[xx0numb0xx]

If I have a mixture of sodium chloride, sodium chlorate, and sodium perchlorate and want to calculate their molar ratio without chemically changing them, how would I go about doing it? This is what I have come up with so far:

Sodium chloride has a K_sp of about 37.9 at 25°C.
Sodium chlorate has a K_sp of about 90.04 at 20°C. (I couldn't find its solubility at 25°C)
Sodium perchlorate has a K_sp of about 293.0 at 25°C.

If I dissolved each together, then
Sodium chloride would have a K_sp of 6.16[Na⁺].
Sodium chlorate would have a K_sp of 9.489[Na⁺].
Sodium perchlorate would have a K_sp of 17.12[Na⁺].

I would VERY slowly add water to the mixture on a magnetic stirrer at 25°C until it completely dissolves. When there is just a small amount left, I would gently heat the solution, put it back on the magnetic stirrer, and wait for it to cool. If some of the salt precipitates out after the solution has cooled back down to 25°C, I would add a small amount of water and repeat the heating/cooling procedure. Once that is finished, I'll know how many grams of the mixture will dissolve per liter of water. That's where I'm stuck. How could I calculate the solubility of Na⁺ from that? Once I have that figured out, I could plug it in and solve for the various K_sp values and convert them into molarity, which I could convert into moles.

[Borek]

If I dissolved each together, then
Sodium chloride would have a K_sp of 6.16[Na⁺].

No idea what you mean by that.

I doubt you will be able to calculate anything and get any reliable result in such a concentrated solution. Our theory is good for diluted solutions, the more concentrated they get, the worse the results are. For really concentrated solutions experimental determination is the best approach I can think of.

[xx0numb0xx]

The K_sp of sodium chloride would be the product of the molar solubility of the sodium ions and chloride ions in question.

K_sp = [Na⁺][Cl^-]

The solubility of sodium chloride at 25°C is 359g/L or 6.16M, so

K_sp = 6.16 * 6.16.

The common ion effect will change the solubility of the sodium ions in question but not affect the solubility of the chloride ions. Therefore, the sodium ions become an unknown.

K_sp = 6.16[Na+]

Do you see where I'm getting at now? I'm just having trouble figuring out how to calculate the solubility of the sodium ions in sodium chloride from the mass solubility (g/L) of the mixture.

Regarding your comment about "our theory" not being very applicable in dilute solutions, that's just completely absurd, no offense. K_sp is meaningless in dilute solutions. K_sp is calculated and applied at the point of saturation, when the solution reaches maximum concentration. When a solution is dilute, there's no way to use K_sp.

[Borek]

The solubility of sodium chloride at 25°C is 359g/L or 6.16M, so

K_sp = 6.16 * 6.16.

The common ion effect will change the solubility of the sodium ions in question but not affect the solubility of the chloride ions. Therefore, the sodium ions become an unknown.

K_sp = 6.16[Na+]

OK, I see where you got it from. It won't work this way when you have several anions in the solution.

Regarding your comment about "our theory" not being very applicable in dilute solutions, that's just completely absurd, no offense. K_sp is meaningless in dilute solutions. K_sp is calculated and applied at the point of saturation, when the solution reaches maximum concentration. When a solution is dilute, there's no way to use K_sp.

AgCl has Ksp of 10^-10, so the saturated solution is 10^-5 M. Quite dilute, despite being saturated.

Do you know what ion activity is? Do you know what ionic strength of the solution is? Do you know how they are related? (hint: nobody knows, we have only some limited estimates).

[xx0numb0xx]

OK, I see where you got it from. It won't work this way when you have several anions in the solution.

If I used recrystallization to remove most of the sodium chloride, would I then be able to find the ratio of chlorate to perchlorate using solubility?

AgCl has Ksp of 10-10, so the saturated solution is 10-5 M. Quite dilute, despite being saturated.

So you're saying that using this technique isn't very effective for higher K_sp values? Is there another method I could use that's relatively simple and doesn't require too much equipment?

Do you know what ion activity is? Do you know what ionic strength of the solution is? Do you know how they are related? (hint: nobody knows, we have only some limited estimates).

I think ionic strength of a solution is related to the amount and charge of the ions in that solution. More ions give more ionic strength and ions with larger charges (such as Mg²⁺ or PO₄^3-) also give more ionic strength, right? I have no clue what ion activity is, though. A quick Google search didn't really help much, either. If I had to make a guess, I'd say that it's a measure of the ability for ions to react. Why? Is high ionic strength and activity related to making K_sp values ineffective when high?

[Borek]

The only approach I can think is the one involving Ksp and mass balances - that is, full equilibrium calculation.

And I strongly suggest you first learn about thermodynamic effects in highly concentrated solutions, Debye-Huckel theory, SIT (specific interaction theory) and so on.

Even using SIT I am not sure I would trust the calculation results.