Partial Quantities Research Articles

Partial molal volumes and partial molal compressibilities of n-alkanes in sodium dodecanoate solutions

Partial molal volumes and partial molal compressibilities have been determined for n-alkanes (C 7–C 10) in aqueous micelle solutions of sodium dodecanoate at 25°C. The partial molal volumes and compressibilities of n-alkanes in micelle solutions are higher than those in water, and resembles the partial molal quantities of liquid n-alkanes. This proves that the alkanes are dissolved in the interior of micelles and that the interior of the micelles resembles liquid hydrocarbon. Separate contributions to the partial molal quantities from the different groups of the molecule have been calculated.

Determination of the specific heat capacity of hemoglobin- and methemoglobin-water mixtures using an adiabatic calorimeter

The specific heat capacity of bovine hemoglobin-, methemoglobin-, and thermally denatured hemoglobin-water mixtures were measured in the temperature range from 10 to 80°C. The partial specific heat capacities for mass fractions of the protein between 0 and 1 were computed. Significant differences of the partial quantities were obtained for the native, respectively denatured state of protein and for the protein in the native state in fluid mixtures, respectively in rather dry mixtures. For mixtures with protein mass fractions up to 0.45, exceeding the value in living human red cells, partial specific heat capacities of either components are found to be constant. The accuracy of the used adiabatic calorimeter will be described briefly.

Volumes and heat capacities of some amino acids in water at 25 °C

The apparent molal volumes and heat capacities of nine amino acids were measured in water at 25 °C with a flow densimeter and a flow microcalorimeter. It is shown that the poor additivity of the standard partial molal quantities of amino acids in water are attributable to the ionization of the two groups NH2 and COOH. The hydration of these ionic groups interfere with each other when they are separated by less than three carbon atoms.

Thermodynamics of the Nonstoichiometric β1 ‐ PtZn Phase Exhibiting the Ll0 Structure

Thermodynamic activities of zinc in the and the phases were determined at 1273°K using an isopiestic method. The theoretical thermodynamic equations by Chang and co‐workers for the nonstoichiometric phases were modified to include the different interactions between the first nearest neighbor and the second nearest neighbor atoms. An analysis of the activity data for the phase at 1273°K in terms of the modified theoretical equation yields the following values: , , and . The thermodynamic data of the α‐phase were evaluated in terms of the subregular solution model. The partial quantities of platinum and the integral quantities for the α‐ and were obtained by means of the Gibbs‐Duhem relationship. A theoretical relationship between the enthalpy of formation and the model parameters for the phases was derived and correlated with the data and other data available in the literature.

Thermodynamics of the solution of hydrogen in LaNi 5 at small hydrogen contents

Partial thermodynamic parameters for the solution of hydrogen in LaNi 5 have been determined by p-c-T methods on unactivated bulk samples of LaNi 5. The relative partial molar enthalpy of solution of hydrogen, at infinite dilution of hydrogen, is −33,9 kJ (g atom H) −1 (~425 K). This is more exothermic than the heat of absorption corresponding to the formation of the hydride phase from the hydrogen-saturated intermetallic compound. The partial molar enthalpy of solution becomes more endothermic with hydrogen content in the region of solubility in the pure intermetallic compound. The partial thermodynamic quantities at infinite dilution have been found to vary with the stoichiometry of the LaNi 5+ x where x varies from −0.2 to + 0.5. The partial molar enthalpy of absorption is most exothermic for the stoichiometric compound.

Heats of dilution of some aqueous rare earth electrolyte solutions at 25.degree.C. 2. Rare earth nitrates

The heats of dilution of the aqueous trinitrates of La, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu have been measured from dilute solution to saturation at 25/sup 0/C. The integral heats of solution of La(NO/sub 3/)/sub 3/.6H/sub 2/O, Nd(NO/sub 3/)/sub 3/.6H/sub 2/O, Gd(NO/sub 3/)/sub 3/+.6H/sub 2/O, Ho(NO/sub 3/)/sub 3/.6H/sub 2/O, Er(NO/sub 3/)/sub 3/.6H/sub 2/O, and Lu(NO/sub 3/)/sub 3/.5H/sub 2/O in water have also been determined. The heat of dilution data were fitted directly to semiempirical polynomials and these polynomials were used to calculate apparent and partial molal heat quantities. The results are compared to available thermodynamic and transport data for the rare earth nitrates.

