Barium is a nonessential element in the human body, but some organisms build exoskeletons using barium sulfate, which has a K_sp of 1.1 $\times$ 10^-10 at 25 $\circ$ C. What is the mass of barium in 1.0 L of a saturated solution of barium sulfate at 25 $\circ$ C?

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Quizplus · Accepted Answer

The solubility product constant (Ksp) for barium sulfate (BaSO4) at 25°C is 1.1 × 10^-10. To find the mass of barium in a saturated solution, we first calculate the molar solubility of BaSO4. Since BaSO4 dissociates into Ba^2+ and SO4^2- in a 1:1 ratio, the concentration of Ba^2+ in a saturated solution is equal to the molar solubility of BaSO4. $$ K_{sp} = [Ba^{2+}][SO_4^{2-}] = (s)(s) = s^2 $$Solving for s (molar solubility):$$ s^2 = 1.1 \times 10^{-10} $$$$ s = \sqrt{1.1 \times 10^{-10}} $$$$ s \approx 1.05 \times 10^{-5} \, M $$To find the mass of barium in 1.0 L of this solution, we convert the molarity of Ba^2+ to moles and then to grams:$$ 1.05 \times 10^{-5} \, mol/L \times 1.0 \, L = 1.05 \times 10^{-5} \, mol $$$$ 1.05 \times 10^{-5} \, mol \times 137.33 \, g/mol \approx 1.44 \times 10^{-3} \, g $$$$ 1.44 \times 10^{-3} \, g = 1.4 \, mg $$Therefore, the mass of barium in 1.0 L of a saturated solution of barium sulfate at 25°C is approximately 1.4 mg.

Barium Is a Nonessential Element in the Human Body, but Some