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 \(\quad K_{\mathrm{sp}}=8.5 \times 10^{-45}\)

Short answer

Least soluble to most soluble: \( \mathrm{Ag}_{2} \mathrm{S} \rightarrow \mathrm{CuS} \rightarrow \mathrm{AgCl} \rightarrow \mathrm{CaF}_{2} \)

Step-by-step solution

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.

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.

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

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.

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.

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.

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.

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.