Salts have varying solubilities in solvents such as water. Some salts dissolve well in water, whereas others are nearly insoluble. The solubility product Ksp is the equilibrium constant for the dissolution of a solid salt into water, and its magnitude is an indicator of the solubility of the salt. Barium sulfate, BaSO4, is used in medical imaging of the gastrointestinal tract because it is opaque to X rays. A barium sulfate solution, sometimes called a cocktail, is ingested by the patient, whose stomach and intestines can then be visualized via X-ray imaging. If a patient ingests 280mL of a saturated barium sulfate solution, how much toxic Ba2+ ion has the patient consumed?

Amount of toxic Ba²+ ingested by the patient = 0.404 mg

Explanation:

The solubility product constant, Ksp for barium sulfate is 1.1 x 10-¹⁰.

Considering the dissociation products of aqueous BaSO₄ solution:

BaSO₄ (aq) ⇄ Ba²+ (aq) + SO₄²- (aq)

Let the concentration of Ba²+ be x and that of SO₄²- be x as well since the mole ratio of the products is 1 : 1

Ksp = [Ba²+] × [SO₄²-]

Ksp = x × x = x²

x² = 1.1 x 10-¹⁰

x = 1.05 × 10-⁵ M

Therefore, the concentration of Ba²+ ions = 1.05 × 10-⁵ M

Volume of saturated barium sulfate ingested by the patient = 280 mL = 0.280 L

Number of moles of Ba²+ ions = molar concentration × volume

Number of moles of Ba²+ = 1.05 × 10-⁵ M × 0.280 L = 2.94 × 10-⁶ moles

Mass of Ba²+ ions = number of moles × molar mass

Molar mass of Ba²+ = 137.33 g/mol

Mass of Ba²+ = 2.94 × 10-⁶ moles × 137.33 g/mol = 4.04 × 10-⁴ g = 0.404 mg

Therefore, amount of toxic Ba²+ ingested by the patient = 0.404 mg