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Chapter 16: Problem 3

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

Short Answer

Expert verified
A solid with a \(K_{sp}\) value of zero in water at 25°C means that the solid is completely insoluble at this temperature, as the equilibrium constant for the dissolution process is equal to zero. This implies the solid does not dissolve in water, and its constituent ions are not present in the solution.

Step by step solution

01

Understand the dissolution process

When an ionic solid dissolves in water, it breaks into its constituent ions. For example, consider a generic solid, AB, dissolving in water: \[ AB(s) \rightleftharpoons A^{(+) } (aq) + B^{(-) } (aq) \] Here, AB is the solid and A^+ and B^- are its ions in aqueous solution. The process reaches an equilibrium in which both the solid and its ions exist together in solution.
02

Write the equilibrium constant expression

To determine the solubility product constant, we need to write the equilibrium constant expression for the dissolution process. Since \(K_{sp}\) represents the mathematical product of the dissociated ions' concentrations raised to the power of their respective stoichiometric coefficients, we have: \[ K_{sp}=[A^+][B^-] \] Keep in mind that the concentration of the solid is not included in the expression, as it is constant throughout the dissolution process.
03

Understand the meaning of a \(K_{sp}\) value of zero

A \(K_{sp}\) value of zero for solid AB means that the equilibrium constant for the dissolution process is equal to zero, which implies that the dissolution process does not occur to any appreciable extent. In other words, solid AB does not dissolve in water at 25°C, and its ions do not exist in the solution.
04

Conclude the result

A solid with a \(K_{sp}\) value of zero means that the solid is completely insoluble in water at 25°C, and the equilibrium condition for its dissolution is such that the solid does not dissociate into its constituent ions in solution.

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Most popular questions from this chapter

On a hot day, a 200.0 -mL sample of a saturated solution of \(\mathrm{PbI}_{2}\) was allowed to evaporate until dry. If 240 mg of solid \(\mathrm{PbI}_{2}\) was collected after evaporation was complete, calculate the \(K_{\mathrm{sp}}\) value for \(\mathrm{PbI}_{2}\) on this hot day.

Tooth enamel is composed of the mineral hydroxyapatite. The \(K_{\mathrm{sp}}\) of hydroxyapatite, $\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{OH},\( is \)6.8 \times 10^{-37}$ . Calculate the solubility of hydroxyapatite in pure water in moles per liter. How is the solubility of hydroxyapatite affected by adding acid? When hydroxyapatite is treated with fluoride, the mineral fluorapatite, \(\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{F}\) , forms. The \(K_{\mathrm{sp}}\) of this substance is \(1 \times 10^{-60}\) . Calculate the solubility of fluorapatite in water. How do these calculations provide a rationale for the fluoridation of drinking water?

The solubility of \(\mathrm{PbCl}_{2}\) increases with an increase in temperature. Is the dissolution of \(\mathrm{PbCl}_{2}(s)\) in water exothermic or endothermic? Explain.

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