Convention I. The mole fractions of the components vary over a wide range (cannot distinguish between solvent and solutes).
To define the normal state, we drop the term $RTlnx_i\gamma_i$ in the equation, $\mu_i=\mu_{I,i}^{^0}+RTlnx_i\gamma_{I,i}$. To do this, we choose a state with, $\gamma_{I,i}\rightarrow 1$ and $x_i\rightarrow 1$, so that $lnx_i\gamma_{I,i}\rightarrow 0$.
The normal state $\mu_{I,i}^{0}=\mu_{i}^{\ast}$ is defined as component i being pure at the temperature and pressure of the solution.
Note that $\mu_i=\left(\frac{\partial G}{\partial n_i}\right)_{T,P,n_{j\neq i}}$ does not depend on the choice of the normal state. However, the activity and the activity coefficient do depend.
Convention II. It applies to solutions in which there is a solvent (A) and solutes (i).
- Solvent (A) \begin{equation} \mu_A=\mu_{II,A}^{0}+RTln\gamma_{II,A}x_A \end{equation} To cancel the Neperian term, we do $x_A\rightarrow 1$ and $\gamma_{II,A}\rightarrow 1$, thus we obtain an ideal dilute solution. Under these conditions $ln\gamma_{II,A}x_A=0$ and $\mu_A=\mu_{II,A}^{0}=\mu_{A}^{\ast}$. The normal state of the solvent is defined as pure solvent A at the temperature and pressure of the solution.
- Solute (i) \begin{equation} \mu_i=\mu_{II,i}^{0}+RTln\gamma_{II,i}x_i \end{equation} when $x_i \rightarrow 1$, $\gamma_{ II,i}\rightarrow 1$ it is true that $ln\gamma_{II,i}x_i=0$. $\mu_{i}^{0}$, is defined as a fictitious state that corresponds to the pure solute i in a state in which each molecule of i experiences the same intermolecular forces as an ideal dilute solution. The definitions of the rest of normal states are the same as in ideal dilute solutions.
For solute i the following holds: $\bar{V}_{II,i}^{0}=\bar{V}_{i}^{\infty}, \bar{H}_{II,i} ^{0}=\bar{H}_{i}^{\infty}, \bar{S}_{II,i}^{\infty}=(\bar{S}_i+RTlnx_i)^{\ infty}$
For an ideally dilute solution $\gamma_{II,A}=1, \gamma_{II,i}=1$