Equilibrium constant different forms

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. 

To derive an equation for the exchange equilibrium constant, one forms the difference between Eqs. 5.40b and 5.40a ... 

The gas-phase equilibrium constants differ from those in aqueous solution by as much as 10" The large differences between the stabilities of the tautomeric forms in the gas phase and in solution once more reveal the dominant influence of solvation on relative molecular stabilities. 

Fig. 1. Ulusuation of the one dimensional lattice model with nearest neighbor interaction. Three different conformations are shown the equilibrium constants for forming each conformation from the oik above it are iiulicated as for the first pair because an isolated randomly coiled site becomes helical (these sites are indicated with ),. s for the second pair, because a randomly coiled site adjacoit to a helical site becomes helical. The statistical weights are Micated at right, with reference to the entirely coiled conformation. The general form is where m is the number of sites in the helical conformation, n is the number of continuous stretches of helical sites (93)...

Figure 1. A simple model of protein/support interactions. The protein is assumed to consist of a partly folded state, F, in equilibrium with the native conformer, Nf, an aggregated form, nF, and an unfolded state, U, which in turn is in equilibrium with a second aggregated form. nU. It is assumed that the protein must at least partially unfold to interact with the packing. The interconversions between these different states are determined by the rate constants shown, and the relative amounts at equilibrium by the ratios of the forward and reverse rate constants (the equilibrium constants). Each form is in turn distributed between mobile phase and sorbent with equilibrium constant Ki. .. K. The time constant, 7 is the reciprocal of the rate constant, so 7. = UK., and 7 = l/K, .

Sta.bilizers. Cyanuric acid is used to stabilize available chlorine derived from chlorine gas, hypochlorites or chloroisocyanurates against decomposition by sunlight. Cyanuric acid and its chlorinated derivatives form a complex ionic and hydrolytic equilibrium system consisting of ten isocyanurate species. The 12 isocyanurate equilibrium constants have been determined by potentiometric and spectrophotometric techniques (30). Other measurements of two of the equilibrium constants important in swimming-pool water report significantly different and/or less precise results than the above study (41—43). A critical review of these measurements is given in Reference 44. 

The acidity of a lydrocarbon can be determined in an analogous way. If the electronic spectra of the neutral and anionic forms are sufficiently different, the concentrations of each can be determined directly, and the equilibrium constant for... 

When a Br nsted plot includes acids or bases with different numbers of acidic or basic sites, statistical corrections are sometimes applied in effect, the rate and equilibrium constants are corrected to a per functional group basis. If an acid has p equivalent dissociable protons and its conjugate base has q equivalent sites for proton addition, the statistically corrected forms of the Br insted relationships are... 

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... 

It is in the same order as the equilibrium constants of CTC of amine-FN. That is, the stronger the ability of an amine to form CTC with electron acceptors, the faster the rate of pholopolymerization. However, under 313-nm irradiation, local excitation plays a principal role and the rate of polymerization is observed to descend in a different order [80] ... 

The form of the expression for Q, known as the reaction quotient, is the same as that for the equilibrium constant, K. The difference is that the partial pressures that appear in Q are those that apply at a particular moment, not necessarily when the system is at equilibrium. By comparing the numerical value of Q with that of K, it is possible to decide in which direction the system will move to achieve equilibrium. 

The quantity Q that appears in this equation is the reaction quotient referred to in Chapter 12. It has the same mathematical form as the equilibrium constant, K the difference is that the terms that appear in Q are arbitrary, initial pressures or concentrations rather than equilibrium values. 

We use a different measure of concentration when writing expressions for the equilibrium constants of reactions that involve species other than gases. Thus, for a species J that forms an ideal solution in a liquid solvent, the partial pressure in the expression for K is replaced by the molarity fjl relative to the standard molarity c° = 1 mol-L 1. Although K should be written in terms of the dimensionless ratio UJ/c°, it is common practice to write K in terms of [J] alone and to interpret each [JJ as the molarity with the units struck out. It has been found empirically, and is justified by thermodynamics, that pure liquids or solids should not appear in K. So, even though CaC03(s) and CaO(s) occur in the equilibrium... 

In principle, Equation (7.28) is determined by equating the rates of the forward and reverse reactions. In practice, the usual method for determining Kkinetic is to run batch reactions to completion. If different starting concentrations give the same value for Kkinetic, the functional form for Equation (7.28) is justified. Values for chemical equilibrium constants are routinely reported in the literature for specific reactions but are seldom compiled because they are hard to generalize. 

Equation (7.28) may not provide a good fit for the equilibrium data if the equilibrium mixture is nonideal. Suppose that the proper form for Kkmetic is determined through extensive experimentation or by using thermodynamic correlations. It could be a version of Equation (7.28) with exponents different from the stoichiometric coefficients, or it may be a different functional form. Whatever the form, it is possible to force the reverse rate to be consistent with the equilibrium constant, and this is recommended whenever the reaction shows appreciable reversibility. 

The solution is illustrated in Fig. 8.15, which shows the equilibrium concentration of methanol for different initial gas mixtures. Note that the maximum methanol concentration occurs for the pure CO + H2 mixture. Hence, in principle, a mixture of just CO and H2 could be used, with minor amounts of CO2, to produce the maximum amount of methanol. However, it is not only the equilibrium constant that matters but also the rate of methanol formation, and one must remember that methanol forms from CO2 not CO. Hence, the rate is proportional to the CO2 pressure and this is why the methanol synthesis is not performed with the simple stoichiometric 3 1 mixture of H2 and CO2 that Eq. (19) suggests. 

Having introduced matters pertaining to the electrochemical series earlier, it is only relevant that an appraisal is given on some of its applications. The coverage hereunder describes different examples which include aspects of spontaneity of a galvanic cell reaction, feasibility of different species for reaction, criterion of choice of electrodes to form galvanic cells, sacrificial protection, cementation, concentration and tempera lure effects on emf of electrochemical cells, clues on chemical reaction, caution notes on the use of electrochemical series, and finally determination of equilibrium constants and solubility products. 

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