}$, promotes dent formation on the surface as revealed by the reflectance photomicrographs, in contrast to the smooth surface in regime I. The HClO$_{4}$ vapours, in regime I$^{\prime}$, also catalyse the gas phase reactions and thus bring down the E$_{\text{s,g}}$ too. The excess heat transferred on to the surface from the gas phase is used to melt AP and hence E$_{\text{s,c}}$, in regime I, corresponds to the melt AP decomposition. It is consistent with the similar variation observed for both the melt layer thickness and $\dot{r}$ as a function of P. Thermochemical calculations of the surface heat release support the thermodynamic model and reveal that the AP sublimation reduces the required critical exothermicity of 1108.8 kJ kg$^{-1}$ at the surface. It accounts for the AP not sustaining combustion in the subcritical regime I$^{\prime}$. Further support for the model comes from the temperature-time profiles of the combustion train of AP. The gas and condensed phase enthalpies, derived from the profile, give excellent agreement with those computed thermochemically. The $\sigma _{\text{p}}$ expressions derived from this model establish the mechanistic distinction of regime I$^{\prime}$ and I and thus lend support to the thermodynamic model. On comparing the deflagration of strand against powder AP, the proposed thermodynamic model correctly predicts that the total enthalpy of the condensed and gas phases remains unaltered. However, 16% of AP particles undergo buoyant lifting into the gas phase in the `free board region' (FBR) and this renders the demarcation of the true surface difficult. It is found that T$_{\text{s}}$ lies in the FBR and due to this, in regime I$^{\prime}$, the E$_{\text{s,c}}$ of powder AP matches with the E$_{\text{s,g}}$ of the pellet. The model was extended to AP/dicarboxylic acids and AP/CTPB mixture. The condensed ($\Delta $H$_{1}$) and gas phase ($\Delta $H$_{2}$) enthalpies were obtained from the temperature profile analyses which fit well with those computed thermochemically. The $\Delta $H$_{1}$ of the AP/succinic acid mixture was found just at the threshold of sustaining combustion. Indeed the lower homologue malonic acid, as predicted, does not sustain combustion. In vaporizable fuels like sebacic acid the E$_{\text{s,c}}$ in regime I$^{\prime}$, understandably, conforms to the AP decomposition. However, the E$_{\text{s,c}}$ in AP/CTPB system corresponds to the softening of the polymer which covers AP particles to promote extensive condensed phase reactions. The proposed thermodynamic model also satisfactorily explains certain unique features like intermittent, plateau and flameless combustion in AP/ polymeric fuel systems.
Phase relations and thermodynamic properties of condensed phases in the system calcium-copper-oxygen
Resumo:
The isothermal sections of the phase diagram for the system Ca-Cu-0 at 1073 and 1223 K have been determined. Several compositions in the ternary system were quenched after equilibration, and the phases present were identified by optical microscopy, X-ray diffraction, and electron probe microanalysis. Two ternary compounds Ca2CuO3 and Cao.8&uO1.9s were identified at 1073 K. However, only Ca2CuO3 was found to be stable at 1223 K. The thermodynamic properties of the two ternary compounds were determined using solid-state cells incorporating either an oxide or a fluoride solid electrolyte. The results for both types of cells were internally consistent. The compound C ~ O . ~ & U Ow~h.i~ch~ c, a n also be represented as Ca15Cu18035h, as been identified in an earlier investigation as Cao.828CuOz. Using a novel variation of the galvanic cell technique, in which the emf of a cell incorporating a fluoride electrolyte is measured as a function of the oxygen potential of the gas phase in equilibrium with the condensed phase electrodes, it has been confirmed that the compound Cao.828CuO1.93 (Ca15Cu18035d) oes not have significant oxygen nonstoichiometry. Phase relations have been deduced from the thermodynamic data as a function of the partial pressure of oxygen for the system Ca-Cu-0 at 873, 1073, and 1223 K.
Resumo:
Expressions for various second-order derivatives of surface tension with respect to composition at infinite dilution in terms of the interaction parameters of the surface and those of the bulk phases of dilute ternary melts have been presented. A method of deducing the parameters, which consists of repeated differentiation of Butler's equations with subsequent application of the appropriate boundary conditions, has been developed. The present investigation calculates the surface tension and adsorption functions of the Fe-S-O melts at 1873 and 1923 K using the modified form of Butler's equations and the derived values for the surface interaction parameters of the system. The calculated values are found to be in good agreement with those of the experimental data of the system. The present analysis indicates that the energetics of the surface phase are considerably different from those of the bulk phase. The present research investigates a critical compositional range beyond which the surface tension increases with temperature. The observed increase in adsorption of sulfur with consequent desorption of oxygen as a function of temperature above the critical compositional range has been ascribed to the increase of activity ratios of oxygen to sulfur in the surface relative to those in the bulk phase of the system.