Tuesday, 23 August 2016

acid base - Q. 36 2018 molar solubility of CaF2 at pH3 given molar solubility at pH7 and pKa of HF



This is Q36 on the 2018 Chemistry Olympiad:


Calcium fluoride, CaFX2, has a molar solubility of 2.1104 molL1 at pH = 7.00. By what factor does its molar solubility increase in a solution with pH = 3.00? The pKa of HF is 3.17 (source).


Here are my steps:



  1. Calculate the solubility product of calcium fluoride from the data at pH=7.


  2. Combine the dissolution and the acid/base reaction to CaFX2(s)+2HX+CaX2+(aq)+2HF(aq)

  3. Calculate the equilibrium constant of the combined reaction from the known constants of the separate reactions.

  4. Calculate the equilibrium concentration of CaX2+ at pH = 3.00

  5. Calculate the molar solubility and compared it to the one given for ph = 7.


The arithmetic is shown on the picture, resulting in a CaX2+ concentration of 4.325104 molL1.


enter image description here


I don't understand what I did wrong as the answer is B, 1.83.


Basically I combined the equilibrium of CaFX2 dissociating and the equilibrium of the formation of HF. I then using the equilibrium product found out the concentration of CaX2+. It would be great if you could show me where I went wrong.




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