Equilibrium dependence on temperature

In setting up the CHARMEN-synthesis formulation, we first choose a number NDj of lean substreams for MSA j, each operating at a selected temperature which lies within the admissible temperature range for the MSA. The number of substreams is dependent on the level of accuracy needed for equilibrium dependence on temperature. Theoretically, an infinite number of substreams should... 

Chemical equilibrium depends on temperature as described by the van t Hoff equation... 

Cyclization of 776 with ortho-esters gave (83JOC1628) [l,2,4]triazolo-[4,3-fc]pyrimido[5,4-< ][ 1,2,4]triazines 777, whereas reaction with sodium nitrite afforded the corresponding tetrazolopyrimidotriazine 778.3-Azido-pyrimido[4,5-e][l, 2,4]triazine 779 exists in a cyclic form as tetrazolo derivative 780, as shown by X-ray analysis (86KGS114). In solution the position of the 779 780 equilibrium depended on temperature and solvent. Higher temperatures favored 779. Azido compound 779 predominated in water, and tetrazolo compound 780 predominated in pyridine. Addition of sodium azide to the aqueous solution shifted the equilibrium toward 780. The... 

Any solid is capable of adsorbing a certain amount of gas, the extent of adsorption at equilibrium depending on temperature, the pressure of the gas and the effective surface area of the solid. The most notable adsorbents are, therefore, highly porous solids, such as charcoal and silica gel (which have large internal surface areas - up to c. 1000 m2 g-1) and finely divided powders. The relationship at a given temperature between the equilibrium amount of gas adsorbed and the pressure of the gas is known as the adsorption isotherm (Figures 5.1, 5.5-5.6, 5.8, 5.11, 5.13). 

The swelling equilibrium depends on temperature and pressure. Both are related to flic corresponding dependencies of solvent activity via its corresponding derivative of the chemical potential ... 

Poisoning effects are often correlated with the poison concentration in the feed stream, which, of course, is the important parameter in practical operation. However, in a more detailed analysis this approach can hardly be justified for other than isothermal tests in gradientless reactors. The adsorption equilibrium depends on temperature and composition of the gas phase which varies through the reactor as well as within the single catalyst pellet. Therefore it appears more rational to correlate the deactivation with the amount of poison present on the catalyst rather than... 

Temperature jump. Chemical equilibrium depends on temperature according to the isochore... 

Equilibrium constants for protein-small molecule association usually are easily measured with good accuracy it is normal for standard free energies to be known to within 0.5 kcal/mol. Standard conditions define temperature, pressure and unit concentration of each of the three reacting species. It is to be expected that the standard free energy difference depends on temperature, pressure and solvent composition AA°a also depends on an arbitrary choice of standard unit concentrations. 

In equilibrium, this describes the coexistence of two different phases (solid and liquid), just as in the case of the Ising model ( hising) with the up and down magnetization phases. When h 0, one of these two phases has a priority. Therefore, a sign change of h -h induces a first-order phase transition. (Note that for modeling reasons h(T) may be assumed to depend on temperature.)... 

Fluid in a container is a combination of hquid and vapor. Before container mpture, the contained liquid is usually in equilibrium with the saturated vapor. If a container mptures, vapor is vented and the pressure in the liquid drops sharply. Upon loss of equilibrium, liquid flashes at the liquid-vapor interface, the liquid-container-wall interface, and, depending on temperature, throughout the liquid. 

Several authors, notably Leland and co-workers (L2), have discussed vapor-liquid equilibrium calculations based on corresponding-states correlations. As mentioned in Section II, such calculations rest not only on the general assumptions of corresponding-states theory, but also on the additional assumption that the characterizing parameters for a mixture do not depend on temperature or density but are functions of composition only. Further, it is necessary clearly to specify these functions (commonly known as mixing rules), and experience has shown that if good results are to be obtained, these... 

As an example, the ratio of the equilibrium vapor pressures for water, Pi6 and water. Pig, depends on temperature and is expressed by the following equation, derived from Faure (1977) (temperature is in kelvins) ... 

Given any two of the four quantities EC, Aik, pH, Pco,/ the other two can always be calculated provided appropriate equilibrium constants are available (the equilibrium constants depend on temperature, salinity and pressure). Hydrogen ion concentration, for example, be calculated from Aik and EC with the equation... 

Hence, the reaction order is seen to depend both on the equilibrium constant K2, which depends on temperature, and the actual partial pressure p2- We shall later see that the latter term for a catalyst is related to the extent that the surface is covered by a reactant. 

The derivative with respect to temperature will give the dependence of equilibrium concentration on temperature itself ... 

When much larger temperature ranges are considered, the basis of the dependence of the equilibrium constant on temperature can more clearly be seen by returning to the relationships... 

The ionization of water is so important in the study of aqueous equilibria that the equilibrium constant is given the special symbol, Kw. It can be seen that, Kw, like all equilibrium constants, depends on temperature. Since Kw is larger (the forward reaction is encouraged) at higher temperatures, the forward reaction must consume heat, so the ionization of water must be endothermic. 

Their potentials in 0.1 N, lmolal, IN and saturated KC1 solutions are 0.3337, 0.2800, 0.2897 and 0.2415 V, respectively. The dilute types reach their equilibrium potentials more quickly and these potentials are less dependent on temperature the SCE has the advantage of being less sensitive to current flow (electrolysis). The AgCl-Ag electrodes are more compact, do not need a liquid function, which makes them exceedingly attractive for analysis in non-aqueous media, and support high temperatures. 

The processes of both seed formation and fibril extension are dependent on temperature and on peptide concentration, with 37°C being required for establishing equilibrium within 24 h with 30 pM Pi 4o- A full description of the assay system may be found elsewhere [97,117], A 4 h reaction time is typically within the linear portion of the time course. This nucleus-dependent assay detects mainly inhibitors that are substoichiometric with the monomeric peptide, which is present at high concentration. It is relatively insensitive to inhibitors that target the monomeric peptide. Whether the inhibitors interact with the growing end of a seed or with a low abundance conformational form of the p peptide that is competent to add to the seed is difficult to determine at this time. Similar dose-response curves are obtained for Congo Red as an inhibitor with either thioflavin T (ThT) fluorescence or filtration of radioiodinated peptide readouts (Fig. 4) Caveats in the interpretation of both the ThT and radiometric filtration assays for the evaluation of putative inhibitors are discussed elsewhere [97]. 

Taking into consideration the findings with tert-butylamine in Section 6.6.1 it may be assumed that in solution the equilibrium of these reactions (Eq. (10)) is mostly shifted to the left side, involving however a rapid exchange of base molecules within the adduct. The equilibrium may depend on temperature and the molarity of B. 

The equilibrium will therefore be shifted towards the most basic isomer, i.e. the one (m-) that forms the most stabilised cation (59) in the ion pair. Cases are also known in which the type of control that is operative is dependent on temperature (see below). 

As equation 2.4.8 indicates, the equilibrium constant for a reaction is determined by the temperature and the standard Gibbs free energy change (AG°) for the process. The latter quantity in turn depends on temperature, the definitions of the standard states of the various components, and the stoichiometric coefficients of these species. Consequently, in assigning a numerical value to an equilibrium constant, one must be careful to specify the three parameters mentioned above in order to give meaning to this value. Once one has thus specified the point of reference, this value may be used to calculate the equilibrium composition of the mixture in the manner described in Sections 2.6 to 2.9. 

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