Models for Chemical Potentials in Solutions

The are various models for the chemical potential in a solution; the simplest is the ideal gas.⁴

The following are definitions that will be used when we discuss solution behavior, but are useful to introduce in the context of ideal gases.

An Ideal Gas Mixture

$$\input{equations/mix-idg}$$ (20-13)

An Ideal Solution

In an ``ideal solution,'' the system is made slightly more complicated by allowing chemical potential to become a function of pressure.

$$\input{equations/ideal-sol}$$ (20-14)

A General Solution

In the general case, a new term (the activity $a_i$) is introduced to generalize the dependence on concentration:

$$\input{equations/gen-sol}$$ (20-15)

$a_i$ is called the ``activity of species $i$''--it is a ``generalized composition.'' Factoring out the $X_i$:

$$\input{equations/activity-def}$$ (20-16)

$\gamma_i$ is called an activity coefficient. In the most general case, it could also be a function of $c_i$, but limiting cases where it is independent of $c_i$ will be discussed later.