Predicting temperature-dependent solubility for solvent selection

During the summer of 2010 I reported on the Solvent Selector web service that Andrew Lang and I constructed. The idea was to flag potential solvents with a high solubility for the reactants and a low solubility for the product, so that the work-up would require a simple filtration.

If available, the Solvent Selector service uses measured solubility values. If not available, it attempts to predict the room temperature solubility using one of two models based on Abraham descriptors.

We now have modified the Solvent Selector so that it takes into account temperature. Andrew has inserted a thermometer icon next to each solvent in the report. When clicked, a plot is displayed over the entire range of temperatures where the solvent is a liquid. Curves for each starting material and the product are provided - and hovering over a data point provides numerical values.

There are several ways this resource could be used by chemists.

For reactions where some starting materials are not soluble enough at room temperature, the reaction could be carried out at a higher temperature. A higher temperature might also be desirable simply to speed up the reaction. Being able to predict the solubility of the product at that higher temperature would allow the course of the reaction to be monitored by the appearance of a precipitate.

For reactions where the solubility of the product is too high at room temperature, the curves could be used to estimate how low one could cool the reaction mixture without any chance that one of the starting materials would precipitate out. For example, consider the following Ugi reaction.


An optimization study was performed and found that methanol and ethanol provided much better yields than THF.(see JoVE article) This makes sense from a solubility standpoint, where the Ugi product room temperature solubility is less than 0.05 M for methanol and ethanol but is 0.26 M for THF Solvent Selector results)


However, by clicking on the thermometer icon for the THF entry, one gets the following temperature curves for solubility.

By hovering over the curve for the Ugi product we find that the predicted solubility in THF at -78C (conveniently a dry ice in acetone bath) is 0.01M, while that for the starting material boc-glycine is 0.65 M, well above the 0.5 M concentration at the start of the reaction. This means that even if the reaction did not take place to a significant extent, we would not expect the starting material to precipitate at -78C. Any precipitate should be the pure product.

Of course another obvious application is for solvent selection for re-crystallization.

How it works

For some time now we have been collecting literature on the temperature dependence of solubility in various systems (live Mendeley collection here - be patient it might take a minute to display). Although equations vary depending on the specific approach there seem to be the following commonalities:

1. An assumption is made that miscibility is reached at the melting point of the solute.
2. The log of the solubility is linearly proportional to the inverse of the temperature in Kelvin.

I have looked into a few examples that we have of solubility over a temperature range and the above do seem to hold. This means that with only a room temperature solubility and a melting point for a given solute, the solubility at any temperature can be interpolated or extrapolated. (The concentration at the miscibility point is calculated from the predicted density of the solute divided by its molecular weight).

Although there are situations where two liquids are not miscible because of extreme dissimilarity (e.g. methanol and hexane), for the most part our experience shows that the first assumption is valid. Also, we are not correcting for changes in density for the solute or solvent at different temperatures. Nevertheless, when only a single solubility measurement in a given solvent and a melting point are known, this simple model may prove to be of use as a rough guide for reaction design or re-crystallization. We'll report on its practicality over time as we put it to use.