Lipids are highly soluble in non-polar solvent but not in polar solvent like water. What is the explanation for this phenomenon from the point of view of their chemistry?
Lipids are non-polar molecules, due to the presence of long chain hydrocarbons. Organic solvents are non-polar solvents whereas water is a polar solvent. We know that, "like dissolves like". So, non-polar molecules are dissolved in non-polar solvents and vice-versa.
It depends on what you mean since fats, sterols, and phospholipids are all called lipids (see for more examples and info https://en.wikipedia.org/wiki/Lipid ). Because of this lipids can be roughly divided in two groups: completely hydrophobic or amphiphilic.
Obviously the first group will only be (completely) soluble in a non-polar (hydrophobic) solvent. While the amphiphilic ones are both hydrophobic and hydrophilic and will be soluble in a non-polar solvent and the most common example of amphiphilic lipids, the phospholipids, can form structures such as vesicles and membranes in aqueous environment. To what degree they are soluble in a hydrophobic solvent depends on how much the ‘balance’ between the hydrophobic and hydrophilic nature of the lipids ‘bents’ towards hydrophobic.
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PS. Take for example DOPG which is soluble in chloroform https://www.anatrace.com/Products/Lipids/LIPIDS/P216-DOPG and DMPG which is soluble in methanol https://www.anatrace.com/Products/Lipids/LIPIDS/D614 In other words DOPG has longer hydrophobic ‘tails’ (C18) than myristic acid (C14) and makes the amphiphilic DOPG more hydrophobic (and hydrophobic enough to be completely soluble in a hydrophobic solvent like chloroform.