Determine the molar solubility of BaF2 in pure water given that the Ksp for BaF2 is 2.45 × 10⁻⁵.
A
2.90 × 10⁻² M
B
1.83 × 10⁻² M
C
1.23 × 10⁻⁵ M
D
4.95 × 10⁻³ M
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1
Start by writing the dissolution equation for BaF2 in water: BaF2(s) ⇌ Ba²⁺(aq) + 2F⁻(aq). This shows that one mole of BaF2 produces one mole of Ba²⁺ ions and two moles of F⁻ ions.
Next, express the solubility product constant (Ksp) in terms of the concentrations of the ions. The Ksp expression for BaF2 is: .
Let the molar solubility of BaF2 be 's'. Therefore, the concentration of Ba²⁺ ions will be 's' and the concentration of F⁻ ions will be '2s' because two fluoride ions are produced for each formula unit of BaF2 that dissolves.
Substitute these concentrations into the Ksp expression: . Set this equal to the given Ksp value: .
Solve for 's' by dividing both sides by 4 and then taking the cube root: . This will give you the molar solubility of BaF2 in pure water.