[xx0numb0xx]

Okay, so at 10°C, silver chloride has a solubility of about 0.001923g per liter of water, and silver carbonate has a solubility of about 0.03489g per liter of water. Converting grams to moles, we get a max of .00001342M for silver chloride and .0001265M for silver carbonate. Let's call concentration of silver chloride x and concentration of silver carbonate y.

If you have a y solution of silver carbonate, then maximum x can be calculated with an ICE box like so:

I		y		0
C		+x		+x
E		y+x		x

(.00001342)² = yx + x²

The same can be done to calculate maximum y in an x solution of silver chloride to get:

(.0001265)² = xy + y²

But now you have two equations and two variables, so it's possible to solve for the variables. You end up with .000001416M for silver chloride and .0001258M for silver carbonate. What do these values mean?

[xx0numb0xx]

I just realized that silver carbonate's formula is Ag₂CO₃ and not AgCO₃. For simplicity's sake, let's replace silver carbonate in this example with a magical silver salt that somehow has the same exact solubility as silver carbonate but has an anion with a -1 charge.

[Borek]

That's not how you do these things. Do you know what Ksp (solubility product) is?

[xx0numb0xx]

That's not how you do these things. Do you know what Ksp (solubility product) is?

Yes, it's the product of the molar solubilities of each ion in the compound, isn't it? So what did I do wrong here?

The K_sp of silver chloride in pure water would simply be its maximum molar concentration squared. The K_sp of silver carbonate would be two times the maximum molar concentration cubed. I did do that part incorrectly, but I mentioned that error in the second post.

For the silver chloride example, after K_sp is calculated, you simply set it equal to the concentration of Ag⁺ at equilibrium (x + initial concentration y) multiplied by the concentration of Cl^- at equilibrium (just x) to get, as I posted before, (.00001342)² = yx + x². What am I doing incorrectly, (besides my mistake with silver carbonate)?

[Borek]

Yes, it's the product of the molar solubilities of each ion in the compound, isn't it?

No, there is no such thing as "molar solubility of an ion".

[xx0numb0xx]

No, there is no such thing as "molar solubility of an ion".

So my terminology is off. That doesn't affect the way I calculated these numbers. I still don't see what I did wrong, and I still want to know if there is any significance to this crossing point of the two equations.

[Borek]

It is not your terminology that is off, it is your understanding of how solubility product works. Please try to read on the subject.

[xx0numb0xx]

It is not your terminology that is off, it is your understanding of how solubility product works. Please try to read on the subject.

I just didn't know how to describe K_sp. I did say "each ion in the compound" and not just "each ion." What I meant was that, for example, in sodium carbonate, which has a molar solubility of .0001265M, the carbonate ion dissolves just as much as the sodium carbonate, so you could say its solubility in sodium carbonate is also .0001265M. For every unit of sodium carbonate that dissolves, two sodium ions dissolve, so you could say it's twice as soluble, having a solubility of 0.0002530M in sodium carbonate. These numbers change when the ions are in different pairs, so the ion itself obviously does not have a solubility. Do you see where I'm coming from? I understand that an ion itself does not have a solubility. I know how to calculate K_sp. I know that it's an equilibrium constant. I know that it describes a saturated solution, where the rate of dissolution and precipitation of a compound are equal. What am I missing, great, wise, and critical Borek? I aspire to achieve your wisdom.

If you could just give me some tips on which aspects of solubility product to read about instead of just telling me to read on the subject, I'd greatly appreciate it.

[Borek]

What am I missing, great, wise, and critical Borek?

You are missing fact that concentrations don't have to be related by stoichiometry. Ksp for AgCl is 10^-10, so in the 1 M solution of HCl concentration of Ag⁺ is just 10^-10 M. When you dissolve several salts with a common ions you will get hit by so called common ion effect. This is what every reasonable general chemistry book will teach you in its solubility/Ksp chapter, and as it is explained quite good in many places I don't see a single reason to write about it again.