Example 4. Thermodynamic Properties of Mixtures

In the examples so far, we have only looked at the Controls, Recorder, and Txy Diagram tabs.  The other tabs show the macroscopic properties that the system exhibits.  Move the z and T controls so that you have a two-phase mixture.  Now examine some of the thermodynamic properties of this mixture.  First look at the Activity Coeffs. tab.  Can you explain in terms of the potential model

   Ubb > Urb > Urr     and     Sb > Sr

why the activity coefficients are so close to unity (the logarithm is close to zero)?  Notice that the infinite dilution value of log gamma for pentane is positive on this plot.  Think of a mixture of essentially all heptane molecules into which we have added only one or two pentane molecules.  Now which type of molecule would the neighboring heptane molecules like to have in their midst?   Because all of the interactions with the pentane molecule are rb and Ubb > Urb, the red molecule will not be bound as tightly in the heptane environment as a blue one would, and the red molecule is pushed out into the vapor phase more easily by blue molecules that want its place. Thus, pentane would exhibit positive deviations from Raoult's law as indicated by the activity coefficient greater than one. Similarly, in the infinite dilution limit for the blue molecules all of the interactions will be rb, and since Urb < Ubb, the blue molecules are more tightly bound than in the pure-component standard state and thus have an activity coefficient less than one in this limit.  What about the intermediate compositions where the activity coefficients in this case have the opposite sign of those at infinite dilution?  The net force on the molecule is not just a function of the relative potential energies of the molecules with which it interacts, but also a function of the relative number of those interactions.  It should be remembered that the pair potentials are really a function of the separation distance between the molecules and so it is a function of the relative numbers of such interactions and the distance over which they operate.  This will be a function of distance and the size of the molecules.  The intermolecular nature of the values of the activity coefficients in the intermediate composition regions can therefore be a fairly complex function of the local structure in the fluid and is not immediately observable from the simple 2-D simulations in this module.

Next look at the Excess G tab. Note that the excess Gibbs energy is fairly close to zero for this nearly idea system, but it is primarily negative indicative of negative deviations from Raoult's law.  This is of course consistent with the predominance of the negative values for the logarithms of the two activity coefficients over the majority of the composition range.  The Gibbs energy of mixing is fairly symmetric as it is predominated by the ideal mixing term.

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More Examples: Example 1 | Example 2 | Example 3 | Example 5