Equilibrium, chemical temperature dependency

The conversions are limited by the position of the chemical equilibrium. The temperature dependency of the equilibrium constant Ki for converting CO and H2 can be expressed by the following equation [3.11] ... 

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... 

The last term in parentheses in Equation 6.66 represents the effect of interfacial tension and curvature on the equilibrium freezing temperature. The basic idea is that curvature produces a difference in pressure between solid and melt. Since the chemical potentials in the two phases are fimctions of pressure, and since they must be equal at equilibrium, the equilibrium freezing temperature depends on curvature (see Problem 6.7). 

The formation of weak secondary valence gels occurs in poor solvents, which will not prevent all secondary valence bonds between the polymer coils by solvation. The solvation equilibrium is temperature dependent, i.e., it increases at higher temperatures. (ii) The chemical gel is a network structure (crosslinked) formed by covalent hnks between polymer chains. Chemically crosslinked materials are formed by copolymerization, chemical modification, or radiation of linear polymers. The crosslinked network will swell but not dissolve, because the covalent CTossUnks cannot be broken by any solvent and the swelhng depends on the degree of crosslinking. 

In high temperature systems, there are also temperature induced mechanisms for corrosion that are dependent upon large temperature differences in the heat transport system. The classic example is the transport of carbon in the form of various oxides in gas cooled systems, resulting in depletion of carbon in one part of the system and the deposition of carbon in another part. Parallel mechanisms have been seen in liquid salt test loops. In this system, the primary concern has been the selective chemical transport of chromium (an alloy constituent of many alloys) from hot to cold locations in the reactor system by uranium, where the equilibrium is temperature dependent ... 

Fluctuations of observables from their average values, unless the observables are constants of motion, are especially important, since they are related to the response fiinctions of the system. For example, the constant volume specific heat of a fluid is a response function related to the fluctuations in the energy of a system at constant N, V and T, where A is the number of particles in a volume V at temperature T. Similarly, fluctuations in the number density (p = N/V) of an open system at constant p, V and T, where p is the chemical potential, are related to the isothemial compressibility iCp which is another response fiinction. Temperature-dependent fluctuations characterize the dynamic equilibrium of themiodynamic systems, in contrast to the equilibrium of purely mechanical bodies in which fluctuations are absent. 

Clausius-Clapeyron equation An equation expressing the temperature dependence of vapor pressure ln(P2/Pi) = AHvapCl/Tj - 1/T2)/R, 230,303-305 Claussen, Walter, 66 Cobalt, 410-411 Cobalt (II) chloride, 66 Coefficient A number preceding a formula in a chemical equation, 61 Coefficient rule Rule which states that when the coefficients of a chemical equation are multiplied by a number n, the equilibrium constant is raised to the nth power, 327... 

Calculations Equilibrium Dissolved gases Rates of reaction Chemical potential and AG with the extent of reaction Henry s Law and the pH of the oceans Temperature dependence of chemistry and the analysis of chemical networks in prebiotic environments... 

Essentially, all reactions that require the formation of a chemical bond with an activation energy of around 100 kJ mol-1 are frozen out at the surface of Titan but are considerably faster in the stratosphere, although still rather slow compared with the rates of reaction at 298 K. Chemistry in the atmosphere of Titan will proceed slowly for neutral reactions but faster for ion-molecule reactions and radical-neutral reactions, both of which have low activation barriers. The Arrhenius equation provides the temperature dependence of rates of reactions but we also need to consider the effect of cold temperatures on thermodynamics and in particular equilibrium. 

The l3C NMR spectrum of the C4H7+ cation in superacid solution shows a single peak for the three methylene carbon atoms (72) This equivalence can be explained by a nonclassical single symmetric (three-fold) structure. However, studies on the solvolysis of labeled cyclopropylcarbinyl derivatives suggest a degenerate equilibrium among carbocations with lower symmetry, instead of the three-fold symmetrical species (13). A small temperature dependence of the l3C chemical shifts indicated the presence of two carbocations, one of them in small amounts but still in equilibrium with the major species (13). This conclusion was supported by isotope perturbation experiments performed by Saunders and Siehl (14). The classical cyclopropylcarbinyl cation and the nonclassical bicyclobutonium cation were considered as the most likely species participating in this equilibrium. 

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. 

The Na salts in THF showed an intermediate behavior, and their spectra revealed an interesting temperature dependence. At + 25°C the spectra were very similar to those of the Li salts, but at - 52°C they had changed to the appearance of the spectra of the K salts. The spectra indicate a fast equilibrium 60 (X = Na) 61 with the latter favored by decreasing temperature. Analysis of the temperature dependence of individual chemical shifts allowed the evaluation of AH°, -6.9 kcal/mol, and AS0, -30 e.u., for this equilibrium (i.e., the contact-ion pairs are favored by entropy but disfavored by enthalpy). A similar effect may explain the temperature dependence of the NMR spectrum of 56. 

The idea that an activated complex or transition state controls the progress of a chemical reaction between the reactant state and the product state goes back to the study of the inversion of sucrose by S. Arrhenius, who found that the temperature dependence of the rate of reaction could be expressed as k = A exp (—AE /RT), a form now referred to as the Arrhenius equation. In the Arrhenius equation k is the forward rate constant, AE is an energy parameter, and A is a constant specific to the particular reaction under study. Arrhenius postulated thermal equilibrium between inert and active molecules and reasoned that only active molecules (i.e. those of energy Eo + AE ) could react. For the full development of the theory which is only sketched here, the reader is referred to the classic work by Glasstone, Laidler and Eyring cited at the end of this chapter. It was Eyring who carried out many of the... 

To avoid the high cost of chemical reflux the dual temperature H2S/H20 exchange was independently suggested by Geib (1946) and Spevack (1957) (GS). The method exploits the fact that the equilibrium constant for isotope exchange is temperature dependent. The scheme is illustrated in Fig. 8.13. To carry out the exchange... 

Based on the solution property of poly (DMAEMA-co-AAm) in response to temperature, the temperature dependence of equilibrium swelling of poly (DMAEMA-c6>-AAm) gel as a function of chemical composition was observed as shown in Figure 6. The transition temperature of copolymer gel between the shrunken and swollen state was shifted to the lower temperature with increases in AAm content in the gel network. This is attributed to the hydrogen bond in the copolymer gel network and its hydrophobic contribution to the LCST Copolymer II gel was selected as a model polymer network for permeation study because it showed the sharp swelling transition around 34°C. 

In order to better understand the detailed dynamics of this system, an investigation of the unimolecular dissociation of the proton-bound methoxide dimer was undertaken. The data are readily obtained from high-pressure mass spectrometric determinations of the temperature dependence of the association equilibrium constant, coupled with measurements of the temperature dependence of the bimolecular rate constant for formation of the association adduct. These latter measurements have been shown previously to be an excellent method for elucidating the details of potential energy surfaces that have intermediate barriers near the energy of separated reactants. The interpretation of the bimolecular rate data in terms of reaction scheme (3) is most revealing. Application of the steady-state approximation to the chemically activated intermediate, [(CH30)2lT"], shows that. 

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