Activity of solutions of condensed systems (liquid, solid)

5.10 Activity of solutions of condensed systems (liquid, solid)

Completely analogously to the fugacity in Eq. (3.79) we now define the activity \(a_k\) to describe non-idealities of mixing with respect to a component \(k\) in the mixture; for the chemical potential of component \(k\) we find

\begin{equation*} \begin{split} a_k &=\;\; x_k \gamma_k\\ \mu_k &=\;\; \mu_k^0 + R\,T\,\ln a_k = \mu_k^0 + R\,T\,\ln x_k + R\,T\,\ln \gamma_k = \mu_k^{id} + \mu_k^{ex}\\ \Rightarrow \mu_k^{id} &=\;\; \mu_k^0 + R\,T\,\ln x_k \quad \mbox{and} \quad \mu_k^{ex} = R\,T\,\ln \gamma_k \end{split} \label{eq:activity} \end{equation*}

(5.30)

Again we introduced an activity coefficient \(\gamma_k\) which is determined by \(\mu_k^{ex}\).
As we will see, the general problem is what kind of state is defined as standard:

For ideal samples: pure component, standard conditions.
For solvents of a liquid solution: pure component.
For solutes of a liquid solution: hypothetical standard.

For the standard state we always assume the pure component and \(\gamma = 1\).
For the notation of the standard states by convention ”A” is the solvent, ”B” is the solute, and ”*” indicates the pure phase.