Equilibrium constant nonideal systems

The low equilibrium constant and the strongly nonideal behavior that causes the forming of the binary azeotropes methyl acetate/methanol and methyl acetate/ water make this reaction system interesting as a possible RD application (33). Therefore, methyl acetate synthesis has been chosen as a test system and investigated in a semibatch RD column. Since the process is carried out under atmospheric pressure, no side reactions in the liquid phase occur (146). 

In each case these parameters represent differences between the state function of the activated complex in a particular standard state and the state function of the reactants referred to in the same standard state. One is giving all the characteristics of a thermodynamic equilibrium constant, although it should be multiplied by a transitional partition function. For ideal systems the magnitude of AH° does not depend on the choice of standard state, and for most of the nonideal systems that are encountered the dependence is slight. For all systems, the magnitudes of AG° and AS0 depend strongly on the choice of standard state, so it is not useful to... 

In earlier sections we have dealt with a variety of methods for determining the chemical potential of species in nonideal solutions. This now provides the groundwork for the study of equilibrium constants. As might be expected, the large variety of ways in which these chemical potentials may be specified is reflected in many different ways for defining equilibrium constants. As usual, care will have to be taken to ensure that these different specifications will actually lead to identically the same characterization of a given physical system. 

Up to this point in our discussion of the equilibrium phenomenon, we have assumed ideal behavior for all substances. In fact, the value of K calculated from the law of mass action is the true value of the equilibrium constant for a given reaction system only if the observed pressures (concentrations) are corrected for any nonideal behavior. 

The equilibrium constant for the generalized reaction may be written in terms of partial pressure p if the components are behaving as ideal gases or thermodynamic functions as activity a or fugacity / may be used for nonideal systems. 

However, we know that the use of equilibrium constants based on concentration is correct only for ideal systems. For reactions at high pressure or in solution, the nonideality of the reaction mixture becomes important and equilibrium constants... 

The low equilibrium constant and the strongly nonideal system thermodynamics that gives rise to the binary azeotropes methyl acetate/methanol and methyl ace-... 

Extension to a nonideal system Minimization of free energy Thermodynamics of reactions in solution Partial molar properties Medium and substituent effects on standard free energy change, equilibrium constant, and activity coefficient General considerations Solvent and solute operators Comments... 

The application of thermodynamics to electrochemical systems also helps us understand potentials at nonstandard conditions and gives us a relationship with the equilibrium constant and reaction quotient. However, we understand now that concentration is not necessarily the best unit to relate to the properties of a solution. Rather, activity of ions is a better unit to use. Using Debye-Hiickel theory, we have ways of calculating the activities of ions, so we can more precisely model the behavior of nonideal solutions. 

For a determined reaction stoichiometry and initial reactant composition, write the equilibrium constant in terms of the extent of reaction for gas-phase, liquid-phase, and heterogeneous reactions for ideal or nonideal systems. 

Depending on the system at hand, the equilibrium ratio AT, may be either constant (as in Henry s law), or a function of temperature, pressure, and/or composition. In this book, the following phase equilibrium models are primarily models dealt with (1) constant relative volatilities, (2) ideal solutions using Raoult s law, and (3) nonideal solutions using a modified Raoult s law and the NRTL activity coefficient model, although other activity coefficient models are also applicable. Each of these three models is briefly discussed here. 

Using Equation 7-12, a curve can be established that shows the relationship between the liquid composition and the equilibrium vapor composition at a constant relative volatility. Figure 7-1 shows curves at a values of 1.4, 2.0, and 4.0, which represent separations of increasing ease. The equilibrium relationships between vapor and liquid compositions for some nonideal binary systems are shown in Figure 7-2. Curve I is a methanol/water system, and Curve II is a water/acetic acid system. Note that these curves no longer are symmetrical like those in Figure 7-1. 

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