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 hydrogen ion concentration
The pH of a solution is defined as the negative logarithm of the hydrogen ion concentration [H⁺]. Mathematically, this is expressed as:
\[ \text{pH} = -\log[H^+] \]

### Step 2: Calculate the hydrogen ion concentration
Given that the pH of the solution is 5, we can find the concentration of hydrogen ions:
\[ [H^+] = 10^{-\text{pH}} = 10^{-5} \, \text{mol/L} \]

### Step 3: Use the ion product of water
The product of the concentrations of hydrogen ions and hydroxyl ions in water at 25°C is given by the ion product constant (Kw):
\[ K_w = [H^+][OH^-] = 10^{-14} \]

### Step 4: Set up the equation to find hydroxyl ion concentration
We can rearrange the equation to solve for the concentration of hydroxyl ions:
\[ [OH^-] = \frac{K_w}{[H^+]} \]

### Step 5: Substitute the known values
Substituting the known values into the equation:
\[ [OH^-] = \frac{10^{-14}}{10^{-5}} \]

### Step 6: Simplify the expression
Now, we simplify the expression:
\[ [OH^-] = 10^{-14 + 5} = 10^{-9} \, \text{mol/L} \]

### Conclusion
Thus, the concentration of hydroxyl ions in the solution is:
\[ [OH^-] = 10^{-9} \, \text{mol/L} \]

### Final Answer
The concentration of hydroxyl ion in the solution is \( 10^{-9} \, \text{mol/L} \).

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