Adsorption of gas mixtures on heterogeneous solid surfaces: I. Extension of Tóth isotherm on adsorption from gas mixtures

It was proved that the partial adsorbed quantities can be calculated from the individual adsorption isotherms. This calculation can be carried out by equations which take into' account the energetical heterogeneity of the surface of adsorbent as well. Thus, the partial isotherms equations which can be applied are as followsV A (p A ,p B ) =p A /[b a + (p A +b AB p B ) m ] 1/m andV B (p A ,p B ) =p B /[b B + (p B +b BA p A ) m ] 1/m wherep A andp B are the partial equilibrium pressures, whileb A ,b B andm are constants which can be determined on the basis of the individual isotherms.

Thermodynamic studies of the phase relationships of nonstoichiometric cerium oxides at higher temperatures

Partial molar thermodynamic quantities for oxygen in nonstoichiometric cerium oxides were determined by thermogravimetric analysis in CO CO 2 mixtures in the temperature range 900–1400°C. Under these conditions compositions within the range 2.00 ⩾ O M ⩾ ∼1.75 could be obtained. A detailed analysis of the data shows that the α′-phase region in the phase diagram, previously described as a grossly nonstoichiometric phase, can be divided into several subregions each consisting of an apparent nonstoichiometric single phase. The finer details of the thermodynamic data, however, suggest that some of these subregions can be further split into ordered intermediate phases with compositions following the series M n O 2 n−2 . Supplementary high-temperature X-ray diffraction studies under vacuum were made at temperatures up to 855°C. At the higher temperatures between 790 and 855°C, a new phase of low symmetry was obtained. Indexing of the powder pattern for this phase showed it to be isostructural with Pr 6O 11 and with a monoclinic unit cell with a = 6.781 ± 0.006Å, b = 11.893 ± 0.009 Å, c = 15.823 ± 0.015 Å, and β = 125.04 ± 0.04°.

Thermodynamics of theβ’-NiZn intermetallic phase exhibiting the CsCl-structure

The thermodynamic activity, partial molar entropy and partial molar enthalpy of zinc have been calculated based on the measurement of partial pressure of zinc above eleven β’-NiZn alloys exhibiting the CsCl-type of structure over the temperature interval 1042 to 1159 K, using the dew-point method. Good correlations are found between theory and experiment for all three partial quantities. Furthermore, from these results and the recently reported data on the f.c.c. terminal solid solutions, the corresponding partial quantities of nickel in β’-NiZn alloys are computed as well as the integral quantities. It is found that the thermal entropy of this phase remains constant with composition, an assumption used by Chang and co-workers in deriving the theoretical equations to account for the compositional variations of the thermodynamic properties for this type of ordered phase. A similar analysis is also made for the thermodynamic properties of the low-tempe rature form of the equi-atomic phase exhibiting the face-centered tetragonal superlattice structure.

Determination of CMC and Partial Specific Volume of Polysorbates 20, 60, and 80 from Densities of Their Aqueous Solutions

The CMC of the surfactants was determined by measuring the density of their aqueous solutions at 24.88° with a new instrument which can measure accurately the change in natural frequency of a hollow oscillator of constant volume when it is filled with a solution of unknown density. The frequency change is transformed into density by calibrating the instrument with liquids of known densities. The CMC values obtained were 12 X 10-3 wt.% for polysorbate 20, 9 X 10-3 wt.% for polysorbate 60, and 6.2 X 10-3 wt.% for polysorbate 80. By applying the intercept method, partial specific volumes of water and the surfactant were obtained from the density of each surfactant solution. These partial quantities indicated that the formation of micelles is associated with an increase in the partial specific volume of the surfactant and a concomitant decrease in that of water.

