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From what I understand, RO is able to remove (or at least considerably reduce) the salts dissolved in water.

But thinking about it just doesn't make sense. RO works by filtering the solution using a membrane with pores so fine that only water can go through them. But elemental ions are WAY smaller than molecules of water.

So how does RO prevents salts from going to the other side?

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  • $\begingroup$ Are you sure those ions are way smaller? Especially if you consider their aqueous layers around them necessary to stabilize their charge? $\endgroup$ – Greg Mar 27 '17 at 23:53
  • $\begingroup$ Elemental ions are definitely not WAY smaller than molecules of water. Besides, they are charged. $\endgroup$ – Ivan Neretin Mar 28 '17 at 5:53
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The short answer is pressure. What you've described above is basically just osmosis, and without applied pressure to overcome the osmotic pressure of the system, reverse osmosis doesn't happen.

This Wikipedia article gives a good description of the concept, and the difference between filtration, osmosis and reverse osmosis:

Osmosis is a natural process. When two solutions with different concentrations of a solute are separated by a semipermeable membrane, the solvent has a tendency to move from low to high solute concentrations for chemical potential equilibration.

Formally, reverse osmosis is the process of forcing a solvent from a region of high solute concentration through a semipermeable membrane to a region of low solute concentration by applying a pressure in excess of the osmotic pressure. The largest and most important application of reverse osmosis is the separation of pure water from seawater and brackish waters; seawater or brackish water is pressurized against one surface of the membrane, causing transport of salt-depleted water across the membrane and emergence of potable drinking water from the low-pressure side.

The membranes used for reverse osmosis have a dense layer in the polymer matrix—either the skin of an asymmetric membrane or an interfacially polymerized layer within a thin-film-composite membrane—where the separation occurs. In most cases, the membrane is designed to allow only water to pass through this dense layer, while preventing the passage of solutes (such as salt ions). This process requires that a high pressure be exerted on the high concentration side of the membrane, usually 2–17 bar (30–250 psi) for fresh and brackish water, and 40–82 bar (600–1200 psi) for seawater, which has around 27 bar (390 psi)[6] natural osmotic pressure that must be overcome.

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