Osmosis is the process; it is essentially diffusion, which is a spontaneous (no energy input required) process as applied to water.
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Hydrolysis is incorrect; that describes a type of chemical reaction in which water breaks a chemical bond.
Photosynthesis is incorrect; that describes the complex process in which energy in light is converted into chemical energy.
Cyclosis is incorrect; that describes the movement of cytoplasm within a cell. There is no spontaneous, net movement of water across a concentration gradient.
This is a very well written essay if I do say so myself I think your teacher will enjoy reading it cause I know I did... And I hope your teacher is proud because not many people walk away from a class with the amount of information by which you have attained you did great :)
