Data equilibrium constants

Electrochemical methods are well established and use relatively inexpensive equipment to produce unique characterization information for molecules and chemical systems qualitative (speciation) and quantitative analytical data, thermodynamic data (equilibrium constants), and kinetic data (heterogeneous and homogeneous reaction rates). 

Based on JANAF or equivalent thermochemical data, equilibrium constants were calculated for the gas-phase equilibria ... 

Commission on Equilibrium Data Equilibrium constants of liquid-liquid distribution reactions. 

VPLQFT is a computer program for correlating binary vapor-liquid equilibrium (VLE) data at low to moderate pressures. For such binary mixtures, the truncated virial equation of state is used to correct for vapor-phase nonidealities, except for mixtures containing organic acids where the "chemical" theory is used. The Hayden-0 Connell (1975) correlation gives either the second virial coefficients or the dimerization equilibrium constants, as required. 

Hammen equation A correlation between the structure and reactivity in the side chain derivatives of aromatic compounds. Its derivation follows from many comparisons between rate constants for various reactions and the equilibrium constants for other reactions, or other functions of molecules which can be measured (e g. the i.r. carbonyl group stretching frequency). For example the dissociation constants of a series of para substituted (O2N —, MeO —, Cl —, etc.) benzoic acids correlate with the rate constant k for the alkaline hydrolysis of para substituted benzyl chlorides. If log Kq is plotted against log k, the data fall on a straight line. Similar results are obtained for meta substituted derivatives but not for orthosubstituted derivatives. 

Decades of work have led to a profusion of LEERs for a variety of reactions, for both equilibrium constants and reaction rates. LEERs were also established for other observations such as spectral data. Furthermore, various different scales of substituent constants have been proposed to model these different chemical systems. Attempts were then made to come up with a few fundamental substituent constants, such as those for the inductive, resonance, steric, or field effects. These fundamental constants have then to be combined linearly to different extents to model the various real-world systems. However, for each chemical system investigated, it had to be established which effects are operative and with which weighting factors the frmdamental constants would have to be combined. Much of this work has been summarized in two books and has also been outlined in a more recent review [9-11]. 

So far the four metal ions have been compared with respect to their effect on (1) the equilibrium constant for complexation to 2.4c, (2) the rate constant of the Diels-Alder reaction of the complexes with 2.5 and (3) the substituent effect on processes (1) and (2). We have tried to correlate these data with some physical parameters of the respective metal-ions. The second ionisation potential of the metal should, in principle, reflect its Lewis acidity. Furthermore the values for Iq i might be strongly influenced by the Lewis-acidity of the metal. A quantitative correlation between these two parameters... 

The text listed below provides more details on how the potentiometric titration data may be used to calculate equilibrium constants. This text provides a number of examples and includes a discussion of several computer programs that have been developed to model equilibrium reactions. 

Long, J. R. Drago, R. S. The Rigorous Evaluation of Spectrophotometric Data to Obtain an Equilibrium Constant, /. Chem. Educ. 1982, 59, 1037-1039. 

Although this experiment is written as a dry-lab, it can be adapted to the laboratory. Details are given for the determination of the equilibrium constant for the binding of the Lewis base 1-methylimidazole to the Lewis acid cobalt(II)4-trifluoromethyl-o-phenylene-4,6-methoxysalicylideniminate in toluene. The equilibrium constant is found by a linear regression analysis of the absorbance data to a theoretical equilibrium model. 

Thermochemical Data. Equilibrium considerations significantly limit alcohol yield at low pressures in the vapor-phase process (116). Consequently, conditions controlling equilibrium constants have been determined and give the following relation, where Tis in K (116,117) ... 

Equimolal proportions of the reactants are used. Thermodynamic data at 298 K are tabulated. The specific heats are averages. Find (1) the enthalpy change of reaction at 298 and 573 K (2) equilibrium constant at 298 and 573 K (3) fractional conversion at 573 K. 

The physical data index summarizes the quantitative data given for specific compounds in the text, tables and figures in Volumes 1-7. It does not give any actual data but includes references both to the appropriate text page and to the original literature. The structural and spectroscopic methods covered include UV, IR, Raman, microwave, MS, PES, NMR, ORD, CD, X-ray, neutron and electron diffraction, together with such quantities as dipole moment, pX a, rate constant and activation energy, and equilibrium constant. 

The basic thermodynamic data for the design of such reactions can be used to assess the dissociation energies for various degrees of dissociation, and to calculate, approximately, tire relevant equilibrium constants. One important source of dissociation is by heating molecules to elevated temperamres. The data below show the general trend in the thermal dissociation energies of a number of important gaseous molecules. 

These data can be used to obtain the value of the equilibrium constant at any temperature and this in turn can be used to calculate the degree of dissociation through the equation for the conceiiuation dependence of the constant on the two species for a single element, die monomer and the dimer, which coexist. Considering one mole of the diatomic species which dissociates to produce 2x moles of the monatomic gas, leaving (1 — jc) moles of the diatomic gas and producing a resultant total number of moles of (1 +jc) at a total pressure of P atmos, the equation for the equilibrium constant in terms of these conceiiU ations is... 

