Selection equilibrium

Table 8.9 Selected Equilibrium Constants in Aqueous Solution at Various...

The thermodynamic properties of to-potactic insertion reaction materials with selective equilibrium are quite different from those of materials in which complete equilibrium can be assumed, and reconstitution reactions take place. Instead of flat plateaus related to polyphase equilibria, the composition-dependence of the potential generally has a flat S-type form. 

In the following, the MO applications will be demonstrated with two selected equilibrium reactions, most important in radical chemistry disproportionation and dimerization. The examples presented will concern MO approaches of different levels of sophistication ab initio calculations with the evaluation of partition functions, semiempirical treatments, and simple procedures employing the HMO method or perturbation theory. 

Selected equilibrium constants and thermodynamic quantities of the mononuclear species are listed in Table I and the distribution of mononuclear ions as a function of pH is shown in Fig. 1. Values have also been reported which show the variation of the protonation constant of HVO, - with variation of added KC1 from 0 to 2 M (15). 

Selected Equilibrium Constants and Thermodynamic Quantities for the Protonation of... 

Metal binding by a hydrous oxide from a 10 7 M solution (SOH + Me2+ SOMe+ + H+) for a set of selected equilibrium constants (see Eqs. (i) - (iii)) and concentration conditions (see text). No corrections have been made for electrostatic interactions (compare Fig. 3.14). The pH edge reflects a narrow pH range in which the metal ion is adsorbed. 

Because there is no obvious reason for selecting equilibrium constants from runs in which the initial solution contained either solid KCI or solid KBr (runs A or B), the calculations that follow are based on average solid compositions and average equilibrium constants of A and B runs for each total composition reported (Table IV). The equilibrium constants for Equation 5 are shown as a function of KBr mole fraction in Figure 1. 

Although most of the commercial adsorptive separation processes are operated under the selective-equilibrium adsorption mechanism, adsorptive separation may also be based on diffusion rates through a permeable barrier which are designated as rate-selective adsorption processes. In some instances there may be a combination of equilibriums as well as rate selective adsorption. A rate-selective adsorption process yields good separation when the diffusion rates of the feed components through the permeable barrier differ by a wide margin. 

Table I. Selected Equilibrium Constants for Aqueous Plutonium Reactions0...

A computer database of critically selected equilibrium constants is found in R. M. Smith, A. E. Martell, and R. J. Motekaitis, NIST Critical Stability Constants cf Metal Complexes Database 46 (Gaithersburg, MD National Institute of Standards and Technology, 2001). Books dealing with the experimental measurement of equilibrium constants include A. Martell and... 

In 1965, Cram established a scale of acidities reaching to the very weak carbon acids by combining data from the various methods.72 The basis of the scale is the value of pKa = 18.5 found by Langford and Burwell for 9-phenylfluorene (2),73 and it includes the equilibrium measurements of Streitwieser and others up to pKa 33. Table 3.1 records some selected equilibrium values in this range. Beyond pAa 33, direct equilibrium methods fail and only the kinetic and organometallic techniques can be used. Cram compared Streitwieser s exchange-rate measurements for triphenylmethane and for cumene (4),74 ... 

There are two general classes of selectivity equilibrium-based and kinetically based. Both types depend on specific interactions of the analyte molecule with the selective layer. In addition, there is also physical selectivity based on the highly specific interaction of the molecule with the electrostatic and electromagnetic fields. The topic of selectivity is broad enough to deserve its own chapter. We examine issues pertaining to selectivity in Chapter 2. 

Table 1.7. Influence of temperature on selected equilibrium constants. 

WATEQ2 consists of a main program and 12 subroutines and is patterned similarly to WATEQF ( ). WATEQ2 (the main program) uses input data to set the bounds of all major arrays and calls most of the other procedures. INTABLE reads the thermodynamic data base and prints the thermodynamic data and other pertinent information, such as analytical expressions for effect of temperature on selected equilibrium constants. PREP reads the analytical data, converts concentrations to the required units, calculates temperature-dependent coefficients for the Debye-HKckel equation, and tests for charge balance of the input data. SET initializes values of individual species for the iterative mass action-mass balance calculations, and calculates the equilibrium constants as a function of the input temperature. MAJ EL calculates the activity coefficients and, on the first iteration only, does a partial speciation of the major anions, and performs mass action-mass balance calculations on Li, Cs, Rb, Ba, Sr and the major cations. TR EL performs these calculations on the minor cations, Mn, Cu, Zn, Cd, Pb, Ni, Ag, and As. SUMS performs the anion mass... 

Population genetics Hardy- Weinberg law, founder effects, mutation-selection equilibrium 412,427,429-433... 

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