Applications Involving the Equilibrium Constant

Knowing the value of the equilibrium constant for a reaction allows us to do many things. For example, the size of K tells us the inherent tendency of the reaction to occur. A value of K much larger than 1 means that at equilibrium, the reaction system will consist of mostly products—the equilibrium lies to the right. For example, consider a general reaction of the type 

That is, at equilibrium [B] is 10,000 times greater than [A]. This means that the reaction strongly favors the product B. Another way of saying this is that the reaction goes essentially to completion. That is, virtually all of A becomes B. 

On the other hand, a small value of K means that the system at equilibrium consists largely of reactants—the equilibrium position is far to the left. The given reaction does not occur to any significant extent. 

What does the value of the equilibrium constant, K, tell us  

Calculating Equilibrium Concentration Using Equilibrium Expressions 

I AIM To learn to calculate equilibrium concentrations from equilibrium constants. 

Another way we use the equilibrium constant is to calculate the equilibrium concentrations of reactants and products. For example, if we know the value of K and the concentrations of all the reactants and products except one, we can calculate the missing concentration. This is illustrated in Example 16.7. 

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Up to this point, we have focused on aqueous equilibria involving proton transfer. Now we apply the same principles to the equilibrium that exists between a solid salt and its dissolved ions in a saturated solution. We can use the equilibrium constant for the dissolution of a substance to predict the solubility of a salt and to control precipitate formation. These methods are used in the laboratory to separate and analyze mixtures of salts. They also have important practical applications in municipal wastewater treatment, the extraction of minerals from seawater, the formation and loss of bones and teeth, and the global carbon cycle. 

At a given temperature, a reaction will reach equilibrium with the production of a certain amount of product. If the equilibrium constant is small, that means that not much product will be formed. But is there anything that can be done to produce more Yes, there is— through the application of Le Chatelier s principle. Le Chatelier, a French scientist, discovered that if a chemical system at equilibrium is stressed (disturbed) it will reestablish equilibrium by shifting the reactions involved. This means that the amounts of the reactants and products will change, but the final ratio will remain the same. The equilibrium may be stressed in a number of ways changes in concentration, pressure, and temperature. Many times the use of a catalyst is mentioned. However, a catalyst will have no effect on the equilibrium amounts, because it affects both the forward and reverse reactions equally. It will, however, cause the reaction to reach equilibrium faster. 

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. 

The condition of equilibrium is also applicable to changes of state that involve heterogenous reactions, and the same methods used for homogenous reactions to obtain expressions of the equilibrium constant are used for heterogenous reactions. One difference is that in many heterogenous reactions one or more of the substances taking part in the change of state is a pure phase at equilibrium. In such cases the standard state of the substance is chosen as the pure phase at the experimental temperature and pressure. The chemical potential of the pure substance in its standard state still appears in Y.k vkPk but the activity of the substance is unity and its activity does not appear in the expression for the equilibrium constant. 

The advantage of bidimensional representation is evident if four reactive components are involved, as in the class of reversible reactions A + B <-> C + D. This situation covers an important number of industrial applications, as the esterification of acids with alcohols. Selecting C as the reference, the transformed variables are XA = xA + xc, XB = xB + xc and XD = xD- xc since v, = 0. The transformed variables sums to one, but only two are used as co-ordinates. Accordingly, the pure components may be placed in the corner of a square diagram, reactants or products on the same diagonal. Figure A. 5 displays the reactive distillation map traced as before for the relative volatilities 4/2/6/1 and the equilibrium constant K t = 5. 

In some early applications [96] to ETs involving compounds with quin-one-like compounds Q, QA Q -A Q=, it was necessary to examine some data on the formation constants of the semiquinone QH, Q + QH2 — 2QH (The H is typically attached to an O or an N.) My impression, after looking at available data, was that the equilibrium constant was approximately the same, provided all three species had the same charge. Looking at the structures, one could see that every atom in a molecule on the left in this reaction corresponded to one on the right that had the same nearest and next nearest neighbor. I then looked at many examples of other pairs of compounds, which I termed conformal pairs and found that the total of heat of combustion of a pair was approximately the same as its conformal pair [97]. 

