Equilibrium point of a reaction

The tools for calculating the equilibrium point of a chemical reaction arise from the definition of the chemical potential. If temperature and pressure are fixed, the equilibrium point of a reaction is the point at which the Gibbs free energy function G is at its minimum (Fig. 3.1). As with any convex-upward function, finding the minimum G is a matter of determining the point at which its derivative vanishes. 

A study of enzyme catalysis is a study of kinetics, which asks the question how fast However, enzymes cannot alter the outcome or direction of a reaction. For instance, if one were to add a small amount of sodium chloride to a large volume of water, we know that the end result will be that the salt will dissolve in the water. However, the time dissolution takes depends on a number of factors What is the temperature Is it being stirred This is kinetics. We also know that a swinging pendulum will eventually come to rest at its equilibrium point, which in this case is its pointing straight down toward the center of Earth. Kinetics describes only the time it takes to reach that point. Enzymes cannot alter the equilibrium point of a reaction, only the time it takes to get there. 

The general conditions which had been assumed to hold for catalytic reactions and which were used to determine whether a substance acted as catalyst, were given earlier in this chapter. They were evolved gradually as more and more reactions of this nature were studied, and it is not surprising therefore that this superstructure of conditions became top-heavy and that some of the conditions assumed to be essential in a catalytic reaction, at times were found not to hold. The question whether the equilibrium point of a reaction is changed by a catalyst is a case in point. If a catalyst only changes the velocity of a reaction, and exerts no other influence whatsoever, as assumed in the 6... 

Aqueous geochemists work daily with equations that describe the equilibrium points of chemical reactions among dissolved species, minerals, and gases. To study an individual reaction, a geochemist writes the familiar expression, known as the mass action equation, relating species activities to the reaction s equilibrium constant. In this chapter we carry this type of analysis a step farther by developing expressions that describe the conditions under which not just one but all of the possible reactions in a geochemical system are at equilibrium. 

Despite the authority apparent in its name, no single rate law describes how quickly a mineral precipitates or dissolves. The mass action equation, which describes the equilibrium point of a mineral s dissolution reaction, is independent of reaction mechanism. A rate law, on the other hand, reflects our idea of how a reaction proceeds on a molecular scale. Rate laws, in fact, quantify the slowest or rate-limiting step in a hypothesized reaction mechanism. 

The thermodynamic feasibility of a reaction with precipitating products can be assessed by comparing the mass action ratio to the equilibrium constant of a reaction. This requires estimation of solubilities, using melting points of reactants in combination with the reaction equilibrium constant [39]. 

Before we discuss redox titration curves based on reduction-oxidation potentials, we need to learn how to calculate equilibrium constants for redox reactions from the half-reaction potentials. The reaction equilibrium constant is used in calculating equilibrium concentrations at the equivalence point, in order to calculate the equivalence point potential. Recall from Chapter 12 that since a cell voltage is zero at reaction equilibrium, the difference between the two half-reaction potentials is zero (or the two potentials are equal), and the Nemst equations for the halfreactions can be equated. When the equations are combined, the log term is that of the equilibrium constant expression for the reaction (see Equation 12.20), and a numerical value can be calculated for the equilibrium constant. This is a consequence of the relationship between the free energy and the equilibrium constant of a reaction. Recall from Equation 6.10 that AG° = —RT In K. Since AG° = —nFE° for the reaction, then... 

The phenomenon of strong association can be viewed as a type of chemical reaction. Indeed, a method that is entirely equivalent to RCMC was developed independently by Smith and Triska [10], and based on the ideas of chemical equilibrium. Smith and Triska call their method the reaction ensemble. We shall refer to both reactive canonical Monte Carlo and the reaction ensemble methods as RCMC, since they are in fact the same. Taking the view of chemical equilibria, we can very concisely write the equations that determine the equilibrium point of a system with n phases and C components. For a system at constant temperature T and pressure p, equilibrium is reached when the total Gibbs free energy G is minimized ... 

It has long been known that the process of esterification may be enormously hastened by the addition of a strong add, such as sulfuric or hydrochloric acid. The equilibrium point of the reaction is not altered by the catalyst only the rate of esterification is increased. ... 

