Problem 76 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

For the following Assertion and Reason, the correct option is [Main Sep. 02, \(\mathbf{2 0 2 0}\) (I)] Assertion (A) : When Cu (II) and sulphide ions are mixed, they react together extremely quickly to give a solid. Reason (R) : The equilibrium constant of \(\mathrm{Cu}^{2+}(\mathrm{aq})+\mathrm{S}^{2-}(\mathrm{aq}) \rightleftharpoons \mathrm{CuS}\) (s) is high because the solubility product is low. (a) Both \(\mathrm{S}\) and \(\mathrm{E}\) are true, and \(\mathrm{E}\) is the correct explanation of \(\mathrm{S}\). (b) Both \(\mathrm{S}\) and \(\mathrm{E}\) are true, but \(\mathrm{E}\) is not the correct explanation of \(\mathrm{S}\). (c) \(\mathrm{S}\) is true but \(\mathrm{E}\) is false. (d) \(\mathrm{S}\) is false but \(\mathrm{E}\) is true.

Step-by-Step Solution

Answer

(a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

Step 1: Understanding the Assertion

The assertion states that when Cu (II) ions and sulfide ions are combined, they react very quickly to produce a solid, CuS. This implies that the reaction proceeds rapidly to form the solid product without significant hesitation.

Step 2: Analyzing the Reason

The reason given is that the equilibrium constant for the formation of copper sulfide (\[\mathrm{Cu}^{2+} + \mathrm{S}^{2-} \rightleftharpoons \mathrm{CuS} \]) is high because the solubility product (Ksp) is low. A low solubility product means that the compound is not very soluble in water, which would lead to high formation of the solid.

Step 3: Linking Assertion with Reason

The high equilibrium constant, caused by the low Ksp, means the reaction proceeds almost entirely to the right to form CuS. This explains the quick formation of the solid when Cu (II) and sulfide ions are mixed, providing a direct link between the reason and the assertion.

Step 4: Conclusion and Choice Justification

Since the high equilibrium constant and low solubility product of CuS justify the reason and support the rapid reaction mentioned in the assertion, both statements (Assertion and Reason) are true, and the reason is indeed the correct explanation for the assertion. Therefore, the correct answer is option (a).

Key Concepts

Solubility Product

The solubility product, often abbreviated as Ksp, is a special type of equilibrium constant. It applies to the dissolving process of sparingly soluble ionic compounds. In essence, it provides a quantitative measure of the compound's solubility. For a given ionic compound separating into its ions in solution, the solubility product is expressed as the product of the molar concentrations of the ions, each raised to the power of its stoichiometric coefficient in the balanced equation.
Ksp is essential in predicting whether a precipitate will form in a solution. The lower the Ksp value, the less soluble the compound is in water, indicating that it will more readily form a solid precipitate when the ionic concentrations exceed the Ksp value. This is crucial in understanding the behavior of compounds like copper sulfide (\(\text{CuS}\)
In the context of the problem, the low Ksp of copper sulfide means that even small amounts of Cu²⁺ and S^2- ions in a solution will result in the rapid formation of a solid. This directly influences reactions and solubility equilibrium, making understanding the solubility product critical for predicting and controlling precipitation reactions.

Equilibrium Constant

An equilibrium constant, denoted as K, provides insight into the extent of a reaction at equilibrium. For reversible reactions, it indicates the ratio of the concentration of the products to the reactants, each raised to the power corresponding to their coefficients in the balanced reaction equation. A large equilibrium constant implies that the reaction heavily favors the formation of products.
In the equilibrium between Cu²⁺ and S^2- ions forming CuS, a high equilibrium constant implies that the forward reaction is strongly favored. This means that, at equilibrium, there is an abundant formation of the solid product, CuS, from its ions. As the equilibrium constant is large, the concentrations of the reactants are low, reflecting the formation of a precipitate.
With a high equilibrium constant in this scenario, the behavior of CuS in solution becomes predictable. Since much of the ionic concentration is transformed into solid CuS quickly, the representation of this principle highlights the reaction favoring the formation of a solid. Thus, understanding the equilibrium constant aids in predicting the position of equilibrium and how reactants and products interact at any given time.

Precipitation Reaction

Precipitation reactions occur when two solutions are mixed and an insoluble solid, known as a precipitate, forms within the solution. These reactions are typically predicted using the solubility product (Ksp) and understanding the equilibrium constant.
During such reactions, if the concentrations of the constituent ions in solution exceed the product of their solubility product, a precipitate forms. As in the case of copper sulfide, when Cu²⁺ and S^2- ions are introduced into the solution, their immediate reaction forms a solid due to the low solubility product, drastically reducing the ionic concentrations in the solution.
Precipitation reactions are hallmark examples of how equilibrium concepts govern practical chemistry processes. They show the direct application of chemical laws in creating solids from solutions, being pivotal in the fields of chemistry involving separation processes, purification, and qualitative analysis of ions in solution. A good understanding of precipitation reactions is hence significant for students tackling problems involving chemical equilibrium and solubility dynamics.