# How to calculate the solubility of CaF₂ at different temperatures?

By 25° Celsius, I used the free energy table for $\small G$ for the reaction and got $\small K_{sp}= 10^{-9.02}$.

I now need to find out what the solubility is by 10, 20 and 30°C. Could you also show what equation you used and how to work out the solubility by one of these other temperatures?

-
Could you elaborate on how you might approach the problem first, rather than asking for a solution, I think it will be a lot more likely to receive an answer that way. –  jonsca Oct 16 '12 at 6:48

## 1 Answer

It depends what you have access to… but if we suppose that you have access to decent thermodynamic tables, here's a hint:

You know how solubility is linked to dissolution reaction (Gibbs) free energy. Now, how does the free energy depend on temperature? In other words, what is $\displaystyle\frac{\partial G}{\partial T}$?

-
I do have access to thermodynamic tables. I tried using the van 't Hoff equation, because there is the relationship between temperature and the K solubility product. However, I am not 100% sure that I am using the right equation and I don't have any way to check if my answers are correct. The answers I get from using the van 't Hoff equation are a little bit counterintuitive. For 10° Celsius, I get a solubility product of Ksp= 10^−9.02 For 20° Celsius, I get a solubility product of Ksp= 10^−9.03 For 30° Celsius, I get a solubility product of Ksp= 10^−9.00 This just seems incorrect to me. –  Erin Oct 16 '12 at 11:59
I think you misread the results. The 20 C reading is the smallest. Assuming that Erin used a constant $\Delta H$, that's not possible. I'd guess that there is a math error involved. –  Paul J. Gans Nov 16 '12 at 19:04