Problem 127 - 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 \(\mathrm{ZnS}\) is aqueous medium (a) \(\mathrm{CuS}>\mathrm{ZnS}>\mathrm{Na}_{2} \mathrm{~S}\) (b) \(\mathrm{ZnS}>\mathrm{Na}_{2} \mathrm{~S}>\mathrm{CuS}\) (c) \(\mathrm{Na}_{2} \mathrm{~S}>\mathrm{CuS}>\mathrm{ZnS}\) (d) \(\mathrm{Na}_{2} \mathrm{~S}>\mathrm{ZnS}>\mathrm{CuS}\)

Step-by-Step Solution

Answer

The correct order is (d) \(\mathrm{Na}_{2} \mathrm{~S} > \mathrm{ZnS} > \mathrm{CuS}\).

Step 1: Understanding Solubility Rules

In aqueous solutions, the solubility of sulfide compounds can be anticipated using the solubility product constant (K_sp). Ionic sulfide compounds generally follow the trend of decreasing solubility with the increase in size and charge, specifically with heavy metal ions like Cu and Zn in comparison to alkali metals like Na.

Step 2: Analyzing Na_2S Solubility

Na₂S, as a salt of an alkali metal (sodium), is very soluble in water. Alkali metal compounds generally dissolve completely in aqueous solutions. Therefore, Na₂S has high solubility.

Step 3: Analyzing CuS Solubility

CuS is a sulfide of a transition metal. It's known for having a very low solubility product, making it poorly soluble compared to many other sulfides. This indicates that CuS will precipitate out more readily than Na₂S and ZnS.

Step 4: Analyzing ZnS Solubility

ZnS, also a sulfide of a transition metal, has a low solubility product, but it is generally considered to have higher solubility than CuS. Thus, ZnS is more soluble than CuS, but still far less soluble than Na₂S.

Step 5: Establishing Correct Solubility Order

Considering the solubility characteristics discussed earlier, we conclude that Na₂S > ZnS > CuS in terms of solubility in aqueous solution. This follows the trend that alkali metal sulfides are highly soluble, while transition metal sulfides have low solubilities.

Key Concepts

Solubility Product Constant (K_sp)

The solubility product constant, abbreviated as \(K_{sp}\), is a numerical value that indicates the extent to which a compound can dissolve in water to form a saturated solution. It specifically applies to sparingly soluble salts. These are the salts that dissolve just enough to establish an equilibrium between the undissolved solid and the ions in solution.

For instance, consider a salt \(AB\) that dissolves according to the equation \(AB \leftrightarrow A^+ + B^-\). The solubility product is expressed as \(K_{sp} = [A^+][B^-]\). A lower \(K_{sp}\) value indicates lesser solubility, meaning the compound doesn’t dissolve well in water.

This concept is critical for understanding why certain sulfides stay precipitated while others dissolve. Transition metal sulfides, having very low \(K_{sp}\) values, are notorious for their limited solubility. In education and experiments, \(K_{sp}\) is pivotal in predicting solubility outcomes and explaining why certain reactions result in solid precipitates.

Transition Metal Sulfides

Transition metals like copper and zinc form sulfides that have distinct solubility characteristics. Due to their chemical properties, these sulfides tend to have low \(K_{sp}\) values, leading to poor solubility in water.

Transition metal sulfides include compounds like \(CuS\) (Copper sulfide) and \(ZnS\) (Zinc sulfide). They are well known for their tendency to form precipitates. This happens because they do not dissolve readily, meaning that in an aqueous solution, they remain mostly as solid rather than ions in the solution.

In our problem scenario, \(CuS\) exhibits a much lower solubility than \(ZnS\), making it the least soluble sulfide in the group. However, both \(CuS\) and \(ZnS\) pale in comparison to alkali metal sulfides like \(Na_2S\), which dissolve almost completely. Understanding these differences is crucial, especially when predicting chemical behavior in various reactions.

Alkali Metal Compounds

Alkali metal compounds, such as \(Na_2S\), generally exhibit high solubility in water. This is due to the nature of alkali metals—like sodium—which form highly soluble salts.

In the periodic table, alkali metals are known for readily dissolving in water, breaking apart into their ions. This characteristic makes \(Na_2S\), in our scenario, the most soluble out of the three compounds.

The high solubility of alkali metal compounds contrasts sharply with the transition metal sulfides, providing a clear example of how different the solubility behaviors can be among different categories of metal sulfides. For students comparing solubility, this property can guide understanding why certain compounds dissolve easily while others do not. This knowledge assists in predicting and controlling chemical solutions and reactions effectively.