Secondary equilibria

If secondary isotope effects arise strictly from changes in force constants at the position of substitution, with none of the vibrations of the isotopic atom being coupled into the reaction coordinate, then a secondary isotope effect will vary from 1.00 when the transition state exactly resembles the reactant state (thus no change in force constants when reactant state is converted to transition state) to the value of the equilibrium isotope effect when the transition state exactly resembles the product state (so that conversion of reactant state to transition state produces the same change in force constants as conversion of reactant state to product state). For example in the hydride-transfer reaction shown under point 1 above, the equilibrium secondary isotope effect on conversion of NADH to NAD is 1.13. The kinetic secondary isotope effect is expected to vary from 1.00 (reactant-like transition state), through (1.13)° when the stmctural changes from reactant state to transition state are 50% advanced toward the product state, to 1.13 (product-like transition state). That this naive expectation... 

Without enzyme catalysis, the secondary KIE is 1.15-1.16. The equilibrium secondary isotope effect was estimated as 1.01-1.03 (but see entry below). 

In the equilibrium-secondary-zone approximation [82, 85] we refine the effective potential along each reaction path by adding the charge in secondary-zone free energy. Thus, in this treatment, we include additional aspects of the secondary subsystem. This need not be more accurate because in many reactions the solvation is not able to adjust on the time scale of primary subsystem barrier crossing [86]. 

As discussed earlier in the secondary structure model, Templeton et al. have shown that the steric arrangement of the methylene links in the novolac resin can have a profound effect on its dissolution rate and on lithographic performance. Using molecular mechanics, these authors have calculated the equilibrium secondary structures of cresol-formaldehyde oligomers. They found that the secondary structure of these molecules determines the relative positions of the hydroxyl groups in the novolac matrix, and hence the possibility of intramolecular hydrogen bonding. ... 

If the short-range repulsive disjoining pressure is large enough, the black spots (secondary films of very low thickness, /12 = 5-10 nm) are stable. They either coalescence or grow in diameter, forming an equilibrium secondary (NBF) thin film (see Fig. 33e). 

We now develop a Rational Expectations (RE) model and apply it to the secondary market model. We show that the corresponding Rational Expectations equilibrium is self-fulfilled and therefore stable. Similar to the BU model, we use superscript r to denote the optimal quantities in the RE model. The key difference between the RE and the BU model is that retailer / makes his decision based on both x, and p, the equilibrium secondary market price in the RE model. We give a formal definition of the RE equilibrium in the following ... 

To date only one equilibrium secondary isotope effect, that on the ionization of formic acid (Sec. IVA,1), has been treated by means of the complete eq. (III-6) with any degree of rigor. In all other cases it has been necessary to make further assumptions. 

An alternative way to improve selectivity for the reaction system in Eq. (2.27) is again to deliberately feed BYPRODUCT to the reactor to shift the equilibrium of the secondary reaction away from BYPRODUCT formation. 

In the above reaction one molecular proportion of sodium ethoxide is employed this is Michael s original method for conducting the reaction, which is reversible and particularly so under these conditions, and in certain circumstances may lead to apparently abnormal results. With smaller amounts of sodium alkoxide (1/5 mol or so the so-called catal3rtic method) or in the presence of secondary amines, the equilibrium is usually more on the side of the adduct, and good yields of adducts are frequently obtained. An example of the Michael addition of the latter type is to be found in the formation of ethyl propane-1 1 3 3 tetracarboxylate (II) from formaldehyde and ethyl malonate in the presence of diethylamine. Ethyl methylene-malonate (I) is formed intermediately by the simple Knoevenagel reaction and this Is followed by the Michael addition. Acid hydrolysis of (II) gives glutaric acid (III). 

Theoretical work by the groups directed by Sustmann and, very recently, Mattay attributes the preference for the formation of endo cycloadduct in solution to the polarity of the solvent Their calculations indicate that in the gas phase the exo transition state has a lower energy than the endo counterpart and it is only upon introduction of the solvent that this situation reverses, due to the difference in polarity of both transition states (Figure 1.2). Mattay" stresses the importance of the dienophile transoid-dsoid conformational equilibrium in determining the endo-exo selectivity. The transoid conformation is favoured in solution and is shown to lead to endo product, whereas the cisoid conformation, that is favoured in the gas phase, produces the exo adduct This view is in conflict with ab initio calculations by Houk, indicating an enhanced secondary orbital interaction in the cisoid endo transition state . 

The small differences m basicity between ammonia and alkylammes and among the various classes of alkylammes (primary secondary tertiary) come from a mix of effects Replacing hydrogens of ammonia by alkyl groups affects both sides of the acid-base equilibrium m ways that largely cancel... 

In a simple liquid-liquid extraction the solute is partitioned between two immiscible phases. In most cases one of the phases is aqueous, and the other phase is an organic solvent such as diethyl ether or chloroform. Because the phases are immiscible, they form two layers, with the denser phase on the bottom. The solute is initially present in one phase, but after extraction it is present in both phases. The efficiency of a liquid-liquid extraction is determined by the equilibrium constant for the solute s partitioning between the two phases. Extraction efficiency is also influenced by any secondary reactions involving the solute. Examples of secondary reactions include acid-base and complexation equilibria. 

In a liquid-liquid extraction, the analyte (or interferent) is extracted from one liquid phase into a second, immiscible liquid phase. When the analyte is involved in secondary equilibrium reactions, it is often possible to improve selectivity by carefully adjusting the composition of one or both phases. 

Nucleation continues by secondary mechanisms and growth continues throughout the run until the batch achieves equilibrium and/or is dumped... 

Equilibrium. In general, primary alcohols are more reactive than secondary alcohols (that is, they tend to displace them), and secondary alcohols tend to displace tertiary alcohols, but in addition, there are considerable differences among different members of the same class. Various alcohols have been compared in this way (4,109). 

Secondary amines cannot form imines, and dehydration proceeds to give carbon-carbon double bonds bearing amino substituents (enamines). Enamines were mentioned in Chapter 7 as examples of nucleophilic carbon species, and their synthetic utility is discussed in Chapter 1 of Part B. The equilibrium for the reaction between secondary amines and carbonyl compounds ordinarily lies far to the left in aqueous solution, but the reaction can be driven forward by dehydration methods. 

If the rate equation contains the concentration of a species involved in a preequilibrium step (often an acid-base species), then this concentration may be a function of ionic strength via the ionic strength dependence of the equilibrium constant controlling the concentration. Therefore, the rate constant may vary with ionic strength through this dependence this is called a secondary salt effect. This effect is an artifact in a sense, because its source is independent of the rate process, and it can be completely accounted for by evaluating the rate constant on the basis of the actual species concentration, calculated by means of the equilibrium constant appropriate to the ionic strength in the rate study. 

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