Problem 191 - A Complete Resource Book in Chemistry for JEE Main

Question

When \(\mathrm{H}_{2} \mathrm{~S}\) is passed through an aqueous solution of an equilimolar mixture of \(\mathrm{Zn}^{2+}\) and \(\mathrm{Pb}^{2+}\) acidified with dilute acetic acid, \(\mathrm{ZnS}\) is not precipitated, because (a) \(\mathrm{K}_{\mathrm{sp}}(\mathrm{ZnS})<\mathrm{K}_{\mathrm{sp}}(\mathrm{PbS})\) (b) \(\mathrm{K}_{\mathrm{sp}}(\mathrm{ZnS})>\mathrm{K}_{\mathrm{sp}}^{\mathrm{sp}}(\mathrm{PbS})\) (c) \(\mathrm{H}_{2} \mathrm{~S}\) decreases the \(\mathrm{K}_{\mathrm{sp}}\) of \(\mathrm{ZnS}\) (d) \(\mathrm{H}_{2} \mathrm{~S}\) increases the \(\mathrm{K}_{\mathrm{sp}}\) of \(\mathrm{PbS}\)

Step-by-Step Solution

Answer

(b) \(\mathrm{K}_{\mathrm{sp}}(\mathrm{ZnS}) > \mathrm{K}_{\mathrm{sp}}(\mathrm{PbS})\).

Step 1: Understand The Reaction

When hydrogen sulfide (\(\mathrm{H}_2 \mathrm{S}\)) is passed through an aqueous solution containing \(\mathrm{Zn}^{2+}\) and \(\mathrm{Pb}^{2+}\) ions, it can react with these ions to form \(\mathrm{ZnS}\) and \(\mathrm{PbS}\) as potential precipitates. The selective precipitation depends on solubility products (\(\mathrm{K}_{\mathrm{sp}}\)).

Step 2: Compare Solubility Products

The solubility product constant (\(\mathrm{K}_{\mathrm{sp}}\)) is a measure of the solubility of an ionic compound. In this context, \(\mathrm{K}_{\mathrm{sp}}(\mathrm{PbS})\) is much lower compared to \(\mathrm{K}_{\mathrm{sp}}(\mathrm{ZnS})\). This indicates that \(\mathrm{PbS}\) is less soluble and precipitates earlier than \(\mathrm{ZnS}\) when \(\mathrm{H}_2 \mathrm{S}\) is added.

Step 3: Analyze the Effect of Dilute Acid

The presence of dilute acetic acid suppresses the ionization of \(\mathrm{H}_2 \mathrm{S}\), reducing the availability of \(\mathrm{S}^{2-}\) ions. The concentration of \(\mathrm{S}^{2-}\) ions is just sufficient to exceed the \(\mathrm{K}_{\mathrm{sp}}\) for \(\mathrm{PbS}\) but not for \(\mathrm{ZnS}\), preventing precipitation of \(\mathrm{ZnS}\).

Step 4: Select the Correct Explanation

The appropriate explanation for \(\mathrm{ZnS}\) not precipitating is that \(\mathrm{K}_{\mathrm{sp}}(\mathrm{ZnS})\) is greater than \(\mathrm{K}_{\mathrm{sp}}(\mathrm{PbS})\), allowing \(\mathrm{PbS}\) to precipitate while \(\mathrm{ZnS}\) remains dissolved. Thus, the correct answer is (b).

Key Concepts

Selective Precipitation

Selective precipitation is a method used in chemistry to separate ions in a solution based on their differing solubilities. When a solution contains multiple ionic species, a precipitating agent can be introduced to selectively precipitate one of the ions, making use of the distinct solubility product (Ksp) values of the compounds formed.
This concept is exemplified when hydrogen sulfide ( H_2 S) is bubbled through an aqueous solution containing both Zn^{2+} and Pb^{2+} ions. It can form precipitates with these ions, creating ZnS and PbS. The lower K_{sp} value of PbS compared to ZnS means PbS is less soluble, resulting in its precipitation first. The reaction proceeds until PbS reaches a solubility threshold and forms a solid, leaving ZnS in the solution.
This technique is particularly useful in laboratory settings where complex mixtures need to be separated into individual components based on specific properties like solubility. Understanding selective precipitation allows chemists to exploit small differences in solubility to achieve separation—a crucial tool in analytical and inorganic chemistry.

Ionic Equilibrium

Ionic equilibrium refers to the state in which the rate of the forward reaction of ionization is equal to the rate of the reverse reaction. This balance indicates no net change in the concentration of ions in solution, a common occurrence in many chemical reactions involving ionic compounds.
In the context of the original problem, ionic equilibrium is key to understanding how PbS precipitates but ZnS does not. The addition of H_2 S leads to an equilibrium involving S^{2-} ions. Due to the presence of dilute acetic acid, the dissociation of H_2 S into S^{2-} is suppressed, maintaining a concentration just above the K_{sp} of PbS but below that of ZnS. Consequently, equilibrium is achieved for precipitating Pb^{2+} ions as PbS, aligning with its lower solubility product constant.
This concept underscores the delicate balance of forces involved in ionic reactions and how changing concentrations can shift equilibria, affecting the outcomes of chemical processes.

Acid-Base Chemistry

Acid-base chemistry explores the behaviors of acids, bases, and their interactions, particularly the transfer of protons ( H^+ ). It often involves the manipulation of the acid and base properties to affect equilibrium and reaction outcomes.
In the problem scenario, dilute acetic acid modifies the environment by influencing the ionization state of H_2 S. The acetic acid, being a weak acid, only partially ionizes in solution. This weak ionization means it can slightly suppress the generation of S^{2-} ions from H_2 S, altering the reaction landscape and influencing which precipitate forms.
Acetic acid's presence exemplifies how acid-base chemistry can control the availability of ions in solution, steering the reaction toward the precipitation of PbS over ZnS. By managing the amount of S^{2-} providing an acidic environment, chemists can dictate which compounds will remain in solution and which will precipitate. This approach is a practical application of acid-base principles, demonstrating the intricate interplay between chemical species in solution.