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Does osmosis happens when we have osmotic pressure difference between the two solutions (that are connected by a membrane)?

Does osmosis happens when we have two solutions of different concentrations?

My professor told that osmosis happens because of the vapour pressure difference between the solutions. But I didn't understand what vapour pressure has to do with osmosis. Can you explain me that, please?

I've been thinking too and is the vapour pressure of a solution numerically equal to the osmotic pressure of that solution? I see this relation because I know the more concentred is the solution the bigger is it's vapour pressure... that's right?

How do I calculate vapour pressure? (Can I use p V = n R T?)

Does density of the solutions has anything to do with osmosis? And what about hidrostatic pressure?

Thank you for the help,

Rafael Andreatta