QuestionJuly 9, 2025

Enter your answer in the provided box. The K_(sp) of metal hydroxide, Ni(OH)_(2) is 5.48times 10^-16 Calculate the solubility of this compound in g/L square g/L

Enter your answer in the provided box. The K_(sp) of metal hydroxide, Ni(OH)_(2) is 5.48times 10^-16 Calculate the solubility of this compound in g/L square g/L
Enter your answer in the provided box. The K_(sp) of metal hydroxide, Ni(OH)_(2) is 5.48times 10^-16 Calculate the solubility of this compound in g/L square g/L

Solution
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Answer

1.13 \times 10^{-4} \text{ g/L} Explanation 1. Write the Dissociation Equation Ni(OH)_2 \rightarrow Ni^{2+} + 2OH^- 2. Express K_{sp} in Terms of Solubility Let solubility be s mol/L. Then, [Ni^{2+}] = s and [OH^-] = 2s. Thus, K_{sp} = [Ni^{2+}][OH^-]^2 = s(2s)^2 = 4s^3. 3. Solve for Solubility s Set 4s^3 = 5.48 \times 10^{-16}, then s^3 = \frac{5.48 \times 10^{-16}}{4}. Calculate s = \sqrt[3]{\frac{5.48 \times 10^{-16}}{4}}. 4. Convert Solubility to g/L Molar mass of Ni(OH)_2 is approximately 92.71 \text{ g/mol}. Solubility in g/L is s \times 92.71.

Explanation

1. Write the Dissociation Equation<br /> $Ni(OH)_2 \rightarrow Ni^{2+} + 2OH^-$<br /><br />2. Express $K_{sp}$ in Terms of Solubility<br /> Let solubility be $s$ mol/L. Then, $[Ni^{2+}] = s$ and $[OH^-] = 2s$. Thus, $K_{sp} = [Ni^{2+}][OH^-]^2 = s(2s)^2 = 4s^3$.<br /><br />3. Solve for Solubility $s$<br /> Set $4s^3 = 5.48 \times 10^{-16}$, then $s^3 = \frac{5.48 \times 10^{-16}}{4}$. Calculate $s = \sqrt[3]{\frac{5.48 \times 10^{-16}}{4}}$.<br /><br />4. Convert Solubility to g/L<br /> Molar mass of $Ni(OH)_2$ is approximately $92.71 \text{ g/mol}$. Solubility in g/L is $s \times 92.71$.
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