Experimental Equilibrium Constants

Although this conversion factor is accurate to seven significant figures, experimental equilibrium constants t3q5ically are accurate to no more than three significant figures, so we round the value of the constant to three... 

Hence the experimental equilibrium constants of Table IV are proportional to the constants for ionization into ion pairs, and the ratios of the if exp reflect differences in the tendency of different molecules to form ion pairs. Since standard free energies are proportional to the logarithms of equilibrium constants, differences in the tabulated free energies represent differences in the standard free energy change for ionization, even though the individual values represent the standard free energy for the overall process of ionization plus dissociation. 

The 2-substituted system has proven especially attractive to modelers because the experimental equilibrium constants are known both in the gas phase and in many different solutions. As a result, the focus of the modeling study can be on the straightforward calculation of the differential solvation free energy of the two tautomers, without any requirement to first accurately calculate the relative tautomeric free energies in the gas phase. However, in 1992 Les et al. [290] suggested that prior experimental data [240,266,288], primarily in the form of ultraviolet spectra in the gas phase and in low-temperature matrices, had been misinterpreted and that the reported equilibrium constants referred to homomeric dimers of tautomers (i.e., (42)2 (43)2). Parchment et al. [291] contested this... 

Several cases exist in which calculations of the entropy change of a reaction from values of the entropy obtained from thermal data and the third law disagree with values calculated directly from measurements of AH and determinations of AG from experimental equilibrium constants. For example, for the reaction... 

Table 6.2 The Preparation of the Experimental Equilibrium Constants for the Extrapolation to 7=0 with the Specific Ion Interaction Method, According to Eq. (6.13)... 

It is straightforward to calculate energies of hydration reactions as a function of the carbonyl compound and, once calibrated on the basis of available experimental data, use this as a criterion for selecting systems which might exist primarily as carbonyl compounds, primarily as carbonyl hydrates or anywhere in between. The disadvantage to such an approach (other than it requiring calculations on both the carbonyl compounds and their respective hydrates) is that it provides very little insight into the factors which influence the equilibrium. Another approach is to focus only on the carbonyl compounds (or only on the hydrates) and look for characteristics which correlate with the experimental equilibrium constants. This is the approach illustrated here. 

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]. 

In this chapter we have seen that acid dissociation constants are needed to calculate the dependence of apparent equilibrium constants on pH. In Chapter 3 we will discuss the calculation of the effects of ionic strength and temperature on acid dissociation constants. The database described later can be used to calculate pKs of reactants at 298.15 K at desired ionic strengths. Because of the importance of pKs of weak acids, Table 1.3 is provided here. More experimental measurements of acid dissociation constants and dissociation constants of complex ions with metal ions are needed because they are essential for the interpretation of experimental equilibrium constants and heats of reactions. A major database of acid dissociation constants and dissociation constants of metal ion complexes is provided by Martell, Smith, and Motekaitis (2001). 

It is possible to distinguish between free ions from associated and covalently bonded species by conductivity measurements, because only free ions are responsible for electrical conductivity in solution [136, 399], Spectrophotometric measurements distinguish between free ions and ion pairs on the one hand, and covalent molecules on the other, because in a first approximation the spectroscopic properties of ions are independent of the degree of association with the counterion [141], The experimental equilibrium constant. Kexp, obtained from conductance data, may then be related to the ionization and dissociation constants by Eq. (2-16). 

A 3rd law analysis of the experimental equilibrium constants tabulated by Cotton and Jenkins (3) using current JANAF... 

A 3rd law analysis of the experimental equilibrium constants tabulated by Cotton and Jenkins (3 ) using current JANAF auxiliary data (4) leads to Dq = 204.8 kcal mol which is 2.6 kcal raol higher than the 202.2 kcal mol derived by Cotton and Jenkins (3 ). Applying this difference to the data of Ryabova and Gurvich ( ) and of Sugden and Schofield (2) as recalculated by... 

The most recent calculations seem to indicate some improvements in the theoretical evaluation of relative tautomer energies. At the 3-21G level the structures are accurate enough for higher-level calculations, which in turn clearly give better relative energies. Here the 6-310 basis set shows the most promise. Another fact to consider is the almost uniform neglect to calculate ASa,b and 8 a 0) even though the vibrational frequencies can be obtained with semiempirical methods. This makes the comparison of the calculated and experimental equilibrium constants even more difficult. 

An uncertain value in the experimental equilibrium constant is az. It is usually underestimated by taking it equal to the apparent (geometrical) surface of the column of unit length. Actually a- can only be larger and so it makes the true Ef1 smaller. 

This section can be closed by listing numerical values of experimental equilibrium constants for the formation of vdW molecules (Table 15). Values are given only for selected temperatures values for other temperatures may be found in the references listed in Table 15. Numerous equilibrium constants for charge-transfer complex formation can be found in Refs. " . 

Table B-3 The preparation of the experimental equilibrium constants for the extrapolation to / = 0 with the specific ion interaction method at 25°C and 1 bar, according to Reaction (B. 12). The linear regression of this set of data is shown in Figure B-1...

In an extension Dewar and co-workers16 have calculated the heats of atomization for many potentially tautomeric compounds and the differences in the values for tautomeric forms are compared with the available experimental equilibrium constants. This and other work on the relationship between tautomeric equilibria and stability of the tautomeric forms of heteroaromatics is discussed further below (Section II,A, 4). 

Table V-37 Compilation of all experimental equilibrium constants found in the literature for aqueous Zr(IV)-carbonate species.

Table V-11 Experimental equilibrium constants (logarithmic values) for Reaction (V.72).

Figure V-49 Extrapolation to 7 = 0 of experimental equilibrium constants for Reaction (V.l 14) determined in NaC104 medium.

The experimental equilibrium constants from the various studies and their source are listed in Table VIII-6. The calculated equilibrium constants at zero ionic strength based on these literature data are discussed below and are summarised in Table VIII-7. Table VIII-6 demonstrates that the agreement of the experimental values is excellent in the cases where the experimental conditions are the same, indicating both a high accuracy and the absence of systematic errors. The uncertainty in the calculated equilibrium constants at zero ionic strength is much larger than the experimental values but this is a result of the uncertainties in the interaction coefficients. 

The best way to find out the equilibrium constant of a particular reaction at a given condition is to do it experimentally. Equilibrium constant depends on temperature, and hence it differs with change in temperature. You should also ask yourself this question. Does the initial concentration of the reactants dictate the equilibrium constant The answer is no. 

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