QuestionAugust 6, 2025

BaSO_(4) is used in diagnostic nuclear medicine techniques because it is highly insoluble. K_(sp)=1.5times 10^-9 25^circ C Calculate the molar solubility of the salt. What is the concentration of Ba2+ions in the saturated solution? [Ba^2+]=[?]times 10^[?]M

BaSO_(4) is used in diagnostic nuclear medicine techniques because it is highly insoluble. K_(sp)=1.5times 10^-9 25^circ C Calculate the molar solubility of the salt. What is the concentration of Ba2+ions in the saturated solution? [Ba^2+]=[?]times 10^[?]M
BaSO_(4) is used in diagnostic nuclear medicine techniques because it is highly insoluble. K_(sp)=1.5times 10^-9 25^circ C Calculate the molar solubility of the salt. What is the concentration of Ba2+ions in the saturated solution? [Ba^2+]=[?]times 10^[?]M

Solution
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Answer

[Ba^{2+}] = 1.22 \times 10^{-5} M Explanation 1. Write the Dissolution Equation BaSO_4(s) \rightleftharpoons Ba^{2+}(aq) + SO_4^{2-}(aq) 2. Express Solubility Product **K_{sp} = [Ba^{2+}][SO_4^{2-}]** 3. Set Up Solubility Expression Let s be the molar solubility of BaSO_4. Then, [Ba^{2+}] = s and [SO_4^{2-}] = s. 4. Substitute into K_{sp} Equation K_{sp} = s \cdot s = s^2 5. Solve for Molar Solubility s^2 = 1.5 \times 10^{-9} s = \sqrt{1.5 \times 10^{-9}} 6. Calculate the Value s \approx 1.22 \times 10^{-5}

Explanation

1. Write the Dissolution Equation<br /> $BaSO_4(s) \rightleftharpoons Ba^{2+}(aq) + SO_4^{2-}(aq)$<br /><br />2. Express Solubility Product<br /> **$K_{sp} = [Ba^{2+}][SO_4^{2-}]$**<br /><br />3. Set Up Solubility Expression<br /> Let $s$ be the molar solubility of $BaSO_4$. Then, $[Ba^{2+}] = s$ and $[SO_4^{2-}] = s$.<br /><br />4. Substitute into $K_{sp}$ Equation<br /> $K_{sp} = s \cdot s = s^2$<br /><br />5. Solve for Molar Solubility<br /> $s^2 = 1.5 \times 10^{-9}$<br /> $s = \sqrt{1.5 \times 10^{-9}}$<br /><br />6. Calculate the Value<br /> $s \approx 1.22 \times 10^{-5}$
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