Which process works by applying pressurized water against a semi-permeable membrane that traps salts and other minerals?

Reverse Osmosis.

Explanation:

This is the mechanisms of water purification for drinking water which is droven by the chenical potential of the solvent.

It involves the use of partiaiy permeable membrane to allow ions, water molecules, solvent molecules to pass through during purification

A pertial permiable menenrane in this prurifiction process is the membrane that allow only water molecules, ions and restricted other unwanted chemical contaminants from passing through it.