Problem 22 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one of the following statements is not correct? (a) \(\mathrm{Cl}-\) is a lewis acid (b) the \(\mathrm{pH}\) of \(10^{-8} \mathrm{M} \mathrm{HCl}\) solution is less than \(7 .\) (c) the ionic product of water at \(25^{\circ} \mathrm{C}\) is \(10^{-14}\) \(\mathrm{mol}^{2} \mathrm{~L}^{-2}\) (d) Bronsted-Lowry theory could not explain the acidic character of \(\mathrm{AlCl}_{3}\).

Step-by-Step Solution

Answer

(a) \( \mathrm{Cl^{-}} \) is not a Lewis acid, so (a) is incorrect.

Step 1: Understanding the Concept of Lewis Acid

A Lewis acid is a substance that can accept a pair of electrons. Therefore, analyzing \( \mathrm{Cl^{-}} \), it is negatively charged, indicating it has extra electrons and cannot accept more. Hence, \( \mathrm{Cl^{-}} \) is not a Lewis acid.

Step 2: Analyzing pH of a Dilute HCl Solution

The pH of a solution is defined as \( pH = -\log[H^+] \). For a very dilute \( 10^{-8} M \) HCl solution, the concentration of hydrogen ions \( [H^+] \) from water also needs consideration. Here, the water contributes \( 10^{-7} M \) \([H^+]\), making the effective \([H^+]\) greater than \( 10^{-7} M \). Thus, the pH is less than 7, consistent with this statement.

Step 3: Confirming Ionic Product of Water

The ionic product of water at \( 25^{\circ} C \) is a well-known constant \( K_w \), which is \( 10^{-14} \mathrm{mol}^2 \mathrm{L}^{-2} \). This statement itself is correct and does not need disputes.

Step 4: Bronsted-Lowry Theory and \( \mathrm{AlCl}_3 \)

The Bronsted-Lowry theory describes acids as proton donors. \( \mathrm{AlCl}_3 \) acts as an acid by accepting electron pairs (acting as a Lewis acid), not by donating protons. Therefore, this theory does not fully explain the acidic nature of \( \mathrm{AlCl}_3 \), confirming this statement is correct.

Key Concepts

Bronsted-Lowry theory

The Bronsted-Lowry theory is a fundamental concept in chemistry that defines acids and bases. According to this theory, an acid is a substance that donates a proton (\(H^+\)) in a reaction, while a base is a substance that accepts a proton. This idea expands the classical definition, allowing for a broader range of substances to be classified as acids and bases.
The theory is particularly useful because it includes reactions in both aqueous and non-aqueous environments. For example:

• \( HCl \) is a Bronsted-Lowry acid because it donates a proton to water, forming \(H_3O^+\).
• \(NH_3\) is a Bronsted-Lowry base because it accepts a proton from water, forming \(NH_4^+\).

However, the Bronsted-Lowry theory doesn't explain all acid-base reactions. Some substances, like \(AlCl_3\), exhibit acidic behavior by accepting electron pairs rather than donating protons. This behavior aligns with the Lewis acid definition rather than Bronsted-Lowry, which highlights the limitations of this theory.
Understanding the differences between these definitions helps chemists determine which theory applies to specific substances, providing a more complete understanding of chemical reactions.

pH calculation

Calculating the pH of a solution is essential for understanding its acidity or basicity. The pH is calculated using the formula:
\[ pH = -\log[H^+] \]
where \([H^+]\) is the concentration of hydrogen ions in the solution.
In the context of a very dilute \(10^{-8} M \) HCl solution, the calculation is slightly tricky. You must consider the hydrogen ions that come from both the added HCl and the natural ionization of water, which contributes an additional \(10^{-7} M\) of \([H^+]\).
This influx makes the effective concentration of hydrogen ions greater than \(10^{-7} M\), resulting in a pH less than 7, indicating an acidic solution. When dealing with very dilute acids, always remember the contribution of water's ionization, ensuring that the pH is accurately represented.

ionic product of water

The ionic product of water, often denoted as \(K_w\), is a critical value in chemistry, representing the equilibrium constant for the self-ionization of water. At 25°C, this constant is \(10^{-14} \ \mathrm{mol}^2\,\mathrm{L}^{-2}\). This signifies that in pure water, the concentration of hydrogen ions \([H^+]\) and hydroxide ions \([OH^-]\) are both \(10^{-7} M\).
This concept is crucial for understanding the balance between acidic and basic solutions:

• If \([H^+]\) increases, \([OH^-]\) decreases, maintaining \(K_w\) at the constant value.
• If \([OH^-]\) increases, \([H^+]\) must decrease proportionally.

This relationship ensures that products of these ion concentrations always equal \(10^{-14}\), preserving the neutrality of water and allowing chemists to calculate pH and pOH in solutions. Understanding \(K_w\) is essential for evaluating different solutions' behaviors beyond simple acid-base reactions.