The magnitude of the anomeric effect depends on the nature of the substituent and decreases with increasing dielectric constant of the medium. The effect of the substituent can be seen by comparing the related 2-chloro- and 2-methoxy-substituted tetrahydropy-rans in entries 2 apd 3. The 2-chloro compound exhibits a significantly greater preference for the axial orientation than the 2-methoxy compound. Entry 3 also provides data relative to the effect of solvent polarity it is observed that the equilibrium constant is larger in carbon tetrachloride (e = 2.2) than in acetonitrile (e = 37.5). 

Kinetic data provide information only about the rate-determining step and steps preceding it. In the hypothetical reaction under consideration, the final step follows the rate-determining step, and because its rate will not affect the rate of the overall reaction, will not appear in the overall rate expression. The rate of the overall reaction is governed by the second step, which is the bottleneck in the process. The rate of this step is equal to A2 multiplied by the molar concentration of intermediate C, which may not be directly measurable. It is therefore necessary to express the rate in terms of the concentrations of reactants. In the case under consideration, this can be done by recognizing that [C] is related to [A] and [B] by an equilibrium constant ... 

Cycloheptatrienes are in many cases in rapid equilibrium with an isomeric bicy-clo[4.1.0]heptadiene. The thermodynamics of the valence isomerism has been studied in a number of instances, and some of the data are given below. Calculate the equilibrium constant for each case at 25°C. Calculate the temperature at which K= for each system. Are the signs of the enthalpy and entropy as you would expect them to be Can you discern any pattern of substituent effects from the data ... 

The exceptions are formaldehyde, which is nearly completely hydrated in aqueous solution, and aldehydes and ketones with highly electronegative substituents, such as trichloroacetaldehyde and hexafluoroacetone. The data given in Table 8.1 illustrate that the equilibrium constant for hydration decreases with increasing alkyl substitution. 

Data Source Equilibrium Constant (k) Mol.Vol. of Associate Density of Associate Molar Refractivity of Associate Refractive Index of Associate... 

Steps 1 and 2 require thermodynamic data. Eigure 2-1 shows the equilibrium constants of some reactions as a function of temperature. The Appendix at the end of this chapter gives a tabulation of the standard change of free energy AG° at 298 K. 

Figure 4-1. Vapor-solid equilibrium constant for (a) methane, (b) ethane, and n-butane. (From Gas Processors Suppliers Association, Engineering Data Book.)...

The equilibrium binding constant for this 1 1 association is Xu = ki/lLi. The Xu values were measured spectrophotometrically, and the rate constants were determined by the T-jump method (independently of the X,j values), except for substrate No. 6, which could be studied by a conventional mixing technique. Perhaps the most striking feature of these data is the great variability of the rate constants with structure compared with the relative insensitivity of the equilibrium constants. This can be accounted for if the substrate must undergo desolvation before it enters the ligand cavity and then is largely resolvated in the final inclusion complex. ... 

John F. Brandts measured the equilibrium constants for the denaturation over a range of pH and temperatures. The data for pH 3 ... 

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

The equilibrium between neutral a and zwitterionic b forms in the case of nicotinic 6 and isonicotinic 7 acids has been studied by Halle in mixtures of DMSO and water (from 0 to 100%) (Scheme 4). The position of the equilibrium is very sensitive to the composition of the solvent and for more than 80% of DMSO, the a form essentially dominates the equilibrium in solution (96CJC613). An analysis of their data shows a perfect linear relationship (r = 1) between the In Kt of the two acids and moderate linear relationships between In Kt and the percentage of DMSO. Johnston has studied the equilibrium 2-hydroxypyridine/2-pyridone in supercritical fluids (propane at 393 K and 1,1-difluoroethane at 403 K) (89JPC4297). The equilibrium constant Kt (pyridone/hydroxypyridine) increases four-fold for a pressure increase of 40 bar in 1,1-difluoroethane. 

Lunazzi et al. [84JCS(P2)1025] reported the first reliable data on the behavior of 1,2,3-triazole 20 in solution (Scheme 21). Using NMR at 300 MHz and lowering the temperature to -98°C they determined not only the equilibrium constant but all the thermodynamic and kinetic parameters = 0.55 kcal mol (CD2CI2) and 1.60 kcal moU (toluene-ds),... 

Equilibrium constants and activation parameters have been determined [76ACS(B)101] [for a review see 82AHC(30)127]. Ionization potentials for tautomeric 2-hydroxyselenophenes have been analyzed by comparison with IP data for compounds derived from either tautomeric form. The enol form could not be detected [75ACS(B)647]. 

Equilibrium Constants Kt = 37a/37b as Determined Using H NMR Spectral Data (Room Temperature) [87JCS(P1)2673]... 

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