English: Chemical potentials for various hypothetical non-ideal substances in solution. Since it is a log scale in mole fraction ${\displaystyle x}$, the ideal ${\displaystyle {\mu }_{\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{a}\mathrm{l}}(x)={\mu }^{\ominus }+RT\ln x}$ appears as a straight line. For each case an ideal line has been drawn with its offset ${\displaystyle {\mu }^{\ominus }}$ chosen to either align in the dilute (${\displaystyle x\to 0}$) or the pure (${\displaystyle x\to 1}$) limits.

The data shown are not for real substances but they do demonstrate realistic features. Their precise parameters were chosen more for graphical convenience.

In order top to bottom:

• An ideal liquid component in an ideal mixture.
• A non-ideal component that deviates positively (above pure-fixed ideal line), such as ethanol in water.
• A non-ideal component that deviates negatively (below pure-fixed ideal line), such as acetone in chloroform.
• A non-ideal solute such as sugar that has a saturation limit (maximum ${\displaystyle x}$). At this point the solute's chemical potential has risen above the chemical potential of the precipitate form (shown as a dot at ${\displaystyle x=1}$), therefore the solute preferentially exists as precipitate (i.e. phase separation would occur into saturated solution and precipitate).
• A non-ideal electrolytic solute such as salt, that dissociates into ions. This is notable for the significant deviations from the ideal line even at low-ish concentrations, due to a ${\displaystyle \sqrt{x}}$ contribution to the non-ideality ("ionic atmosphere effects" aka "salt effects"). This square root contribution makes it converge painfully slowly to the dilute limit, though it does so eventually. Also note that this is the average chemical potential per ion, e.g. for salt NaCl this would be the chemical potential ${\displaystyle \frac{1}{2}({\mu }_{{\mathrm{N}\mathrm{a}}^{+}}+{\mu }_{{\mathrm{C}\mathrm{l}}^{-}})=\frac{1}{2}{\mu }_{\mathrm{N}\mathrm{a}\mathrm{C}\mathrm{l}}={\mu }_{\frac{1}{2}\mathrm{N}\mathrm{a}\mathrm{C}\mathrm{l}}}$, and the chemical potential of NaCl itself would be twice this (with twice the slope!).

The corresponding plot of activity coefficients is here: Activity coefficients vs log mole fraction.svg