Equilibrium constant association

While a number of proteins have been crystallized in this manner, the majority of studies have focused on a robust system comprising the tetrameric protein streptavidin and the vitamin biotin. The choice of this system is primcirily motivated by the strong bond between biotin and streptavidin (having an association equilibrium constant, Ka Tbe binding properties were recently... 

This experiment describes a characterization analysis in which the degree of association, equilibrium constant, and hydrogen bond energy are measured for benzyl alcohol and phenol in CCI4. 

Figure 29. Graph of the Logarithm of the Water/Methanol Association Equilibrium Constant against the Reciprocal of the Absolute Temperature...

Confusingly, all of these terms are in current use to express the position of the equilibrium between a ligand and its receptors. The choice arises because the ratio of the rate constants k and k can be expressed either way up. In this chapter, we take KA to be k, kA and it is then strictly a dissociation equilibrium constant, often abbreviated to either dissociation constant or equilibrium constant. The inverse ratio, k+l k x, gives the association equilibrium constant, which is usually referred to as the affinity constant. 

Each independent Reaction 3.22 in the system has an associated equilibrium constant Kj at the temperature of interest and, hence, a mass action equation of the... 

The reaction has an associated equilibrium constant K, which is understood to carry Boltzman terms accounting for electrostatic effects of any surface complexa-tion reactions embedded within the redox reaction. The reaction s activity product at any point in the simulation is given by,... 

Now we combine the two elementary steps to obtain the overall equation and its associated equilibrium constant. 

Creation and Elimination of Schottky Defects These defects can form at the crystal surface or vanish by diffusing to the surface. The equation describing this and the associated equilibrium constant is... 

It is important to know that the defect equilibria that apply to the pure material, and the associated equilibrium constants, also apply to the doped material. The only additional information required is the nature and concentration of the dopant. To illustrate the construction of a diagram, an example similar to that given in Chapter 7 will be presented, for a nonstoichiometric phase of composition MX, nominally containing M2+ and X2- ions, with a stoichiometric composition MXl 0. In this example, it is assumed that the relevant defect formation equations are the same as those given in Chapter 7 ... 

Chemical equilibrium. The polymer concentrations in the ideal gas phase of water are related to the association equilibrium constants according to the expression ... 

Undoubtedly one of the most used LFER in transition metal chemistry involves electron transfer rate constants and associated equilibrium constants in outer sphere redox reactions. These are an unusual class of reactions in chemistry since bonds are only stretched or contracted in the formation of the activated complex. They therefore lend themselves well to theoretical treatment. We shall have more to say about these reactions in Chap. 5. It is sufficient here to state the simple form of the LFER with an example (Fig. 2.8). For the reaction... 

Any reacting system occuring with a change in electric moment, AM, will show a dependence of the associated equilibrium constant K on the electric-field strength E... 

In order to better understand the detailed dynamics of this system, an investigation of the unimolecular dissociation of the proton-bound methoxide dimer was undertaken. The data are readily obtained from high-pressure mass spectrometric determinations of the temperature dependence of the association equilibrium constant, coupled with measurements of the temperature dependence of the bimolecular rate constant for formation of the association adduct. These latter measurements have been shown previously to be an excellent method for elucidating the details of potential energy surfaces that have intermediate barriers near the energy of separated reactants. The interpretation of the bimolecular rate data in terms of reaction scheme (3) is most revealing. Application of the steady-state approximation to the chemically activated intermediate, [(CH30)2lT"], shows that. 

The variation of the association equilibrium constant, with reciprocal temperature is shown in Figure 6. These data yield a value of = -29.8 kcal mol for the enthalpy change in reaction (4), and AA = -26 cal mol K for the corresponding entropy change. As discussed previously, a combination of the... 

At 298 K, k TIh 6 X 10 s and when multiplied by which is an association equilibrium constant (with units of molarity ), the units M s of k correspond to those of a bimolecular rate constant. 

Fig. 59. A general representation of the binding of n molecules of hetaeron, L, to an eluite E. Each binding step has an associated equilibrium constant, Ki, for e formation of species containing / molecules of hetaeron from the reaction of a species containing i - 1 molecules of hetaeron with hetaeron. As a consequence, the retention factor can have a complex dependence on hetaeron concentration the relationship is given by Eq. (109).

Ka is the association equilibrium constant and is inverse proportional to the dissociation equilibrium constant Kd ... 

Table 4. Dimensionless self- and inter-association equilibrium constants values determined from miscible polymer blends scaled to a common reference volume (100 cm /mol) [83]...

The free energy change (AG°) associated with this process is a measure of the relative stability of the HG complex. For a complex that forms spontaneously, that is, self-assembles in the solution phase, AG° < 0. The free energy is related to the association equilibrium constant by the well-known thermodynamic equation ... 

Statistical thermodynamics is used to obtain the partition function for species strongly bound to the surface (i.e., chemisorbed species). This approach can be used to derive the Langmuir adsorption isotherm, and to estimate the associated equilibrium constant, discussed in Section 11.5.3. The situation in which the adsorbed species is more weakly bound, and moves freely across the surace is considered in Section 11.5.4. 

The two possible reactions of the HCOf ion and the associated equilibrium constants are the following. 

In such a case, the condition that the polymer is formed by a mixed association of monomer units would be reflected in the numerical value of the association equilibrium constant. The value for unlike association differs from that for like association by a factor pp since the Keq is referred to Ma moles of monomer for like particle association and to Ma/p moles of each monomer for unlike particle association, while the measurements are referred to systems both containing Ma moles of monomer. Alternately it can be shown that this factor arises from a statistical entropy contribution. 

Schwager F, Marand E, Davis RM. 1996. Determination of self-association equilibrium constant of ethanol by FTIR spectroscopy. J Phys Chem 100 19268-19272. 

The term hydrolysis implies a reaction in which the O-H bonds of water molecules are ruptured. Consider the following equilibria and associated equilibrium constants K which are set up in aqueous solution ... 

Kd is an important property of a receptor-ligand system. A ligand with a small KD is said to have a high affinity for the receptor. Affinity is related to binding energy, and the standard free energy of binding can be determined from the association equilibrium constant, KA, or /KV) (Equation 5.10). 

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