Systematic Treatment of Molar Solubility

[Big-Daddy]

How do we systematically calculate the molar solubility of a substance with regards to its K_sp? In other words, where does the value of "molar solubility" fit into the equilibrium calculations?

This should build up so that I can understand how to systematically treat the common ion effect, among other equilibria, if necessary. For example, if I want to know what the molar solubility is of my salt when, if it dissolves, it will undergo hydrolysis of the anion, or complex formation, or both (so we would need to consider acid/base equilibria and K_f at the same time as K_sp), how do I set up the equilibrium expressions to solve to get my molar solubility? This would come from an understanding of how exactly to calculate "molar solubility" in relation to equilibria in general.

I suspect that a major step is to note that Ksp = the equilibrium concentrations of the two ions of the salt, to the power of their coefficients in the molecular formula respectively, multiplied together, ONLY when the molar solubility is actually reached - until then, their equilibrium concentrations will multiply to a lower value than the Ksp only. That still leaves me unclear as to exactly what "molar solubility" is and how we would go about calculating it in situations with many equilibria going around.

 

[Borek]

This is not different from the general equilibrium calculations that we discussed in the past. Ksp is just one of the equilibrium equations, that has to be used together wit all other equilibria, mass balances and charge balance. Molar solubility is something that you can easily calculate AFTER you know all equilibrium concentrations. If, for any reason, solution is not saturated then yes, Q < Ksp.

 

[Big-Daddy]

This is not different from the general equilibrium calculations that we discussed in the past. Ksp is just one of the equilibrium equations, that has to be used together wit all other equilibria, mass balances and charge balance. Molar solubility is something that you can easily calculate AFTER you know all equilibrium concentrations. If, for any reason, solution is not saturated then yes, Q < Ksp.

1.) OK, so if the solution is not saturated then we cannot use the K_sp expression in the equilibrium calculations. However, this would not affect our attempt to find molar solubility anyway as the solution will be saturated and only then do we work out molar solubility (and then we can also use the K_sp expression in our equilibrium calculations).

2.) Will the molar solubility simply be the analytical concentration of the cation (in the same way as defined for the mass balance) divided by the coefficient of the cation in the molecular formula of the salt (and also the same thing, for the anion, both of these methods giving the same value)?

3.) Let's say I've added Ag₂SO₄ to solution and this has established an equilibrium not according to K_sp (the K_sp value is known but the solution is not saturated). Now I want to find out how much AgCl (with a known K_sp value) I can add, i.e. molar solubility of AgCl. Is there any way/how would we do this calculation?

 

[Borek]

2.) Will the molar solubility simply be the analytical concentration of the cation (in the same way as defined for the mass balance) divided by the coefficient of the cation in the molecular formula of the salt (and also the same thing, for the anion, both of these methods giving the same value)?

Can be, but doesn't have to. Your cation can be complexed and then to calculate the molar solubility you will need to sum concentrations of all forms of the cation (followed by division by the stoichiometric coefficient).

3.) Let's say I've added Ag₂SO₄ to solution and this has established an equilibrium not according to K_sp (the K_sp value is known but the solution is not saturated). Now I want to find out how much AgCl (with a known K_sp value) I can add, i.e. molar solubility of AgCl. Is there any way/how would we do this calculation?

If the solution is not saturated, the only way to calculate concentration of Ag⁺ is from the mass balance - you should know how much Ag₂SO₄ were put into the mix. If you don't know it, you can't solve the problem

 

[Big-Daddy]

Can be, but doesn't have to. Your cation can be complexed and then to calculate the molar solubility you will need to sum concentrations of all forms of the cation (followed by division by the stoichiometric coefficient).

OK so let's redefine as the molar solubility is the initial concentration of the cation added to the solution (which is equal to the cation's mass balance, which would include all species containing the cation multiplied by the stoichiometric coefficient of the cation in those species, and this total sum of concentrations is the initial concentration of the cation), which can be divided by the stoichiometric coefficient of the cation in the original salt's molecular formula to reach the molar solubility. Or the same thing for the anion.

If the solution is not saturated, the only way to calculate concentration of Ag⁺ is from the mass balance - you should know how much Ag₂SO₄ were put into the mix. If you don't know it, you can't solve the problem

You can have how many moles of Ag₂SO₄ were originally put in the solution, and the Ksp of Ag₂SO₄, but Ag₂SO₄ is not being added until saturation. Can you work it out then? Since Ksp ≠ [Ag⁺]²*[SO₄^2-] unless the solution is saturated, which it here is not ...

 

[Big-Daddy]

Help?

 

[morrobay]

If I am correctly understanding [Ag⁺] before saturation as part of your question :
Then can you get at this with electrode potentials ? Where E^∅ saturated =
[Ag⁺(aq)] ,E value,[?]/Ag electrode + .059 lg[Ag⁺aq]
Where [Ag(+)aq] on right side is silver concentration in saturated solution.
From the Nernst equation. E = E^∅ + (RT/zF) ln[M^z+]
E=E^∅+(.059)/z) lg[Ag^z+]
E^∅ at electrode potential at 1mole/liter
Each 10x lowering of [Ag+] lowers potential by (.059/z) volts

 

[Borek]

You can have how many moles of Ag₂SO₄ were originally put in the solution, and the Ksp of Ag₂SO₄, but Ag₂SO₄ is not being added until saturation. Can you work it out then? Since Ksp ≠ [Ag⁺]²*[SO₄^2-] unless the solution is saturated, which it here is not ...

If you know initial moles of Ag₂SO₄ you put them into the mass balance for silver and if the solution is not saturated, you simply drop Ksp from the set of equations.

 

[Big-Daddy]

If you know initial moles of Ag₂SO₄ you put them into the mass balance for silver and if the solution is not saturated, you simply drop Ksp from the set of equations.

Thank you.