[shackdaddy836]

Hey, I'm trying to study for an exam I have. There's this really hard question on solubility that I'm having an extremely tough time solving. Here it is:


What is the solubility of Al(OH)₃ at 25^oC in 1.0M NaF solution? The K_sp for Al(OH)₃ is 3.0x10^-34, and the K_f for AlF₆^3- is 4.0x10¹⁹, all at 25^oC.
The answer is 1.5x10^-4 M but I have no clue how to get to it. I've asked 6 different people in my class and they are all having trouble too.


I already know I need to multiply K_f and K_sp together to find K_overall. Then I thought I was supposed to create two reactions and combine them:
1) Al(OH)₃ + 3NaF  AlF₃ + 3NaOH
2) AlF₃ + 3F  AlF₆^3-
Overall) Al(OH)₃ + 3NaF + 3F AlF₆^3- + 3NaOH
But then I'm lost after that...

[shackdaddy836]

We have two practice tests that are basically identical in content covered so an alternative to this question would be:

What is the solubility of Cu(OH)₂ at 25^oC in 1.0M NH₃ solution? The Ksp for Cu(OH)₂ is 2.2x10^-20, and the Kf for Cu(NH₃)₄²⁺ is 5.6x10¹¹, all at 25^oC.

The answer for this one is 1.5x10^-3 M

Basically the same question but I thought it might help...

[Borek]

What is the solubility of Al(OH)₃ at 25^oC in 1.0M NaF solution? The K_sp for Al(OH)₃ is 3.0x10^-34, and the K_f for AlF₆^3- is 4.0x10¹⁹, all at 25^oC.

Solubility is most likely quite low, so we can simplify the problem in several ways.

1. We can assume concentration of F^- doesn't change and is 1M all the time (that will have to be checked once the calculations are done).

2. We can assume all dissolved Al³⁺ is complexed, so the concentration of AlF₆^3- equals solubility (that will have to be checked as well).

3. If 2 is right, there is a simple dependence between concentrations of OH^- and AlF₆^3- (that will again require checking, as it may happen solubility is so low presence of OH^- from water autodissociation plays an important role).

At this moment you have three equations - Ksp, Kf, and the one mentioned in 3, and two unknowns - [Al³⁺] and [AlF₆^3-] - simply solve for [AlF₆^3-], as per 2 that's the solubility. Then check if all assumptions hold.

Copper problem is slightly different, as presence of ammonia means already high concentration of OH^-.