Problem 94
Question
Order the following solids (a-d) from least soluble to most soluble. Ignore any potential reactions of the ions with water. a. \(\mathrm{AgCl} \quad K_{\mathrm{sp}}=1.6 \times 10^{-10}\) b. \(\mathrm{Ag}_{2} \mathrm{S} \quad K_{\mathrm{sp}}=1.6 \times 10^{-49}\) c. \(\mathrm{CaF}_{2} \quad K_{\mathrm{sp}}=4.0 \times 10^{-11}\) d. CuS \(\quad K_{\mathrm{sp}}=8.5 \times 10^{-45}\)
Step-by-Step Solution
Verified Answer
Least soluble to most soluble: \( \mathrm{Ag}_{2} \mathrm{S} \rightarrow \mathrm{CuS} \rightarrow \mathrm{AgCl} \rightarrow \mathrm{CaF}_{2} \)
1Step 1: List the solids with their corresponding \(K_{sp}\) values
:
a. \(\mathrm{AgCl}, \quad K_{\mathrm{sp}}=1.6 \times 10^{-10}\)
b. \(\mathrm{Ag}_{2} \mathrm{S}, \quad K_{\mathrm{sp}}=1.6 \times 10^{-49}\)
c. \(\mathrm{CaF}_{2}, \quad K_{\mathrm{sp}}=4.0 \times 10^{-11}\)
d. \(\mathrm{CuS}, \quad K_{\mathrm{sp}}=8.5 \times 10^{-45}\)
2.
2Step 2: Arrange the solids from lowest \(K_{sp}\) value to highest \(K_{sp}\) value
:
b. \(\mathrm{Ag}_{2} \mathrm{S}, \quad K_{\mathrm{sp}}=1.6 \times 10^{-49}\) (least soluble)
d. \(\mathrm{CuS}, \quad K_{\mathrm{sp}}=8.5 \times 10^{-45}\)
a. \(\mathrm{AgCl}, \quad K_{\mathrm{sp}}=1.6 \times 10^{-10}\)
c. \(\mathrm{CaF}_{2}, \quad K_{\mathrm{sp}}=4.0 \times 10^{-11}\) (most soluble)
3.
3Step 3: Order the solids from least soluble to most soluble
:
From the ordered list of \(K_{sp}\) values, we can now order the given solids from least soluble to most soluble:
- Least soluble: \(\mathrm{Ag}_{2} \mathrm{S}\)
- Second least soluble: \(\mathrm{CuS}\)
- Second most soluble: \(\mathrm{AgCl}\)
- Most soluble: \(\mathrm{CaF}_{2}\)
Key Concepts
SolubilityAgClAg2SCaF2CuS
Solubility
Solubility is a property that tells us how much of a substance (solute) can dissolve in a solvent to form a solution.
In chemistry, when a solid dissolves in a liquid, it reaches a point where no more can dissolve, known as "saturation."
The measure of this saturation is called the solubility product constant ( K_{sp} ). It reflects the maximum concentration of ions that can exist in equilibrium in a solution of the solute.
- **Lower K_{sp} values:** Indicate less solubility. - **Higher K_{sp} values:** Indicate greater solubility.
For our example, by comparing the K_{sp} values of different compounds, we can determine their relative solubility.
In chemistry, when a solid dissolves in a liquid, it reaches a point where no more can dissolve, known as "saturation."
The measure of this saturation is called the solubility product constant ( K_{sp} ). It reflects the maximum concentration of ions that can exist in equilibrium in a solution of the solute.
- **Lower K_{sp} values:** Indicate less solubility. - **Higher K_{sp} values:** Indicate greater solubility.
For our example, by comparing the K_{sp} values of different compounds, we can determine their relative solubility.
AgCl
Silver chloride (AgCl) is a compound with a K_{sp} value of 1.6 × 10^{-10}, signifying its relatively limited solubility in water.
AgCl is used in photographic films and some antimicrobial applications due to its low solubility.
When AgCl dissolves, it dissociates as follows:
\[\text{AgCl (s) } \rightleftharpoons \text{ Ag}^+ \text{(aq) } + \text{ Cl}^- \text{(aq)} \]
- **Practical implications:** Since it's not very soluble, concentrations of Ag^+ and Cl^- ions in the solution remain low, meaning it precipitates easily.- **Applications:** The limited solubility allows it to be useful in detecting or restricting chloride ions in various solutions.
