what determine molecule's solubility or lack of solubility in water

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A: Please check my hand written answer

Osmosis

In simple words, osmosis is the slow, gradual movement of a liquid through a membrane. But there are nuances to this process. For instance, there has to be an imbalance in the distribution of solute in the liquid on either side of the membrane, which has to be semipermeable. The liquid in the region with a lower solute concentration moves to the region with a higher concentration, thereby displacing the solution in the process. The objective is to equalize the concentration of molecules on both sides of the membrane; the displacement of liquid can be viewed as a byproduct of this equalization. Since there is no energy required to carry osmosis, it is considered a passive process.