Problem 85 - A Complete Resource Book in Chemistry for JEE Main

Question

At \(25^{\circ} \mathrm{C}\) the \(\mathrm{pH}\) of solution containing \(0.10 \mathrm{M}\) sodium acetate and \(0.03 \mathrm{M}\) acetic acid is [pKa value of \(\left.\mathrm{CH}_{3} \mathrm{COOH}=4.57\right]\) (a) \(3.24\) (b) \(4.59\) (c) \(5.09\) (d) \(6.67\)

Step-by-Step Solution

Answer

The pH of the solution is 5.09, which corresponds to option (c).

Step 1: Understand the Concept

To find the pH of a buffer solution, we use the Henderson-Hasselbalch equation, which relates the pH, the pKa, and the concentrations of the acid and its conjugate base.

Step 2: Recall the Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is given by: \[ pH = pKa + \log\left(\frac{[A^-]}{[HA]}\right) \] where \([A^-]\) is the concentration of the base (sodium acetate in this case) and \([HA]\) is the concentration of the acid (acetic acid).

Step 3: Insert Known Values

Given in the problem: - \( pKa = 4.57 \) - \([A^-] = 0.10 \text{ M} \) - \([HA] = 0.03 \text{ M} \) Insert these values into the equation: \[ pH = 4.57 + \log\left(\frac{0.10}{0.03}\right) \]

Step 4: Calculate the Ratio

Calculate the ratio of the concentrations: \[ \frac{0.10}{0.03} = 3.33 \]

Step 5: Calculate the Logarithm

Calculate the logarithm of the ratio: \[ \log(3.33) \approx 0.52 \]

Step 6: Compute the pH

Substitute the logarithmic value back into the equation: \[ pH = 4.57 + 0.52 = 5.09 \] Thus, the pH of the solution is 5.09.

Key Concepts

Understanding Buffer Solution

A buffer solution resists changes in its pH when small amounts of acid or base are added. This stability is especially useful in chemical reactions and biological processes, where a stable pH is often required. The buffer solution consists of a weak acid and its conjugate base. - In our context, acetic acid (\(\mathrm{CH}_3 \mathrm{COOH}\) ) and sodium acetate (\(\mathrm{CH}_3 \mathrm{COONa}\)) create the buffer. - The acid donates protons (\(\mathrm{H}^+\)), while the conjugate base can accept them.

For example, adding a strong acid to the solution will push the reaction towards the acetate ion accepting the extra protons, minimizing pH change. Therefore, understanding buffer solutions help in understanding how to control the pH of a solution.

Basics of pH Calculation

The pH scale measures how acidic or basic a solution is, ranging from 0 to 14. Lower values represent acidic solutions, while higher values indicate basic solutions. The pH calculation for buffer solutions is often performed using the Henderson-Hasselbalch equation.- The equation: \[ pH = pKa + \log\left(\frac{[A^-]}{[HA]}\right) \] helps in predicting the pH by linking together the acid dissociation constant (\(pKa\)) and the concentrations of the acid and conjugate base.

In practical terms, this equation helps in understanding how the concentrations of the acid/base components affect pH, and thus in preparing buffer solutions with desired pH levels.

Role of Acetic Acid in Buffer Solutions

Acetic acid (\(\mathrm{CH}_3 \mathrm{COOH}\)) is a weak acid that partially dissociates in solution. Its role in a buffer is to provide the reservoir of protons (\(\mathrm{H}^+\)) that can react with added bases.- It dissociates as follows: \[ \mathrm{CH}_3 \mathrm{COOH} \rightleftharpoons \mathrm{CH}_3 \mathrm{COO}^- + \mathrm{H}^+ \] - The presence of acetic acid ensures that as the base concentration increases, the solution can still maintain its pH.

This happens by shifting the equilibrium to produce more \(\mathrm{H}^+\) ions when needed, exemplifying the 'buffering action' that prevents drastic pH changes during reactions.

Sodium Acetate as the Conjugate Base

Sodium acetate, \(\mathrm{CH}_3 \mathrm{COONa}\), acts as the conjugate base in the buffer system. When dissolved in water, it dissociates completely, providing acetate ions (\(\mathrm{CH}_3 \mathrm{COO}^-\)), which accept protons.- The dissociation can be represented as: \[ \mathrm{CH}_3 \mathrm{COONa} \rightarrow \mathrm{CH}_3 \mathrm{COO}^- + \mathrm{Na}^+ \]- These acetate ions are crucial for reacting with and neutralizing added hydronium ions (\(\mathrm{H}_3\mathrm{O}^+\)) when an acid is added.

Thus, sodium acetate helps in maintaining the pH by ensuring that the equilibrium between acetic acid and acetate ions can dynamically respond to changes, showcasing the power of buffers in stabilizing solutions.