We have now seen and used several expressions for the chemical potential of a substance or component in a mixture. For a one-component ideal gas we had

(1)where

For a mixture of ideal gases it can be shown that for each component,
*i*, the chemical potential is given by,

(2)For a nonideal gas we used the fugacity,

(3)For a mixture of nonideal gases it can be shown that,

(4)only now the fugacity of component

(5)For ideal solutions we found that,

(6)These expressions for chemical potential all have the form of a reference or standard state chemical potential plus

(7)The quantity,

All of the special cases we have been considering so far can be reconciled to this definition of activity. Thus, for an ideal gas mixture,

for a nonideal gas mixture, for an ideal solution, and so on. In a nonideal solution we would have to just write Equation 7 again,(7)In Equation 7 all the nonidealities of the solution are absorbed into the activity. We will see a more convenient way to write this below under the heading "activity coefficient."

We can find the activity of a component of a nonideal solution from measurements of the vapor pressure of that component in the vapor in equilibrium with the solution. We know that the chemical potential of a component must be the same in the vapor as in the liquid. that is, from Equations 2 and 7 we obtain,

(8a, b)but for pure component

(9)(Note: When dealing with liquid solutions it is customary to write the chemical potential of the pure liquid as

Subtracting Equation 9 from Equation 8b yields,

(10a, b)so that

(11)If the solution were ideal

**Activity Coefficient**

Sometimes it is convenient to write the activity as the product of an ideal part times a nonideality correction part. For example, in a real solution we might write,

(12)or, in a real gas we would write,

(13)so that

(14)In the latter case we already know that

(15)so that

(16)In the case of the nonideal gas γ → 1 as

(17)from which we conclude that for a nonideal solution,

(18)

In general, the activity coefficient is a unitless parameter that
contains all of the nonideality of a system.

WRS

From here you can:

Copyright 2004, W. R. SalzmanReturn to the local Table of Contents,

Return to the Table of Contents for the Dynamic Text, or

Return to the WRS Home Page.

Permission is granted for individual, noncommercial use of this file.

salzman@arizona.edu

Last updated 21 Oct 04

salzmanindex