Problem 100 - Chemistry

Question

Order the following solids (a–d) from least soluble to most soluble. Ignore any potential reactions of the ions with water. a. \(\mathrm{AgCl} \quad K_{s p}=1.6 \times 10^{-10}\) 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. \(\mathrm{CuS} \quad K_{\mathrm{sp}}=8.5 \times 10^{-45}\)

Step-by-Step Solution

Answer

The order of the solubility of these solids based on their Ksp values is Ag2S < CuS < AgCl < CaF2, from least soluble to most soluble.

Step 1: List the given Ksp values for each solid

For each solid, we have the following Ksp values: a. AgCl: \(K_{sp} = 1.6 \times 10^{-10}\) b. Ag2S: \(K_{sp} = 1.6 \times 10^{-49}\) c. CaF2: \(K_{sp} = 4.0 \times 10^{-11}\) d. CuS: \(K_{sp} = 8.5 \times 10^{-45}\)

Step 2: Identify the least soluble solid

From the given Ksp values, we can see that the solid with the lowest Ksp value is Ag2S with a Ksp of \(1.6 \times 10^{-49}\). This means that Ag2S is the least soluble solid among the four.

Step 3: Identify the next least soluble solid

After Ag2S, the solid with the next lowest Ksp value is CuS with a Ksp of \(8.5 \times 10^{-45}\). This implies that CuS is the second least soluble solid among the four.

Step 4: Identify the next least soluble solid

The solid with the next lowest Ksp value after CuS is AgCl with a Ksp of \(1.6 \times 10^{-10}\). This indicates that AgCl is the third least soluble solid among the four.

Step 5: Identify the most soluble solid

Finally, the remaining solid is CaF2, which has a Ksp value of \(4.0 \times 10^{-11}\). By default, CaF2 is the most soluble solid among the four.

Step 6: Order the solids from least soluble to most soluble

Taking all steps into account, we can order the solids as follows: 1. Ag2S (least soluble): \( K_{sp} = 1.6 \times 10^{-49} \) 2. CuS: \( K_{sp} = 8.5 \times 10^{-45} \) 3. AgCl: \( K_{sp} = 1.6 \times 10^{-10} \) 4. CaF2 (most soluble): \( K_{sp} = 4.0 \times 10^{-11} \) Thus, the order of the solubility of these solids is Ag2S < CuS < AgCl < CaF2.

Key Concepts

Ksp (Solubility Product Constant)

The solubility product constant, often represented as \( K_{sp} \), is a key concept in understanding how soluble a compound is in water. It's specifically used for ionic compounds. Essentially, \( K_{sp} \) is a mathematical representation of the solubility of a solid in a solution.
It indicates the level at which a compound dissolves to form its constituent ions. The smaller the \( K_{sp} \) value, the less soluble the compound is.
To comprehend how \( K_{sp} \) works, let's consider a generic ionic compound \( AB \) that dissolves according to the equation: \[ AB(s) \rightleftharpoons A^+(aq) + B^-(aq) \]Here, \( K_{sp} \) would be expressed as:\[ K_{sp} = [A^+][B^-] \]The brackets denote the concentration of ions, and their product gives us the \( K_{sp} \) value.
For instance, for calcium fluoride \( (CaF_2) \), the equation is:\[ CaF_2(s) \rightleftharpoons Ca^{2+}(aq) + 2F^-(aq) \]And so, the \( K_{sp} \) is:\[ K_{sp} = [Ca^{2+}][F^-]^2 \] Understanding this helps predict how much of a compound can be dissolved in a solution before it becomes saturated.

Solubility Ranking

Solubility ranking is the process of arranging compounds based on their solubility. It's often determined by comparing their \( K_{sp} \) values. In general, the higher the \( K_{sp} \) value, the more soluble the compound is in water.
This ranking can be used to predict which compounds will dissolve more readily.
In the given exercise, the solids were ranked as: - Ag2S (least soluble)- CuS- AgCl- CaF2 (most soluble)This order was determined by their respective \( K_{sp} \) values, starting from the lowest for Ag2S, which is \( 1.6 \times 10^{-49} \), up to the highest for CaF2, with a \( K_{sp} \) of \( 4.0 \times 10^{-11} \).
By knowing the \( K_{sp} \) values, one can make educated guesses on the relative solubilities of different compounds. This kind of ranking is crucial in fields like chemistry and environmental science, where solubility determines the behavior and distribution of substances in various environments.

Ionic Compounds

Ionic compounds are chemical compounds composed of ions held together by electrostatic forces, known as ionic bonds. These compounds typically form when metals transfer electrons to non-metals, resulting in a positive metal ion \( (cation) \) and a negative non-metal ion \( (anion) \).
A classic example of an ionic compound is sodium chloride (NaCl), commonly known as table salt.
The properties of ionic compounds include:

• High Melting and Boiling Points: Because of strong ionic bonds.
• Conductivity When Dissolved: Ionic compounds conduct electricity when dissolved in water, allowing ions to move freely.
• Generally Soluble in Water: Many ionic compounds dissolve in water, a polar solvent, due to the interaction between water molecules and ions.

The solubility of ionic compounds is essential as it determines how substances dissolve or react in solutions.
This knowledge is necessary for various applications, from understanding reactions in aquatic systems to everyday products like soap.
In the context of the exercise, knowing about ionic compounds helps explain why these solids dissolve to varying extents, based on their \( K_{sp} \) values, reflecting their tendency to dissociate into ions.