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 solution of NH₄OH that is 1% dissociated, we can follow these steps:

### Step 1: Determine the concentration of OH⁻ ions
Given that NH₄OH is 1% dissociated, we first need to find the concentration of OH⁻ ions produced from this dissociation.

1. **Initial concentration (C)** of NH₄OH = 0.001 M.
2. **Degree of dissociation (α)** = 1% = 0.01 (as a fraction).

The concentration of OH⁻ ions can be calculated using the formula:
\[ \text{Concentration of OH}^- = \alpha \times C \]
Substituting the values:
\[ \text{Concentration of OH}^- = 0.01 \times 0.001 = 0.00001 \, \text{M} = 10^{-5} \, \text{M} \]

### Step 2: Calculate pOH
Now that we have the concentration of OH⁻ ions, we can calculate the pOH using the formula:
\[ \text{pOH} = -\log[\text{OH}^-] \]
Substituting the concentration:
\[ \text{pOH} = -\log(10^{-5}) = 5 \]

### Step 3: Calculate pH
We know that:
\[ \text{pH} + \text{pOH} = 14 \]
Now we can find the pH:
\[ \text{pH} = 14 - \text{pOH} = 14 - 5 = 9 \]

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

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