AgCl is used in photographic films and some antimicrobial applications due to its low solubility.
When AgCl dissolves, it dissociates as follows:
\[\text{AgCl (s) } \rightleftharpoons \text{ Ag}^+ \text{(aq) } + \text{ Cl}^- \text{(aq)} \]
- **Practical implications:** Since it's not very soluble, concentrations of Ag^+ and Cl^- ions in the solution remain low, meaning it precipitates easily.- **Applications:** The limited solubility allows it to be useful in detecting or restricting chloride ions in various solutions.
Ag2S
Silver sulfide (Ag_2S) has an extremely low K_{sp} value of 1.6 × 10^{-49}, making it one of the least soluble compounds.
This compound typically forms in atmospheric conditions, such as tarnish on silverware.
Its dissolution equation is:
\[\text{Ag}_2\text{S (s) } \rightleftharpoons 2\text{ Ag}^+ \text{(aq) } + \text{ S}^{2-} \text{(aq)} \]
- **Practical implications:** The low solubility means Ag_2S remains mostly solid under ordinary conditions.- **Behavior:** Most of the compound will not dissolve even in the presence of water.
This compound typically forms in atmospheric conditions, such as tarnish on silverware.
Its dissolution equation is:
\[\text{Ag}_2\text{S (s) } \rightleftharpoons 2\text{ Ag}^+ \text{(aq) } + \text{ S}^{2-} \text{(aq)} \]
- **Practical implications:** The low solubility means Ag_2S remains mostly solid under ordinary conditions.- **Behavior:** Most of the compound will not dissolve even in the presence of water.
CaF2
Calcium fluoride (CaF_2) with a K_{sp} value of 4.0 × 10^{-11} has relatively more solubility compared to other compounds like AgCl or CuS.
This compound dissolves by the following reaction:
\[\text{CaF}_2 \text{(s)} \rightleftharpoons \text{Ca}^{2+} \text{(aq)} + 2\text{ F}^- \text{(aq)} \]
- **Natural occurrence:** CaF_2 is found naturally as the mineral fluorite.- **Uses:** It's an important source of fluoride ions and used in applications like producing hydrofluoric acid.
Despite a relatively higher K_{sp}, it is still considered sparingly soluble, balancing utility and stability in many chemical processes.
This compound dissolves by the following reaction:
\[\text{CaF}_2 \text{(s)} \rightleftharpoons \text{Ca}^{2+} \text{(aq)} + 2\text{ F}^- \text{(aq)} \]
- **Natural occurrence:** CaF_2 is found naturally as the mineral fluorite.- **Uses:** It's an important source of fluoride ions and used in applications like producing hydrofluoric acid.
Despite a relatively higher K_{sp}, it is still considered sparingly soluble, balancing utility and stability in many chemical processes.
CuS
Copper(II) sulfide (CuS) has a very low solubility with a K_{sp} value of 8.5 × 10^{-45}.
It typically exists as a black precipitate and is used in the production of solar cells and certain pigments.
When it dissolves, the reaction is:
\[\text{CuS (s) } \rightleftharpoons \text{Cu}^{2+} \text{(aq) } + \text{S}^{2-} \text{(aq)} \]
- **Practical implications:** Its limited solubility leads to CuS precipitating out of solution in many chemical reactions.- **Environment:** CuS is often found in copper-rich mineral deposits and contributes to the characteristic green and blue colors in some minerals.
This low solubility is crucial in contexts where selective precipitation is needed.
It typically exists as a black precipitate and is used in the production of solar cells and certain pigments.
When it dissolves, the reaction is:
\[\text{CuS (s) } \rightleftharpoons \text{Cu}^{2+} \text{(aq) } + \text{S}^{2-} \text{(aq)} \]
- **Practical implications:** Its limited solubility leads to CuS precipitating out of solution in many chemical reactions.- **Environment:** CuS is often found in copper-rich mineral deposits and contributes to the characteristic green and blue colors in some minerals.
This low solubility is crucial in contexts where selective precipitation is needed.
Other exercises in this chapter
Problem 90
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