# Ion exchange and stability constants

• Maharg
In summary, 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.
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+]

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.

--

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.

Maharg said:
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:

Maharg said:
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.

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?

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.

--

## 1. What is ion exchange and how does it work?

Ion exchange is a process in which ions in a solution are exchanged for other ions on a solid surface. This is typically done using a resin or polymer material with charged sites that can attract and hold different ions. The exchange occurs when the solution is passed through the resin, and the desired ions are released into the solution while the unwanted ions are retained by the resin.

## 2. What is a stability constant in ion exchange?

A stability constant, also known as an equilibrium constant, is a measure of how strongly an ion is bound to a resin. It is represented by the symbol Kd and is calculated by dividing the concentration of the bound ions by the concentration of the free ions.

## 3. How is the stability constant affected by pH?

The stability constant is highly dependent on the pH of the solution. This is because the charge of the resin and the ions can change with the pH, affecting their ability to interact and exchange. Generally, the higher the pH, the stronger the binding between the ions and the resin.

## 4. What factors can influence the stability constant?

Aside from pH, other factors that can affect the stability constant include temperature, ionic strength of the solution, and the nature of the resin. Temperature can affect the rate of exchange, while ionic strength can affect the affinity of the ions for the resin. The type of resin used can also have different binding capacities and selectivity for different ions.

## 5. How is the stability constant used in practical applications?

The stability constant is an important parameter in designing and optimizing ion exchange processes. It can help determine the best conditions for maximum removal of unwanted ions, as well as predict the efficiency and capacity of the resin. Additionally, stability constants are used in environmental and chemical analysis to determine the presence and concentration of certain ions in a solution.

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