Choices for Standard States in Gamma Methods

The gamma-phi and gamma-gamma methods involve activity coefficients, which measure how component fugacities in a real mixture deviate from those in an ideal solution. Many kinds of ideal solutions are available, and yet all have one common attribute every ideal solution has each fugacity linear in its mole fraction. 

But while we can pick any straight line and use it to represent an ideal-solution fugacity, in practice we always choose a line that intersects or lies tangent to the curve for the real fugacity at the standard-state pressure. This means that we choose fi%T, P°, x° ) = fi(T, P°, x° ) at some composition x then, at that composition, the activity coefficient must be unity. At other mole fractions, the fugacity of the ideal solution is given by the equation for the straight line. 

Here Ax, = X - x° and the derivative is constant with composition because it represents the slope of the ideal-solution straight line. For binary mixtures, this derivative is well defined but for multicomponent mixtures, it is not, because many ways exist to vary one mole fraction while constraining others. The resolution of this ambiguity provides alternative standard states for multicomponent mixtures, as we shall see. 

When we choose a standard state, we are merely identifying a particular ideal solution on which to base an activity coefficient. The standard state may be real or hypothetical, so long as it is weU-defined and so long as a value for its fugacity can be obtained. Ultimately the choice of standard state is made for computational convenience normally this means either that reliable models for y, exist, or else that the value of Yi is close to unity over the states of interest. When neither of these conditions pertain, we should consider changing the standard state. In many situations the appropriate choice is one of the possibilities discussed in 10.2.1-10.2.3 however, when the mole fraction is not a convenient measure of composition, such as occurs for mixtures of electrolytes or of polymers, then other standard states may be preferred. 

1 Fugacities Based on Pure-Component Standard States 

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