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

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

Step 1: Identify Lewis Acid

A Lewis acid is a substance that can accept a pair of electrons. The chloride ion, \(\mathrm{Cl}^-\), has a full octet and tends to donate electrons rather than accept them. Therefore, \(\mathrm{Cl}^-\) cannot act as a Lewis acid.

Step 2: Analyze pH of Dilute HCl Solution

Calculating the pH of a \(10^{-8} \mathrm{M} \mathrm{HCl}\) solution involves considering the autoionization of water. In such a dilute solution, the contribution of \(\mathrm{H}^+\) from water is significant, resulting in a pH close to 7, not less than 7. Hence, this statement is incorrect.

Step 3: Evaluate Ionic Product of Water

The ionic product of water,\(~K_w\), at \(25^{\circ}\mathrm{C}\) is well known to be \(10^{-14} \mathrm{mol}^{2} \mathrm{~L}^{-2}\). This is a fundamental property of water at room temperature and is correct.

Step 4: Examine Bronsted-Lowry Theory Application

The Bronsted-Lowry theory defines acids as proton donors, but \(\mathrm{AlCl}_3\) acts as a Lewis acid by accepting electrons, not donating protons. Thus, the theory doesn't explain the acidic behavior of \(\mathrm{AlCl}_3\), affirming the statement as correct.

Key Concepts

pH Calculation

Understanding pH calculation is crucial to grasp acidity and alkalinity in various substances. The pH scale ranges from 0 to 14, with 7 being neutral. Values below 7 indicate acidity, while values above 7 denote alkalinity. To calculate the pH, you'll use the formula: \( pH = -\log [H^+] \), where \([H^+]\) is the concentration of hydrogen ions in the solution.

In the context of a \(10^{-8} M\, HCl\) solution, the pH calculation becomes slightly more complex. Given the dilute concentration, the autoionization of water plays a significant role. In pure water at 25°C, \([H^+]\) from water itself is \(10^{-7} M\). Hence, when calculating the overall \([H^+]\) concentration for such dilute solutions, you need to account for both the \(HCl\) and the water. This contributions usually result in a pH around 7, contrary to less than 7, leading to errors if not carefully considered.

Ionic Product of Water

The ionic product of water \((K_w)\) is an important parameter in understanding water's chemical nature. At 25°C, \(K_w\) is defined as \(10^{-14} mol^2 L^{-2}\). It represents the product of the concentrations of hydrogen ions \([H^+]\) and hydroxide ions \([OH^-]\) in water:

\[ K_w = [H^+][OH^-] = 10^{-14} \ mol^2 \ L^{-2} \]

This relationship indicates that increasing the concentration of one ion will result in a decrease in the other to maintain the equilibrium balance. It is vital to remember that temperature changes can affect \(K_w\), but at room temperature (25°C), this value is constant. Utilizing \(K_w\) is essential for calculating pH and understanding the behavior of acidic and basic solutions.

Bronsted-Lowry Theory

The Bronsted-Lowry theory is a cornerstone of acid-base chemistry. It defines acids as proton donors and bases as proton acceptors. This theory broadens the concept of acids and bases beyond the classic Arrhenius definitions, which were limited to aqueous solutions.

While it explains many acid-base reactions, there are limitations. For instance, the theory doesn't encompass substances like \(AlCl_3\) that exhibit acidic behavior through electron pair acceptance rather than proton donation. This is where the Lewis theory comes into play as it categorizes acids not just by their ability to donate protons but also by their ability to accept electron pairs. Thus, while Bronsted-Lowry provides a useful framework, it doesn't entirely capture all acidic or basic characteristics of substances.