It is very important to realise that the affinity of the condensed substances is measured by an expression which involves the concentrations of the saturated vapours together with the equilibrium constant characteristic of the same reaction in the gaseous state This conclusion depends upon the assumption that the pressure or concentration of a saturated vapour is a true measure of the reactivity of the condensed substance The above expression is of great impoitance foi it allows us to calculate the affinity of condensed reactions from measurements made upon the substances m the gaseous state This point will be referred to again in discussing the application of Nernst s Heat Theorem to gaseous reactions... 

Equilibrium Measurements. Measurements of the temperature dependence of equilibrium constants of reactions involving transition metal-alkyl bond disruption yield values of aH from which BDE s can be deduced through appropriate thermodynamic cycles. The first example of this application involved the determination of the Co-C BDE of Py(DH)2Co-CH(CH )Ph from measurements of the equilibrium constant of reaction 17, according to Equations 17-19 (28,29). 

With diatomic molecules, energies of dissociation may be determined in various other ways. One method depends upon the variation with temperature of the equilibrium constant of the dissociation, and application of the thermodynamic relation din JT/dT = AUjBT, A second method involves determinations, based upon measurements of explosion temperatures, of the apparent specific heat of the partially dissociated gas. 

Another case that is important in many applications involves the motion of a drop in a liquid containing a surfactant, which can be adsorbed at the drop s surface [2]. The motion of the drop results in that, due to the constant stretching of the surface, the surface density of adsorbed surfactant molecules in the front part of the surface will be smaller than in the case of the drop s equilibrium with the solution. In the rear part of the drop, the surface density will exceed the density at equilibrium. Because, unlike the surface of a solid particle, the surface of a drop is mobile, the motion of the liquid will cause surfactant molecules to drift to the rear part of drop and accumulate there. Accumulation of surfactant results in a decreased surface tension in the rear part of the drop. On the other hand, the increase of surfactant concentration in the rear part leads to the appearance of a surface diffusion flux in the opposite direction - from the rear to the front. This... 

From the EQCM data (see Fig. 14.4), it may be concluded that the thermodynamic analysis in Eqs. 14.7-14.9 is likely to be applicable on the voltammetric time scale due to the slow rate of the dissolution/reprecipitatiOTi process involving Red (solid) and Red(ionic liquid). As per Eqs. 14.5 and 14.6, the processes that contribute to the voltammetry are assumed to be (1) oxidation of Red(solid) to Ox (solid), which is accompanied by charge neutralization involving the insertion of [PFe] (2) dissolution of [Ox][PFg](solid) with the equilibrium relationship between the dissolved species (Ox (ionic liquid)) and [PFg] (ionic liquid), and [Ox] [PFe] (solid) at the particle/ionic liquid interface being governed by the equilibrium constant K, and (3) reduction of solution-phase Ox" to solution-phase Red. Thus, overall the processes to be modelled are as follows ... 

The application of thermodjtnamics to chemical reactions enables equilibrium constants to be calculated from a knowledge of the macroscopic thermal, or microscopic molecular, properties of the reactants (A and B) and the products (C and D). Using statistical thermodynamics [20], the equilibrium constant for a reaction involving gas-phase species, can be expressed, in terms of the per unit volume partition functions, (q, /V), for the reactants and products, by... 

To test the applicability of the cross relation to HAT, a set of 17 organic reactions have been compiled in which cross and self-exchange rate constants have all been measured under similar conditions (the self-exchange rate for 9,10-dihydroanthracene (DHA) has been estimated by applying the cross relation).These reactions, indicated with a in Table 1.2, involve oxyl radicals abstracting H from O-H and C-H bonds. The equilibrium constants are either available under the same conditions or have been adjusted using the solvent corrections described below. 

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