Problem 92 - A Complete Resource Book in Chemistry for JEE Main

Question

Identify the correct order of solubility of \(\mathrm{Na}_{2} \mathrm{~S}, \mathrm{CuS}\) and \(\mathrm{ZnS}\) in aqueous medium. (a) \(\mathrm{Na}_{2} \mathrm{~S}>\mathrm{CuS}>\mathrm{ZnS}\) (b) \(\mathrm{Na}_{2} \mathrm{~S}>\mathrm{ZnS}>\mathrm{CuS}\) (c) \(\mathrm{CuS}>\mathrm{ZnS}>\mathrm{Na}_{2} \mathrm{~S}\) (d) \(\mathrm{ZnS}>\mathrm{Na}_{2} \mathrm{~S}>\mathrm{CuS}\)

Step-by-Step Solution

Answer

(b) \mathrm{Na}_{2} \mathrm{~S} > \mathrm{ZnS} > \mathrm{CuS}

Step 1: Understanding the Solubility Product

The solubility of a compound in an aqueous medium is primarily determined by its solubility product constant (Ksp). The lower the Ksp value, the less soluble the compound is.

Step 2: Analyze the Compounds

We recognize that \(\mathrm{Na}_{2} \mathrm{~S}\) is a soluble sulfide of a Group 1 metal, whereas \(\mathrm{CuS}\) and \(\mathrm{ZnS}\) are sparingly soluble sulfides of transition metals. Generally, Group 1 metal sulfides, such as \(\mathrm{Na}_{2} \mathrm{~S}\), are much more soluble in water compared to transition metal sulfides.

Step 3: Arrange Based on General Solubility

Given the high solubility of alkali metal sulfides, \(\mathrm{Na}_{2} \mathrm{~S}\) will be the most soluble. \(\mathrm{CuS}\) and \(\mathrm{ZnS}\) both have low solubility, but generally, \(\mathrm{ZnS}\) is slightly more soluble than \(\mathrm{CuS}\) due to its slightly higher \(\Ksp\).

Step 4: Conclude the Order of Solubility

Thus, the order from most soluble to least soluble is \(\mathrm{Na}_{2} \mathrm{~S} > \mathrm{ZnS} > \mathrm{CuS}\).

Key Concepts

Solubility Product Constant (Ksp)

The solubility product constant, commonly denoted as \( K_{sp} \), is a key concept in understanding the solubility of compounds in an aqueous medium. Essentially, \( K_{sp} \) is an equilibrium constant for a solid substance dissolving in water to form its constituent ions. It directly correlates with how soluble a compound is; the higher the \( K_{sp} \), the more soluble the compound. This makes \( K_{sp} \) a vital tool in predicting the behavior of salts in solution.
For example, consider a generic salt \( AB \) dissolving as \( AB(s) \rightarrow A^+(aq) + B^-(aq) \). The \( K_{sp} \) expression would be \( [A^+][B^-] \). The concentration of the ions at equilibrium helps us understand how much of the salt dissolves in water.
If you are comparing solubility levels, it's important to refer to their \( K_{sp} \) values. A lower \( K_{sp} \) indicates a less soluble compound, providing a simple way to rank the solubility of different substances.

Group 1 Metal Sulfides

Group 1 metal sulfides generally possess high solubility due to the unique properties of alkali metals. These elements, which include sodium, potassium, and others, have one electron in their outer shell. This configuration enhances their ability to form soluble compounds. Sodium sulfide (\( \mathrm{Na}_2 \mathrm{S} \)) is an excellent example.
This compound disassociates readily in water, and its high solubility can be attributed to the strong affinity of sodium ions for water molecules. This is a typical trait across Group 1 sulfides, making them more soluble compared to sulfides from other metal groups.

• High reactivity due to single valence electron
• Results in greater solubility
• Commonly used in industrial applications for this reason

Transition Metal Sulfides

Transition metal sulfides, such as copper sulfide (\( \mathrm{CuS} \)) and zinc sulfide (\( \mathrm{ZnS} \)), generally have low solubility in water. This is primarily due to the nature of transition metals. These elements have partially filled \( d \)-orbitals, resulting in the formation of less soluble compounds.
Unlike Group 1 metals, transition metals form compounds where the metal-sulfur bonds are more covalent, leading to decreased solubility.

• The lower solubility is reflected by smaller \( K_{sp} \) values
• Shows a tendency to form precipitates in aqueous solutions
• Important in processes like metallurgy where such characteristics are needed

Copper sulfide is known to be very insoluble, resulting in a much smaller \( K_{sp} \) than that of zinc sulfide. Hence, \( \mathrm{CuS} \) and \( \mathrm{ZnS} \) are ranked based on their solubility: \( \mathrm{ZnS} \) being slightly more soluble than \( \mathrm{CuS} \).