Transformation equilibrium

AH = latent heat of transformation = equilibrium temperature (absolute). 

The wave and pulse patterns of nonreactive separation processes, as well as the integrated reaction separation processes illustrated above, can be easily predicted with some simple graphical procedures derived from Eqs. (4) and (5). The behavior crucially depends on the equilibrium function y(x) in the nonreactive case, and on the transformed equilibrium function Y(X) in the reactive case. In addition to phase equilibrium, the latter also includes chemical equilibrium. An explicit calculation of the transformed equilibrium function and its derivatives is only possible in special cases. However, in Ref. [13] a numerical calculation procedure is given, which applies to any number of components, any number of reactions, and any type of phase and reaction equilibrium. 

Fig. 5.7. Transformed equilibrium function of a reactive distillation process with a reaction of type 2 A B + C and a mixture with constant relative volatilities (schematic)...

In summary, we find that the transformed equilibrium function provides useful insight not only into the steady-state behavior but also in to the transient behavior. This was illustrated here with a very simple example. However, an application to more complicated examples is straightforward, as shown in Ref. [13]. 

Figure 2.4 illustrates how the transformed equilibrium Gibbs free energy ArG ° varies with pH of the solution. Because of the hydrogen ion generated in the reference reaction of Equation (2.13), the reaction becomes more favorable as pH increases. Near pH of 7, the ArG ° is approximately —36 kJ mol-1. 

Figure 2.4 Transformed equilibrium Gibbs free energy as a function of pH, predicted from Equation (2.17), using the reference Keq = 0.1, and the pK values from Table 2.1.

Here (A rG °)j is the standard transformed equilibrium Gibbs free energy for reaction j, which may be obtained from a standard chemical reference source. 

Since the stability condition for a chemical reaction is (dA/de) < 0, the heat capacity at constant composition is always less than the heat capacity of a system that remains in equilibrium as it receives heat. Certain fluid molecules, such as supercooled liquid glycerin, can vibrate but not rotate freely, which is called libration. As the temperature increases, more molecules rotate, and the variable s becomes the extent of libration-rotation transformation. If the transformation equilibrium is reached rather slowly, the heat capacity (Cp e) will be lower than the heat capacity measured in slow heating. 

In muscle tissue or gl-aph preparations reaction GL-(-PU iAL- -KQ proceeds with equal velocity from either side and reaches equilibrium at 50% transformation (equilibrium constant=1) in less than 10 minutes with pigeon breast muscle (34), in 60 minutes with g -aph (115). th Cohen s enzyme preparation (60) equilibrium was not attained in 2 hours, but the ratio of initial reaction velocity constants (monomolecular)... 

Equation (F.8) shows that can be developed in a Taylor s series about the transformed equilibrium positions (g ) as well, but the variables are now the transformed displacements Su( ). Confining ourselves to the harmonic energy, we therefore obtain... 

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