[Luckenberg99]

I am trying to find a correlation between the concepts written in the title. I am having some difficulties, so I would like to know if the following reasoning can be considered correct.

In general terms, a substance is polar when it has a non-zero total dipole moment, just think of water, chloroform, etc. However, when we talk about solubilities and solvents, it is not quite correct to estimate polarity through dipole moment alone, but it is more appropriate to use the dielectric constant: a high dielectric constant is associated with strongly polar substances, while a low dielectric constant is associated with low-polar or apolar substances.

This is shown by the fact that the dipole moment of water and chloroform are very similar, but their polarity is very different, as the dielectric constant of chloroform is very low, so it is an almost apolar solvent, although it has a dipole moment similar to water. Thus, it can be said that the dipole moment is more of a general and "physical" concept.

Having said that, it is possible to correlate what has been said with solubility: like dissolves like, so very polar substances (i.e., with high dielectric constant) will solubilize in equally strongly polar substances, as the molecules of each substance form similar intermolecular interactions with each other (in this case, the main interaction would be hydrogen bonding).

Conversely, apolar substances (with low dielectric constant) will solubilize in apolar substances (similar intermolecular interactions prevail: London interactions).

Thus, apolar substances will not dissolve in polar substances, because the intermolecular interactions formed between the molecules of each substance are different: for example, an alkane will not dissolve in water because water prefers to form stronger interactions with itself, rather than forming weaker interactions with the alkane.

What to do, however, when we don't have the dielectric constant? A little rule of thumb can be used to predict solubility: if there is one polar group in the molecule for every 4-5 carbon atoms, then the substance can be considered strongly polar and will be soluble in equally polar solvents (water). Beyond this limit, the substance will be soluble in less polar solvents, such as organic solvents.

Thank you for any feedback

[Enthalpy]

This only needs few refinements.

For polar molecules to build a liquid with high permittivity (water, glycol carbonate, etc), they must aggregate in big organized groups, on which kT acts less strongly. So while the dipole moment is a molecule's attribute, the permittivity depends strongly on the temperature and abnormally on the concentration.

This resembles ferromagnetism versus paramagnetism.

Hydrogen bonds organize groups more efficiently than the dipole moment does, yes, and this can increase the permittivity.

[Vidya]

I think the simple way of thinking is if the organic molecule has more electronegative atoms  or more OH groups then it has more polarity and is more soluble in polar solvent.

[Enthalpy]

Solubility in water near RT:
 5g/L CH₃Cl
17g/L CH₂Cl₂
 8g/L CHCl₃
0.8g/L CCl₄