Final answer:
To find the pH of the solution, calculate the concentration of fluoride ions using the weight of calcium fluoride and the volume of water. Then, apply the equilibrium expression with the given Kₐ to find the hydroxide ion concentration. Finally, calculate the pOH and subtract it from 14 to find the pH.
Step-by-step explanation:
The pH of a solution made by dissolving 5.36 grams of calcium fluoride (CaF2) can be determined by first finding the molarity of the fluoride ions (F-). Calcium fluoride is slightly soluble in water and will dissociate according to the equation:
CaF2 (s) → Ca²⁺ (aq) + 2F¯ (aq)
Next, we apply this stoichiometry to find the molarity of fluoride ions in the solution. This will then be used with the given Kₐ (or K₁ in the case of fluoride ion, here denoted as Kᵤ for simplicity) of fluoride to find the concentration of hydroxide ions (OH-), using the equilibrium relationship:
F¯ (aq) + H₂O (l) ⇌ HF (aq) + OH¯ (aq)
Once the [OH-] is known, we can calculate the pOH of the solution, which can be used to find the pH:
pH = 14 - pOH
In this example, we would use the reaction stoichiometry and the Kᵤ of the fluoride ion to first determine the concentration of fluoride ions in the solution. Given that the dissociation of CaF2 leads to twice as many fluoride ions as calcium ions, the concentration of fluoride ions would be double the concentration of calcium ions. Using the provided information, the molarity of the fluoride ions can be calculated and then the pH of the solution can be determined.