Equilibrium constant Keq

Because the equilibrium constant, Keq, and the standard free-energy change, AG°, both measure whether a reaction is favored, they are mathematical related by the equation... 

Our inhibitor design strategy was based on the premise that structural modifications in the base of purine riboside that enhance purine base hydration without impairing the binding of the hydrated species to the ADA binding site would result in purine riboside (PR) analogues with high ADA inhibitory potency. Since the apparent inhibition constant (Kj (app)) is related to the hydration equilibrium constant (Keq) and the inhibitory constant for the hydrated molecule (Kj ) by... 

There is an important difference in this behavior between an exothermic reaction and an endothermic reaction. Fran equation 3.1-5, the van t Hoff equator, the equilibrium constant (Keq) decreases with increasing T for an exothermic reaction, and increases for an endothermic reaction. The behavior of f eq(T) corresponds to this. 

In chemical equilibrium, the forward and reverse reaction rates are equal and there is no net production of intermediates. The equilibrium constant Keq is given as the ratio of reactants in equilibrium. For the elementary reaction shown in Eq. (21), we obtain... 

For reversible enzymatic reactions, the Haldane relationship relates the equilibrium constant KeqsNith the kinetic parameters of a reaction. The equilibrium constant Keq for the reversible Michaelis Menten scheme shown above is given as... 

In general, the relationship between the equilibrium constant Keq and the free energy AG can be given by... 

The cardinal feature of catalysis is that the equilibrium constant of a chemical reaction is unaffected by the presence of a catalyst. This is true as long as the concentration of the catalyst is insignificant relative to the concentra-tion(s) of the least abundant reactant(s) or product(s). Thus for an uncatalyzed reaction (A B) with rate constants k+ and k- (for the forward and reverse rates, respectively), the equilibrium constant K q = k+lk-. In the presence of catalyst, the rate constants are increased, say to xk+ and yk-, and the new equilibrium constant Keq = xk+lyk- = (xly) k+/k-) = x y)K q. Because the rate enhancement in the presence of enzyme will always be the same for forward and reverse reactions, x = y, such that Ksq must still equal K q. 

An oft-suggested check on the initial rate condition is that, over the duration of the assay, the initial substrate concentration (ie., [S]) should not decrease by more than 5% (and ideally, significantly less). However, the validity of this suggestion depends on a number of other factors. If the reaction equilibrium constant Keq favors substrate(s), rather than product(s), then 10% conversion may amount to a significant fraction of that attainable... 

The equilibrium constant (Keq) for this reaction takes the form ... 

Figure 12.4 Comparison of the mass action ratio and equilibrium constants for peptide synthesis in different solvents at aw 0.70, at 30°C [45]. The light bars are equilibrium constants (Keq) obtained from four individual experiments.

The direction of a reaction can be assessed straightforwardly by comparing the equilibrium constant (Keq) and the ratio of the product solubility to the substrate solubility (Zsat) [39]. In the case of the zwitterionic product amoxicillin, the ratio of the equilibrium constant and the saturated mass action ratio for the formation of the antibiotic was evaluated [40]. It was found that, at every pH, Zsat (the ratio of solubilities, called Rs in that paper) was about one order of magnitude greater in value than the experimental equilibrium constant (Zsat > Keq), and hence product precipitation was not expected and also not observed experimentally in a reaction with suspended substrates. The pH profile of all the compounds involved in the reaction (the activated acyl substrate, the free acid by-product, the antibiotic nucleus, and the product) could be predicted with reasonable accuracy, based only on charge and mass balance equations in combination with enzyme kinetic parameters [40]. 

Water gas shift and steam reforming reactions producing H2 under rich conditions (reactions R6 and R7 in Table III, respectively) start to be significantly active at the temperatures above 300 °C (cf. Fig. 22c. These reactions result in a different actual CO C3H6 H2 concentration ratio inside the monolith in comparison with the raw exhaust gas, or the synthetic rich inlet gas mixture used in the lab experiments (Koci et al., 2007b). The reactions with water are characterized by the evaluated rate constants kj T) as well as by the thermodynamic equilibrium constants Keq(7). 

