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I know from class that water travels to where the solute concentration is higher. I have no problem visualizing it if it's just "salt." What if there are multiple types of solutes? For example, if solute A is more concentrated in the cell and solute B is more concentrated outside, which way would the water move? Is there something that takes into account multiple solute concentrations?

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The effects of multiple solutes are often considered additive, although things may get complicated at higher concentrations. In general one considers the effect of these solutes on the "activity" of water on both sides of the membrane. The difference in water activities results in an osmotic potential gradient.

There are two concepts that are useful to describe what you are interested in. One is osmolarity (or osmolality), which is the effective total concentration of solutes potentially resulting in osmotic pressure buildup across a membrane. The membrane may in this case be permeable to some of these substances however. A second concept is tonicity, which is essentially the same but considers only substances which are not freely transported across the relevant membrane. For an introduction to these topics you can read Ref. 1.

Related concepts are the total osmotic pressure and the colloid osmotic pressure$^2$. The first represents the osmotic pressure expected to result from all solutes (salts and colloids), both assumed unable to freely diffuse through the membrane. In the second case only the colloid is assumed unable to traverse the membrane.

Reference

(1) Vujovic, P.; Chirillo, M.; Silverthorn, D. U. Learning (by) Osmosis: An Approach to Teaching Osmolarity and Tonicity. Advances in Physiology Education 2018, 42 (4), 626–635. https://doi.org/10.1152/advan.00094.2018.

(2) Silbey, R. J.; Alberty, R. A.; Bawendi, M. G. Physical Chemistry, 4th ed.; Wiley: Hoboken, NJ, 2005.

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