Problem 8 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

As per Hardy-Schulze formulation, the flocculation values of the following for ferric hydroxide sol are in the order:(a) \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]<\mathrm{K}_{2} \mathrm{CrO}_{4}<\mathrm{KBr}=\mathrm{KNO}_{3}=\mathrm{AlCl}_{3}\) (b) \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]<\mathrm{K}_{2} \mathrm{CrO}_{4}<\mathrm{AlCl}_{3}<\mathrm{KBr}<\mathrm{KNO}_{3}\) (c) \(\mathrm{AlCl}_{3}>\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]>\mathrm{K}_{2} \mathrm{CrO}_{4}>\mathrm{KBr}=\mathrm{KNO}_{3}\) (d) \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]>\mathrm{AlCl}_{3}>\mathrm{K}_{2} \mathrm{CrO}_{4}>\mathrm{KBr}>\mathrm{KNO}_{3}\)

Step-by-Step Solution

Answer

The flocculation values are in order (a): \(\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]<\mathrm{K}_{2}\mathrm{CrO}_{4}<\mathrm{KBr}=\mathrm{KNO}_{3}=\mathrm{AlCl}_{3}\).

Step 1: Understanding Hardy-Schulze Rule

The Hardy-Schulze rule states that the flocculation value of a precipitating ion is inversely proportional to its valency. This means that ions with higher charges will have lower flocculation values than those with lower charges.

Step 2: Identify Charges of Ions

For the given options, identify the charges on the ions. The ferric hydroxide sol is positively charged, so we are interested in the negative ions. - \(\text{K}_3[\text{Fe}(\text{CN})_6]: \text{Fe}(\text{CN})_6^{3-}\)- \(\text{K}_2\text{CrO}_4: \text{CrO}_4^{2-}\)- \(\text{AlCl}_3: \text{Al}^{3+}\text{ (not applicable as it is a positive ion)}\)- \(\text{KBr} \text{ and } \text{KNO}_3: \text{Br}^- \text{ and } \text{NO}_3^-\) Note: AlCl\( _3 \) as a salt applies to the Al\( ^{3+} \) ion which does not participate in flocculation since it's positively charged.

Step 3: Rank the Ions Based on Charge

Using the Hardy-Schulze rule, rank the ions based on their negative charges:1. \(\text{Fe}(\text{CN})_6^{3-}\) has the highest charge.2. \(\text{CrO}_4^{2-}\) has a moderate charge.3. \(\text{Br}^-\) and \(\text{NO}_3^-\) both have charges of \(-1\).

Step 4: Determine Correct Order from Options

According to the Hardy-Schulze principle and the ion charges analyzed:\(\text{Fe}(\text{CN})_6^{3-}\) < \(\text{CrO}_4^{2-}\) < \text{Br}^- = \text{NO}_3^-Therefore, the correct order based on flocculation values would be option (a):\[\text{K}_3[\text{Fe}(\text{CN})_6]<\text{K}_2\text{CrO}_4<\text{KBr}=\text{KNO}_3=\text{AlCl}_3\]

Step 5: Verify Against the Given Options

Cross-checking with the answer choices:- Option (a): Matches \(\text{K}_3[\text{Fe}(\text{CN})_6]<\text{K}_2\text{CrO}_4<\text{KBr}=\text{KNO}_3=\text{AlCl}_3\) aligns with the Hardy-Schulze rule and the ion charges.- Option (b) and (c) and (d) do not follow the Hardy-Schulze principle based on charges of the ions.

Key Concepts

Flocculation Values

Flocculation values play a critical role in understanding the behavior of colloids in a solution. According to the Hardy-Schulze rule, flocculation value refers to the minimum concentration of a salt needed to cause the flocculation, or precipitation, of a colloid. This value is essential because it helps determine how easily ions will cause particles in a colloid to aggregate and settle out of the solution.
For example, in the context of ferric hydroxide sol, different salts have varying flocculation values due to the differing effectiveness of their negative ions in neutralizing the positive charge on the ferric hydroxide particles. The lower the flocculation value, the more effective the ion is at precipitating the sol. This principle has practical applications in water treatment processes, where appropriate salts are chosen to remove impurities from water by causing them to clump together and settle.

Ion Charges

The charge of ions in a solution significantly influences their capacity to cause flocculation. According to Hardy-Schulze's rule, ions that carry a higher negative charge are more effective at causing the precipitation of positively charged colloids. This is because a higher negative charge can better neutralize the positive charges on the colloidal particles.
In the context of the solution provided, consider the ions like \([\text{Fe}(\text{CN})_6^{3-}]\), which have a charge of \(-3\), compared to singly negative ions like \(\text{Br}^-\) and \(\text{NO}_3^-\). The triple negative charge makes \(\text{Fe}(\text{CN})_6^{3-}\) more efficient at flocculating the positively charged ferric hydroxide colloids than the singly negative ions. Thus, higher charged ions have lower flocculation values compared to those with lesser charges.

Precipitating Ions

Precipitating ions are those capable of causing a colloidal system to combine and separate from the dispersion medium as a precipitate. In a positively charged colloidal sol like ferric hydroxide, negatively charged ions from different salts will act as precipitating ions.
Recognizing which ions are precipitating is critical for predicting the order of flocculation values. This is because only the ions with a charge opposing the colloidal particles' charge can effectively cause aggregation. Specifically, in our context, ions like \(\text{Fe}(\text{CN})_6^{3-}\) are potent precipitating ions due to their high negative charge, efficiently neutralizing the positive charge.

Valency and Flocculation

Valency has a direct and profound effect on flocculation, as outlined by the Hardy-Schulze rule. Valency refers to the measure of an ion's combining power, closely related to the number of electrons lost or gained. The rule states that precipitating ions with higher valency have stronger flocculating power.
Practically, this means ions with high valency are more efficient in causing the flocculation of oppositely charged colloids. In the solution example, ions such as \(\text{Fe}(\text{CN})_6^{3-}\) have a valency of three, making them more effective at neutralizing the positive charges on the colloidal particles than ions like \(\text{Br}^-\) or \(\text{NO}_3^-\), which have a valency of one. This results in lower flocculation values and more effective aggregation and settlement of colloidal particles.