Equilibrium constant special meanings

Solubility equilibrium constants, such as (20) and (22), are given a special name—the solubility product. It is symbolized K,p. A low value of K,p means the concentrations of ions are low at equilibrium. Hence the solubility must be low. Table 10-11 lists solubility products for some common compounds. 

No general discussion of the multitude of behaviour patterns, especially as regards dependence on concentration of catalyst, or of components of a syncatalyst, can be profitable at this stage. As for the termination reactions - our special concern here - this kinetic pattern implies that Vt is of first order, Vt of zero order, with respect to monomer. This means that k3 or k4 contain a term k iplky, they may also contain one or more equilibrium constants - depending on the nature of the catalytic system. 

What does the equilibrium expression mean It means that, for a given reaction at a given temperature, the special ratio of the concentrations of the products to reactants defined by the equilibrium expression will always be equal to the same number—namely, the equilibrium constant K. For example, consider a series of experiments on the ammonia synthesis reaction... 

A special problem arises if the molecular property measured in the course of the determination of the equilibrium constant is also dependent on the temperature. For example, the temperature dependence of the absorbance may render impossible the use of spectrophotometry in the determination of thermodynamic data from the equilibrium constants relating to various temperatures. In such cases AH may be obtained by means of a separate calorimetric measurement, and the entropy term is found in the usual manner from this AH value and from AG calculated from the equilibrium constants, relating to a single temperature ... 

Generally speaking, there are two main problems in learning thermodynamics. One, of course, is to learn the details of the specialized procedures in one s disciphne, which in our case involves chemical reactions, activities, fugacities, equilibrium constants, and so on. The other, either more or less important depending on your point of view, is to understand thermodynamics as a whole - what is it, what do the variables mean, and how does it relate to other branches of science In this book, the first four chapters deal mostly with this latter problem, and the rest of the book with the details. 

Equation (2.60) is a very common relation between reaction rate constant and chemical equilibrium constant. In addition, the exponential of K represents special physical meaning. 

This equilibrium lies far to the left (indicating that very little ionization has taken place). This means that the concentrations of hydrogen ions and hydroxide ions are very small. At 25°C, [H+] = [OH ] = 1.00 x 10 M. A special equilibrium constant, K, known as the ion product constant for water, is based on this ionization and is defined as follows at 25°C. 

Prediction or measurement of u is of paramount importance for assessing transport of chemicals in rivers. The following discussion will be restricted to the special case of stationary uniform flow. This means that at a fixed location the discharge Q is constant, the cross section A does not change in size or shape, and the surface slope remains constant. With these assumptions, an equilibrium between the gravitational... 

The vapor curve KLMNP gives the composition of the vapor as a function of the temperature T, and the liquid curve KKMSP gives the composition of die liquid as a function of die temperature. These two curves have a common point M. The state represented by M is that in which the two states, vapor and liquid, have the same composition xaB on die mole fraction scale. Because of die special properties associated with systems in this state, the Point M is called an azeotropic point and the system is said to form an azeotrope. In an azeotropic system, one phase may be transformed to the other at constant temperature, pressure and composition without affecting the equilibrium state. This property justifies the name azeotropy, which means a system diat boils unchanged. 

The Gibbs phase rule is the basis for organizing the models. In general, the number of independent variables (degrees of freedom) is equal to the number of variables minus the number of independent relationships. For each unique phase equilibria, we may write one independent relationship. In addition to this (with no other special stipulations), we may write one additional independent relationship to maintain electroneutrality. Table I summarizes the chemical constituents considered as variables in this study and by means of chemical reactions depicts independent relationships. (Throughout the paper, activity coefficients are calculated by the Debye-Hiickel relationship). Since there are no data available on pressure dependence, pressure is considered a constant at 1 atm. Sulfate and chloride are not considered variables because little specific data concerning their equilibria are available. Sulfate may be involved in a redox reaction with iron sulfides (e.g., hydrotroilite), and/or it may be in equilibrium with barite (BaS04) or some solid solution combinations. Chloride may reach no simple chemical equilibrium with respect to a phase. Therefore, these two ions are considered only to the... 

Mathematical solutions of coupled rate equations are available for a variety til special cases,16 but approximate solutions informed by experimental data concerning the relative rates of contributing reactions are more the rule. For the iructions in Eq. 1.48, as an example, it is known2,7 that the second reaction comes to equilibrium very much faster than the first and that, in the first icaclion, the forward rate is much smaller than the backward rate. Thus the rate o formation of bicarbonate from the hydration of C02 is limited by the rate of lot mation of true carbonic acid (at pH < 8). With respect to Eqs. 1.53a and I s tc, this means that, on the time scale of formation of species C (H2CO ), the iale of increase of the concentration of species D (OH ) is nil. Moreover, the i onccnlralion of species B (11,0) is effectively constant in aqueous solution and... 

Michaelis and Menten (1913) treated the special case where k2 k-i- Under this assumption, K reduces to 1/ATi and the first reaction is effectively at equilibrium. Their overall rate expression corresponds to the final form in Eq. (2.5-30). though their constant K has a different meaning. Thus, it is not possible to test the accuracy of the Michaelis-Menten equilibrium assumption by reaction rate experiments in the quasi-steady-state region. Rather, one would need additional measurements very early in the reaction to allow calculation of the rate coefficients fci, k-i. and k2-... 

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