What is the driving force behind osmosis in biology?

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Let's say there are two parts in a container, one part is pure water and the other part is some solution. There is a membrane blocking the solution particles from moving to the other side. So eventually, water will be pulled to the solution side to make it less concentrated.

My question is, what is the force that pull the water to the other side?
 
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Welcome to PF, Youknowme.
Well, to start with, it has to be a semi-permeable membrane as opposed to a solid one. If the solution in question is saline, for instance, the membrane must have holes of a size that H20 can pass through but NaCl can't.
Unfortunately, I can't explain why the saline 'wants' to be diluted. Someone else here can, though.
 
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Isn't it purely statistical mechanics? There are vastly more 'mixed' states than totally separated states?
 
Yes. If there are "more" (higher concentration of) water molecules on one side, they are statistically more likely to pass through the membrane than water molecules on the other side.
 
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There are holes in the membrane that allow water to pass through. The water molecules move roughly, so two water molecules, one on each side, are each equally likely to happen to pass through the membrane.

And since there are more water molecules on one side than the other, overall there is more chance of water moving in that direction. The "force" is pressure and it comes from the kinetic energy and that random motion of the molecules. More water on one side than the other means more pressure.