Equilibrium constant nonideal behavior

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). 

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. 

To gain some appreciation for the effect of nonideal behavior on the calculation of equilibrium constants, consider the data in Table 6.5, which show the values of Kp (at 723 K) for the reaction... 

It is very important to note at this point that the equilibrium constants are customarily given without units. The reason for this is beyond the scope of this text, but it involves corrections for the nonideal behavior of the substances taking part in the reaction. When these corrections are made, the units cancel out and the corrected K has no units. Thus we will not use units for K in this text. 

The fundamental equation for the rate constant, Eq. (2-58), contains the assumption that the reactants (and the activated complex as well) are ideal, namely, that all components have activity coefficients of unity at all concentrations. The assumption of ideality is implicit in Eq. (2-57), in which the equilibrium constant K is related to concentrations rather than activities. For reactions in the gas phase the restriction to ideality is not, in general, a serious limitation, since departure from ideal behavior will be slight at the moderate densities commonly used. In solution, however, ionized solutes are far from ideal even at low concentrations, and even nonionized solutes exhibit significant nonideal behavior at concentrations frequently used in rate studies. 

Using commercial extractants at medium-high concentrations and eliminating purification processes usually imply a nonideal behavior of the liquid phases taking part in the extraction reaction. Thus, the thermodynamic equilibrium constant will be... 

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. 

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