Answer:
The majority of the molecules move from higher to lower concentration, although there will be some that move from low to high. The overall (or net) movement is thus from high to low concentration.
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It is easiest to tell if a solution is saturated if there is residue on the bottom. If it crystallized, the solution is saturated. If it is a supersaturated solution, there will not be crystallization unless more of the solute is added, at which point all of it will crystallize.