Chapter 10: Problem 76
Write the solubility product expression for each of the following salts. (a) \(\mathrm{BaCrO}_{4}\) (b) \(\mathrm{CaCO}_{3}\) (c) \(\mathrm{PbF}_{2}\) (d) \(\mathrm{Ag}_{2} \mathrm{~S}\)
Short Answer
Expert verified
(a) \(K_{sp} = [\mathrm{Ba}^{2+}][\mathrm{CrO}_{4}^{2-}]\); (b) \(K_{sp} = [\mathrm{Ca}^{2+}][\mathrm{CO}_{3}^{2-}]\); (c) \(K_{sp} = [\mathrm{Pb}^{2+}][\mathrm{F}^{-}]^2\); (d) \(K_{sp} = [\mathrm{Ag}^{+}]^2[\mathrm{S}^{2-}]\).
Step by step solution
01
State the dissociation equation for BaCrO4
The salt \(\mathrm{BaCrO}_{4}\) dissociates in water as follows: \[\mathrm{BaCrO}_{4(s)} \rightleftharpoons \mathrm{Ba}^{2+}_{(aq)} + \mathrm{CrO}_{4}^{2-}_{(aq)} \]
02
Write the solubility product expression for BaCrO4
The solubility product \(K_{sp}\) for \(\mathrm{BaCrO}_{4}\) is written as: \[K_{sp} = [\mathrm{Ba}^{2+}][\mathrm{CrO}_{4}^{2-}]\]
03
State the dissociation equation for CaCO3
The salt \(\mathrm{CaCO}_{3}\) dissociates in water as follows: \[\mathrm{CaCO}_{3(s)} \rightleftharpoons \mathrm{Ca}^{2+}_{(aq)} + \mathrm{CO}_{3}^{2-}_{(aq)} \]
04
Write the solubility product expression for CaCO3
The solubility product \(K_{sp}\) for \(\mathrm{CaCO}_{3}\) is written as: \[K_{sp} = [\mathrm{Ca}^{2+}][\mathrm{CO}_{3}^{2-}]\]
05
State the dissociation equation for PbF2
The salt \(\mathrm{PbF}_{2}\) dissociates in water as follows: \[\mathrm{PbF}_{2(s)} \rightleftharpoons \mathrm{Pb}^{2+}_{(aq)} + 2\mathrm{F}^{-}_{(aq)} \]
06
Write the solubility product expression for PbF2
The solubility product \(K_{sp}\) for \(\mathrm{PbF}_{2}\) is written as: \[K_{sp} = [\mathrm{Pb}^{2+}][\mathrm{F}^{-}]^2\]
07
State the dissociation equation for Ag2S
The salt \(\mathrm{Ag}_{2}\mathrm{~S}\) dissociates in water as follows: \[\mathrm{Ag}_{2} \mathrm{~S}_{(s)} \rightleftharpoons 2\mathrm{Ag}^{+}_{(aq)} + \mathrm{S}^{2-}_{(aq)} \]
08
Write the solubility product expression for Ag2S
The solubility product \(K_{sp}\) for \(\mathrm{Ag}_{2} \mathrm{~S}\) is written as: \[K_{sp} = [\mathrm{Ag}^{+}]^2[\mathrm{S}^{2-}]\]
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Dissociation Equations
In chemistry, when referring to a salt dissolving in water, we often talk about dissociation equations. These equations describe the process in which an ionic compound separates into its individual ions in a solution. This is key in understanding the ionic balance in solutions. For instance, the salt \( \mathrm{BaCrO}_{4} \) will dissociate in water to form ions like \( \mathrm{Ba}^{2+} \) and \( \mathrm{CrO}_4^{2-} \). This can be written as:
- \( \mathrm{BaCrO}_4(s) \rightleftharpoons \mathrm{Ba}^{2+}_{(aq)} + \mathrm{CrO}^{2-}_{4(aq)} \)
Solubility Equilibria
The concept of solubility equilibria revolves around the balance between dissolved ions and undissolved solid in a saturated solution. It's where the dissolution and precipitation rates of a salt are equal, resulting in no net change in concentration. This equilibrium is defined by the solubility product constant, \( K_{sp} \).
- For \( \mathrm{BaCrO}_4 \), the \( K_{sp} \) expression is \( [\mathrm{Ba}^{2+}][\mathrm{CrO}_4^{2-}] \).
- This concept exemplifies dynamic equilibrium, a fundamental principle in chemistry.
Sparingly Soluble Salts
Sparingly soluble salts are ionic compounds with limited solubility in water. This means only a small amount dissolves to produce a saturated solution. While they don’t dissolve completely, understanding them is vital in areas like geochemistry and pharmaceuticals.
- Examples include \( \mathrm{Ag}_2 \mathrm{S} \) and \( \mathrm{PbF}_2 \).
- For instance, the dissolution of \( \mathrm{PbF}_2 \) is represented by the equation \( \mathrm{PbF}_2(s) \rightleftharpoons \mathrm{Pb}^{2+}_{(aq)} + 2\mathrm{F}^{-}_{(aq)} \), with the \( K_{sp} \) given by \( [\mathrm{Pb}^{2+}][\mathrm{F}^{-}]^2 \).