Dissolution Thermodynamics - What is the standard state in units of mole fraction?

I have recently been working on a project that involves the correlation of mole fraction solubility using the Apelblat equation (in simplified form: $\ln\chi = A +\frac{B}{T}$), which can allegedly be used to compute some of the standard state thermodynamic quantities associated with the dissolution process via the van't Hoff equation ($\Delta H\_s^{\circ} = -R \frac{d \ln K\_d}{dT^{-1}} = -R \frac{d \ln \chi}{dT^{-1}}$). This seems to be the common approach in the literature that I have seen so far, and doing a fit with some experimental data gives a fine fit and reasonable values for $\Delta H^{\circ}$ and $\Delta S^{\circ}$, but if we attempt to use the typical $\Delta G^{\circ} = -RT\ln K$ relation we run into some trouble due to the definition of the mole fraction unit. Essentially, since the mole fraction of solute in solution will always be less than unity, it appears that this "standard state" Gibb's free energy will *always* be positive. This appears to defy the obvious experimental observation that the solute dissolves at STP.


This causes questions to arise about what necessarily is meant for a standard thermodynamic change when working with mole fraction solubilities. Given how prolific this sort of analysis has been in the literature I have read, I am puzzled that this point seems to not have been explored very much. My initial instinct to resolve this issue to to convert the mole fraction to molarity, while multiplying the thermodynamic quantities found through the Apelblat coefficients by the same factor to get something more reasonable, but I am not sure how much this throws the entire idea of Apelblat correlation to the wind.


Anyways, my main question is **what is meant by standard state when working with units of mole fraction** in dissolution thermodynamics?


