Effective equilibrium constant

Activity ceofficients, surface and absorption effects, equilibrium constants of reactions... 

In catalysis applications, the tunable solvent properties result in a variety of effects, such as controllable component and catalyst solubilities. Moreover, it is possible that kinetic rates are affected by both temperature and pressure effects, equilibrium constants are shifted in favor of the desired products, and selectivity and yields are increased by manipulating the solvent s dielectric constant or by controlling the temperature in highly exothermic reactions through an adjustment of the solvent s heat capacity [18-23]. 

Consider the mass action law given by Eq. (63). In the A-C binary at atom fraction the effective equilibrium constant can be obtained from Eq. (82) with / 14 = -/ 34 to write the mass action law as... 

For p + 0, we rearrange the equilibrium constant expression to incorporate activity coefficients into an effective equilibrium constant, K, at the given ionic strength. 

For simplicity, we omit activity coefficients, but you do know how to use them. You would solve the problem with all activity coefficients equal to 1, find the ionic strength, and then compute activity coefficients with the Davies equation. Then you would compute effective equilibrium constants incorporating activity coefficients and solve the problem again. After each iteration, you would find a new ionic strength and a new set of activity coefficients. Repeat the process until ionic strength is constant. Wow You are smart ... 

To use activity coefficients, first solve the equilibrium problem with all activity coefficients equal to unity. From the resulting concentrations, compute the ionic strength and use the Davies equation to find activity coefficients. With activity coefficients, calculate the effective equilibrium constant K for each chemical reaction. K is the equilibrium quotient of concentrations at a particular ionic strength. Solve the problem again with K values and find a new ionic strength. Repeat the cycle until the concentrations reach constant values. 

Relative concentrations of ATP, ADP, and AMP as a function of the adenylate energy charge. The adenylate kinase reaction was assumed to be at equilibrium, and a value of 1.2 was used for its effective equilibrium constant in the direction shown in the equation in the text. 

It can be seen from this equation that the effective equilibrium constant Kbisphas is a function of the phase ratio a. Within limits, the equilibrium can be shifted in the desired direction by controlling and shifting a. If the reaction is of the form A + B <=> C + D, Eq. (12.7) is equivalent to Eq. (12.6). 

Figure 12.1 Dependence of the effective equilibrium constant 7fbiphas on the phase ratio a (from Chaplin, 1990).

Thermodynamic effects Equilibrium constants for replacing Y by another ligand Z or, in certain cases, for the formation of a complex with lower coordination number, i.e., the difference in free energy between two ground states of known structure. 

Effective equilibrium constants in 0.1 M CaCl2 were measured by Cavanaugh (14) or estimated by the Radian equilibrium program (26). As given in Table IV, these constants include the effects of ionic strength and ion pairing on the activity of the anions. Ion pairs, such as CaSO, are not treated as separate species, but are accounted for as an effect on the activity of simple ions, such as SO3. 

The basis of the treatment discussed here is (1) postulation of an apparent or effective equilibrium constant for the reaction that occurs simultaneously and interactively in both phases and (2) finding a relationship between this and the true equilibrium constants in the individual phases. Such an approach (Martinek et al., 1977, 1980, 1981a,b Martinek and Semenov, 1981a,b Semenov et al.. 

Figure 18.1 Effective equilibrium constant for the reaction A volume ratio a (from Martinek et al., 1981a).

D8. In the leaching of sugar from sugar cane, water is used as the solvent. Typically about 11 stages are used in a countercurrent Rotocel or other leaching system. On a volumetric basis liquid flow rate/solid flow rate = 0.95. The effective equilibrium constant is i% = 1.18, where m = (concentration, g/liter, in liquid)/(concentration, liter, in solid) fSchwartzberg. 19801. If pure water is used as the inlet solvent, predict the recovery of sugar in the solvent. 

D9. Experimental data for the leaching of sugar from sugar cane with water shows that a reasonable value for the effective equilibrium constant y/x = n is 1.18 where y and x are the solute... 

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