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As you learned in Chapter 7 , most metal hydroxides are sparingly soluble in water. Write balanced chemical equations describing the dissolving of the following metal hydroxides in water. Write the expression for \(K_{\mathrm{sp}}\) for each process. a. \(\mathrm{Cu}(\mathrm{OH})_{2}(s)\) b. \(\mathrm{Cr}(\mathrm{OH})_{3}(s)\) c. \(\mathrm{Ba}(\mathrm{OH})_{2}(s)\) d. \(\operatorname{Sn}(\mathrm{OH})_{2}(s)\)

Short Answer

Expert verified
a. Cu(OH)\(_2\)(s) \(\rightleftharpoons\) Cu\(^{2+}\)(aq) + 2 OH\(^{-}\)(aq); \(K_{sp}\) = [Cu\(^{2+}\)] [OH\(^{-}\)]\(^{2}\) b. Cr(OH)\(_3\)(s) \(\rightleftharpoons\) Cr\(^{3+}\)(aq) + 3 OH\(^{-}\)(aq); \(K_{sp}\) = [Cr\(^{3+}\)] [OH\(^{-}\)]\(^{3}\) c. Ba(OH)\(_2\)(s) \(\rightleftharpoons\) Ba\(^{2+}\)(aq) + 2 OH\(^{-}\)(aq); \(K_{sp}\) = [Ba\(^{2+}\)] [OH\(^{-}\)]\(^{2}\) d. Sn(OH)\(_2\)(s) \(\rightleftharpoons\) Sn\(^{2+}\)(aq) + 2 OH\(^{-}\)(aq); \(K_{sp}\) = [Sn\(^{2+}\)] [OH\(^{-}\)]\(^{2}\)

Step by step solution

01

Write the balanced chemical equations

We will write down the balanced chemical equations representing the dissolving of each metal hydroxide in water. a. Cu(OH)\(_2\)(s) \(\rightleftharpoons\) Cu\(^{2+}\)(aq) + 2 OH\(^{-}\)(aq) b. Cr(OH)\(_3\)(s) \(\rightleftharpoons\) Cr\(^{3+}\)(aq) + 3 OH\(^{-}\)(aq) c. Ba(OH)\(_2\)(s) \(\rightleftharpoons\) Ba\(^{2+}\)(aq) + 2 OH\(^{-}\)(aq) d. Sn(OH)\(_2\)(s) \(\rightleftharpoons\) Sn\(^{2+}\)(aq) + 2 OH\(^{-}\)(aq)
02

