Equilibrium constant exchange

The equilibrium constant (exchange constant) for this equilibrium is given by... 

Note that when the value of one of the previous equilibrium constants, exchange constants, or solubility products is taken from other sources, attention should be paid to the definition. For example, the solubility product of Ca(OH)2 is commonly defined as... 

In this equation, the primes on the imaginary parts indicate that the Lamior frequencies and coupling constants will be different. Also, if the equilibrium constant for the exchange is not 1, then the forward and reverse rates will not be equal. Note that the 1,2 block, in the top right, represents the rate from site 2 into site 1. 

In tlie case of mutual AB exchange this matrix can be simplified. The equilibrium constant must be 1, so /r k . Also, is equal to Mg and vice versa, and the couplmg constant is the same. For instance, if L is the Liouville matrix for one site, then the Liouville matrix for the other site is P LP, where P is the matrix describing the pemuitation. 

The solubility of hydrogen chloride in solutions of aromatic hydrocarbons in toluene and in w-heptane at —78-51 °C has been measured, and equilibrium constants for Tr-complex formation evaluated. Substituent effects follow the pattern outlined above (table 6.2). In contrast to (T-complexes, these 7r-complexes are colourless and non-conducting, and do not take part in hydrogen exchange. 

The equilibrium constant for this ion-exchange reaction, which is also called the selectivity coefficient, is... 

TABLE 16-7 Equilibrium Constants for Polystyrene DVB Cation and Anion Exchangers... 

The exchange reaction TaCUlg) + Si = Ta + SiCUlg) has the equilibrium constant given by... 

Althoi h the equilibrium constant for hydration is unfavorable, the equilibrium between an aldehyde or ketone and its hydrate is established rapidly and can be detected by isotopic exchange, using water labeled with 0, for example ... 

The distribution coefficient is an equilibrium constant and, therefore, is subject to the usual thermodynamic treatment of equilibrium systems. By expressing the distribution coefficient in terms of the standard free energy of solute exchange between the phases, the nature of the distribution can be understood and the influence of temperature on the coefficient revealed. However, the distribution of a solute between two phases can also be considered at the molecular level. It is clear that if a solute is distributed more extensively in one phase than the other, then the interactive forces that occur between the solute molecules and the molecules of that phase will be greater than the complementary forces between the solute molecules and those of the other phase. Thus, distribution can be considered to be as a result of differential molecular forces and the magnitude and nature of those intermolecular forces will determine the magnitude of the respective distribution coefficients. Both these explanations of solute distribution will be considered in this chapter, but the classical thermodynamic explanation of distribution will be treated first. 

Cobalt, tetraamminepyrophosphato-structures, 1, 202, 203 Cobalt, tetraammine(sarcosine)-chirality, 1,198 Cobalt, triammine-structure, 1, 8—10 Cobalt, tricarbonato-reactions, 1,22 Cobalt, tricarbonylnitroso-exchange reactions, 1, 290 Cobalt, trichloro-equilibrium constant, 1, 517 Cobalt, trichlorobis(triethylphosphine)-structure, 1, 45... 

Objections were raised to other results of these authors derived by viscometric techniques. Thus the viscometric technique led to the erroneous value 119) of 1, instead of 4, as required by symmetry, for the equilibrium constant of the athermal exchange l20> ... 

Kaplan and Thornton (1967) used three different sets of vibrational frequencies to estimate the zero-point energies of the reactants and products of the equilibrium, which provided three different isotope exchange equilibrium constants 1-163, 1-311 and 1-050. The value 1-311 is considered to be most reasonable, whereas the others are rejected as unrealistic for the case in hand. Calculations using the complete theory led to values that varied from 1-086 to 1-774 for different sets of valence-force constants for the compounds involved. 

There is a very special case for self-exchange reactions in which the left side of the equation is identical to the right side. Accordingly, there is no free energy change in the reaction, and the equilibrium constant ( fn) must be unity (Eq. 9.29). 

The complex has been separated by ion exchange and characterised by direct analysis . The complex has a distinctive absorption spectrum (Fig. 11), quite unlike that of Np(V) and Cr(III). The rate coefficient for the first-order decomposition of the complex is 2.32 x 10 sec at 25 °C in 1.0 M HCIO. Sullivan has obtained a value for the equilibrium constant of the complex, K = [Np(V) Cr(III)]/[Np(V)][Cr(III)], of 2.62 + 0.48 at 25 °C by spectrophotometric experiments. The associated thermodynamic functions are AH = —3.3 kcal. mole" and AS = —9.0 cal.deg . mole . The rates of decay and aquation of the complex, measured at 992 m/t, were investigated in detail. The same complex is formed when Np(VI) is reduced by Cr(II), and it is concluded that the latter reaction proceeds through both inner- and outer-sphere paths. It is noteworthy that the substitution-inert Rh(lII), like Cr(III), forms a complex with Np(V) °. This bright-yellow Np(V) Rh(III) dimer has been separated by ion-exchange... 

Natural systems may be quite complex. For example, the enantiomerization of phenoxyalkanoic acids containing a chiral side chain has been studied in soil using H20 (Buser and Muller 1997). It was shown that there was an equilibrium between the R- and 5-enantiomers of both 2-(4-chloro-2-methylphenoxy)propionic acid (MCPP) and 2-(2,4-dichlorophenopxy)propionic acid (DCPP) with an equilibrium constant favoring the herbicidally active / -enantiomers. The exchange reactions... 

Several theoretical models, such as the ion-pair model [342,360,361,363,380], the dyneuaic ion-exchange model [342,362,363,375] and the electrostatic model [342,369,381-386] have been proposed to describe retention in reversed-phase IPC. The electrostatic model is the most versatile and enjoys the most support but is mathematically complex euid not very intuitive. The ion-pair model emd dynamic ion-exchange model are easier to manipulate and more instructive but are restricted to a narrow range of experimental conditions for trtilch they might reasonably be applied. The ion-pair model assumes that an ion pair is formed in the mobile phase prior to the sorption of the ion-pair complex into the stationary phase. The solute capacity factor is governed by the equilibrium constants for ion-pair formation in the mobile phase, extraction of the ion-pair complex into the stationary phase, and the dissociation of th p ion-pair complex in the... 

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