The hydrogen ion concentration of the oceans is about `2xx10^(-9)` M. What is the pH?

Options

A. `8.85`
B. `9.3`
C. `7.85`
D. `8.7`

Answer

To find the pH of the ocean water given the hydrogen ion concentration, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given hydrogen ion concentration**:
The hydrogen ion concentration \([H^+]\) is given as \(2 \times 10^{-9} \, \text{M}\).

2. **Use the pH formula**:
The formula to calculate pH is:
\[ \text{pH} = -\log[H^+] \]

3. **Substitute the given concentration into the formula**:
\[ \text{pH} = -\log(2 \times 10^{-9}) \]

4. **Apply the logarithmic property**:
Using the property of logarithms, \(\log(AB) = \log(A) + \log(B)\), we can break it down:
\[ \text{pH} = -\log(2) - \log(10^{-9}) \]

5. **Calculate \(-\log(10^{-9})\)**:
The logarithm of \(10^{-9}\) is:
\[ -\log(10^{-9}) = 9 \]

6. **Find \(-\log(2)\)**:
The value of \(-\log(2)\) is approximately \(-0.301\). Therefore:
\[ \text{pH} = -0.301 + 9 \]

7. **Combine the values**:
\[ \text{pH} = 9 - 0.301 = 8.699 \]

8. **Round the result**:
The pH value can be rounded to:
\[ \text{pH} \approx 8.7 \]

### Final Answer:
The pH of the ocean water is approximately **8.7**.