Excess Properties

An alternative to the rather abstract partial molar property approach to solution nonideality is the "excess" property method, which describes solutions in terms of their deviations from ideal behavior. Using an A-B binary solution with enthalpy as the generic thermodynamic property, the excess property formulation for the solution enthalpy is:

The first two terms on the right represent the combined enthalpies of the pure components and hex is the excess enthalpy and is due solely to nonideality of the solution

Since the partial molar properties and the excess properties describe the same physical phenomenon, they must be related. The connection between hex and the partial molar enthalpies is obtained by equating the right hand sides of Eqs (7.16) and (7.21):

A direct connection between h A and hex can be obtained by substituting Eq (7.19) into the second term on the right-hand side of Eq (7.22), dividing the resulting equation by xB, and taking the derivative with respect to xA. This procedure yields:

Knowledge of hex as a function of xA gives hA - hA from Eq (7.23) and Eq (7.22) then yields h B - hB. The utility of this approach is that (at least for the enthalpy), the excess property is amenable to experimental determination.

Example: xA moles of pure liquid A and xB = 1- xA moles of pure B, both at temperature T, are mixed in a vessel maintained in a large water bath also held at temperature T. As a result of forming the solution, the temperature of the water bath is observed to increase by AT. How is this temperature rise related to the excess enthalpy of solution?

Upon combining the two pure components, the enthalpy of the solution is less than that of the pure components by hex. Because formation of the solution occurs at constant pressure, the First law (Sect. 3.4) requires that the enthalpy change appear as heat transferred from the solution to the water bath. This exchange of heat causes the water bath to increase in temperature. With CP denoting the specific heat of water, the excess enthalpy of the solution is:

A variant of this example is analyzed in problem 7.2.

Like partial molar quantities, excess functions apply to solution properties other than enthalpy: volume, internal energy, entropy, Helmholz free energy, and Gibbs free energy. As discussed in the next section, the last of these is particularly important.

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How to find excess properties in thermodynamics?
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