Temperature-dependent equilibrium constants

Table 2.3 Corrected equations for the calculation of temperature-dependent equilibrium constants based on publications of Reimschuessel and co-workers [21]...

Transesterification is the main reaction of PET polycondensation in both the melt phase and the solid state. It is the dominant reaction in the second and subsequent stages of PET production, but also occurs to a significant extent during esterification. As mentioned above, polycondensation is an equilibrium reaction and the reverse reaction is glycolysis. The temperature-dependent equilibrium constant of transesterification has already been discussed in Section 2.1. The polycondensation process in the melt phase involves a gas phase and a homogeneous liquid phase, while the SSP process involves a gas phase and two solid phases. The respective phase equilibria, which have to be considered for process modelling, will be discussed below in Section 3.1. 

The relative importance of the dissolved species will be dependent upon the type of process under consideration. For example, in the magnesium oxide process, magnesium is one of the dominant species while sodium is one of the dominant species in the regenerative sodium process. A general list of equilibria is presented in Table 1. Expressions of the following form have been developed for the temperature dependent equilibrium constants (y). 

K is the temperature dependent equilibrium constant T is the absolute temperature in degrees Kelvin and B, C, D, and E are constants. Numerical values of these constants are presented in Table 2. 

The most significant chemical equilibria present in flue gas scrubbing slurries are outlined. Expressions for temperature dependent equilibrium constants are presented that are suitable for the temperature ranges encountered in scrubbing applications. Expressions for activity coefficients of ions and ion-pairs are presented that are suitable for the ranges of ionii strengths encountered for this type of applications. 

Instead, the reaction proceeds to an equilibrium point, where both products and reactants remain. The equilibrium composition is dependent upon both the initial composition and final temperature. Fortunately, the equilibrium concentrations can be determined by a temperature dependent equilibrium constant, K, and the following equation. 

Here and Kq2 are the temperature-dependent equilibrium constants for reactions G3 and G2 respectively. 

Temperature-dependent equilibrium constants for carbonate are shown in table 13.1 (Larson and Buswell, 1942). Equations 13.4 and 13.5 can result in more alkaline waters due to the generation of OH- this is typical of what may be found in lakes and streams due to high carbonates in the drainage basin. The percolation of H2O through soils results in the enrichment of CO2 from plant and microbial decay processes forming H2CO3 which can... 

In addition to the two ODE for the extents of reactions, reaction kinetics are required. The reaction rate expressions describe reversible kinetics with a temperature-dependent equilibrium constant. The temperature dependence of the reaction rate constant is assumed to obey Arrhenius law. However, for the proposed methodology this is of minor importance since isothermal cell operation is assumed. 

The thermodynantic driving force (AG) for each of the S-state transitions has been estimated from measurements of the temperature-dependent equilibrium constants for the fight-induced transient intermediate states P680+/Yz and Yz /WOC(Mn). These values were then placed on... 

Rawling and Toguri [66RAW/TOG] (see Appendix A) presented an expression for the temperature dependent equilibrium constant ... 

Due to the different properties of the selenide phases studied, different temperature spans were employed, viz. 620 to 810 K for HgSe(cr), 970 to 1370 K for CdSe(cr), and 1170 to 1410 K for ZnSe(cr). The expression for the temperature-dependent equilibrium constant presented in [72FLO] is based on the combined information from all three systems studied. 

Kb is the temperature dependent equilibrium constant which is defined as (Borgars and Campbell, 1974) ... 

Answer. Let s begin with the kinetic rate law in terms of partial pressures and the temperature-dependent equilibrium constant from thermodynamics ... 

If a chemical reaction takes place, in separation apparatus at constant pressure Z(T) is the chemical, temperature dependent, equilibrium constant. Eq. (1-139) is... 

At equilibrium conditions the Gibbs energy expression 2.8 equals to zero and allows one to define the equilibrium state in terms of the measurable temperature-dependent equilibrium constant K q,... 

Reaction (2-1) proceeds as a homogeneous reaction until the crystal has achieved a new minimum of the total free energy as given by the temperature dependent equilibrium constant of eq. (2-1) ... 

CALCULATE THE TEMPERATURE DEPENDENT EQUILIBRIUM CONSTANTS AND THE SATURATION PRESSURE OF HATER... 

In the microkinetic model, site blocking is described in terms of the equilibrium between gas phase H2S and adsorbed H2S using a temperature-dependent equilibrium constant [36]. While H2S dissociates on the surface to form HS and S species, the fit of the microkinetic model did not improve when decomposition steps were added, suggesting rapid reversibility (at least in the presence of significant H2 partial pressures). Adsorbed S is known to deactivate nearby sites [37,38] - in other words, the surface can be substantially deactivated by sub-monolayer H2S. 

The temperature dependent equilibrium constants can be calculated, for example, by the functions derived by Cherednichenko (1953) and Bissett (1977) (with Tin K) ... 

Equation 18.60 shows that statistical thermodynamics can calculate temperature-dependent equilibrium constants from partition functions. Because the partition functions themselves are ultimately determined from the energy levels of the chemical species, we see once again how a knowledge of energy levels—obtained from spectroscopy—helps us make thermodynamic predictions about chemical reactions. 

Graphically, this leads to a plot similar to the case of the temperature dependent equilibrium constant shown above in the section on equUibrimn. We see that we can plot a logarithm of the pressure against reciprocal Kelvin temperature and expect to find a straight line with a negative slope. 

Any reversible dissociation can be expressed in accordance with the Law of Mass Action which states at equilibrium, the mathematical product of the concentrations of the substances formed by a chemical reaction divided by the product of the concentrations of the reactants in that reaction is equal to a constant . This constant is called the temperature-dependent equilibrium constant,... 

The proton transfer between the imine and enamine tautomers of 2-phenacylquinolines 24 (Scheme 5.18) in solution is slow on the NMR timescale [56]. This enables quantification of the tautomeric forms by examining 5(H-11), i5(C-ll), and 3(N-1) in CDCI3 solution NMR spectra as well as calculation of both the temperature-dependent equilibrium constants fCp and the free energy differences AGj of the tautomers [56]. 

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