Equilibrium constants, estimation

The major absorption in the 31P n.m.r. spectrum of an equimolar solution of penta-phenoxyphosphorane and sodium phenoxide in DMF-acetonitrile is due to the hexaphenoxyphosphate anion, as predicted from the low equilibrium constant estimated for equation (2) (page 35).27 Catechol and phosphorus oxychloride in refluxing benzene gave the spirophosphorane(108), which with triethylamine gave the salt (109).45 On the basis of its 31P chemical shift in DMF solution, (108) was formulated86 as the free six-co-ordinate acid (110), but it seems probable that DMF is... 

We have seen how a comparison of the equilibrium constant estimated from kinetic data for the forward and reverse directions (i.e. K = kf/k ) with that obtained by measurements on the equilibrated system, may be used to provide strong support (or otherwise) for a particular reaction scheme (see also Chap. 8 Pd(II)). The kinetic approach may be useful also for providing information on thermodynamic data not otherwise easily available. 

Using the equilibrium constants estimated by Guthrie (12) for hemi-orthoamide tetrahedral intermediates (derived from N,N-dimethylformamide and N,N-di-methylacetamide) and the activation parameters described in Table 2, it was possible to obtain the free energy of activation for the breakdown UG ieav) and for conformational change (aG onf) of the tetrahedral interme.-diates derived from the N-benzyl-N-methyl derivatives of formamide, acetamide and propionamide. These values are the following. 

EXAMPLE 7-8 From the above equilibrium constants, estimate the solubility of silver chloride in solutions containing chloride at the following concentrations 10 , 10 , 10 1, and 2 M. What is the minimum solubility, and at what chloride ion concentration does it occur ... 

Fe(diAMHsar)] i+ cation these states have very close energy characteristics (AH is approximately 100 cm-i), the equilibrium constant is practically temperature-independent. The choice of a pure spin or a spin-orbital model affects the equilibrium constant estimation but not AH. The /4ff value is well described by both models (Fig. 8) except the one for [Fe(diAMHsar)] + tetracation, in which case the first model gives much better agreement with the experimental data [241-243]. 

Equilibrium constants estimated for the Schlenk equilibria of ethylmagnesium bromide (iodide) and phenylmagnesium bromide (iodide) in diethyl ether are shown in Table 3. Equilibria lie strongly to the side of the alkyl- and arylmagnesium halides for both substituents [27]. 

For kaolinite, the dissolution reaction is the reverse of reaction 6.25 and has an equilibrium constant estimated to be The equilibrium expression for this reaction is then... 

Application of DPP to the mechanism The electroreduction of the system Cd(II)-EDTA, already extensively studied [14, 124] by DC and AC polarography, has been chosen as an example of the elucidation of the electrode mechanism by the DPP technique [120]. Rate constants kp and and the equilibrium constant estimated by this method can hence be compared with literature data. In buffered solu-... 

Table 27 Rate parameters and equilibrium constants estimated for reactions (25)—(27) and(29)—(31) at 298.2 K = 1.0 mol dm" (NaHCOa/NaClO ) (data...

One can write acid-base equilibrium constants for the species in the inner compact layer and ion pair association constants for the outer compact layer. In these constants, the concentration or activity of an ion is related to that in the bulk by a term e p(-erp/kT), where yp is the potential appropriate to the layer [25]. The charge density in both layers is given by the algebraic sum of the ions present per unit area, which is related to the number of ions removed from solution by, for example, a pH titration. If the capacity of the layers can be estimated, one has a relationship between the charge density and potential and thence to the experimentally measurable zeta potential [26]. 

Within the same approximation, we estimate that the equilibrium constant... 

This method provides a reasonable estimate of the piQ, provided that the weak acid is neither too strong nor too weak. These limitations are easily appreciated by considering two limiting cases. For the first case let s assume that the acid is strong enough that it is more than 50% dissociated before the titration begins. As a result the concentration of HA before the equivalence point is always less than the concentration of A , and there is no point along the titration curve where [HA] = [A ]. At the other extreme, if the acid is too weak, the equilibrium constant for the titration reaction... 

Estimation of fct for Reversible Reactions When the reaction is of the form A B, where B is a nonvolatile product and the equilibrium constant is defined by Cg = K Ca, the expressions for computing /cl become extremely complex. A good discussion of this situation is given in Mass Tran.sfer by Sherwood, Pigford, and Wilke (McGraw-Hill, New York, 1975, p. 317). Three limiting cases are hsted below ... 

