Yield, thermodynamic

Equilibrium constants involving each compound were evaluated using the partial pressures by the third law method. Accepting the heats of formation of WF5 and WF obtained from bomb calorimetry, the values for WF (n = 1 to 4) could be extracted by iterative fitting to partial pressure data. The W/02/F2 and W/S/F2 systems were also examined to give heats of formation of tungsten oxo- and thiofluorides. This experimentally simple technique yields thermodynamic data on high-temperature species inaccessible to conventional calorimetry. 

Condensation theory is based on thermodynamic equilibrium. More than a century s worth of experiments have yielded thermodynamic data (entropy and enthalpy of formation, plus heat capacity) for elements and compounds. Equations of state describing the stabilities of different compounds under various conditions can be calculated from these data, as briefly described in Box 7.1. Because liquids are not normally stable at the low pressures appropriate for space, the compounds in condensation calculations are generally solid minerals, but liquids can exist at higher pressures (achievable if areas of the nebula with enhanced dust concentrations relative to gas were vaporized). 

Calorimetric (DSC) measurements yield thermodynamic properties of duplex melting in these oligonucleotides independent of any assumptions concerning the model of melting, such as a cooperative all-or-none process versus a noncooperative, multiple-stage melting process. Comparison of calorimetric enthalpies with van t Hoff enthalpies obtained either from the manipulation of heat capacity curves outlined in equations (16.19) to (16.22), or from optical or NMR measurements [equations (16.14) to (16.17)] allows conclusions to be drawn concerning the size of the cooperative unit. If the two... 

The ability to polymerize readily via selective oxidation utilizing the abundant and cheap oxidant 02 often represents a desirable low-cost method for upgrading the value of a raw material. The most successful example is the oxidative polymerization of 2,6-dimethylphenol to yield poly(2,6-dimethyl-l,4-phenylene ether) with copper-amine catalysts under an 02 atmosphere at room temperature. Thiophenol also has a labile hydrogen but is rapidly oxidized to yield thermodynamically stable diphenyl disulfide. This formation is based on the more facilitated formation of S—S bond through radical coupling [82] in comparison with the formation of C—S—C bond through the coupling with the other molecules in the para position (Eq. 9). 

Adsorption isotherms represent a relationship between the adsorbed amount at an interface and the equilibrium activity of an adsorbed particle (also the concentration of a dissolved substance or partial gas pressure) at a constant temperature. The analysis of adsorption isotherms can yield thermodynamic data for the given adsorption system. Theoretical adsorption isotherms derived from statistical and kinetic data, and using the described assumptions (see 3.1), are known only for the gas-solid interface or for dilute solutions of surfactants (Gibbs). Those for the system gas-solid are of a few basic types that can be thermodynamically predicted81. From temperature relations it is possible to calculate adsorption and activation energies or rate constants for individual isotherms. Since there are no theoretically founded equations of adsorption isotherms for dissolved surfactants on solids, the adsorption of gases on solides can be used as a starting point for an interpretation. 

Electrochemical measurement of pHa via Eq. (8.3) senses hydronium ion activity rather than its concentration. Hence, electrochemical evaluations of dissociation constants (Af ) yield thermodynamic quantities... 

A mixture of lower selenium fluorides is obtained by the reaction between heated selenium (210 °C) and fluorine, highly diluted with argon. FSeSeF and the other species are detected by IR spectroscopy. UV irradiation of matrix-isolated FSeSeF yields thermodynamically less stable Se=SeF2. ... 

On summarizing, one can state that in particular our knowledge of the thermochemistry of trimer and tetramer alkali halide species is increased by the recent investigations (cf. Table 19). Further investigations, carried out earlier than those in Table 19 and yielding thermodynamic data, have been reported for the species (NaCl) (i = 3, 4) [493], (LiFlj, and (LiCllj [90]. 

Electric discharge reactions which yield thermodynamically unstable products are of interest to synthetic chemists, because such products are often difficult to prepare by other methods. Many fascinating compounds of unusual structure have been isolated from discharge reactions. Although such syntheses usually have low efficiencies, they are nevertheless of interest to chemists who hope to discover new types of compounds. In this review, some of the available data are systematized, and likely directions for future research are indicated. 

