Calculating the solubility of calcium

Question

Assignment:

Question 1. Tooth enamel consists of hydroxyapatite, Ca₅(PO₄)₃OH (K_sp = 6.8×10^-37).  Fluoride ion added to drinking water reacts w/Ca₅(PO₄)₃OH to form the more tooth decay-resistant fluorapatite, Ca₅(PO₄)₃F (K_sp =1.0×10^-60).  Fluoridated water has dramatically decreased cavities among children. Calculate the solubility of Ca₅(PO₄)₃OH and of Ca₅(PO₄)₃F in water.

Question 2. A 35.00 mL solution of .2500 M HF is titrated with a standardized .1532 M solution of NaOH at 25^?C.

(a)  What is the pH of the HF solution before titrant is added?

(b)  How many milliliters of titrant are required to reach the equivalence point?

(c)  What is the pH at .50 mL before the equivalence point?

 (d)  What is the pH at the equivalence point?

(e)  What is the pH at .50 mL after the equivalence point?

Provide complete and step by step solution for the question and show calculations and use formulas.