Table 4-1 lists some rate constants for acid-base reactions. A very simple yet powerful generalization can be made For normal acids, proton transfer in the thermodynamically favored direction is diffusion controlled. Normal acids are predominantly oxygen and nitrogen acids carbon acids do not fit this pattern. The thermodynamicEilly favored direction is that in which the conventionally written equilibrium constant is greater than unity this is readily established from the pK of the conjugate acid. Approximate values of rate constants in both directions can thus be estimated by assuming a typical diffusion-limited value in the favored direction (most reasonably by inspection of experimental results for closely related... 

The differenee in reaction rates of the amino alcohols to isobutyraldehyde and the secondary amine in strong acidic solutions is determined by the reactivity as well as the concentration of the intermediate zwitterions [Fig. 2, Eq. (10)]. Since several of the equilibrium constants of the foregoing reactions are unknown, an estimate of the relative concentrations of these dipolar species is difficult. As far as the reactivity is concerned, the rate of decomposition is expected to be higher, according as the basicity of the secondary amines is lower, since the necessary driving force to expel the amine will increase with increasing basicity of the secondary amine. The kinetics and mechanism of the hydrolysis of enamines demonstrate that not only resonance in the starting material is an important factor [e.g., if... 

However, estimates of equilibrium constants (see for instance. Comprehensive Coordination... 

Although AGrxn depends on both enthalpy and entropy, there are many reactions for which the entropy contribution is small, and can be neglected. Thus, if AHjxn = AErxn, wc cuu estimate equilibrium constants for such reactions by the following equation ... 

Molecular orbital calculations have been used to estimate equilibrium constants, although up to the present these attempts have not met with much success. Using calculations of this type, 2- and 4-hydroxypyridine 1-oxide were predicted to be more stable than 1-hydroxypyrid-2- and -4-one by ca. 20 kcal/mole, which corresponds to a ratio of ca. 10 between the forms. It was later shown experimentally that, at least in the series of 4-substituted compounds, there is very little energy difference between the forms and that the ratio between them is about unity. Molecular orbital calculations for... 

One interesting problem frequently recurring in heterocyclic chemistry, particularly with respect to nitrogen heterocycles, is tautomeric equilibria. Too many methods are available for the elucidation of equilibrium positions and tautomeric equilibrium constants (Kj) to adequately review the whole question here. However, the Hammett equation provides one independent method this method has the advantage that it can be used to predict the equilibrium position and to estimate the equilibrium constant, even in cases where the equilibrium position is so far to one side or the other that experimental determination of the concentration of the minor component is impossible. The entire method will be illustrated using nicotinic acid as an example but is, of course, completely general. 

Thus, estimates of tautomeric equilibrium constants are available without any experimental data except the necessary a- and p-values. 

Tautomeric Equilibrium Constants Kt = [ll/]/[21/] OF Substituted Tetrazoles 27 in DMSO Estimated from NMR Studies... 

To apply the Equilibrium Law to acid solutions, a chemist must know the numerical value of the equilibrium constant, KA. Experiments which provide this information require the measurement of hydrogen ion concentration. Acid-sensitive dyes, such as litmus, offer the easiest estimate of [H+]. 

The following experiment was performed to determine the equilibrium constant in (43). A 1.22 gram sample of benzoic acid was dissolved in 1.00 liter of water at 25°C. With dyes whose color is sensitive to acidity (indicators) the concentration of H+(aq) was estimated to be 8 X 10 4 M. 

The parameters indexed with a are connected with the nucleation step or other effects occurring only once per triple helix. Parameters denoted by s are related with the equilibrium constants of the propagation steps and are ordered to be independent of the position of the reacting chain segment. This implies that end effects are neglected. Since the same dependences are valid for AH° and AS, with the help of their chain length dependence we can determine AG by extrapolation up to 3 n - 2 = 0, and thus, a can be estimated it depends neither on temperature nor on the chain length. 

Unionized mercuric acetate is also a mercurating species, for the second-order rate coefficient for mercuration of benzene by mercuric acetate in acetic acid at 25 °C is 0.41 x 10"7. If mercuration took place via ionized acetate ion pairs HgOAc+OAc" for which AT, the equilibrium constant can be estimated at 2 x 10"8, then since the rate of mercuration by this ion pair will be approximately the same as by the acetoxymercury perchlorate ion pair for which k2 the second-order rate coefficient has been determined (above) as 0.37x10"3 at 25 °C, the observed second-order rate should be 2 x 10"8 x0.37 x 10"3 = 0.74xl0-11. This is so different from the rate actually observed that mercuration by the ion pair can be eliminated which leaves ionized mercurcy acetate as the only possible mercurating species439. 

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