The other common category of calorimetry is differential methods, in which the thermal behavior of the substance being measured is compared to that of a reference sample whose behavior is known. In differential scanning calorimetry (DSC), the instrument measures the difference in power needed to maintain the samples at the same temperature. In differential thermal analysis (DTA), the samples are heated in a furnace whose temperature is continuously changed (usually linearly), and the temperature difference between the sample and the reference sample as a function of time can yield thermodynamic information. DSC and DTA are most commonly used for determining the temperature of a phase transition, particularly for transitions involving solids. In addition, DSC experiments can yield values for the enthalpy of a phase transition or the heat capacity. Commercial DSC and DTA instruments are available. 

One should always remember that it is difficult to proceed from thermodynamic measurements to molecular properties. This is particularly true in multicomponent systems. That is, water-water and water-protein interactions are inextricably mixed with protein-protein interactions when one measures partial molal quantities. Assumptions and experiments beyond those yielding thermodynamic information are needed to determine what is happening at the molecular level. The major cause... 

A study by means of ion exchange yields thermodynamic data for zirconium sulphate complexes. The study confirmed the finding of [49CON/MCV] that no hydrolysis and polymerisation occur at log, [Zr] < - 4 in 2 M HCIO4. 

Research at the Shell laboratories has focused on the use of shape-selective zeolites, notably ferrierite (PER), for the latter conversion. The data in Fig. 10 show that at temperatures as low as 350 C the maximum isobutene yield (thermodynamics) can be achieved. 

The one-electron reduction potential of interest is then calculated from the equilibrium constant and the one-electron reduction potential of the redox reference couple using Nemst s equation (AE° = 0.0591 log K). While electrochemical techniques often yield irreversible oxidation potentials, pulse radiolysis usually yields thermodynamically correct one-electron reduction potenticils, provided the reactions are fast... 

It is a common practice to employ thermal stress and pH changes to unfold the protein [21,22], as these are often encountered during the pharmaceutical development of protein drugs. A pH range of 5 to 7 is desired for formulation development [23]. Temperature-dependent studies yield thermodynamic information such as Tm and AG and the stability of the protein. To determine the Tm and AG, a simple two-state model for unfolding is assumed [24, 25]. 

It is likely that the study of electrides would be more widespread if thermal stability at room temperature could be achieved. The recent success in synthesizing a sodide and potasside that are stable at room temperature provided the incentive to find aza-based complexants that will permit the crystallization of stable electrides. The cation of choice would be Li", because there would be no competition from Li. an alkalide that has never been made. A number of candidates were tried, from methylated cyclens to fully methylated azacryptands to ada-manzane-like complexants. Thus far none produced a crystalline electride of known structure. When the cation is kinetically able to leave the complexant. dissociation without decomposition occurs. The aza complexants used to date apparently do not form strong enough complexes to yield thermodynamically stable electrides. although aikalides can be made in some cases. The search for the ideal aza complexant continues. 

Thermodynamic Data of Formation. The standard enthalpy of formation of gaseous PH3, fH298 = 5.4 1.7 kJ/mol, was calculated from the heats of the explosive decomposition of PH3/SbH3 mixtures with white phosphorus as the reference state and is the recommended value different experimental values are given in Phosphor C, 1965, pp. 10/1. The experimentally determined value yields AfG29s=13.4 and AfHo=13.39 kJ/mol [27]. Calculations from molecular constants with standard methods yielded thermodynamic data of formation and the equilibrium constant for the formation of PH3 as an ideal gas the reference states used were crystalline a white phosphorus (0 to 195 K), crystalline p white phosphorus (195 to 317 K), the melt (317 to 1180 K), and an ideal P2 gas at higher temperatures. Selected results are as follows [28] ... 

The measured quantity can be weight loss (TGA), a mechanical quantity (TMA) or a comparison between the behavior of two specimens (DTA) which, when properly calibrated, yields thermodynamic quantities that compare favorably with older, more conventional calorimetric techniques. Since the measurement time and equipment costs for scanning calorimetry (DSC) are orders of magnitude lower, the DSC has essentially replaced the conventional adiabatic calorimeter and finds a place in nearly every modern analytical laboratory. 

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