Polystyrene and acetone are not soluble in water because they are non-polar substances.
A polar substance is a substance that has opposite charges on two ends of the molecule. In polar molecules, a dipole moment exists in the molecule and accounts for its interaction with water.
Water is a polar solvent. It can only dissolve polar molecules. Since polystyrene and acetone are both non-polar substances, polystyrene dissolves in acetone and not in water.
This agrees with the principle in chemistry that like dissolves like.
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