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This is in the case of extracting plant oil using a solvent extraction method for the purposes of biodiesel production.

In a paper, it is stated that increased oil yield may be due to the 'increase in oil solubility at a higher temperature' when cottonseed oil was extracted using hexane and ethanol (separately) as solvents. But it does not elaborate on why this occurs.

I had a search online, and I understand that the solubility of solids improve due to increased kinetic energy which allows the solute particles to gain more movement and break apart in the solvent. Gases seem to be the opposite. But what happens for liquids?

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It can have thermodynamic, kinetic and structural reasons.

Higher temperature helps to neglect energy difference between intermolecular bonds, what increase solubility. Entropy raise due mixing helps either. But during extractions, solubility is seldom the limiting factor.

The extraction rate depends on temperature. Regardless of if it is more soluble at higher temperature or not, it dissolves and gets extracted faster. With the same effort, one gets higher yield at higher temperature, unless there is a product deterioration at higher temperature.

Another factor may be stronger desintegration of plant structure to have better access to embedded oil.

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Gases are all infinitely miscible. Gaseous molecules can occupy the whole available volume, whatever their interactions. Liquids should have the same behavior. But they don't behave like gases. Sometimes they are not miscible. Why ? The reason is the existence of H-bonds ( or other van der Wals forces).

When water is to be mixed with another substance (solid or liquid), a lot of H-bonds have to be broken. And this operation requires a lot of energy. This may be accepted if enough new H-bonds are made between water and the new solute. This happens with substances like methanol and ethanol for example. Furthermore, entropy increases. But if the number of new H-bonds is too small, as with octanol or higher alcanols, Nature is reluctant to separate water molecules from one another. Not enough new H-bonds are created in the mixture. As a consequence, the two liquids stay separated, even though it is against entropy gain.

But at high temperature, H-bonds are not so strong in pure water. At boiling point, they nearly disappear. So it is easier to mix polar substances in boiling water than at room temperature.

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