Equilibrium constant relation between

The free energy AG can also be related to the equilibrium constant K between the free and the bound state of drug and receptor ... 

In some systems, particularly metal oxides or nitrides, different states of oxidation of the metal or metals could be assumed or actually determined. Expressions for equilibrium constants related to reactions between the atoms in different oxidation states could be set up in terms of the mole fractions of the reacting species. The expressions for the chemical potentials could also be written in terms of these mole fractions. As an example, consider the substance Uj l,Pul02 x. The question might be to determine how the pressure of oxygen varies with the value of x at constant temperature and constant y. We assume that the uranium is all in the oxidation state of +4 and that the plutonium exists in the +3 and +4 oxidation states for positive values of x. The equilibrium change of state is... 

This equation is essentially an equilibrium constant relationship between the electron and hole concentrations in the semiconductor. It is much like the ionization constant expression for the dissociation of water, which can be related to the concentrations of H+(aq) and OH (aq) through the relationship [H+][OH ] = /fw = 1 x 10 " M. The only difference between these two expressions is that the temperature dependence of the water dissociation equilibrium constant is contained implicitly in the value of K, but is explicit in the relationship expressed by equations (5) and (6). The most important point to remember is that increases in the sample temperature will produce exponential increases in the electron and hole concentrations for an intrinsic semiconductor. Thus, the conductivity of intrinsic semiconductors increases exponentially with temperature. In contrast, the conductivity of metals decreases with increasing temperature. ... 

This equation is essentially an equilibrium constant relationship between the electron and hole concentrations in the semiconductor. It is much like the ionization constant expression for the dissociation of water, which can be related to the concentrations of H+(aq) and OH (aq) through the relationship [H+][OH ] = = I y. 10 MT The only... 

Sufficiently close to thermodynamic equilibrium the relation between the fluxes and forces can be described by linear relations with phenomenological constants, L ... 

As described in the preceding section the defect reactions and equilibria can be described as chemical reactions and treated in terms of the law of mass action. It is emphasised that the equilibrium constants relate activities of the structure elements involved in the defect reaction, but under ideal conditions and when the stmcture elements can be assumed to be randomly distributed over the available sites, the activities equal the concentrations of the stmcture elements. This is a valid assumption for very dilute solutions. However, for larger defect concentrations interactions take place between the defects, etc. and in principle activities should be used instead of concentrations. 

Where y is the contribution of dispersive forces and y is the contribution of specific interaction forces such as H-bonding, dipole-dipole, acid-base, etc. The IGC method was successfully applied in recent years to determine the surface properties of divided solids 45,46), From gas chromatographic measurements, Vg is determined by using equation (1). Vg relates to the equilibrium constant K between the adsorbed solute and the polymer surface as follows ... 

As the solubility coefficient S is the equilibrium constant relating the distribution of the permeant molecules between the fluid phase and the polymer phase, i.e. 

One can write acid-base equilibrium constants for the species in the inner compact layer and ion pair association constants for the outer compact layer. In these constants, the concentration or activity of an ion is related to that in the bulk by a term e p(-erp/kT), where yp is the potential appropriate to the layer [25]. The charge density in both layers is given by the algebraic sum of the ions present per unit area, which is related to the number of ions removed from solution by, for example, a pH titration. If the capacity of the layers can be estimated, one has a relationship between the charge density and potential and thence to the experimentally measurable zeta potential [26]. 

This important relation between the temperature derivative of the equilibrium constant K and the standard... 

Conformational free energy simulations are being widely used in modeling of complex molecular systems [1]. Recent examples of applications include study of torsions in n-butane [2] and peptide sidechains [3, 4], as well as aggregation of methane [5] and a helix bundle protein in water [6]. Calculating free energy differences between molecular states is valuable because they are observable thermodynamic quantities, related to equilibrium constants and... 

One of the fundamental equations of thermo dynamics concerns systems at equilibrium and relates the equilibrium constant K to the dif ference in standard free energy (A6°) between the products and the reactants... 

In the case of hydrogen, for example, at a teiuperamre of 2500 K, the equilibrium constant for dissociation has the value, calculated from the tlrermo-dynamic relation between the Gibbs energy of formation and the equilibrium constant of 6.356 x 10 " and hence at a total pressure of 10 atmos, the degree of dissociation is 0.126 at 2500 K, which drops to 8.32 x 10 at 2000 K. 

This relation defines the equilibrium constant between reactants and products, =... 

LP Hammett. Some relations between reaction rates and equilibrium constants. Chem Rev 17 125-136, 1935. 

Because of the dynamic equilibrium between neutral species and their anions, the rate constants for reactions 2 and 3 and those for reactions 4 and 5 cannot be evaluated separately. The relation between and the above constants is... 

It is well accepted that tautomerism relates to the equilibrium between two or more different tautomers e.g., it corresponds to determining if the structure of a compound is, for instance, a pyridone or an hydroxypyridine. The kinetic aspects are often neglected and when the tautomeric equilibrium constant, Kt, is equal to 1 (e.g., for imidazole), the problem may seem... 

In a solution containing such particles, the conditions for equilibrium in all possible proton transfers must be satisfied simultaneously, In terms of these proton energy levels, we may say that this is made possible by the additivity of the J values. In Fig. 38 the values of J for the three proton transfers have been labeled J1, J2, and J3. From the relation J3 = Ji + Ji) we may obtain at once a relation between the values of Kx, and hence between the equilibrium constants K. In the proton transfer labeled Jt the number of solute particles remains unchanged, whereas in J4 and Jt the number of solute particles is increased by unity. 

Now look at the numerical values of the equilibrium constants. The K s listed range from 10+1 to 10 16, so we see there is a wide variation. We want to acquire a sense of the relation between the size of the equilibrium constant and the state of equilibrium. A large value of K must mean that at equilibrium there are much larger concentrations present of products than of reactants. Remember that the numerator of our equilibrium expression contains the concentrations of the products of the reaction. The value of 2 X 10,s for the K for reaction (19) certainly indicates that if a reaction is initiated by placing metallic copper in a solution containing Ag+ (for example, in silver nitrate solution), when equilibrium is finally reached, the concentration of Cu+2 ion, [Cu+2], is very much greater than the square of the silver ion concentration, [Ag+]2. 

The acid-base equilibrium constant for the Me residue can be determined by spectroscopic pH titration. An example for the titration is shown in Fig. 2. The electrostatic potential

difference between the apparent pK on the charged surface (pKobs) and that on an intrinsic neutral surface (pK1) by... 

Table 9.3 summarizes the relations between equilibrium constants. 

The effect of temperature on the equilibrium composition arises from the dependence of the equilibrium constant on the temperature. The relation between the equilibrium constant and the standard Gibbs free energy of reaction in Eq. 8 applies to any temperature. Therefore, we ought to be able to use it to relate the equilibrium constant at one temperature to its value at another temperature. 

To find the quantitative relation between the equilibrium constants for the same reaction at two temperatures T, and T2, we note that Eq. 8 allows us to write the relation... 

The units of AG are joules (or kilojoules), with a value that depends not only on E, but also on the amount n (in moles) of electrons transferred in the reaction. Thus, in reaction A, n = 2 mol. As in the discussion of the relation between Gibbs free energy and equilibrium constants (Section 9.3), we shall sometimes need to use this relation in its molar form, with n interpreted as a pure number (its value with the unit mol struck out). Then we write... 

At equilibrium, the rates of the forward and reverse reactions are equal. Because the rates depend on rate constants and concentrations, we ought to be able to find a relation between rate constants for elementary reactions and the equilibrium constant for the overall reaction. 

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