Van't Hoff factor and Ksp

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Aug 31, 2017
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Hi, Could someone please explain what's the relation between Van't Hoff factor and Ksp?
I'm going through EK 1001 and the answer to question 556 says " It is wrong to compare Ksp's of salts that break up into different numbers of particles. For example, we can't compare the Ksp values for CaCO3 and Na2CO3, since they dissociate into two and three ions, respectively."

I've found a similar post to mine, but the answers didn't really help me:
Solubilities, van't Hoff factor, and Ksp

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Van't hoff is just a term to describe how many ions are present in a salt and is much more relevant when determining diffusion

Ksp = or 2s^2, 3s^3 etc
where s is solubility and the power/coefficient on the s is the amount of ions

If you had a different number of ions, you'd have drastically different Ksp values making the salts essentially incomparable
The van't Hoff Factor is utilized for colligative properties by accounting for the ways that the particles of a solute can break up into when interacting in solution.

For Ksp's, there's a reason that you can only compare them with regards to solubility when you have the same stoichiometric ratios. Write out a general Ksp solubility expression for CaCO3. You'd get Ksp = * = s^2. Now, do the same for Na2CO3. You'd get Ksp = [2s]^2 * = 4s^3. Suppose Ksp of CaCO3 was hypothetically 4. Suppose it was 6 for the Na2CO3. Try solving for s in both of these cases. You'd get a value of 2 for the first equation and a value of approximately 1.14 for the second equation. In other words, the stoichiometric ratios of the ions can make a significant difference in solubility. If you were to just compare Ksp's for two equations with different stoichiometric ratios, you could deceive yourself in what the true nature of the solubilities of the systems are.