A buffer solution is prepared by mixing equal concentration of acid (ionisation constant `K_(a)`) and a salt. The pH of buffer is

Options

A. `pK_(a) + 7`
B. `14 - pK_(a)`
C. `pK_(a)`
D. `pK_(a) + 1`

Explanation

To find the pH of a buffer solution prepared by mixing equal concentrations of an acid and its salt, we can follow these steps:

### Step 1: Understand the Buffer Solution
A buffer solution consists of a weak acid and its conjugate base (salt). The weak acid partially ionizes in solution, and the salt provides the conjugate base.

### Step 2: Use the Henderson-Hasselbalch Equation
The pH of a buffer solution can be calculated using the Henderson-Hasselbalch equation:
\[ \text{pH} = pK_a + \log\left(\frac{[\text{Salt}]}{[\text{Acid}]}\right) \]
where:
- \( pK_a = -\log(K_a) \)
- \([\text{Salt}]\) is the concentration of the salt (conjugate base).
- \([\text{Acid}]\) is the concentration of the weak acid.

### Step 3: Set the Concentrations Equal
In this case, we are given that the concentrations of the acid and the salt are equal:
\[ [\text{Salt}] = [\text{Acid}] \]
Let’s denote the concentration as \( C \). Therefore:
\[ \text{pH} = pK_a + \log\left(\frac{C}{C}\right) \]

### Step 4: Simplify the Logarithmic Term
Since the concentrations are equal, the ratio becomes:
\[ \frac{C}{C} = 1 \]
Thus, the logarithm of 1 is:
\[ \log(1) = 0 \]

### Step 5: Calculate the pH
Substituting back into the Henderson-Hasselbalch equation, we have:
\[ \text{pH} = pK_a + 0 \]
Therefore, the pH of the buffer solution is simply:
\[ \text{pH} = pK_a \]

### Conclusion
The pH of the buffer solution is equal to the \( pK_a \) of the weak acid used in the solution.