Problem 1 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Arrange the following solutions in the decreasing order of \(\mathrm{pOH}\) : (A) \(0.01 \mathrm{M} \mathrm{HCl}\) (B) \(0.01 \mathrm{M} \mathrm{NaOH}\) (C) \(0.01 \mathrm{M} \mathrm{CH}_{3} \mathrm{COONa}\) (D) \(0.01 \mathrm{M} \mathrm{NaCl}\) (a) \((\mathrm{A})>(\mathrm{C})>(\mathrm{D})>(\mathrm{B})\) (b) \((\mathrm{A})>(\mathrm{D})>(\mathrm{C})>(\mathrm{B})\) (c) \((\mathrm{B})>(\mathrm{C})>(\mathrm{D})>(\mathrm{A})\) (d) \((\mathrm{B})>(\mathrm{D})>(\mathrm{C})>(\mathrm{A})\)

Step-by-Step Solution

Answer

(b) (A) > (D) > (C) > (B)

Step 1: Understand pOH

The pOH of a solution is a measure of its hydroxide ion (OH^-) concentration. It can be calculated as \(\mathrm{pOH} = -\log_{10}[\text{OH}^-]\). A higher pOH indicates a lower hydroxide concentration and thus a more acidic solution.

Step 2: Calculate pOH of 0.01 M HCl (A)

HCl is a strong acid and dissociates completely in water: HCl \rightarrow H^+ + Cl^-. Hence, it does not contribute to the OH^- concentration, as it increases the H^+ concentration. Using the relation \(\mathrm{pH} + \mathrm{pOH} = 14\), we find pOH by first calculating pH: \(\mathrm{pH} = -\log_{10}[\text{H}^+] = 2\). Hence, \(\mathrm{pOH} = 14 - 2 = 12\).

Step 3: Calculate pOH of 0.01 M NaOH (B)

NaOH is a strong base and dissociates completely: NaOH \rightarrow Na^+ + OH^-. The hydroxide concentration is \(0.01 \text{ M}[\text{OH}^-]\), so \(\mathrm{pOH} = -\log_{10}[0.01] = 2\).

Step 4: Calculate pOH of 0.01 M CH3COONa (C)

CH3COONa is the salt of a weak acid (CH3COOH) and a strong base (NaOH). In solution, it forms a basic solution as CH3COO^- partially hydrolyzes to produce OH^- ions. Let x be the concentration of OH^- formed, then we use the kb of CH3COO^- to estimate pOH. Since this needs a more advanced calculation, for simplicity, note that pOH will be more than 7 but less than 12, as it's a weak base salt.

Step 5: Calculate pOH of 0.01 M NaCl (D)

NaCl is a neutral salt, meaning it does not affect the pH or pOH significantly; hence it should remain neutral at 7. Its pOH, therefore, is \(\mathrm{pOH} = 14 - 7 = 7\).

Step 6: Rank the solutions by pOH

Now, rank the solutions in decreasing order of pOH: \((A)\, \mathrm{pOH}=12 > (D)\, \mathrm{pOH}=7 > (C)\, \mathrm{pOH}>7 > (B)\, \mathrm{pOH}=2\). The order is thus (A) > (D) > (C) > (B).

Key Concepts

Acid-Base Equilibrium

Acid-base equilibrium is an essential concept in chemistry that describes how acidic or basic a solution is based on its ion concentrations. In any water-based (aqueous) solution, water molecules can dissociate into hydrogen ions ( ankind{H^+} ankind{)}) and hydroxide ions ( ankind{OH^-} ankind{)}). This dissociation is affected by the presence of acids or bases, shifting the equilibrium and altering the solution's properties.

For acids, they increase the concentration of ankind{H^+} ankind{ in a solution, which affects the pH and pOH values. Bases, on the other hand, contribute ankind{OH^-} ankind{ ions and thus modify the pOH levels directly. Understanding the interplay of these ions in solution helps predict and explain the behavior and nature of different chemicals.

Strong Acids and Bases

Strong acids and bases are characterized by their complete dissociation in water, leading to significant changes in the ankind{H^+} ankind{ or ankind{OH^-} ankind{ concentrations. Examples include hydrochloric acid (HCl), a strong acid, which fully dissociates to release ankind{H^+} ankind{ ions. This leads to an increase in acidity and a low pH.

Similarly, sodium hydroxide (NaOH) is a strong base. It dissociates fully, providing a high concentration of ankind{OH^-} ankind{ ions, thereby decreasing the pOH and increasing the pH of the solution. These properties make strong acids and bases powerful reagents in chemical reactions and crucial in understanding pOH order when analyzing acidic or basic solutions.

Salt Hydrolysis

Salt hydrolysis may alter the pH and pOH of a solution. When salts like sodium acetate ( ankind{CH_3COONa} ankind{)} dissolve in water, the ions can interact with water molecules, modifying the solution's acidity or basicity. This is due to the salt being formed from the conjugate base of a weak acid (such as acetic acid, ankind{CH_3COOH} ankind{)}, and a strong base (NaOH).

During hydrolysis, the acetate ion ( ankind{CH_3COO^-} ankind{)} can react with water to produce ankind{OH^-} ankind{ ions, making the solution basic. The hydrolyzed product's pOH must be calculated cautiously, as it generally falls between that of neutral and strongly basic solutions, depending on factors like the extent of ionization of the weak acid.

pH and pOH relationship

pH and pOH are interconnected measures that describe a solution's acidity and basicity, respectively. The relationship is expressed by the equation ankind{pH + pOH = 14} ankind{ for water at 25°C. This means if you know one, you can easily find the other.

The pH scale ranges from 0 to 14, with 7 being neutral. If a solution's pH is lower than 7, it is acidic, while a pH higher than 7 indicates a basic solution. Similarly, the pOH scale follows the opposite pattern: lower values imply basic solutions, and higher values suggest acidic solutions.

• A strong acid like HCl has a low pH and a high pOH.
• A strong base like NaOH will demonstrate a low pOH.

Understanding this relationship is crucial for analyzing solution properties and solving chemical equilibrium problems.