Chemical equilibrium ratios, comparing

ILLUSTR.ATION 13.1-6 Comparing Chemical Equilibrium Ratios... 

Let us finally consider implications of these findings for reaction mechanisms in metalloproteins. Therefore, we must take into account that, much like with Sabatier s approach, considerations about thermodynamic stability, which might go as a static phenomenon if it were not for the fact that chemical equilibrium is nothing but the ratio of forward and reverse reaction rates, hence it also is about dynamics and might be compared to other reaction rates, this approach being encouraged by the well-known structure-reaction rate relationships for both (at least benzenoid aromatic) substrates and square-planar or octahedral coordination complexes ... 

We examine the ratio of Cg and and compare it with the ratio expechxi for chemical equilibrium. The ratio of Cr/Ca for the steady state is, dividing equation 138 by equation 10,... 

At equilibrium, in order to achieve equality of chemical potentials, not only tire colloid but also tire polymer concentrations in tire different phases are different. We focus here on a theory tliat allows for tliis polymer partitioning [99]. Predictions for two polymer/colloid size ratios are shown in figure C2.6.10. A liquid phase is predicted to occur only when tire range of attractions is not too small compared to tire particle size, 5/a > 0.3. Under tliese conditions a phase behaviour is obtained tliat is similar to tliat of simple liquids, such as argon. Because of tire polymer partitioning, however, tliere is a tliree-phase triangle (ratlier tlian a triple point). For smaller polymer (narrower attractions), tire gas-liquid transition becomes metastable witli respect to tire fluid-crystal transition. These predictions were confinned experimentally [100]. The phase boundaries were predicted semi-quantitatively. 

In this section the distinction between dissolved and sorbed species is introduced into the box model concept in the simplest possible manner, that is, by assuming a reversible linear equilibrium relationship between the dissolved concentration, C (molm 3), and the species sorbed on solids, Cs(mol kg 1). (The units m3 and kgs refer to water volume and solid mass, respectively.) The sorption/ desorption process shall be fast compared to other processes which affect the chemical (e.g., mixing, chemical transformation). As discussed in Chapter 9 (Eq. 9-7), the (observed) solid-water distribution ratio Kd is defined by. 

In the feed Is sufficiently high so that carbon cannot be present at equilibrium, the equilibrium composition can be calculated from consideration of only Chemical Reactions I and II. Accordingly, the activities of each of the species can be calculated If the equilibrium constants, Kj and KII and value of n are known provided the activity ratio Inequalities given In Equation 1 are met. If the Inequalities of Equation 1 are not met, coke deposition Is possible. Values of the n at which the equalities of Equation 1 are met represent the minimum steam/methane ratio, n., at which no carbon deposition will take place at equilibrium. Figure 1 displays n versus temperature, T. Extending the analysis to Include Chemical Reaction III permits the calculation of the equilibrium coke laydown as a function of n and T shown In Figure 2. These curves will be used later to compare with the corresponding kinetic curves obtained experimentally. 

As compared to the corresponding agalacto compound 6, the presence of Gal residues 6 and 6 introduces a change in the chemical shift of the H-l atoms of the peripheral GlcNAc residues 5 and 5 from 8 4.558 to 4.582. However, this extension has virtually no effect upon the chemical shifts of the H-l atoms of Man residues 3, 4, and 4. Interestingly, the H-l atom of Man-4 and also that of Man-4 each yields two separated doublets which must be ascribed to the two anomeric forms of 7. From the relative intensities of these doublets, it may be concluded that the anomers of this oetasaccharide occur in the ratio of ot /3 = 2 1. Apparently, the chain length does not affect the anomeric-equilibrium constant. 

For part (a), we write the appropriate chemical equations and solubility product expression, designate the equilibrium concentrations, and then substitute into the solubility product expression. For part (b), we recognize that NaF is a soluble ionic compound that is completely dissociated into its ions. MgF2 is a slightly soluble compound. Both compounds produce F ions so this is a common ion effect problem. We write the appropriate chemical equations and solubility product expression, represent the equilibrium concentrations, and substitute into the solubility product expression. For part (c), we compare the molar solubilities by calculating their ratio. 

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