Thermodynamic functions for the α solid solution in the system niobium-molybdenum-nitrogen Activity coefficients, excess partial quantities and interaction coefficients

On the basis of experimental results, part of which have been published previously 1, activity coefficients, excess partial quantities and interaction coefficients for the solution of nitrogen in niobium-molybdenum alloys are derived by means of which the effect of molybdenum on the solubility of nitrogen in niobium or the effect of niobium on the solubility of nitrogen in molybdenum is quantitatively described. For temperatures between 1600 ° and 2400 °C and for nitrogen concentrations in the range of the α niobium-molybdenum-nitrogen solid solution the following equations are obtained: x N = p 1 2 N2 exp [ (−17.6 + 4.6x Mo) R ] exp [ −(−46.0 + 38.6x Mo)· 10 3 RT ] for x Mo≦ 0.4 and x N = p 1 2 N2 exp [ (− 6.3 − 18.7x Nb) R ] exp [ − (19.9 − 93.3x Nb) · 10 3 RT ] for x Nb≦ 0.4 . Here x n , x Mo and x Nb denote the atom fraction of nitrogen, molybdenum and niobium in the α solution; p N2 is the nitrogen pressure in atm, T the absolute temperature in °K and R the gas constant.

Use of Gibbs equation in irreversible thermodynamics. I. Gibbs and Gibbs-Duhem equations and definition of partial quantities in specific variables

Use of Gibbs equation in irreversible thermodynamics. I. Gibbs and Gibbs-Duhem equations and definition of partial quantities in specific variables

Oxygen decomposition pressures and thermodynamic data for nonstoichiometric berkelium berkelium oxide

A unique, highly sensitive system for the quantitative measurement of decomposition pressures of small samples was used to obtain equilibrium oxygen decomposition pressures over a 1·22 mg sample of nonstoichiometric 249Bk oxide. The temperature and pressure range investigated was 852°–1150°C and from 10 −7 to 10 −20atm O 2, respectively. These conditions were sufficient to enable examination of nearly the entire compositional range between BkO 2 and Bk 2O 3. Partial thermodynamic quantities were derived and found to be a function of composition but independent of temperature. The shapes of the equilibrium decomposition pressure isotherms were used to deduce the possible condensed phase relationships in this oxide system.

The thermodynamics of ternary solid solutions containing both substitutional and interstitial solute atoms

The partial configurational thermodynamic functions of the interstitial species in ternary solid solutions containing both substitutional and interstitial solute atoms have been derived in the first order or quasichemical approximation. These functions are shown to give the correct behavior in the limits of infinite temperature (where they reduce to zero-order statistics), and in the limit where the substitutional solute and solvent become identical. Several conclusions concerning the atomic interactions have been made from the form of the partial thermodynamic quantities and comparisons with previous models for this type of solution have been made.

Thermodynamics of the chemostat

AbstractPractical equations are written for the transfer rates of substrates and products into and out of cells growing in the chemostat, the rates of heat production and of biomass production, and the exchange rates of heat and matter between the chemostat and its surroundings. These rate equations together with partial molal quantities of the substrates and the products at their steady state concentrations in the chemostat, and with thermodynamic quantities of biomass, are combined to give equations for the rate of entropy production due to irreversible processes in the chemostat and for the rate of entropy exchange between the chemostat and its surroundings. In addition, expressions are obtained using practical thermodynamics quantities, for calculating the minimum entropy content and the enthalpy of formation of cells growing in the chemostat under defined steady state conditions.

The measurement of the thermodynamic properties of NiO−MnO solid solutions by a solid electrolyte cell technique

The activity of NiO in NiO−MnO solid solutions has been measured using the cell Ni, NiO |Zr0.85 Ca0.15 O1.85|Ni, [NiO]s.s. in the temperature range 900° to 1200°C for compositions between 0 and 80 mol pct NiO. The activity-composition relationships for MnO have been determined by integration of the Gibbs-Duhem equation, and the partial and integral thermodynamic quantities for the system have been calculated. The system exhibits a positive deviation from ideal behavior with a maximum heat of mixing of 850±150 cals per mole, and a positive excess entropy of mixing of 0.24±0.1 cal per mole °C was detected at the equimolar composition.

