What is ideal solubility?

An explanatory video by Prof. Simon Gaisford – Pharma Drama

Welcome to Pharma Drama, the channel where we look at the science of healthcare and healthcare products. In this video I’m going to explain the concept of ideal solubility – so if that sounds ideal, get yourself a drink and then let’s make a start.

I have already discussed the concepts of solubility and dissolution – just click on the links to the videos and it would help a lot if you watched them before we discuss ideal solubility!

Assuming you’re OK with the concepts of solubility and dissolution, then I can remind you that the process of dissolution can be considered to proceed in two steps, each with an associated change in energy, and we note that the overall enthalpy of solution is the sum of the enthalpy of fusion and the enthalpy of mixing. One consequence of this is that the enthalpy of solution is influenced by the polymorphic form of drug, because different crystalline forms will have different melting temperatures and enthalpies of fusion. There is, however, another special case which we can consider and that is when the enthalpy of mixing is zero. In other words, this is when there is no net change in energy when solute molecules interact with solvent molecules. In this special case we say that mixing is ideal.

Ideal mixing is interesting because it means the enthalpy of solution is dependent only on the enthalpy of fusion of the dissolving solid and, although I won’t derive it here, it allows us to calculate the solubility of a compound directly if we know its melting temperature and enthalpy of fusion. We call this the ideal solubility, and it represents the solubility of the compound assuming the enthalpy of mixing is zero. One point to note is that the equation calculates the mole fraction of the solute – I know, mole fractions are a tricky concept and there’s a video on concentrations to help you with that! We only need the melting temperature and enthalpy of fusion of a material to calculate ideal solubility, and we can determine both of these values from a single differential scanning calorimetry measurement – this is very handy early in the preformulation stage of development when not a lot of material may be available.

Let me give you an example. The melting temperature of aspirin is 137 oC and its enthalpy of fusion is 28.80 kJ/mol. What is its ideal solubility? The calculation is shown on the screen – once we make sure all the units are correct, we find that the mole fraction of aspirin at ideal solubility is 0.037. If you prefer more conventional units, that’s 370g/L. In other words, if there was no enthalpy of mixing between aspirin and a solvent, we should be able to dissolve 370g of drug per litre.

How does that compare with the measured solubilities of aspirin in various solvents? You can see the numbers in the table on the screen. In THF the measured solubility is almost the same as the ideal solubility and in water it’s… absolutely nowhere near! What does this tell you about the type of interaction between aspirin and the various solvents? Let me give you a moment to think about that…

It tells you that the mixing interaction is almost zero (or ideal) in THF and gets increasing unfavourable as we go down the table (if mixing were favourable, the experimental solubility would be above ideal). It also tells you that the interaction with water is particularly terrible! This is seen a lot with pharmaceutical compounds. Water is a polar solvent, and unless the drug substance is polar the mixing interaction is usually unfavourable. Note also that THF and methanol are solvents that are frequently used to increase the solubility of poorly water-soluble compounds and I hope you can see from this table why that might be. I should note here though that ideal solubility only considers enthalpy of fusion and in reality there are other factors that may influence dissolution and solubility, including entropy, ionisation, dielectric constants and so on. Also, ideal solubility can’t be calculated for amorphous forms, as they have no enthalpy of fusion. Nevertheless, ideal solubility is an interesting parameter to calculate because when combined with actual solubility data it gives an insight into how the solute interacts (or not) with the solvent.

I said earlier that two polymorphs of a drug should have different ideal solubilities so let me show you an example. On the screen are data for two polymorphs of indomethacin – you can see each form has a different enthalpy of fusion and melting temperature. When their ideal solubilities are calculated you can see that they are in fact different. The form with the higher melting temperature has the lower ideal solubility (which makes sense – the only barrier to dissolution when ideal is breaking of molecules from the solid). This is one of the reasons different physical forms of the same drug have different solubilities!

Right, that’s all we need to know about ideal solubility. I hope that made sense. If it did, please hit the like button and consider subscribing as it really helps the channel. Otherwise, thank you so much for watching, and I’ll see you again soon.