Solubility of BaSO4 in 4M HCl solution

[christian0710]

Hi can anyone help me out with this problem?


This is how far I came

BaSO4 +H(+) <---> SO4+H2O +Ba
s 4-s s s

ksp = [SO4][Ba]/[H+] = s^2/[4-s]

So I saturated the solution in s, so the H+ will be 4M-s at equilibrium,

But it's not correct :(
What am I doing wrong?

 

[Borek]

Your reaction equation is nonsensical.

Start with a correct Ksp formula. Then remember that SO₄^2- gets protonated to HSO₄^- - so you have to take the second dissociation constant Ka2 into account.

 

[christian0710]

Oops forgot something

BaSO4 +H(+) <---> HSO4+H2O +Ba(+2)

This must be the right formula.
So if we saturate BaSO4 with s, and we start with 4M HCl (= 4M H+) then we must get s HSO4 at equilibrium and s Ba. Or is my logic off? Ksp=[reactants ]/[products ]

 

[christian0710]

I'm good at sulubility products in water, but when it get's to acids, i lack a bit understanding, that's why i i want gain the right logic.

 

[Borek]

BaSO4 +H(+) <---> HSO4+H2O +Ba(+2)

It is still nonsensical and can't be balanced.

Ksp=[reactants ]/[products ]

That's not the way we usually write Ksp.

 

[christian0710]

So if i take a easy example

Mg(OH)2 ---- Mg2+ +2OH
s s 2s

Ksp =[Mg][OH]^2 = (s)(2s)^2

Is this not correct?

Can you help me with the reaction? I'm not quite sure how to write it :(

 

[Borek]

Ksp =[Mg][OH]^2

OK, now write Ksp for barium sulfate.

 

[christian0710]

Ksp = [Ba][SO4]

 

[christian0710]

And you said that "SO42- gets protonated to HSO4-"

So perhaps the second Ksp= [HSO4]/[H+][SO4]?

I've never done a problem like this, so It's hard for me to imagine what the method is (combining two ksp) But do you equate the two solubility product expressions?

 

[christian0710]

Woa, just saw your website! Perhaps I should begin reading some of the pH calculations you write now and then.

 

[Borek]

There is no second Ksp, there is one Ksp that you already wrote.

Your problem now is how to calculate what fraction of sulfuric acid is in the form of SO₄^2- that is present in Ksp formula. This is where Ka2 comes into play.

 

[christian0710]

SO4 + H3O(+) <-----> HSO4
------- 4M-x -----------x

Ka2 for this reaction is 10^-(1,99) (because pKa=1,99)

So Ka2 =[HSO4]/[H3O+] = [x]/[4-x] Korrekt?

 

[Borek]

So Ka2 =[HSO4]/[H3O+]

Close, but no.

Ka describes the dissociation, not protonation. Can you write reaction equation for the HSO₄^- dissociation, and then write correct reaction quotient? One that doesn't miss any important reactant nor product?

 

[christian0710]

Ahh yes that makes sense, Ka is the acid constant, so we need to have the acid as reactant. It's the reverse i assume?

HSO4(-) + H2O <-----> SO4(2-) + H3O(+)
---x-------------------------------4M-x--

So I know for sure that we start with 4M [H+], so we must end with 4M-x, which is the amount added to SO4 to form HSO4, right?

Ka = [SO4][H+]/[HSO4]

 

[Borek]

I am almost 100% sure you can safely assume 4M and ignore x. Even if not, you can easily check if the assumption was correct after finding the solution.

 

[christian0710]

Okay, so we have two reactions and two balance equations.
BaSO4 <----> Ba(+2) + SO4(2-)
---0--------------s---------s+ (at equilibrium)
HSO4(-) + H2O <-----> SO4(2-) + H3O(+)
--x-------------------------------4M

So how do we approach this HSO4 dissociation? Do we say, We start with with 4M of H+ from HCl dissociation. And we start with x moles of SO4 (from the BaSO4), and at equilibrium we get x moles of HSO4 (Or do we start with x moles of HSO4? (this is where is get confused)

We have the following expressions from the equations.

Ksp = [Ba][SO4]=s^2

Ka = [SO4][H+]/[HSO4] =

 

[Borek]

We start with 4M H⁺ and x moles of SO₄^2-.

You are missing mass balance - how does the amount of Ba²⁺ depend on the amount of SO₄^2- and HSO₄^-?

 

[christian0710]

Thank you for taking this in steps, I can see how we need to approach this problem in parts now.
If i look at the two reactions, this would make sense, no?

[Ba] =[SO4] - [HSO4]

So when you say we start with x moles of SO4 I assume "we" assume that we start with a solution of BaSO4 which dissolves into the x SO4, that we add to our HSO4 dissociation equation?

 

[Borek]

Something like that. SO₄^2- is consumed by protonation, which shifts the solubility equilibrium to the right.

At this stage it is just a matter of solving system of three equations.