Equilibrium constant Gibbs free energy relationship

Equilibrium constant—Gibbs free energy relationship... 

Let us call the melt phase a and the solid phase with complete immiscibility of components y. P is constant and fluids are absent. The Gibbs free energy relationships at the various T for the two phases at equilibrium are those shown in figure 7.2, with T decreasing downward from Ty to Tg. The G-X relationships observed at the various T are then translated into a T-X stability diagram in the lower part of the figure. 

What is the mathematical relationship that relates the Gibbs free energy to the equilibrium constant. 

K can often be calculated from the relationships of thermodynamics, if the Gibbs free energy for the chemical reaction can be obtained. For a gaseous reaction in which the equilibrium constant Kp is determined from equilibrium pressures of each component, the following expressions may be written ... 

The two thermodynamic equations that are most useful for simple kinetic and binding experiments are (1) the relationship between the Gibbs free energy change and the equilibrium constant of a reaction. 

The thermodynamic criterion for the equilibria CaCO, ) = Ca0(,) + C02 (,) is AG ° = -RT n Kp, where AG° is the change in Gibbs free energy of the reactants and products in their standard state, R is the gas constant, and Kp is the equilibrium constant. For this equilibria, A p = pco, for pressure in units of atmospheres. Values for AG are tabulated in the form AG° = a+ bT combining these expressions yields an exponential relationship between the partial pressure of CO2 and temperature for the above equilibria. Complete derivations and discussion of these equations may be found in physical chemistry textbooks such as references [13] and [14]. 

Linear free energy relationship (LFER) — For various series of similar chemical reactions it has been empirically found that linear relationships hold between the series of free energies (-> Gibbs energy) of activation AG and the series of the standard free energies of reactions AGf, i.e., between the series of log fc (k -rate constants) and log K (Kt - equilibrium constants) (z labels the compounds of a series). Such relations correlate the - kinetics and -> thermodynamics of these reactions, and thus they are of fundamental importance. The LFER s can be formulated with the so-called Leffler-Grunwald operator dR ... 

Since the equilibrium distribution coefficient Kassoc l is related to the overall energy change in Gibbs free energy AGassoc, for the separation process carried out at constant pressure P and constant molar volume V of the solvent, then the capacity factor K, also takes on the well-known fundamental thermodynamic dependency through the relationships ... 

Equation (2-80) expresses the retention of an ionizable basic analyte as a function of pH and three different constants ionization constant adsorption constant of ionic form of the analyte (7 bh+) and adsorption constant of the neutral form of the analyte (T b)- These three constants describe three different equilibrium processes, and they have their own relationships with the system temperature and Gibbs free energy with respect to the particular analyte form. 

As shown above, the equilibrium constants are not fundamental quantities only the Gibbs free energy changes for a given reaction are unique. This, however, does not detract from the overall utility of equilibrium constants. Consider the relationships... 

Understand the relationships among Gibbs free energy, chemical potential, reaction quotients (Q), the equilibrium constant, and the saturation index SI). 

Hence, for the conditions under which most protein-hgand interactions are studied, Eq. 3.13 describes fhe relationship between fhe fhermodynamic parameter AG° and a reaction characteristic (fhe equilibrium constant) fhat can be measured experimentally. Because fhe change in Gibbs free energy is related to the change in enfhalpy and entropy by AG°=AH° - TAS°, Eq. 3.13 can be rearranged to... 

The numerical values of the equilibrium constants can of course be converted to standard Gibbs free-energy changes through the relationship ln(K) = —AG°/RT and it is frequently of interest to attempt interpretations of these free energies in terms of contributions of various individual interactions to the overall value. There... 

The relationship between the chemical equilibrium constant K and the Gibbs free energy is... 

In Section 17-12 we studied the relationship between the standard Gibbs free energy change, AG , and the thermodynamic equilibrium constant, K... 

Knowledge Required (1) The relationship of the change in Gibbs Free Energy, AG , and the equilibrium constant. (2) Interpretation of dJGf data to determine relative values of equilibrium constants. 

Skill 26.1 Recognize the relationships among enthalpy, entropy, Gibbs free energy, and the equilibrium constant. 

An equation that describes the quantitative relationship between the enthalpy, the entropy and the equilibrium constant was developed by J. Willard Gibbs, a professor of mathematical physics at Yale in the late nineteeth century. He defined a new quantity, now called the Gibbs free energy (G), which describes the balance between the enthalpy and entropy factors for a chemical reaction. 

The equilibrium constant at 25 °C is calculated directly from tabulations of the Gibbs free energy of formation. Once this value is known, the equilibrium constant can be calculated at any other temperature. To obtain the equation that governs the variation of the equilibrium constant with temperature, the starting point is ea. 00.5). which provides the relationship between the Gibbs free energy, temperature, pressure, and composition ... 

The measurement of formal potentials allows the determination of the Gibbs free energy of amalgamation (cf Eq. 1.2.27), acidity constants (pATa values) (cf. Eq. 1.2.32), stability constants of complexes (cf. Eq. 1.2.34), solubility constants, and all other equilibrium constants, provided that there is a definite relationship between the activity of the reactants and the activity of the electrochemical active species, and provided that the electrochemical system is reversible. Today, the most frequently applied technique is cyclic voltammetry. The equations derived for the half-wave potentials in dc polarography can also be used when the mid-peak potentials derived from cyclic voltammograms are used instead. Provided that the mechanism of the electrode system is clear and the same as used for the derivation of the equations in dc polarography, and provided that the electfode kinetics is not fully different in differential pulse or square-wave voltammetry, the latter methods can also be used to measure the formal potentials. However, extreme care is advisable to first establish these prerequisites, as otherwise erroneous results will be obtained. 

We leam to determine the standard reduction potentials based on the standard hydrogen electrode reference and use them to calculate the emf of a cell and hence the spontaneity of a cell reaction. A relationship exists between a cell s emf, the change in the standard Gibbs free energy, and the equilibrium constant for the ceU reaction. (19.3 and 19.4)... 

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