Calculate pH of 0.001 M `NH_(4)OH`, when it is 1% dissociated in the solution :

Options

A. 5
B. 2.96
C. 9.04
D. 11.4

Explanation

To calculate the pH of a 0.001 M NH₄OH solution that is 1% dissociated, follow these steps:

### Step 1: Determine the dissociation of NH₄OH
Given that NH₄OH is a weak base, we know that it will dissociate in water as follows:
\[ \text{NH}_4\text{OH} \rightleftharpoons \text{NH}_4^+ + \text{OH}^- \]

### Step 2: Calculate the concentration of OH⁻ ions
The concentration of OH⁻ ions can be calculated using the formula:
\[ [\text{OH}^-] = C \cdot \alpha \]
Where:
- \( C \) is the concentration of the base (0.001 M)
- \( \alpha \) is the degree of dissociation (1% = 0.01)

Substituting the values:
\[ [\text{OH}^-] = 0.001 \, \text{M} \cdot 0.01 = 0.00001 \, \text{M} = 10^{-5} \, \text{M} \]

### Step 3: Calculate pOH
Using the concentration of OH⁻ ions, we can calculate pOH:
\[ \text{pOH} = -\log[\text{OH}^-] \]
Substituting the value:
\[ \text{pOH} = -\log(10^{-5}) = 5 \]

### Step 4: Calculate pH
We know that:
\[ \text{pH} + \text{pOH} = 14 \]
Thus, we can find pH:
\[ \text{pH} = 14 - \text{pOH} = 14 - 5 = 9 \]

### Final Answer
The pH of the 0.001 M NH₄OH solution when it is 1% dissociated is approximately **9**.

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