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Colligative properties are properties that are affected by the number of solute molecules dissolved in the solution. True or false?

I think the statement is false, and the correct one should use "number of solute particles". I asked my TA and he said the molecule version is true, although I show him an example that $\ce{H2CO3}$ can dissolve water in many ways to create different sets of miles for $(\ce{CO3^2-},$ $\ce{HCO3-},$ $\ce{H+}).$ In this case, one mole of molecules $(\ce{H2CO3})$ can result in different total numbers of particles.

However, my TA said that $\ce{CO3^2-},$ $\ce{HCO3-},$ and $\ce{H+}$ can be considered as different molecules. I still don't satisfy with his answer though.

Could someone explain it for me, whether I am right or wrong.

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It's not good notation on the TAs part. IUPAC defines a molecule as having to be electrically neutral. I see what they are intending, but solute particles would be more correct. This is why, as you noted, compounds that dissolve into ions produce a greater effect than the number of original molecules would suggest and molecules that aggregate in solution have a smaller effect. Equations for colligative properties depend on the van't Hoff factor, which essentially converts from the original number of molecules to the number of distinct particles.

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True. Colligative properties depend only on the number of solute particles, not on the nature of the solute particles. This results in vapor pressure lowering, boiling point elevation, freezing point depression and change in the osmotic pressure.

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