Problem 92 - A Complete Resource Book in Chemistry for JEE Main

Question

The pKa of a weak acid is \(4.8\). What should be the ratio of \([\) acid \(] /[\mathrm{salt}]\), if a buffer of \(\mathrm{pH}=5.8\) is required? (a) \(0.1\) (b) 10 (c) 1 (d) 2

Step-by-Step Solution

Answer

The ratio of [acid]/[salt] should be 0.1.

Step 1: Understanding the Problem

We need to find the ratio of concentrations of the weak acid and its salt in a buffer solution with a given pH. The pKa of the weak acid is provided, and we will use the formula for pH of a buffer.

Step 2: Henderson-Hasselbalch Equation

The equation to use is the Henderson-Hasselbalch equation: \[ ext{pH} = ext{pKa} + ext{log}rac{[ ext{salt}]}{[ ext{acid}]} \]Here, pH is 5.8 and pKa is 4.8.

Step 3: Substitute and Rearrange

Substitute the given pH and pKa values into the Henderson-Hasselbalch equation:\[ 5.8 = 4.8 + ext{log}rac{[ ext{salt}]}{[ ext{acid}]} \]Rearrange the equation to solve for the log ratio:\[ ext{log}rac{[ ext{salt}]}{[ ext{acid}]} = 5.8 - 4.8 \]

Step 4: Calculate the Log Ratio

Calculate the difference on the right side of the equation:\[ ext{log}rac{[ ext{salt}]}{[ ext{acid}]} = 1.0 \]

Step 5: Convert Logarithm to Ratio

Take the antilog to calculate the ratio. Since \( ext{log10}(x) = y \) then \( x = 10^y \):\[ rac{[ ext{salt}]}{[ ext{acid}]} = 10^1 = 10 \]

Step 6: Determine Final Ratio

Since the equation requires the \( rac{[ ext{acid}]}{[ ext{salt}]} \) ratio, invert the calculated ratio:\[ rac{[ ext{acid}]}{[ ext{salt}]} = rac{1}{10} = 0.1 \]

Key Concepts

Buffer Solutions

A buffer solution is a special type of solution that resists changes in its pH level, even when small amounts of an acid or a base are added. This stability is crucial for many chemical reactions and biological processes, which often require very specific pH levels to proceed correctly.
Buffer solutions are usually made from a weak acid and its conjugate base, or a weak base and its conjugate acid. The magic of a buffer solution lies in this combination, which helps maintain the pH within a narrow range.

• They work by neutralizing added acids or bases to maintain a consistent pH.
• They are often used in biological and chemical applications where a stable pH is needed for reactions to occur properly.
• The effectiveness of a buffer is often described by its buffer capacity, which is the amount of acid or base it can absorb without significant pH change.

In this exercise, the buffer solution is made of a weak acid and its salt, which provides its conjugate base. The balance between these components and their concentrations determines the buffer's pH.

Weak Acids

Weak acids are a type of acid that do not completely dissociate in solution. This means they don't release all their hydrogen ions (H⁺ ions) into the solution when dissolved in water. Unlike strong acids, which fully dissociate, weak acids establish an equilibrium between the dissociated ions and the undissociated acid molecules.
The strength of a weak acid is characterized by its dissociation constant, known as the acid dissociation constant ( ka ). The pKa is simply the negative logarithm of ka , giving an idea about the acid's strength. A larger pKa value indicates a weaker acid, as it dissociates less in solution.

• Common examples include acetic acid ( ch3cooh ) and formic acid ( hcooh ).
• Weak acids are important in buffer solutions as they provide the necessary resistance to pH changes.
• The given problem involves a weak acid with a pKa of 4.8, which means it has moderate acidity.

pH Calculation

Calculating pH is essential in understanding the acidity or basicity of a solution. For buffer solutions, the Henderson-Hasselbalch equation provides a straightforward method to find the pH based on the concentrations of the acid and its salt. The Henderson-Hasselbalch equation is:\[ \text{pH} = \text{pKa} + \log \frac{[\text{salt}]}{[\text{acid}]}\]This equation is a handy tool when working with buffer solutions, as it links the concentrations and the pH directly. In this formula:

• \( \text{pH} \) is the measure of acidity in the buffer solution.
• \( \text{pKa} \) gives insight into the acid strength, with the provided value for this weak acid being 4.8.
• \([\text{salt}]/[\text{acid}]\) is the ratio of the concentrations of the conjugate base (from the salt) and the weak acid.

By rearranging and solving this equation, one can find the required concentration ratio to maintain a desired pH of 5.8. The process involves simple log calculations: first determining the log ratio and then using antilog to find the concentration ratio.