The position of equilibrium of any chemical reaction is given by its equilibrium constant, Keq (sometimes expressed simply as K). For the generalized reaction... 

Each acid has a characteristic tendency to lose its proton in an aqueous solution. The stronger the acid, the greater its tendency to lose its proton. The tendency of any acid (HA) to lose a proton and form its conjugate base (A-) is defined by the equilibrium constant (Keq) for the reversible reaction... 

Pure water ionizes slightly, forming equal numbers of hydrogen ions (hydronium ions, H30+) and hydroxide ions. The extent of ionization is described by an equilibrium constant, Keq =... 

Under the equilibrium condition (8.18), where the remaining terms AG°, R, and T are all constants, the reaction quotient Q must itself become a constant, which we identify as the equilibrium constant Keq ... 

The equilibrium constant Keq, (8.27d), thereby factors into enthalpic and entropic terms ... 

Exercise 4-10 a. Calculate AH° from bond energies for the conversion of 1-hexene to cyclohexane at 25° and from this, with AS0 as —20.7 e.u. per mole, calculate the equilibrium constant Keq from Equation 4-2. For comparison, calculate the equilibrium constant that would be expected if the degrees of disorder of the reactants and the products were equal (i.e., AS0 = 0). b. How large can AS0 be at 25° for a reaction before our 15 kcal rule starts to give incorrect answers ... 

How could we have predicted which product would be favored The first step is to decide whether the prediction is to be based on (1) which of the two products is the more stable, or (2) which of the two products is formed more rapidly. If we make a decision on the basis of product stabilities, we take into account AH° values, entropy effects, and so on, to estimate the equilibrium constants Keq for the reactants and each product. When the ratio of the products is determined by the ratio of their equilibrium constants, we say the overall reaction is subject to equilibrium (or thermodynamic) control. Equilibrium control requires that the reaction be reversible. 

The [sym-dodeca-13C] benzophenone (equation 313) has been synthesized via Friedel-Crafts phenylation of carbon tetrachloride and subsequent dehalogenation of the product using [per-13C] benzene. Ci2Dio13CO and Ci2Hio13CO were applied637 in the EPR and MS study of the electron transfer from ketyls to isotopically substituted ketones (equation 311-313). The equilibrium constants Keq at —75°C, for electron transfer from the anion radicals of polyatomic hydrocarbons (A -) to their isotopic analogues (B),... 

Dissociation of the dithionite ion can proceed both in aqueous and in nonaqueous media. There is a special equation to determine the average values of the equilibrium constants (Keq) of the formation of S02 from S204 (Lough McDonald 1987), namely, Keq = [SO2 ]2/ [S2On0 - 0.5 [S02 ]. ... 

Table 2-1 Equilibrium Constants (Keq) of Electron-Transfer Reactions... 

If a reaction in an aqueous solution is at equilibrium, an equilibrium constant (Keq) may be calculated if the activities of all of the products and reactants are known. (However, in practice, Keq is approximated by using molar concentrations instead of activities.) In general, reactions have the following format, where a moles of substance A reacts with b moles of substance B to form c moles of substance C and d moles of substance D ... 

Fig. 7.34 Theoretical SWV curves for a reversible EE mechanism coupled to a very fast chemical reaction. AT) = OmV, Sw = 50mV, AEs = 5mV. The values of the chemical equilibrium constant Keq are 0.01 (a), 1 (b), and 100 (c). The dimensionless net current (A) and their forward (b) components are shown. Reproduced from [51 ] with permission...

One can also derive a relationship between temperature and the equilibrium constant Keq and the standard free enthalpy AH°. If the following reversible reaction is operational... 

Experimentally, temperature is commonly used to bring about systematic structural changes in the RNA. To illustrate, consider the thermal equilibrium between a population of folded and unfolded RNA molecules, F U (for now ignore the existence of intermediates), governed by the equilibrium constant Keq = c j/cF. It can be shown that the change in concentration of the folded population is related to a temperature change by (Bernasconi, 1976)... 

The Equilibrium Constant Keq in the direction of nucleoside synthesis had been reported by Kalckar (5.) as approximately 35-50. Equilibration of known initial concentrations of R-l-P,... 

---