In a mixture of weak acid and its salt, the ratio of concentration of salt to acid is increased ten fold. The pH of the solution

Options

A. decrease ten fold
B. increases ten fold
C. increases by one
D. decreases by one.

Explanation

To solve the problem, we will use the Henderson-Hasselbalch equation, which relates the pH of a solution to the pKa of the acid and the ratio of the concentrations of the salt and the acid.

### Step-by-Step Solution:

1. **Understanding the Henderson-Hasselbalch Equation**:
The equation is given by:
\[ \text{pH} = \text{pK}_a + \log\left(\frac{[\text{Salt}]}{[\text{Acid}]}\right) \]
where \([\text{Salt}]\) is the concentration of the salt and \([\text{Acid}]\) is the concentration of the weak acid.

2. **Initial Condition**:
Let’s denote the initial concentration of the salt as \([\text{Salt}]_1\) and the concentration of the acid as \([\text{Acid}]_1\). The initial pH can be expressed as:
\[ \text{pH}_1 = \text{pK}_a + \log\left(\frac{[\text{Salt}]_1}{[\text{Acid}]_1}\right) \]

3. **Change in Concentration**:
According to the problem, the ratio of the concentration of salt to acid is increased tenfold. Therefore, we have:
\[ \frac{[\text{Salt}]_2}{[\text{Acid}]_2} = 10 \cdot \frac{[\text{Salt}]_1}{[\text{Acid}]_1} \]
This means:
\[ [\text{Salt}]_2 = 10 \cdot [\text{Salt}]_1 \quad \text{and} \quad [\text{Acid}]_2 = [\text{Acid}]_1 \]

4. **New pH Calculation**:
Now, we can calculate the new pH using the Henderson-Hasselbalch equation:
\[ \text{pH}_2 = \text{pK}_a + \log\left(\frac{[\text{Salt}]_2}{[\text{Acid}]_2}\right) \]
Substituting the new concentrations:
\[ \text{pH}_2 = \text{pK}_a + \log\left(\frac{10 \cdot [\text{Salt}]_1}{[\text{Acid}]_1}\right) \]
This can be simplified to:
\[ \text{pH}_2 = \text{pK}_a + \log(10) + \log\left(\frac{[\text{Salt}]_1}{[\text{Acid}]_1}\right) \]
Since \(\log(10) = 1\), we have:
\[ \text{pH}_2 = \text{pK}_a + 1 + \log\left(\frac{[\text{Salt}]_1}{[\text{Acid}]_1}\right) \]
Thus, we can express \(\text{pH}_2\) in terms of \(\text{pH}_1\):
\[ \text{pH}_2 = \text{pH}_1 + 1 \]

5. **Conclusion**:
If the initial pH was \(\text{pH}_1\), the new pH after increasing the salt concentration tenfold will be:
\[ \text{pH}_2 = \text{pH}_1 + 1 \]

### Final Answer:
The pH of the solution after increasing the salt concentration tenfold is \(\text{pH}_1 + 1\).