Solubilities, van't Hoff factor, and Ksp

[jaybird12]

I understand quantitatively why when a compound with a given Ksp dissociates into more particles, the solubility increases. Ksp = 4x^3 instead of Ksp = x^2 and all that. But for some reason, I can't understand it qualitatively. Can someone explain why compounds that dissociate into more particles more soluble at the same Ksp?

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[Teleologist]

I understand quantitatively why when a compound with a given Ksp dissociates into more particles, the solubility increases.

Please clarify what you mean by this. I have no clue what this is saying.

Can someone explain why compounds that dissociate into more particles more soluble at the same Ksp?

Can you provide an example?

 

[jaybird12]

Sorry. What I mean is, I understand how the equations tell you that if you have two compounds with an identical Ksp, but one dissociates into 3 ions and the other only dissociates into 2 ions, the one that dissociates into 3 ions is more soluble.
For example, EK's 1001 Questions in Chem #534 asks for which compound is the least soluble in water. I initially narrowed it down to FeCO3 with a Ksp of 2.1 x 10^-11 and Ag2CO3 with a Ksp of 8.1 x 10^-12. If all the compounds dissociate into the same number of particles, you can directly compare the Ksp values, and the compound with the lowest Ksp value has the lowest solubility. But here, FeCO3 dissociates into 2 particles, and Ag2CO3 dissociates into 3, so you have to actually find the solubility (x) using the Ksp. FeCO3's Ksp = x^2, so solubility = 1.4 x 10^-11 mol/L. Ag2CO3's Ksp = 4x^3, so solubility = 1.3 x 10^-4 mol/L. FeCO3 is more soluble, as the equations show, even though it has a higher Ksp.
It's not a big deal because the equations can always show that a compound with a greater van't Hoff value is more soluble, but I'm trying to find a more fundamental or intuitive explanation as to why a compound that breaks into more particles is more soluble than another compound, even if they had the same Ksp.

 

[Czarcasm]

Sorry. What I mean is, I understand how the equations tell you that if you have two compounds with an identical Ksp, but one dissociates into 3 ions and the other only dissociates into 2 ions, the one that dissociates into 3 ions is more soluble.
For example, EK's 1001 Questions in Chem #534 asks for which compound is the least soluble in water. I initially narrowed it down to FeCO3 with a Ksp of 2.1 x 10^-11 and Ag2CO3 with a Ksp of 8.1 x 10^-12. If all the compounds dissociate into the same number of particles, you can directly compare the Ksp values, and the compound with the lowest Ksp value has the lowest solubility. But here, FeCO3 dissociates into 2 particles, and Ag2CO3 dissociates into 3, so you have to actually find the solubility (x) using the Ksp. FeCO3's Ksp = x^2, so solubility = 1.4 x 10^-11 mol/L. Ag2CO3's Ksp = 4x^3, so solubility = 1.3 x 10^-4 mol/L. FeCO3 is more soluble, as the equations show, even though it has a higher Ksp.
It's not a big deal because the equations can always show that a compound with a greater van't Hoff value is more soluble, but I'm trying to find a more fundamental or intuitive explanation as to why a compound that breaks into more particles is more soluble than another compound, even if they had the same Ksp.

It's sort of unusual that you're bringing up van't hoff factor here since that term is generally applied for colligative properties in general. Van't hoff factor represents the number of 'stuff' in a solution. In other words, the total number solutes that would dissolve in some substance/solvent, assuming it behaves ideally and would dissociate 100%. On a conceptual basis, the solubility of a salt probably has to do with lattice energy (kqq/r) and entropy changes within the solution it's dissolving in. It's a little bit complex to reason why something is more soluble than something else, at least for MCAT purposes. Should you have to make that comparison, it would probably be explained in a passage. As far as the comparison you're making though, the "x" term (molar solubility) is used to assess or compare relative solubilities of different compounds (including those that dissociate into more particles). We use this x term to make this comparison. Even though say, an MX3 salt may have more stuff in a solution than an MX salt, to say the MX3 salt is more soluble would be incorrect. It may have more stuff in the solution but can have a considerably lower molar solubility ("x" value). Not sure if this helps clear things up.

 

[Teleologist]

It's not a big deal because the equations can always show that a compound with a greater van't Hoff value is more soluble, but I'm trying to find a more fundamental or intuitive explanation as to why a compound that breaks into more particles is more soluble than another compound, even if they had the same Ksp.

Well, you won't find what you're looking for because your premise is incorrect.

Consider the hydrolysis of silver sulfide. We get four ions upon hydrolysis. Compare that to silver chloride, which, upon hydrolysis, only gives us two ions and nothing else. Silver sulfide is the much more stable salt however.

 

[jaybird12]

Okay, thanks!