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Chapter 17: Problem 52

(a) True or false: "solubility" and "solubility-product constant" are the same number for a given compound. (b) Write the expression for the solubility- product constant for each of the following ionic compounds: \(\mathrm{MnCO}_{3}, \mathrm{Hg}(\mathrm{OH})_{2},\) and \(\mathrm{Cu}_{3}\left(\mathrm{PO}_{4}\right)_{2}\).

Short Answer

Expert verified
(a) The statement is false, as solubility and solubility-product constant are not the same number for a given compound. (b) The solubility-product constant expressions are as follows: \(K_{sp}(\mathrm{MnCO}_{3}) = [\mathrm{Mn}^{2+}][\mathrm{CO}_{3}^{2-}]\), \(K_{sp}(\mathrm{Hg}(\mathrm{OH})_{2}) = [\mathrm{Hg}^{2+}][\mathrm{OH}^-]^2\), and \(K_{sp}(\mathrm{Cu}_{3}\left(\mathrm{PO}_{4}\right)_{2}) = [\mathrm{Cu}^{2+}]^3[\mathrm{PO}_{4}^{3-}]^2\).

Step by step solution

01

Part (a) - Solubility vs Solubility-Product Constant

Solubility is a measure of how much solute can dissolve in a given solvent, typically measured in moles per liter (M). The solubility of a compound depends on temperature, pressure, and the nature of the solvent. The solubility-product constant (Ksp) is a value that represents the equilibrium between a solid ionic compound and its dissolved ions. The Ksp of a compound is a constant value for a given temperature. Therefore, the solubility and solubility-product constant are not the same number for a given compound. So, the statement is false.
02

Part (b) - Expression for Solubility-Product Constant for MnCO3

The dissolution of MnCO3 in water can be represented as: \[\mathrm{MnCO}_{3}(s) \rightleftharpoons \mathrm{Mn}^{2+}(aq) + \mathrm{CO}_{3}^{2-}(aq)\] The solubility-product constant expression (Ksp) for MnCO3 is: \[K_{sp} = [\mathrm{Mn}^{2+}][\mathrm{CO}_{3}^{2-}]\]
03

Part (b) - Expression for Solubility-Product Constant for Hg(OH)2

The dissolution of Hg(OH)2 in water can be represented as: \[\mathrm{Hg}(\mathrm{OH})_{2}(s) \rightleftharpoons \mathrm{Hg}^{2+}(aq) + 2\mathrm{OH}^{-}(aq)\] The solubility-product constant expression (Ksp) for Hg(OH)2 is: \[K_{sp} = [\mathrm{Hg}^{2+}][\mathrm{OH}^-]^2\]
04

Part (b) - Expression for Solubility-Product Constant for Cu3(PO4)2

The dissolution of Cu3(PO4)2 in water can be represented as: \[\mathrm{Cu}_{3}\left(\mathrm{PO}_{4}\right)_{2}(s) \rightleftharpoons 3\mathrm{Cu}^{2+}(aq) + 2\mathrm{PO}_{4}^{3-}(aq)\] The solubility-product constant expression (Ksp) for Cu3(PO4)2 is: \[K_{sp} = [\mathrm{Cu}^{2+}]^3[\mathrm{PO}_{4}^{3-}]^2\]

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Most popular questions from this chapter

Baking soda (sodium bicarbonate, \(\mathrm{NaHCO}_{3}\) ) reacts with acids in foods to form carbonic acid \(\left(\mathrm{H}_{2} \mathrm{CO}_{3}\right),\) which in turn decomposes to water and carbon dioxide gas. In a cake batter, the \(\mathrm{CO}_{2}(g)\) forms bubbles and causes the cake to rise. \((\mathbf{a})\) A rule of thumb in baking is that \(1 / 2\) teaspoon of baking soda is neutralized by one cup of sour milk. The acid component in sour milk is lactic acid, \(\mathrm{CH}_{3} \mathrm{CH}(\mathrm{OH}) \mathrm{COOH}\). Write the chemical equation for this neutralization reaction. (b) The density of baking soda is \(2.16 \mathrm{~g} / \mathrm{cm}^{3}\). Calculate the concentration of lactic acid in one cup of sour milk (assuming the rule of thumb applies), in units of mol/L. (One cup \(=236.6 \mathrm{~mL}=48\) teaspoons \() .(\mathbf{c})\) If \(1 / 2\) teaspoon of baking soda is indeed completely neutralized by the lactic acid in sour milk, calculate the volume of carbon dioxide gas that would be produced at a pressure of \(101.3 \mathrm{kPa}\), in an oven set to \(177^{\circ} \mathrm{C}\).

The value of \(K_{s p}\) for \(\mathrm{Cd}(\mathrm{OH})_{2}\) is $2.5 \times 10^{-14} .(\mathbf{a})$ What is the molar solubility of \(\mathrm{Cd}(\mathrm{OH})_{2} ?(\mathbf{b})\) The solubility of \(\mathrm{Cd}(\mathrm{OH})_{2}\) can be increased through formation of the complex ion \(\mathrm{CdBr}_{4}^{2-}\left(K_{f}=5 \times 10^{3}\right) .\) If solid \(\mathrm{Cd}(\mathrm{OH})_{2}\) is added to a NaBr solution, what is the initial concentration of NaBr needed to increase the molar solubility of \(\mathrm{Cd}(\mathrm{OH})_{2}\) to $1.0 \times 10^{-3} \mathrm{~mol} / \mathrm{L} ?$

Which of these statements about the common-ion effect is most correct? (a) The solubility of a salt MA is decreased in a solution that already contains either \(\mathrm{M}^{+}\) or \(\mathrm{A}^{-} .\) (b) Common ions alter the equilibrium constant for the reaction of an ionic solid with water. \((\mathbf{c})\) The common-ion effect does not apply to unusual ions like \(\mathrm{SO}_{3}^{2-} .(\mathbf{d})\) The solubility of a salt MA is affected equally by the addition of either \(\mathrm{A}^{-}\) or a noncommon ion.

For each statement, indicate whether it is true or false. (a) The solubility of a slightly soluble salt can be expressed in units of moles per liter. (b) The solubility product of a slightly soluble salt is simply the square of the solubility. (c) The solubility of a slightly soluble salt is independent of the presence of a common ion. (d) The solubility product of a slightly soluble salt is independent of the presence of a common ion.

A 10.0-mL sample of \(0.250 \mathrm{MHNO}_{3}\) solution is titrated with $0.100 M$ KOH solution. Calculate the pH of the solution after the following volumes of base have been added: (a) \(20.0 \mathrm{~mL}\), (b) \(24.9 \mathrm{~mL}\) (c) \(25.0 \mathrm{~mL}\) (d) \(25.1 \mathrm{~mL}\), (e) \(30.0 \mathrm{~mL}\).
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