A Concrete Example

To fix this idea even further, consider a brine solution with watery-ice and salty-water. The quantity of interest may be the temperature (or temperatures) that an average composition of $C_{\mbox{NaCl}} = 0.07$ has an icy-phase in equilibrium with a watery-phase. One possible state of the system may be:

$C^{\mbox{icy}}_{\mbox{NaCl}} = 0.0005$ and $C^{\mbox{watery}}_{\mbox{NaCl}} = 0.09$

which completely determines the phase fractions.

Note that this doesn't determine what the extent (i.e. $N^{\mbox{icy}}_{\mbox{total}}$ and $N^{\mbox{watery}}_{\mbox{total}}$) of the system is--it only produces derived intensive quantities.