Problem 54 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following statements about \(\mathrm{pH}\) and \(\mathrm{H}^{+}\) ion concentration is incorrect? (a) addition of one drop of concentrated \(\mathrm{HCl}\) in \(\mathrm{NH}_{4} \mathrm{OH}\) solution decreases \(\mathrm{pH}\) of the solution (b) a solution of the mixture of one equivalent of each of \(\mathrm{CH}_{3} \mathrm{COOH}\) and \(\mathrm{NaOH}\) has a \(\mathrm{pH}\) of 7 (c) \(\mathrm{pH}\) of pure neutral water is not zero (d) a cold and concentrated \(\mathrm{H}_{2} \mathrm{SO}_{4}\) has lower \(\mathrm{H}^{+}\)ion concentration than a dilute solution of \(\mathrm{H}_{2} \mathrm{SO}_{4}\)

Step-by-Step Solution

Answer

(d) is incorrect; concentrated H₂SO₄ has higher H⁺ ion concentration.

Step 1: Understanding pH Changes

Adding a drop of concentrated HCl to an NH₄OH solution introduces more H⁺ ions. Because the pH is the negative logarithm of the hydrogen ion concentration, increasing the H⁺ concentration decreases the pH of the solution, making it more acidic.

Step 2: Mixing Equimolar Strong Base and Weak Acid

When one equivalent of CH₃COOH (acetic acid) is mixed with one equivalent of NaOH (a strong base), the base neutralizes the acid, forming water and sodium acetate. Sodium acetate is a salt that, when dissolved in water, creates a weakly basic solution due to hydrolysis, resulting in a pH greater than 7.

Step 3: pH of Pure Water

The pH of pure water at 25°C is 7, which is neutral. The statement that pure neutral water does not have a pH of zero is true because a pH of zero would indicate a highly acidic solution.

Step 4: Evaluating H⁺ Ion Concentrations in Different Solutions

Cold and concentrated H₂SO₄ is a very strong acid with a high concentration of H⁺ ions. In contrast, a dilute solution of H₂SO₄ will have fewer H⁺ ions per unit volume. Thus, the statement that concentrated H₂SO₄ has a lower H⁺ ion concentration than a dilute solution is incorrect.

Key Concepts

Hydrogen Ion Concentration

Hydrogen ion concentration is a crucial factor in determining the acidity of a solution. When acid molecules disassociate in water, they release hydrogen ions (H⁺). The more H⁺ ions present, the more acidic the solution becomes.
This is measured using the pH scale, which ranges from 0 to 14. The pH is calculated as the negative logarithm of the H⁺ ion concentration, \( \text{pH} = -\log [\text{H}^+] \). This means that as H⁺ ion concentration increases, pH decreases, making the solution more acidic. Conversely, fewer H⁺ ions mean a higher pH, indicating a more basic or alkaline solution.
Understanding these relationships helps explain why adding an acid to a solution lowers the pH.

Acid-Base Neutralization

Acid-base neutralization involves a chemical reaction where an acid and a base react to form water and a salt.
This process typically neutralizes the effects of each reactant, leading to a pH closer to neutral. For example, if you mix acetic acid (CH₃COOH), a weak acid, with sodium hydroxide (NaOH), a strong base, they react to produce sodium acetate (CH₃COONa) and water.
The sodium acetate may further undergo hydrolysis in water, increasing the solution's pH slightly above 7, making it slightly basic rather than neutral. This illustrates why equimolar mixtures of a strong base and weak acid do not have a pH of exactly 7, despite neutralization.

Acetic Acid and Sodium Hydroxide

Both acetic acid and sodium hydroxide play specific roles in acid-base reactions. Acetic acid (CH₃COOH) is a weak acid, which means it doesn't completely dissociate in water. Sodium hydroxide (NaOH), on the other hand, is a strong base, fully dissociating to release hydroxide ions (OH⁻).
When combined in equivalent amounts, NaOH completely neutralizes the acetic acid, forming sodium acetate and water. Sodium acetate, left in solution, can influence the pH to become slightly basic due to its anion, acetate. This phenomenon of achieving a solution pH above 7, despite neutralization theoretically resulting in a neutral state, can be attributed to the properties of the resulting salt.

Properties of Pure Water

Pure water exhibits unique properties, with a neutral pH of 7 at 25°C. This occurs due to the balance of H⁺ and OH⁻ ions.
Any disturbance, such as temperature changes, can alter this delicate balance. Although pure water at a neutral pH is often discussed, it's crucial to understand that water's pH reflects its inherent impurities or any dissolved substances.
A pH of zero for pure water is a misconception since this value is reserved for highly acidic solutions. Pure water's unique balance of ions allows it to maintain neutrality, playing a vital role in numerous biological and chemical systems.