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Polar Vs. Nonpolar and Oil vs Water

Hello,  I have become a little confused because of certain explanations on the web and in textbooks concerning polar and nonpolar molecules. It is my understanding that polar molecules attract one another (dipole-dipole), and that nonpolar molecules can also attract one another (London Dispersion). However, is it not true that non polar molecules will be attracted to polar molecules as well? It seems oversimplification to state that nonpolar molecules only attract nonpolar, and polar molecules only attract polar.

The reason I ask this is because nonpolar substances have transient charges, while polar molecules maintain their charge. Two nonpolar molecules with random transient charges versus one molecule with transient charge and a molecule with a steady charge (polar) lead me to believe that polar-nonpolar interactions would be stronger than nonpolar interactions were  it not for one thing: Polar molecules attract each other more strongly. Thus, water-oil would have better attraction than oil-oil were it not for the fact that water-water interactions through hydrogen bonding was so strong. Thus, the oil appears to be "repeled" when in all actuality it is excluded. Is this a correct train of thought? Are there instances other than oil and water that could better relay this concept? Thanks for your time.

All molecules have attractions between them in London forces (weak). So there is some attraction between non-polar oil moecules, though weak. Water is polar (permanently) and as well as London forces, there are the much stronger attractions which are dipole to dipole and specifically called hydrogen bonds. The London forces are not important.

You also have the problem that polar and non-polar do not mix, so oil floats on water so there is little interaction between them. Oil and petrol would mix as they are both non-polar with weak London forces between them. Water and ethanol (slightly polar because of the -O-H group) so mix because relatively strong hydrogen bonding occurs between the O of one molecule with the H of the other.