Problem 225 - A Complete Resource Book in Chemistry for JEE Main

Question

Acetic acid solution was \(66.6 \%\) neutralized by adding a base. If \(\mathrm{pK}_{a}\) of acetic acid is \(4.7\), the \(\mathrm{pH}\) of the above solution is approximately

Step-by-Step Solution

Answer

The pH of the solution is approximately 5.0.

Step 1: Understand the Problem

We need to find the pH of a solution where acetic acid is 66.6% neutralized by a base. We are given the \( \mathrm{pK}_a \) of acetic acid as \( 4.7 \).

Step 2: Recall the Henderson-Hasselbalch Equation

The pH of a buffer solution is given by the Henderson-Hasselbalch equation: \[ \mathrm{pH} = \mathrm{pK}_a + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right) \] where \([\text{A}^-]\) is the concentration of the conjugate base, and \([\text{HA}]\) is the concentration of the acid.

Step 3: Calculate the Ratio of Conjugate Base to Acid

Since the solution is 66.6% neutralized, 66.6% of the acetic acid has been converted into its conjugate base. Therefore, the ratio \( \frac{[\text{A}^-]}{[\text{HA}]} \) is \( \frac{66.6}{33.4} \), which simplifies to \( 2 \).

Step 4: Apply the Henderson-Hasselbalch Equation

Substitute the values into the equation: \[ \mathrm{pH} = 4.7 + \log(2) \]. The value of \( \log(2) \) is approximately \( 0.301 \).

Step 5: Calculate the Final pH

Add \( 4.7 \) and \( 0.301 \) to find the pH: \[ \mathrm{pH} = 4.7 + 0.301 = 5.001 \]. Thus, the pH of the solution is approximately \( 5.0 \).

Key Concepts

Acetic Acid

Acetic acid is an important organic compound with the chemical formula \( \text{CH}_3\text{COOH} \). It is a weak acid, meaning it's only partially ionized in solution. This property is crucial when considering buffer solutions, as only a fraction of the acetic acid molecules donate protons to form acetate ions (\( \text{CH}_3\text{COO}^- \)), which serve as the conjugate base.
The ionization of acetic acid can be represented as follows:
\[\text{CH}_3\text{COOH} \rightleftharpoons \text{CH}_3\text{COO}^- + \text{H}^+\]
Understanding this equilibrium is key to working with acetic acid in buffer systems. The degree to which acetic acid dissociates in solution is expressed by its acidity constant, denoted as \( K_a \). A relatively high \( K_a \) value would indicate a stronger acid, but for acetic acid, \( pK_a = 4.7 \) is typical, confirming its weak acidic nature.
Uses of acetic acid span from household vinegar to industrial applications, highlighting its role in creating stable environments in chemical reactions.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a fundamental tool used to estimate the pH of buffer solutions. It relates pH to the concentration of an acid and its conjugate base in equilibrium. The equation is written as:
\[\text{pH} = \text{pK}_a + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)\]
In this equation:

• \(\text{pH}\) is the measure of acidity or basicity of the solution.
• \([\text{A}^-]\) is the concentration of the conjugate base, which results from the partial dissociation of the weak acid.
• \([\text{HA}]\) is the concentration of the remaining undissociated weak acid.

This equation is particularly useful when calculating the pH of solutions where a specific percentage of a weak acid is neutralized with a base, as shown in the original exercise. By knowing \(\text{pK}_a\) and the ratio of \([\text{A}^-]\) to \([\text{HA}]\), one can easily determine the pH. It's the backbone of many calculations in acid-base chemistry, making it a versatile and powerful tool for chemists.

Neutralization in Chemistry

Neutralization is a chemical reaction where an acid and a base interact to form a salt and water, often resulting in changes in pH. In the context of the acetic acid exercise, the neutralization process refers to the reaction between acetic acid and a base, which leads to partial conversion of the acid to its conjugate base:
\[\text{CH}_3\text{COOH} + \text{OH}^- \rightarrow \text{CH}_3\text{COO}^- + \text{H}_2\text{O}\]
This conversion doesn't go to completion when working with buffers, meaning some acetic acid remains, maintaining the ability to resist drastic pH changes. During neutralization, the proportion of acid to base alters until equilibrium is reached. This balance is crucial for buffer systems.
Buffers are able to effectively soak up \(\text{H}^+\) (protons) or release them, depending on the conditions imposed on the system. This quality makes them indispensable in biochemical and chemical environments where stable pH is necessary, such as in the human body and industrial processes. Special systems like these rely on the principles of acid-base neutralization to maintain their pH balance as intended.