Ion exchange and stability constants

[Maharg]

Homework Statement

In natural water containing 0.9 mmol/L calcium and 12 ug/L fulvic acid, determine the
fraction of the fulvic acid that is bound to calcium (i.e. the ratio between the concentration of Ca-FA and total concentration of FA binding sites), assuming that calcium is the only metal presentin a significant concentration.

The pH of the water is 5.0, the conditional stability constant Kf (Ca-FA) is 1.2x103 and the
binding sites on FA is 5 mmol/g.

Homework Equations

FA = H+ + Org-

Org- + Ca2+ = Org-Ca2+

H2O = H+ OH-

Told to find ratio Ca-Org-/Org-

The Attempt at a Solution

Found concentration of FA binding sites = 60 umol/L
then concentration H+ = 50 umol/L
and Ca2+ = 900 umol/L

The professor told us we'll need those reactions but I'm unsure why we need the Water reaction.

Also confused how to get A- as we don't know the equilibrium constant for Fa = H+ + Org- and I've looked it up to see if fulvic acid is strong to find out if it dissociates completely. I don't the next step. If someone could just suggest how I properly do the next step.

I think I have to eventually do Kf = Org-Ca2+/[Org-][Ca2+]

 

[Borek]

Your notation is hard to follow, as it is inconsistent (FA, Org-, A- - I can guess what you mean, but it distracts).

You are given conditional stability constant - most likely for a pH 5.0. If so, you don't need information about fulvic acid dissociation constant.

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[Maharg]

The reactions I listed were given by my professor when I asked him for help and it left me a bit more confused. I assumed he just meant Org- is same as A-.

Do I need to calculate H+? I am just looking for Ca2+Fa/Fa right?\

DO I just calculate Kf = Ca2+FA/[FA][Ca2+]

I also want to thank you Borek you've helped me a few times in the past before and I appreciate it.

 

[Borek]

I assumed he just meant Org- is same as A-.

Probably.

Do I need to calculate H+? I am just looking for Ca2+Fa/Fa right?

DO I just calculate Kf = Ca2+FA/[FA][Ca2+]

That's my bet - go from here, ignoring pH and fulvic acid protonation. Just take care:

Found concentration of FA binding sites = 60 umol/L

That's not the number I got.

I also want to thank you Borek you've helped me a few times in the past before and I appreciate it.

You are welcome.

 

[Maharg]

My answer isn't making sense.

I did the calculations. So I had

Kf = [CaFA]/[Ca2+][FA]

1.2E3 = [CaFA]/ (0.9E-3)(6E-8)

= 6.5E- 5 mol/L

But this is higher than my FA value. Somehow I'm coming up with more Ca-FA binds then total binding sites. What step am I missing?

 

[Borek]

You are not taking into account mass balance of fulvic acid.

But you don't have to calculate concentration of neither complex nor free fulvic acid! See if you can rearrange Kf expression to get ratio on one side.

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