The pH of a solution which is three times as acidic as pure water is

Options

A. 6.7
B. 3.5
C. `7.0`
D. 6.523

Answer

To solve the problem of finding the pH of a solution that is three times as acidic as pure water, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the pH of Pure Water**:
- The pH of pure water is 7. This is a neutral pH.

2. **Determine the Concentration of H⁺ Ions in Pure Water**:
- The relationship between pH and hydrogen ion concentration [H⁺] is given by the formula:
\[ \text{pH} = -\log[H^+] \]
- For pure water:
\[ 7 = -\log[H^+] \]
- Therefore, we can find the concentration of H⁺ ions:
\[ [H^+] = 10^{-7} \text{ M} \]

3. **Calculate the H⁺ Ion Concentration for the New Solution**:
- The new solution is three times as acidic as pure water. This means:
\[ [H^+] = 3 \times 10^{-7} \text{ M} \]

4. **Calculate the pH of the New Solution**:
- Now, we will use the pH formula again:
\[ \text{pH} = -\log[H^+] \]
- Substituting the concentration we found:
\[ \text{pH} = -\log(3 \times 10^{-7}) \]

5. **Use Logarithmic Properties**:
- We can separate the logarithm:
\[ \text{pH} = -(\log 3 + \log(10^{-7})) \]
- This simplifies to:
\[ \text{pH} = -\log 3 - (-7) = -\log 3 + 7 \]

6. **Calculate the Value of pH**:
- The value of \(-\log 3\) is approximately \(-0.477\).
- Therefore:
\[ \text{pH} \approx 7 - 0.477 = 6.523 \]

7. **Final Answer**:
- The pH of the solution that is three times as acidic as pure water is approximately **6.52**.