Problem 234 - A Complete Resource Book in Chemistry for JEE Main

Question

When \(0.01\) mole of \(\mathrm{NaOH}\) are added to a litre of buffer solution, its \(\mathrm{pH}\) changes from \(4.745\) to \(4.815\). The buffer capacity of the buffer solution is \(0.07 \mathrm{y}\). The value of \(\mathrm{y}\) is

Step-by-Step Solution

Answer

The value of \( y \) is approximately 2.04.

Step 1: Understand buffer capacity

Buffer capacity is defined as the number of moles of an acid or base that must be added to 1 liter of a buffer solution to change its pH by 1 unit.

Step 2: Apply buffer capacity formula

We know that the buffer capacity \( \text{Buffer capacity} = \frac{\text{Number of moles of base added}}{\Delta \text{pH}} \). Here, \( \Delta \text{pH} = 4.815 - 4.745 = 0.070 \), and \( \text{Number of moles of base added} = 0.01 \).

Step 3: Substitute values into the formula

Substitute the known values into the equation: \[ 0.07y = \frac{0.01}{0.070} \].

Step 4: Solve for \( y \)

Calculate \( y \) by rearranging and solving the equation: \[ y = \frac{0.01}{0.070 \times 0.07} = 2.04 \].

Key Concepts

Buffer Solution

A buffer solution is a special type of solution that helps maintain a stable pH, even when small amounts of an acid or base are added. This means it has the ability to resist changes in pH. Buffer solutions usually consist of a weak acid and its conjugate base, or a weak base and its conjugate acid. These components work together to neutralize added acids or bases, thus maintaining a relatively stable pH.

• Buffer solutions are critical in many biological systems, where maintaining a consistent pH is essential for processes and reactions.
• Common examples of buffer solutions include acetic acid (a weak acid) and sodium acetate (its conjugate base).

When you add a base like \( ext{NaOH}\), it reacts with the weak acid in the buffer to minimize the pH change. Conversely, if an acid is added, the conjugate base neutralizes it.

pH Change

pH change in a solution refers to the alteration in the acidity or basicity of that solution. pH is a measure of the concentration of hydrogen ions \[ ext{H}^+ \] in a solution, with lower pH values being more acidic and higher values being more basic.
When a small amount of acid or base is added to a buffer solution, the pH will only alter slightly, not dramatically. This is a primary characteristic of a buffer solution's function. For instance, in our example, the pH changed from 4.745 to 4.815 when \(0.01\) mole of \( ext{NaOH} \) was added. This indicates the buffer's effectiveness in maintaining pH stability despite external additions.

• The change \( ext{∆pH} \) was only \(0.070\), showcasing how a buffer absorbs the addition and neutralizes it accordingly.

Understanding and calculating pH changes help in assessing the buffer's ability to function effectively in various conditions.

Buffer Capacity Formula

The buffer capacity formula provides a way to measure the efficiency of a buffer solution in resisting pH changes. It is defined as the number of moles of acid or base that need to be added to a liter of buffer solution to change its pH by one unit. This is an important metric in chemistry. The formula is given by:
\[ ext{Buffer capacity} = \frac{ ext{Number of moles of base added}}{\Delta ext{pH}} \]
For a practical example, if you add \(0.01\) mole of \( ext{NaOH} \) to a buffer and its pH changes by \(0.070\), you can calculate its buffer capacity.

• Substituting the values into the buffer capacity formula results in: \(rac{0.01}{0.070}\).
• This calculates the buffer capacity before considering specific buffers, which signifies the ability to resist changes.

The result provides insights not just into the buffer solution's effectiveness but also highlights how much acid or base the solution can counteract without significant pH shifts. This is crucial for maintaining desired pH conditions in chemical and biological systems.