Higher the amount of acid or base used to produce a definite change of pH in a buffer solution,higher will be its buffer capacity. Buffer capacity of solution is maximum under the following conditions:
[Salt]= [Acid] (in acid buffer), [Salt] = [Base] (in base buffer) pH of a buffer solution lies in the range given below: pH = `pK_(a)pm1`,
In other words, any buffer solution can be used as buffer up to two pH units only, depending upon the value of `pK_(a)`, or `pK_(b),`. A buffer is said to be efficient when `pH =pK_(a)`, or pOH= `pK_(b)`
The bulfer capacity is equal to :

Options

A. `(Deltan)/(DeltapH)`
B. `(pH)/(Deltan)`
C. `pK_(a)=pm1`
D. none of these

Answer

To solve the question regarding buffer capacity, we need to understand the concept of buffer solutions and how their capacity is defined. Let's break it down step by step.

### Step-by-Step Solution:

1. **Understanding Buffer Capacity**:
- Buffer capacity refers to the ability of a buffer solution to resist changes in pH upon the addition of small amounts of acid or base. It is defined as the amount of acid or base (in moles) required to change the pH of the buffer solution by one unit.

**Hint**: Remember that buffer capacity is about how much acid or base can be added before the pH changes significantly.

2. **Conditions for Maximum Buffer Capacity**:
- The buffer capacity is maximum when the concentration of the salt is equal to the concentration of the acid in an acidic buffer, or when the concentration of the salt is equal to the concentration of the base in a basic buffer.

**Hint**: Think about how the balance between the acid and its conjugate base (or base and its conjugate acid) affects the buffer's ability to maintain pH.

3. **pH Range of Buffer Solutions**:
- The pH of a buffer solution is typically within the range of \( pK_a \pm 1 \) for acidic buffers, and \( pK_b \pm 1 \) for basic buffers. This means that any buffer can effectively maintain pH within two units of its \( pK_a \) or \( pK_b \).

**Hint**: Use the \( pK_a \) or \( pK_b \) values to determine the effective pH range of a buffer.

4. **Efficiency of a Buffer**:
- A buffer is considered efficient when the pH of the solution is equal to \( pK_a \) for acidic buffers or \( pK_b \) for basic buffers. This is the point where the buffer can best resist changes in pH.

**Hint**: Efficiency is all about the balance between the acid and its conjugate base.

5. **Mathematical Expression of Buffer Capacity**:
- Mathematically, buffer capacity (β) can be expressed as:
\[ \text{Buffer Capacity} = \frac{\Delta n}{\Delta pH} \]
where \( \Delta n \) is the number of moles of acid or base added, and \( \Delta pH \) is the change in pH.

**Hint**: Think of buffer capacity as a ratio that tells you how much change in pH occurs for a given amount of acid or base added.

6. **Conclusion**:
- Based on the above understanding, the correct expression for buffer capacity is:
\[ \text{Buffer Capacity} = \frac{\Delta n}{\Delta pH} \]
- Therefore, the answer to the question is that the buffer capacity is equal to the number of moles of acid or base required to change the pH of a buffer solution by one unit.

### Final Answer:
The buffer capacity is equal to \( \frac{\Delta n}{\Delta pH} \).