Concentration from equilibrium constant

Calculate equilibrium constants from concentration data. 

Calculate an equilibrium constant from concentration measurements (Section 15.5). 

The pioneering work of Gilkerson and co-workers [122-130] and Huyskens and colleagues [131,132] allows the determination of the corresponding equilibrium constants from conductivity measurements. If all equilibria, Eq. (4)-(6), are involved, the association constants of an electrolyte without (K l) and with (KA ) addition of the ligand at concentration cL of the ligand L are given by the relationship [132]... 

Examples through illustrate the two main types of equilibrium calculations as they apply to solutions of acids and bases. Notice that the techniques are the same as those introduced in Chapter 16 and applied to weak acids in Examples and. We can calculate values of equilibrium constants from a knowledge of concentrations at equilibrium (Examples and), and we can calculate equilibrium concentrations from a knowledge of equilibrium constants and initial concentrations (Examples, and ). 

The effect of pressure on chemical equilibria and rates of reactions can be described by the well-known equations resulting from the pressure dependence of the Gibbs enthalpy of reaction and activation, respectively, shown in Scheme 1. The volume of reaction (AV) corresponds to the difference between the partial molar volumes of reactants and products. Within the scope of transition state theory the volume of activation can be, accordingly, considered to be a measure of the partial molar volume of the transition state (TS) with respect to the partial molar volumes of the reactants. Volumes of reaction can be determined in three ways (a) from the pressure dependence of the equilibrium constant (from the plot of In K vs p) (b) from the measurement of partial molar volumes of all reactants and products derived from the densities, d, of the solution of each individual component measured at various concentrations, c, and extrapolation of the apparent molar volume 4>... 

The concentration of M = I(T3 molar. Suppose we want to reduce the concentration of M to 10 5. When we calculate the equilibrium constant from the first example and then calculate the required concentration ofLatM= 1(T5 molar we find the following rule of thumb if an excess ofL is needed, keep [L] the same and lower fM] only ... 

In this section, you learned that the expression for the reaction quotient is the same as the expression for the equilibrium constant. The concentrations that are used to solve these expressions may be different, however. When Qc is less than Kc, the reaction proceeds to form more products. When Qc is greater than Kc, the reaction proceeds to form more reactants. These changes continue until Qc is equal to Kc. Le Chatelier s principle describes this tendency of a chemical system to return to equilibrium after a change moves it from equilibrium. The industrial process for manufacturing ammonia illustrates how chemical engineers apply Le Chatelier s principle to provide the most economical yield of a valuable chemical product. 

EXAMPLE 9.5 Determining the equilibrium constant from equilibrium concentrations... 

One of the most useful applications of standard potentials is the calculation of equilibrium constants from electrochemical data. The techniques we are going to develop here can be applied to reactions that involve a difference in concentration, the neutralization of an acid by a base, a precipitation, or any chemical reaction, including redox reactions. It may seem puzzling at first that electrochemical data can be used to calculate the equilibrium constants for reactions that are not redox reactions, but we shall see that this is the case. 

In some cases, the reaction rates are very fast and a pseudoequilibrium approach is used to model the system (4.30). This approach consists of assuming that the concentration of species is always close to the equilibrium conditions and hence, they can be calculated using equilibrium constants from the values of other species present in the reaction system. This approach is especially important for the modeling processes in which the reaction rates are fast and when the kinetic rates are ill-defined (because of a large number of species or a lack of experimental data that makes difficult the kinetic analysis)... 

Cogly, Butler and Grunwald were the first who determined solvation equilibrium constants from chemical shift measurements. The chemical shifts of water in propylene carbonate containing various salts were extrapolated to zero water concentration. The dependence of the chemical shift of water at infinite dilution in PC... 

On the surface, the combination of cation exchanger and anion exchanger would mean that pure water is produced. As shown in Equations (16.1) and (16.2), however, the unit process of ion exchange is governed by equilibrium constants. The values of these constants depend upon how tightly the removed ions from solution are bound to the bed exchanger sites. In general, however, by the nature of equilibrium constants, the concentrations of the affected solutes in solution are extremely small. Practically, then, we may say that pure water has been produced. 

It is conventional, however, to omit the concentration of water from mass action expressions and instead to absorb its value into a revised equilibrium constant. The concentration of water is 55.4 M thus, Eq. [1-14] can be rewritten as... 

Calculating equilibrium constants from pressures or concentrations... 

Fig. 7. Fraction of thallium(III) present in the various species in aqueous solution of 50 mM Tl(III) as a function of the total chloride concentration (mM) (a) in 3 M HCIO4 [equilibrium constants from Woods et al. (90)] (b) in 3 M HCIO4 + 1 M NaC104 [equilibrium constants from Ahrland and Johansson (92)].

Peq for a gas phase reaction is defined in terms of the partial pressures of reactants and products. At times it is more convenient to express the reactivity of a substance in terms of moles or molecules per unit volume. The equilibrium constant in concentration terms is obtained from Peq by using the Ideal Gas equation ... 

Since this equilibrium constant involves concentrations it is, by definition, a non-ideal constant, and in principle may show an ionic strength dependence. Generally the experimental measurement is the pH, found either directly from the pH of the given solution, or, more accurately, from a pH titration. The rigorous definition of pH is ... 

Figure A-17 Distribution diagram for the Th(IV)-hydroxide system in 3 M (Na)Cl, using the best set of equilibrium constants from Model 111-B (Table A-29). Note that many of the complexes suggested there occm in such low concentrations that they are not seen in the figures.

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