Barium sulfate (BaSO₄) is a slightly soluble salt, with K_sp = 1.1 × 10⁻¹⁰. What mass of Ba²⁺ ions will be present in 1.0 L of a saturated solution of barium sulfate?

Question

Quizplus · Accepted Answer

From the given value of the solubility product constant, we can write:
BaSO4 ⇌ Ba2+ + SO42-
At equilibrium, let x be the concentration of Ba2+ and SO42- ions. Since the solubility is slightly soluble, we can assume that the concentration of Ba2+ and SO42- ions formed will be very small compared to the concentration of BaSO4.
Therefore, [Ba2+][SO42-] = KS1U1B1spS1U1B0 = 1.1 × 10S1U1P1−S1S1P0S1U1P110S1S1P0
Let the concentration of Ba2+ and SO42- ions be x. Therefore, at equilibrium, the concentration of Ba2+ and SO42- ions formed will also be x. Hence, we can write:
x^2 = 1.1 × 10S1U1P1−S1S1P0S1U1P110S1S1P0
x = sqrt(1.1 × 10S1U1P1−S1S1P0S1U1P110S1S1P0) = 1.0 × 10S1U1P1−S1S1P0S1U1P10S1S1P0 M
So, the molar mass of BaSO4 = 137.3 + 32.1 + 4(16.0) = 233.3 g/mol
Therefore, the mass of BaSO4 present in 1.0 L of saturated solution is:
mass = concentration × molar mass = 1.0 × 10S1U1P1−S1S1P0S1U1P10S1S1P0 × 233.3 g/mol = 0.0023 g
Since 1 mol BaSO4 produces 1 mol Ba2+ and 1 mol SO42-, the mass of Ba2+ ions present in 1.0 L of saturated solution is also 0.0023 g.
The molar mass of Ba2+ is 137.3 g/mol. Therefore, the number of moles of Ba2+ ions present in 1.0 L of saturated solution is:
moles = mass / molar mass = 0.0023 g / 137.3 g/mol = 1.68 × 10S1U1P−S1S1P3S1U1P−S1S1P2S1U1P−S1S1P4S1S1P0 mol
Since 1 mole of Ba2+ ions is present in 1 mole of BaSO4, the number of moles of Ba2+ ions is equal to the number of moles of BaSO4.
Therefore, the mass of Ba2+ ions present in 1.0 L of saturated solution is 0.0023 g, which is the same as the mass of BaSO4 present in solution. However, the mass of BaSO4 corresponds to the mass of Ba2+ and SO42- ions combined. Therefore, the mass of Ba2+ ions present in 1.0 L of saturated solution is only half of 0.0023 g, which is 0.0014 g (Option C).

Barium Sulfate (BaSO4) Is a Slightly Soluble Salt, with Ksp

Barium Sulfate (BaSO₄) Is a Slightly Soluble Salt, with K_sp