Conversely, if we were initially to add only C and D to the reaction vessel, calculation of the total free energy of the system as the reaction proceeded to form A and B would produce a curve of the form shown by the dashed line on the right-hand side of Fig. 3-2, In each case the reaction only proceeds spontaneously, or without any external help, as long as the value of Gf decreases. Because of this there exists, at a certain extent of reaction, a point where Gr is at a minimum. This point can be spontaneously reached from either the product or reactant side, and it is the equilibrium point of the system. Thus we may state that the equilibrium condition of a reaction is the point at which Gr is a minimum. Also, we may deduce that reaction in the direction that decreases Gr is spontaneous while reaction in the direction that increases Gr is not spontaneous or will not occur in a closed system. 

Equilibrium concentrations of a reaction represent the point of lowest free energy available to the system. 

In chemistry, the most important purpose of thermodynamics is to determine the equilibrium point of a chemical reaction and to predict whether a reaction is spontaneous under defined conditions. Thermodynamics cannot supply any information on the rate at which the reaction takes place. 

It is evident that the abrupt change of the potential in the neighbourhood of the equivalence point is dependent upon the standard potentials of the two oxidation-reduction systems that are involved, and therefore upon the equilibrium constant of the reaction it is independent of the concentrations unless these are extremely small. The change in redox potential for a number of typical oxidation-reduction systems is exhibited graphically in Fig. 10.15. For the MnO, Mn2+ system and others which are dependent upon the pH of the... 

Here, the sign of equality (=) has been replaced by the double oppositely directed arrows (s=) called a sign of reversibility. Such a reaction is called a reversible reaction. The reversibility of reactions can be detected when both the forward and the reverse reactions occur to a noticeable extent. Generally, such reactions are described as reversible reactions. The most important criterion of a reaction of this type is that none of the reactants will become exhausted. When the reaction is allowed to take place in a closed system from where none of the substances involved in the reaction can escape, one obtains a mixture of the reactants and the products in the reaction vessel. Every reversible reaction, depending on its nature, will after some time reach a stage when the reactants and the products coexist in a state of balance, and their amounts will remain unaltered for unlimited time. Such a state of a chemical reaction is called chemical equilibrium, and the point of such an equilibrium varies only with temperature. 

As equation 2.4.8 indicates, the equilibrium constant for a reaction is determined by the temperature and the standard Gibbs free energy change (AG°) for the process. The latter quantity in turn depends on temperature, the definitions of the standard states of the various components, and the stoichiometric coefficients of these species. Consequently, in assigning a numerical value to an equilibrium constant, one must be careful to specify the three parameters mentioned above in order to give meaning to this value. Once one has thus specified the point of reference, this value may be used to calculate the equilibrium composition of the mixture in the manner described in Sections 2.6 to 2.9. 

Brinkley (1947) published the first algorithm to solve numerically for the equilibrium state of a multicomponent system. His method, intended for a desk calculator, was soon applied on digital computers. The method was based on evaluating equations for equilibrium constants, which, of course, are the mathematical expression of the minimum point in Gibbs free energy for a reaction. 

The dissolution rate, according to the theory, does not depend on the mineral s saturation state. The precipitation rate, on the other hand, varies strongly with saturation, exceeding the dissolution rate only when the mineral is supersaturated. At the point of equilibrium, the dissolution rate matches the rate of precipitation so that the net rate of reaction is zero. There is, therefore, a strong conceptual link between the kinetic and thermodynamic interpretations equilibrium is the state in which the forward and reverse rates of a reaction balance. 

In geochemical modeling, we prefer to use rate laws that predict the net rather than the forward reaction rate, to avoid the possibility of a reaction running past the point of equilibrium and continuing in a simulation, impossibly, against the thermodynamic drive. The net reaction rate r is the difference between the forward rate, given by the rate law above, and the rate at which reaction proceeds in the reverse direction,... 

Several chemical geothermometers are in widespread use. The silica geothermometer (Fournier and Rowe, 1966) works because the solubilities of the various silica minerals (e.g., quartz and chalcedony, Si02) increase monotonically with temperature. The concentration of dissolved silica, therefore, defines a unique equilibrium temperature for each silica mineral. The Na-K (White, 1970) and Na-K-Ca (Fournier and Truesdell, 1973) geothermometers take advantage of the fact that the equilibrium points of cation exchange reactions among various minerals (principally, the feldspars) vary with temperature. 

And we see a further point the equilibrium constant K of a reaction is a direct function of A Gr according to the van t Hoff isotherm (Equation (4.55)). If the overall energy of reaction remains unaltered by the catalyst, then the position of equilibrium will also remain unaltered. 

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