QuestionJuly 13, 2025

What is the molar solubility of Ni_(3)PO_(4) in a 1.00L solution of 0.00300M solution of Ni^+ Ni_(3)PO_(4)Ksp=4.5^ast 10^-18 Answer

What is the molar solubility of Ni_(3)PO_(4) in a 1.00L solution of 0.00300M solution of Ni^+ Ni_(3)PO_(4)Ksp=4.5^ast 10^-18 Answer
What is the molar solubility of Ni_(3)PO_(4) in a 1.00L solution of 0.00300M solution of Ni^+ Ni_(3)PO_(4)Ksp=4.5^ast 10^-18 Answer

Solution
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Answer

1.29 \times 10^{-5} M Explanation 1. Write the Dissolution Equation Ni_3(PO_4)_2 \rightleftharpoons 3Ni^{2+} + 2PO_4^{3-} 2. Express K_{sp} in Terms of Concentrations K_{sp} = [Ni^{2+}]^3[PO_4^{3-}]^2 3. Substitute Known Values Let s be the molar solubility of Ni_3(PO_4)_2. Then, [PO_4^{3-}] = 2s and [Ni^{2+}] = 0.00300 + 3s. 4. Simplify Assumptions Assume 3s \ll 0.00300, so [Ni^{2+}] \approx 0.00300. 5. Solve for s Substitute into K_{sp}: 4.5 \times 10^{-18} = (0.00300)^3(2s)^2. Solve for s: s = \sqrt{\frac{4.5 \times 10^{-18}}{(0.00300)^3 \times 4}}. 6. Calculate s s = \sqrt{\frac{4.5 \times 10^{-18}}{2.7 \times 10^{-8}}} = \sqrt{1.6667 \times 10^{-10}} = 1.29 \times 10^{-5} M.

Explanation

1. Write the Dissolution Equation<br /> $Ni_3(PO_4)_2 \rightleftharpoons 3Ni^{2+} + 2PO_4^{3-}$<br /><br />2. Express $K_{sp}$ in Terms of Concentrations<br /> $K_{sp} = [Ni^{2+}]^3[PO_4^{3-}]^2$<br /><br />3. Substitute Known Values<br /> Let $s$ be the molar solubility of $Ni_3(PO_4)_2$. Then, $[PO_4^{3-}] = 2s$ and $[Ni^{2+}] = 0.00300 + 3s$.<br /><br />4. Simplify Assumptions<br /> Assume $3s \ll 0.00300$, so $[Ni^{2+}] \approx 0.00300$.<br /><br />5. Solve for $s$<br /> Substitute into $K_{sp}$: $4.5 \times 10^{-18} = (0.00300)^3(2s)^2$.<br /> Solve for $s$: $s = \sqrt{\frac{4.5 \times 10^{-18}}{(0.00300)^3 \times 4}}$.<br /><br />6. Calculate $s$<br /> $s = \sqrt{\frac{4.5 \times 10^{-18}}{2.7 \times 10^{-8}}} = \sqrt{1.6667 \times 10^{-10}} = 1.29 \times 10^{-5}$ M.
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