Solubility

The forces of attraction between particles are the key to understanding. These forces cause bond creation resulting in a release of energy.

Ionic substances tend to dissolve in water

If an ionic substance dissolves it is because the forces of attraction of the water molecules (polar) for the ions is greater than the force of attraction the ions have for one another. The water molecules have dipoles (partial separation of electrical charge) that are attracted to the opposite charges of the ionic substance. The partial negative charge on the oxygen of the water is attracted to the positive ions of the ionic substance and the partial positives on the hydrogens of the water are attracted to the negative ions. See demo

Examples - ionic

NaCl sodium chloride

Soluble because the force of attraction between the positive singly charged sodium and the singly negatively charged chloride ions is weaker than the bonds formed between the water and the ions.

Al₂O₃ aluminium oxide

Insoluble because the forces of attraction between the small 3+ aluminium and the small 2- oxide ions are much greater than the bonds that would be formed between the water and the ions

Ionic substances tend to dissolve in polar solvents

Covalent substances and non polar solvents

Covalent substances are held together by Van der Waal's forces. These forces get larger as the molecule increases in size and hence larger molecules are more difficult to dissolve. Non-polar solvents often have large relative molecular masses to help dissolve the non-polar solutes.

Examples of non-polar solvents

Polar solvents also attract other molecules through Van der Waal's forces but as polar solvents are usually very small molecules this attraction is very small.

Examples - covalent

Hexane + water

Consequently water attracts other water molecules much more so than water attracts, for example, hexane molecules. Hexane molecules attract other hexane molecules much more so than hexane molecules attract water. There is just no reason for the hexane to dissolve in water...and so it doesn't. Hexane is INSOLUBLE in water

Hexane + xylene

Hexane (C₆H₁₄ non-polar) however is attracted to xylene (C₈H₁₀ non-polar) - in fact slightly more so than it is attracted to other hexane molecules and so the xylene carres the hexane off into solution. Hexane is SOLUBLE in xylene.

Summary

Polar substances dissolve in polar solvents, non-polar substances dissolve in non-polar solvents. "Like dissolves like"