Generalized partial quantities from Pitzer's expansion and pseudocritical rules

AIChE JournalVolume 16, Issue 5 p. 889-890 Communication to the Editor Generalized partial quantities from Pitzer's expansion and pseudocritical rules Michael S. Morgan, Michael S. Morgan Massachusetts Institute of Technology, Cambridge, MassachusettsSearch for more papers by this authorRobert C. Reid, Robert C. Reid Massachusetts Institute of Technology, Cambridge, MassachusettsSearch for more papers by this author Michael S. Morgan, Michael S. Morgan Massachusetts Institute of Technology, Cambridge, MassachusettsSearch for more papers by this authorRobert C. Reid, Robert C. Reid Massachusetts Institute of Technology, Cambridge, MassachusettsSearch for more papers by this author First published: September 1970 https://doi.org/10.1002/aic.690160533Citations: 1AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL No abstract is available for this article.Citing Literature Volume16, Issue5September 1970Pages 889-890 RelatedInformation

溶融アルミニウム-インジウム合金の熱力学的研究

In order to clarify thermodynamic properties of the molten aluminum-indium alloy system, the values of electromotive force for the following reversible galvanic cell have been determined in the temperature range 700° to 950°C.(This article is not displayable. Please see full text pdf.) The activities derived show considerable positive deviations from Raoult’s law as expected from the phase diagram. The experimental results agree with the activities estimated from the liquidus line, or those derived from Lumsden’s model. The activity coefficients at infinite dilution were determined at 700°C to be 11.4 and 13.2 for aluminum and indium, respectively. Limits of the miscibility gap and the location of critical point which had involved uncertainty were confirmed with the observed lines of electromotive force. Various partial and integral thermodynamic quantities were derived from experimental data, and it was found that the heats of mixing obtained were in good agreement with those determined directly with calorimeter by Wittig. Furthermore, the interaction energy and the short-range order in this liquid alloy have been evaluated by the aid of the theory of quasichemical approach, and the results obtained show reasonable agreements with those derived by the classical thermodynamic method.

The Holmium‐Hydrogen System

Pressure‐temperature‐composition data were obtained to study the nature of the holmium‐hydrogen system. A Sieverts‐type apparatus was employed to perform measurements in the temperature range, 250°–950 °C, in the composition range, Ho to , and at pressures from 10−4 to 630 Torr. The existence of three homogeneous phases was established: holmium solid solution, the dihydride, and the trihydride phases. The limits of hydrogen solid solution in each of the phases were determined from discontinuities in the isothermal plots. Equilibrium plateau decomposition relationships were determined from van't Hoff plots in the two‐phase regions , , The differential heats of reaction in these two regions are, and , respectively. The differential entropies of reaction are, and , respectively. Relative partial molal and integral thermodynamic quantities were calculated for the system.The dissociation pressure equation for the holmium solid solution dideuteride plateau region was determined for comparison purposes The enthalpy of reaction to form the dideuteride phase in , and the entropy of reaction is .

Etude du systeme uranium-hydrogene aux pressions elevees

The system uranium-hydrogen was investigated for pressure-temperature-concentration equilibria, up to 150 atm and 860° C. The hydrogen solubility in uranium and the hydride hypo-stoichiometry increase considerably with temperature. At 820° C and about 83 atm, the compositions of the solid solution < U, H > and of the hydride UHs-z become equal. Above this temperature, the system forms only a continuous solid solution. The equilibrium diagram U-UH 3 for the three variables pressure-temperature-concentration has been established from these results. The hydride loses its pyrophoric character when cooled in hydrogen. The partial and total thermodynamic quantities related to the solid solution < U, H > and to the hydride UH 3- x are computed as functions of composition at various temperatures.