The `P^(H)` of a solution is 3.0. This solution is diluted by 100 times. Then the `P^(H)` of the resulting solution is

Options

A. 5
B. 7
C. 1
D. 11

Answer

To solve the problem, we need to determine the pH of a solution after it has been diluted by 100 times. The initial pH of the solution is given as 3.0.

### Step-by-Step Solution:

1. **Understanding pH and Hydrogen Ion Concentration**:
The pH of a solution is defined as:
\[ \text{pH} = -\log[H^+] \]
where \([H^+]\) is the concentration of hydrogen ions in moles per liter (M).

2. **Calculating Initial Hydrogen Ion Concentration**:
Given that the initial pH is 3.0, we can calculate the initial concentration of hydrogen ions:
\[ [H^+] = 10^{-\text{pH}} = 10^{-3} \text{ M} \]

3. **Dilution of the Solution**:
When the solution is diluted by 100 times, the concentration of hydrogen ions will also decrease by a factor of 100. Therefore, the new concentration of hydrogen ions after dilution is:
\[ [H^+]_{\text{new}} = \frac{[H^+]_{\text{initial}}}{100} = \frac{10^{-3}}{100} = 10^{-5} \text{ M} \]

4. **Calculating the New pH**:
Now, we can calculate the pH of the diluted solution using the new hydrogen ion concentration:
\[ \text{pH}_{\text{new}} = -\log[H^+]_{\text{new}} = -\log(10^{-5}) = 5 \]

5. **Final Answer**:
Thus, the pH of the resulting solution after dilution is **5**.

### Summary:
The pH of the solution after being diluted by 100 times is **5**.