Equilibrium constant free energy change

For a system at equilibrium, the free energy change, AG, at constant temperature and pressure is zero. Let two phases, a and (3, of the same substance, in equilibrium at a temperature T and pressure P, be considered. If the two phases are reversibly converted into one another (a (3) by withdrawing or supplying heat, the system is always in equilibrium, and AG is zero. It readily follows that the molar free energy of the substance in the two phases in equilibrium is the same... 

At equilibrium the free energy changes associated with the second and third stages are zero. For the first stage at, constant temperature T ... 

Know the effect of temperature on equilibrium constants, free energy, and entropy and enthalpy changes. 

Here we have divided both sides of the equation by nF to isolate the cell potential in the equation. This equation also resembles the Nernst equation (Equation 13.4), and it is easy to see how it arises. At equilibrium, the free energy change is zero and the reaction quotient, Q, is equal to the equilibrium constant, K. 

Having calculated the standai d values AyW and S" foi the participants in a chemical reaction, the obvious next step is to calculate the standard Gibbs free energy change of reaction A G and the equilibrium constant from... 

It is known that the order of acidity of hydrogen halides (HX, where X = F, Cl, Br, I) in the gas phase can be successfully predicted by quantum chemical considerations, namely, F < Cl < Br < I. However, in aqueous solution, whereas hydrogen chloride, bromide, and iodide completely dissociate in aqueous solutions, hydrogen fluoride shows a small dissociation constant. This phenomenon is explained by studying free energy changes associated with the chemical equilibrium HX + H2O + HjO in the solu-... 

At equilibrium, the ratio of concentrations is an equilibrium constant, so we can write the standard free energy change for the process as... 

In any of these forms, this relationship allows the standard-state free energy change for any process to be determined if the equilibrium constant is known. More importantly, it states that the equilibrium established for a reaction in solution is a function of the standard-state free energy change for the process. That is, AG° is another way of writing an equilibrium constant. 

The equilibrium constants determined by Brandts at several temperatures for the denaturation of chymotrypsinogen (see previous Example) can be used to calculate the free energy changes for the denaturation process. For example, the equilibrium constant at 54.5°C is 0.27, so... 

Hexokinase catalyzes the phosphorylation of glucose from ATP, yielding glncose-6-P and ADR Using the values of Table 3.3, calculate the standard-state free energy change and equilibrium constant for the hexokinase reaction. 

The production of ammonia is of historical interest because it represents the first important application of thermodynamics to an industrial process. Considering the synthesis reaction of ammonia from its elements, the calculated reaction heat (AH) and free energy change (AG) at room temperature are approximately -46 and -16.5 KJ/mol, respectively. Although the calculated equilibrium constant = 3.6 X 108 at room temperature is substantially high, no reaction occurs under these conditions, and the rate is practically zero. The ammonia synthesis reaction could be represented as follows ... 

The standard free-energy change for a reaction M + X - MX is also related to the equilibrium constant for the corresponding reaction... 

Because the equilibrium constant, Keq, and the standard free-energy change, AG°, both measure whether a reaction is favored, they are mathematical related by the equation... 

What typically happens for an energetically unfavorable reaction to occur is that it is "coupled" to an energetically favorable reaction so that the overall free-energy change for the two reactions together is favorable. To understand what it means for reactions to be coupled, imagine that reaction 1 does not occur to any reasonable extent because il has a small equilibrium constant and is energetically unfavorable that is, the reaction has AG > 0. 

The equation just written is generally applicable to any system. The equilibrium constant may be the K referred to in our discussion of gaseous equilibrium (Chapter 12), or any of the solution equilibrium constants (Rw Ra, Rj, K, . . . ) discussed in subsequent chapters. Notice that AG° is the standard free energy change (gases at 1 atm, species in solution at 1M). That is why, in the expression for K, gases enter as their partial pressures in atmospheres and ions or molecules in solution as their molarities. 

One of the most important characteristics of a cell is its voltage, which is a measure of reaction spontaneity. Cell voltages depend on the nature of the half-reactions occurring at the electrodes (Section 18.2) and on the concentrations of species involved (Section 18.4). From the voltage measured at standard concentrations, it is possible to calculate the standard free energy change and the equilibrium constant (Section 18.3) of the reaction involved. 

As pointed out previously, the value of the standard cell voltage, E°, is a measure of the spontaneity of a cell reaction. In Chapter 17, we showed that the standard free energy change, AG°, is a general criterion for reaction spontaneity. As you might suppose, these two quantities have a simple relation to one another and to the equilibrium constant, K, for the cell reaction. 

Equations (9.7) and (9.8) define K, the equilibrium constant for the reaction.b It is sometimes referred to as the thermodynamic equilibrium constant. As we shall see, this ratio of activities can be related to ratios of pressure or concentration which, themselves, are sometimes called equilibrium constants. But K, as defined in equations (9.7) and (9.8), is the fundamental form that is directly related to the free energy change of the reaction. 

Furthermore, even if we accept the use of A s and B s as rate constants with a ratio determined by detailed balance, there are many problems associated with evaluating the free energy changes (see e.g. Ref. [26]) and it is unlikely that they are simply related to equilibrium crystals. 

In the introductory chapter we stated that the formation of chemical compounds with the metal ion in a variety of formal oxidation states is a characteristic of transition metals. We also saw in Chapter 8 how we may quantify the thermodynamic stability of a coordination compound in terms of the stability constant K. It is convenient to be able to assess the relative ease by which a metal is transformed from one oxidation state to another, and you will recall that the standard electrode potential, E , is a convenient measure of this. Remember that the standard free energy change for a reaction, AG , is related both to the equilibrium constant (Eq. 9.1)... 

There is a very special case for self-exchange reactions in which the left side of the equation is identical to the right side. Accordingly, there is no free energy change in the reaction, and the equilibrium constant ( fn) must be unity (Eq. 9.29). 

Enzymes accelerate reaction rates by lowering the activation barrier AGp. While they may undergo transient modification during the process of catalysis, enzymes emerge unchanged at the completion of the reaction. The presence of an enzyme therefore has no effect on AG for the overall reaction, which is a function solely of the initial and final states of the reactants. Equation (25) shows the relationship between the equilibrium constant for a reaction and the standard free energy change for that reaction ... 

The second law of thermodynamics states that the total entropy of a system must increase if a process is to occur spontaneously. Entropy is the extent of disorder or randomness of the system and becomes maximum as equilibrium is approached. Under conditions of constant temperature and pressure, the relationship between the free energy change (AG) of a reacting system and the change in entropy (AS) is expressed by the following equation, which combines the two laws of thermodynamics ... 

The standard free energy change can be calculated from the equilibrium constant... 

We need two equations. We calculate the free energy change for the reaction using Equation, and Equation links free energy with the equilibrium constant. 

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