pH of a solution is 5. Its hydroxyl ion concentration is

Options

A. `5 M`
B. `10 M`
C. `10^(-5)M`
D. `10^(-9)M`

Answer

To find the hydroxyl ion concentration from the given pH of a solution, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given pH**:
- The pH of the solution is given as 5.

2. **Calculate the concentration of hydrogen ions [H⁺]**:
- The formula for pH is:
\[ \text{pH} = -\log[H^+] \]
- Rearranging this formula to find [H⁺]:
\[ [H^+] = 10^{-\text{pH}} = 10^{-5} \, \text{M} \]

3. **Use the ion product of water (Kw)**:
- At 25°C, the ion product of water (Kw) is:
\[ K_w = [H^+][OH^-] = 10^{-14} \]

4. **Calculate the concentration of hydroxyl ions [OH⁻]**:
- We can rearrange the equation for Kw to find [OH⁻]:
\[ [OH^-] = \frac{K_w}{[H^+]} = \frac{10^{-14}}{10^{-5}} \]
- Simplifying this gives:
\[ [OH^-] = 10^{-14 + 5} = 10^{-9} \, \text{M} \]

5. **Conclusion**:
- The concentration of hydroxyl ions [OH⁻] in the solution is:
\[ [OH^-] = 10^{-9} \, \text{M} \]

### Final Answer:
The hydroxyl ion concentration is \( 10^{-9} \, \text{M} \).

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