[Loler]

Hello everyone,

This is probably pretty simple and I am just getting confused but it is not clear to me.

There is something I don't understand. The solubility of gypsum in pure water at 25°C is about 2g/L. That means, maximum concentration of 11.6 mM of Ca²⁺ and SO₄^2-.

What I don't understand is when I try to calculate what the concentration of Ca²⁺ and SO₄^2- would be from the solubility product constant (k_sp= 2.4x10^-5), I get around 5 mM of Ca²⁺ and SO₄^2-. So I don't understand what's going on here, why the difference between 5 mM and 11.6 mM?

[chenbeier]

What you calculated is correct.
I couldnt find an english webside of this problem.
On this german one it is mentioned.

http://www.aqion.de/site/165

At the end it says it has something to do with the activity coefficients and complesing of CaSO₄(aq)

Schlußfolgerungen

Die beiden Ergebnisse unterscheiden sich deutlich voneinander:
          
(10a)    analytische Lösung (mit Taschenrechner):    5.1 mM
(10b)    numerische Lösung (chem. Thermodynamik):    15.6 mM

Die Ursachen für das Versagen des analytischen Lösungsansatzes liegen vor allem in zwei Punkten:

    Vernachlässigung der Komplexbildung (insbesondere für CaSO4(aq))
    Vernachlässigung der Aktivitätskorrekturen (bei Ionenstärke I = 42 mM, γ = 0.48

[Enthalpy]

That paragraph claims that for CaSO₄, there is no effect by the activity coefficients
https://en.wikipedia.org/wiki/Solubility_equilibrium#Dissolution_with_dissociation

With gypsum, crystallization water needs a small correction, which does not explain the discrepancy.

Grain size of the solid has an influence too
https://link.springer.com/article/10.1134/S0016702917010062

[Borek]

That paragraph claims that for CaSO₄, there is no effect by the activity coefficients

I don't think it says anything like that, care to quote the exact statement you refer to?

Unless my back of the envelope calculations are wrong using ionic strength and activity coefficients is perfectly enough to get 11.1 mmol/L, quite close to 11.6. There are plenty of other equilibria involved, so the difference left doesn't look surprising at all.

[Enthalpy]

Did I read it improperly? Quoting
https://en.wikipedia.org/wiki/Solubility_equilibrium#Dissolution_with_dissociation
For 2:2 and 3:3 salts, such as CaSO4 and FePO4, the general expression for the solubility product is the same as for a 1:1 electrolyte
K_sp = [A][ B] = [A]² = [ B]²
and in the table,
Salt     p     q    Solubility S
CaSO₄    1     1    √Ksp

This would be a bizarre convention indeed. Have I been misled by Wiki? The CRC handbook computes K_sp from ΔG of reactions written like
Ca₂(SO₄)₂ 2(Ca²⁺) + 2(SO₄)^2-
which is more consistent with salts of unsymmetrical charges, and would also answer nicely the initial question.

But here for BaSO₄ and PbCrO₄
https://www.chem.purdue.edu/gchelp/howtosolveit/Equilibrium/Solubility_Products.htm
they only write, like Wiki,
K_sp = [Ba²⁺][SO₄^2-]
K_sp = [Pb²⁺][CrO₄^2-]

So I'm lost. Varying conventions?

[Borek]

The CRC handbook computes K_sp from ΔG of reactions written like
Ca₂(SO₄)₂ 2(Ca²⁺) + 2(SO₄)^2-

Haven't seen anything like that 

That is: it would be OK for a compound with Ca₂(SO₄)₂ formula, which - as far as I am aware - gypsum is not. I suppose they explain the convention and the reasoning behind somewhere.

But here for BaSO₄ and PbCrO₄
https://www.chem.purdue.edu/gchelp/howtosolveit/Equilibrium/Solubility_Products.htm
they only write, like Wiki,
K_sp = [Ba²⁺][SO₄^2-]
K_sp = [Pb²⁺][CrO₄^2-]

That's the way it was defined in all books I can think of.

Basically it is not different from any other equilibrium reaction, we just assume solid activity of 1, then for simple salts

A_nB_m nA^m+ + mB^n-

and

[tex]K_{sp} = [A^{m+}]^n[B^{n-}]^m[/tex]

(unless n and m are not coprimes, in which case coefficients become different, but it is trivial in general).

[Enthalpy]

The CRC handbook writes it over the table "Solubility product constants":
M_mX_n(s) mMⁿ⁺(aq) + nX^m-(aq)
without any explicit exception about m=n nor about non-trivial common divisors.
Then it goes on with ΔG for that reaction and deduces K_sp.

Is their reader supposed to understand that the equation is implicitly simplified for m=n like in CaSO₄?
That would be consistent with the online Purdue paper and with the Wiki article I quoted.

Or does the CRC's table keep m and n when they are equal? I believe so, because their ΔG mentions m and n moles together with the charges, I quote:
ΔG = mΔG(Mⁿ⁺,aq) + nΔG(X^m-,aq) - ΔG(M_mX_n,s)
and Log(Ksp) = -ΔG/(RT)
Then Ksp = [Ba²⁺]²[SO₄^2-]²
which reconciles Ksp and the solubility in Loler's data (which is also the CRC's data).

So my impression is that both conventions coexist when m=n or when m and n have a non-trivial common divisor.

[Borek]

Is their reader supposed to understand that the equation is implicitly simplified for m=n like in CaSO₄?

That would be my understanding, that's how we write reaction equations and formulas by convention - using the lowest integer coefficients.

If they go against that convention they should IMHO explicitly mention it, as it is asking for troubles.

What Ksp value do they list for BaSO₄?

[Enthalpy]

1.07×10^-10 BaSO₄
7.10×10^-5  CaSO₄
9.92×10^-29 FePO₄.2H₂O


I just wonder about the data...  In the "Physical constants of inorganic compounds" table in the CRC hdbk, 100cm³ of cold water dissolve
0.3g  of CaSO₄.1/2H₂O
0.24g of CaSO₄.2H₂O
How is that consistent? We can't prevent dissolved CaSO₄.1/2H₂O from crystallizing as CaSO₄.2H₂O, can we?

Explicitly mention it: perhaps the author meant that mMⁿ⁺(aq) + nX^m-(aq) was the most unequivocal way to tell it, but an additional word of caution would have been welcome to my opinion.

[Borek]

1.07×10^-10 BaSO₄
7.10×10^-5  CaSO₄

As far as I am aware these values are always quoted for the [X²⁺][SO₄^2-] product.

I just wonder about the data...  In the "Physical constants of inorganic compounds" table in the CRC hdbk, 100cm³ of cold water dissolve
0.3g  of CaSO₄.1/2H₂O
0.24g of CaSO₄.2H₂O
How is that consistent? We can't prevent dissolved CaSO₄.1/2H₂O from crystallizing as CaSO₄.2H₂O, can we?

You would need nucleation for the other type of crystal to grow up, so if the thermodynamics is right (doesn't make one of them much more stable) the other may not appear.

Explicitly mention it: perhaps the author meant that mMⁿ⁺(aq) + nX^m-(aq) was the most unequivocal way to tell it, but an additional word of caution would have been welcome to my opinion.

Yes.