Extrema in free energy of a solution? I am a high school student reading about the second law of thermodynamics, and one of the equations given was the free energy change in dilution.
$$\Delta G_{\text{dil}} = -RT \log(C_1/C_2)$$
This implies that as you make a solution more dilute, the free energy decreases. However this equation does not take into account the entropy change in breaking a solid crystal, which I would expect to be highly positive as the crystal is a highly symmetric arrangement. Also it assumes ideal solution.
If we take into account the entropy change in breaking up the solid crystal, we see that the free energy increases while diluting, and also increases in breaking up the solid , that is, concentrating. So I would expect a minima in the free energy vs concentration curve. My guess is it might be the saturation point?
Is my reasoning correct? If it is, then is it possible to calculate the minima?
For Gibbs Free Energy, the standard equation is ΔG=ΔH−TΔS. The overall change in Gibbs Free Energy will depend, at least in part, on the enthalpy of dissolution for the specific substance. As for entropy, increasing entropy by breaking up the crystal decreases Gibbs Free Energy. The saturation point is where ΔG for the dissolution equals zero: where ΔH = TΔS. As ΔH and ΔS vary depending on the particulars of the solute and solvent, the saturation point also varies.
The equation you cite is specifically for when you have two solutions, so the dissolution of the solid is not described by it. Since the saturation point depends on the enthalpy of dissolution, you can't use the log equation to find it.