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Chapter 15: Problem 3

You are browsing through the Handbook of Hypothetical Chemistry when you come across a solid that is reported to have a \(K_{\mathrm{sp}}\) value of zero in water at \(25^{\circ} \mathrm{C}\). What does this mean?

Short Answer

Expert verified
A \(K_{sp}\) value of zero for a solid in water at \(25^{\circ} \mathrm{C}\) indicates that the solid is completely insoluble in water at this temperature, and the concentration of its ions in a saturated solution is essentially zero.

Step by step solution

01

Explanation of Solubility Product Constant (\(K_{sp}\))

The solubility product constant, \(K_{sp}\), is a measure of the solubility of a slightly soluble ionic compound in water. It is the product of the concentrations of the ions in a saturated solution, each raised to the power of their stoichiometric coefficient. A high \(K_{sp}\) value implies that the substance is highly soluble in water, while a low \(K_{sp}\) value indicates that the substance is poorly soluble in water.
02

Interpretation of the \(K_{sp}\) Value

In this case, the given \(K_{sp}\) value is zero. Mathematically, a \(K_{sp}\) value of zero means that the concentrations of the constituent ions in the saturated solution are essentially zero. This implies that the solid is completely insoluble in water at \(25^{\circ} \mathrm{C}\).
03

Conclusion

A \(K_{sp}\) value of zero for a solid in water at \(25^{\circ} \mathrm{C}\) means that the solid is not soluble in water at this temperature, and the concentration of its ions in a saturated solution is essentially zero.

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Most popular questions from this chapter

Sodium tripolyphosphate \(\left(\mathrm{Na}_{5} \mathrm{P}_{3} \mathrm{O}_{10}\right)\) is used in many synthetic detergents. Its major effect is to soften the water by complexing \(\mathrm{Mg}^{2+}\) and \(\mathrm{Ca}^{2+}\) ions. It also increases the efficiency of surfactants, or wetting agents that lower a liquid's surface tension. The \(K\) value for the formation of \(\mathrm{MgP}_{3} \mathrm{O}_{10}^{3-}\) is \(4.0 \times 10^{8} .\) The reaction is \(\mathrm{Mg}^{2+}(a q)+\mathrm{P}_{3} \mathrm{O}_{10}^{5-}(a q) \rightleftharpoons \mathrm{MgP}_{3} \mathrm{O}_{10}^{3-}(a q)\) Calculate the concentration of \(\mathrm{Mg}^{2+}\) in a solution that was originally \(50 .\) ppm \(\mathrm{Mg}^{2+}(50 . \mathrm{mg} / \mathrm{L} \text { of solution) after } 40 . \mathrm{g}\) \(\mathrm{Na}_{5} \mathrm{P}_{3} \mathrm{O}_{10}\) is added to \(1.0 \mathrm{L}\) of the solution.

Calculate the molar solubility of \(\mathrm{Al}(\mathrm{OH})_{3}, K_{\mathrm{sp}}=2 \times 10^{-32}\).

The overall formation constant for \(\mathrm{HgI}_{4}^{2-}\) is \(1.0 \times 10^{30}\) That is, $$ 1.0 \times 10^{30}=\frac{\left[\mathrm{HgI}_{4}^{2-}\right]}{\left[\mathrm{Hg}^{2+}\right]\left[\mathrm{I}^{-}\right]^{4}} $$ What is the concentration of \(\mathrm{Hg}^{2+}\) in \(500.0 \mathrm{mL}\) of a solution that was originally \(0.010\) \(M\) \(\mathrm{Hg}^{2+}\) and \(0.78\) \(M\) \(\mathrm{I}^{-} ?\) The reaction is $$\mathrm{Hg}^{2+}(a q)+4 \mathrm{I}^{-}(a q) \rightleftharpoons \mathrm{HgI}_{4}^{2-}(a q)$$

The \(K_{\mathrm{sp}}\) for lead iodide \(\left(\mathrm{PbI}_{2}\right)\) is \(1.4 \times 10^{-8} .\) Calculate the solubility of lead iodide in each of the following. a. water b. \(0.10 M \operatorname{Pb}\left(\mathrm{NO}_{3}\right)_{2}\) c. \(0.010 M\) NaI

Write balanced equations for the dissolution reactions and the corresponding solubility product expressions for each of the following solids. a. \(\mathrm{AgC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) b. \(\mathrm{Al}(\mathrm{OH})_{3}\) c. \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\)
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