Write the expressions for \(K_{sp}\) for each metal hydroxide

We will now write down the \(K_{sp}\) expressions for each metal hydroxide. For a general reaction: AB(s) \(\rightleftharpoons\) A\(^{n\text{+}}\)(aq) + B\(^{n\text{-}}\)(aq), the \(K_{sp}\) expression can be written as: \(K_{sp}\) = [A\(^{n+}\)][B\(^{n-}\)] Here, we will use this concept to derive expressions for the given metal hydroxides: a. Cu(OH)\(_2\)(s) \(\rightleftharpoons\) Cu\(^{2+}\)(aq) + 2 OH\(^{-}\)(aq) \(K_{sp}\) = [Cu\(^{2+}\)] [OH\(^{-}\)]\(^{2}\) b. Cr(OH)\(_3\)(s) \(\rightleftharpoons\) Cr\(^{3+}\)(aq) + 3 OH\(^{-}\)(aq) \(K_{sp}\) = [Cr\(^{3+}\)] [OH\(^{-}\)]\(^{3}\) c. Ba(OH)\(_2\)(s) \(\rightleftharpoons\) Ba\(^{2+}\)(aq) + 2 OH\(^{-}\)(aq) \(K_{sp}\) = [Ba\(^{2+}\)] [OH\(^{-}\)]\(^{2}\) d. Sn(OH)\(_2\)(s) \(\rightleftharpoons\) Sn\(^{2+}\)(aq) + 2 OH\(^{-}\)(aq) \(K_{sp}\) = [Sn\(^{2+}\)] [OH\(^{-}\)]\(^{2}\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Metal Hydroxides
Metal hydroxides are compounds consisting of a metal cation bonded to hydroxide ions (OH鈦). These are often characterized by their low solubility in water, meaning they do not dissolve readily. This can be puzzling for students because it contrasts with many ionic compounds which freely dissolve in water. However, the metal hydroxides have stronger ionic bonds and lattice structures that require more energy to break apart.
To assess the solubility of these compounds, we often perform dissolution tests in water. When they dissolve, they dissociate into their respective ions. Still, due to their low solubility, only a small concentration will dissociate. This dissociation is crucial for reactions in aqueous solutions as it defines the concentration of available metal ions and hydroxide ions.
For example, when copper(II) hydroxide (Cu(OH)鈧) dissolves in water, it separates into Cu虏鈦 ions and OH鈦 ions. As a rule of thumb, each metal hydroxide's solubility can significantly vary, thus making this a central concept in understanding reactions in inorganic chemistry.
Dissolution Equations
Dissolution equations describe the process by which a compound breaks down into its constituent ions in a solution. These equations are important because they offer a visual understanding of how compounds interact with water at the molecular level.
In dissolution equations for metal hydroxides, the solid formula of the compound (like Cu(OH)鈧) is shown on the left, and on the right, you see the ions it breaks down into when dissolved in water (like Cu虏鈦 and OH鈦). This can be represented as:
- Cu(OH)鈧(s) 鈬 Cu虏鈦(aq) + 2 OH鈦(aq).
Here, the double arrows indicate the reversible nature of the dissolution process, emphasizing that not all components dissolve completely. Each equation must balance, considering both the charge and the number of atoms involved. This balancing ensures the conservation of mass and the uniform distribution of charges in the solution.
Further, each metal hydroxide has unique coefficients, indicating how many ions of each type are produced per formula unit of the solid, influenced by its stoichiometry. These equations form the basis for predicting how solutions will behave in chemical processes.
Solubility Product Constant (Ksp)
The Solubility Product Constant, abbreviated as Ksp, is a measure that describes the extent to which a compound can dissolve in water. It is a specific type of equilibrium constant used in the context of solubility equilibria, especially for sparingly soluble compounds like metal hydroxides.
The Ksp takes into consideration the concentrations of the ions produced in the dissolution of the compound. For a general dissolution reaction, for example, AB(s) 鈬 A鈦(aq) + B鈦(aq), the Ksp expression is expressed as:
  • Ksp = [A鈦篯[B鈦籡
Thus, the Ksp expression is derived by the product of the concentrations of the ions each raised to the power of their coefficients from the balanced equation.
In terms of metal hydroxides, such as Cr(OH)鈧 dissolving as Cr鲁鈦(aq) + 3 OH鈦(aq), the corresponding Ksp expression will be:
  • Ksp = [Cr鲁鈦篯 [OH鈦籡鲁
The larger the value of Ksp, the more soluble the compound is. Understanding these constants helps predict the conditions under which a particular compound will precipitate or remain soluble, a vital aspect of chemical reactions and processes in solutions.

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Most popular questions from this chapter

Suppose the reaction system $$ \mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) $$ has already reached equilibrium. Predict the effect of each of the following changes on the position of the equilibrium. Tell whether the equilibrium will shift to the right, will shift to the left, or will not be affected. a. Any liquid water present is removed from the system. b. \(\mathrm{CO}_{2}\) is added to the system by dropping a chunk of dry ice into the reaction vessel. c. The reaction is performed in a metal cylinder fitted with a piston, and the piston is compressed to decrease the total volume of the system. d. Additional \(\mathrm{O}_{2}(g)\) is added to the system from a cylinder of pure \(\mathrm{O}_{2}\).

The three common silver halides ( \(\mathrm{AgCl}, \mathrm{AgBr},\) and \(\mathrm{AgI}\) ) are all sparingly soluble salts. Given the values for \(K_{\mathrm{sp}}\) for these salts below, calculate the concentration of silver ion, in \(\mathrm{mol} / \mathrm{L},\) in a saturated solution of each salt.

The equilibrium constant for the reaction $$ \mathrm{H}_{2}(g)+\mathrm{F}_{2}(g) \rightleftharpoons 2 \mathrm{HF}(g) $$ has the value \(2.1 \times 10^{3}\) at a particular temperature. When the system is analyzed at equilibrium at this temperature, the concentrations of both \(\mathrm{H}_{2}(g)\) and \(\mathrm{F}_{2}(g)\) are found to be \(0.0021 M\). What is the concentration of \(\mathrm{HF}(g)\) in the equilibrium system under these conditions?

Suppose \(K=4.5 \times 10^{-3}\) at a certain temperature for the reaction $$ \mathrm{PCl}_{5}(g) \rightleftharpoons \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) $$ If it is found that the concentration of \(\mathrm{PCl}_{5}\) is twice the concentration of \(\mathrm{PCl}_{3},\) what must be the concentration of \(\mathrm{Cl}_{2}\) under these conditions?

The solubility product constant, \(K_{\mathrm{sp}},\) for calcium carbonate at room temperature is approximately \(3.0 \times 10^{-9}\). Calculate the solubility of \(\mathrm{CaCO}_{3}\) in grams per liter under these conditions.

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