Thermodynamic equilibrium constant relating free-energy change

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. 

It is important to note that, for any given temperature, the [thermodynamic] equilibrium constant is directly related to the standard change in free energy. Since, at any given temperature, the free energy in the standard state for each reactant and product, G°, is independent of the pressure, it follows that the standard change in free energy for the reaction, AfG°, is independent of the pressure.g Therefore, at constant temperature, the equilibrium constant K. .. is also independent of the pressure. That is,... 

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)... 

The retention factor is related to the thermodynamic equilibrium constant K for solute binding by k = (IK, where f is the phase ratio of the column. The free-energy change for the chromatographic process is expressed by... 

Perhaps the most important equation relates the thermodynamic equilibrium constant K° to the standard free energy change AG° of the reaction ... 

The free energy change (AG°) associated with this process is a measure of the relative stability of the HG complex. For a complex that forms spontaneously, that is, self-assembles in the solution phase, AG° < 0. The free energy is related to the association equilibrium constant by the well-known thermodynamic equation ... 

An important thermodynamic result is that the free-energy change can be related to the reaction equilibrium constant. Begin by considering again the reaction of Eq. 9.3, which describes chemical conversion of A and B to X and Y in the molar ratios shown. If the reaction proceeds by some infinitesimal amount dS, then the number of moles of each chemical species changes by an amount... 

We have from equilibrium thermodynamics Relation 3.50 between standard free-energy change, AG°, and equilibrium constant, K, and from transition-state... 

The thermodynamic equilibrium constants are related to the overall standard unitary free energy changes associated with the transfer of the solutes from the mobile to the stationary phase such that... 

Section 14.7 discusses direction of change from the point of view of thermodynamics, relating Q to the Gibbs free energy change and the equilibrium constant. 

Thermodynamics The equilibrium constant for dissolving an ionic substance is known as the solubility product. It is related to a Gibbs free energy change that depends on a balance of lattice energy and solvation energies, together with an entropy contribution. 

Thermodynamic data give us a means of quantitatively expressing stability. Now we need to explore the relationship between structure and reactivity. The quantitative description of reactivity is called chemical kinetics. A fundamental thermodynamic equation relates the equilibrium constant for a reaction to the free-energy change associated with the reaction ... 

In thermodynamic terms, the equilibrium constant is related to the free energy change (AG°) of the reaction... 

Finally, the quasi-equilibrium statistical thermodynamics part of Equation (8.107) may be substituted for by the standard expression relating equilibrium constant to a standard Gibbs free energy change for the equilibrium (see Chapter 7), with the result that Equation (8.107)... 

It is known from thermodynamics that the equilibrium constant of a chemical reaction is related to the standard free energy change by the equation... 

Solvation of ionic materials is based on an equilibrium constant known as the solubility product. It arises from thermodynamic considerations and is directly related to the Gibbs free energy change (see Chapter 16). This in turn is related to three components lattice energy (see Chapter 8), solvation energy (see Chapter 8), and entropy (see Chapter 9). 

The equilibrium position is dictated by the thermodynamics of the reaction, and the equilibrium constant is directly related to the standard free energy change for the reaction. So we can determine equilibrium constants from tabulated thermodynamic information. Alternatively, experimental measurements of K can also provide a route to thermodynamic data. 

Practical separations with a porous column packing in SEC are performed close to equilibrium conditions. Elutions are performed at flow rates around 1 mL/min when Yr is independent of flow rate. Although many theoretical models have been proposed for polymer separations in SEC, thermodynamic treatments provide a sound representation of separation behavior. For a separation operating at equilibrium conditions, the standard free-energy change AG° for the transfer of solute molecules from the mobile phase to the stationary phase at constant temperature T is related to Ksec by... 

One of the most important results of chemical thermodynamics is an equation relating the standard free-energy change for a reaction to the equilibrium constant. Before we look at this equation, we must discuss the thermodynamic form of the equilibrium constant that occurs in that equation. 

The standard free-energy change, standard emf, and equilibrium constant are all related. Knowing one, you can calculate the others. Electrochemical measurements can therefore provide equilibrium or thermodynamic information. 

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