pH of a solution is 5. Thus. the concentration of hydroxyl ion in the solution is

Options

A. `9 mol L^-1`
B. `5 mol L^-1`
C. `10^-5 mol L^-1`
D. `10^-9 mol L^-1`

Answer

To find the concentration of hydroxyl ions (OH⁻) in a solution with a pH of 5, we can follow these steps:

### Step 1: Understand the relationship between pH and H⁺ concentration
The pH of a solution is defined as:
\[ \text{pH} = -\log[H^+] \]
Given that the pH is 5, we can write:
\[ 5 = -\log[H^+] \]

### Step 2: Calculate the concentration of H⁺ ions
To find [H⁺], we can rearrange the equation:
\[ \log[H^+] = -5 \]
Now, converting from logarithmic form to exponential form gives:
\[ [H^+] = 10^{-5} \text{ moles per liter} \]

### Step 3: Use the ion product of water to find [OH⁻]
The product of the concentrations of hydrogen ions and hydroxyl ions in water at 25°C is given by:
\[ [H^+][OH^-] = 10^{-14} \]
Substituting the value of [H⁺] we found:
\[ (10^{-5})[OH^-] = 10^{-14} \]

### Step 4: Solve for [OH⁻]
To find [OH⁻], we can rearrange the equation:
\[ [OH^-] = \frac{10^{-14}}{10^{-5}} = 10^{-9} \text{ moles per liter} \]

### Conclusion
Thus, the concentration of hydroxyl ions (OH⁻) in the solution is:
\[ [OH^-] = 10^{-9} \text{ moles per liter} \]

### Final Answer
The correct option is 10⁻⁹ moles per liter.

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