Equilibrium constants relationship with standard Gibbs energy

By starting with the relationship between standard Gibbs energy change and the equilibrium constant, the van t Hoff equation—relating the equilibrium constant and temperature—can be written (equation 13.25). With this equation, tabulated data at 25 °C can be used to determine equilibrium constants not just at 25 °C but at other temperatures as well. 

Keeping in mind the relationship between the standard Gibbs energy and the equilibrium constant, it is very easy to modify the Langmuir isotherm, taking into account the variation of AG g with 0. To do this, we replace AGj g in Eq. (11.4) by AG0 and combine with Eq. (11.10), to obtain... 

The Van t Hoff isotherm establishes the relationship between the standard free energy change and the equilibrium constant. It is of interest to know how the equilibrium constant of a reaction varies with temperature. The Varft Hoff isochore allows one to calculate the effect of temperature on the equilibrium constant. It can be readily obtained by combining the Gibbs-Helmholtz equation with the Varft Hoffisotherm. The relationship that is obtained is... 

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 ... 

Because it applies mostly to electrolytes, it is discussed in Chapter 15. Briefly, Helgeson models the behavior of solutes by developing equations for the standard state partial molar volume (Helgeson and Kirkham 1976) and standard state partial molar heat capacity (Helgeson et al. 1981) as a function of P and T, with adjustable constants such that they can be applied to a wide variety of solutes. If you know these quantities (V°, C°p), you can calculate the variation of the standard state Gibbs energy, and that leads through fundamental relationships to equilibrium constants, enthalpies, and entropies. 

The relationship (Equation 4.3) that correlates energy change with equilibrium constant involves standard enthalpy (AH°), temperature (K), and standard entropy (AS°) and is called the Gibbs standard free energy (AG°) ... 

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