Question

Question #4159a

Answer 1

You need to conside osmolarity, not molarity.

Explanation:

Osmosis is all about the movement of solvent particles through a semi-permeable membrane from a region of lower solute concentration to a region of higher solute concentration.

Solvent molecules moving away from a less concentrated solution will make that solution more concentrated. Likewise, solvent molecules moving into a more concentrated solution will make that solution more dilute.

This is important because the ratio that exists between the number of solute particles and the number of solvent particles in a solution will affect osmosis.

Osmolarity is used to determine exactly how many moles of solute particles, called osmoles, you get per liter of solution. In essence, osmolarity does not depend on what type of solute particles you have, but rather on how many of them you have.

In your case, calcium chloride, `"CaCl"_2`, and sodium chloride, `"NaCl"`, are both ionic compounds that dissociate completely in aqueous solution.

However, as you noted, the former produces 3 particles per formula unit, while the latter only produces 2 particles per formula unit.

This means that two solutions of equal molarities will have different osmolarities. Let's say that you have `"1-M"` samples of both solutions

`"For CaCl"_2: " "1color(red)(cancel(color(black)("mole CaCl"_2)))/"L" * "3 osmoles"/(1color(red)(cancel(color(black)("mole CaCl"_2)))) = "3 osmoles/L"`

`"For NaCl: " 1color(red)(cancel(color(black)("mole NaCl")))/"L" * "2 osmoles"/(1color(red)(cancel(color(black)("mole NaCl")))) = "2 osmoles/L"`

In this case, you can see that one liter of water will have a smaller solute-to-solvent ratio in the case of a calcium chloride solution than in the case of a sodium chloride solution.

So if your calcium chloride solution is isotonic with the potato, you can conclude that both this solution and the potato have the same number of solute particles per liter, i.e. the same osmolarity.

This means that the sodium chloride solution is actually hypotonic to the potato and the calcium chloride solution.

What molarity would be needed for the sodium chloride solution in order for it to be isotonic with the potato? Work your way backward to get

`3color(red)(cancel(color(black)("osmoles")))/"L" * "1 mole NaCl"/(2color(red)(cancel(color(black)("osmoles")))) = "1.5 moles/L"`

So, as a conclusion, two solutions of the same molarity that have different osmolarities will not be isotonic.