A 0.01 M ammonia solution is `5%` ionised. Its pH will be

Options

A. 11.8
B. 10.69
C. 7.22
D. 12.24

Answer

To find the pH of a 0.01 M ammonia solution that is 5% ionized, we can follow these steps:

### Step 1: Determine the concentration of hydroxide ions (OH⁻)
Given that ammonia (NH₃) is a weak base and is 5% ionized, we can calculate the concentration of hydroxide ions produced.

- **Concentration of ammonia (C)** = 0.01 M
- **Degree of ionization (α)** = 5% = 5/100 = 0.05

Using the formula for the concentration of hydroxide ions:
\[ [\text{OH}^-] = C \times \alpha \]
Substituting the values:
\[ [\text{OH}^-] = 0.01 \, \text{M} \times 0.05 = 0.0005 \, \text{M} = 5 \times 10^{-4} \, \text{M} \]

### Step 2: Calculate the pOH
Now, we can calculate the pOH using the concentration of hydroxide ions:
\[ \text{pOH} = -\log[\text{OH}^-] \]
Substituting the value we found:
\[ \text{pOH} = -\log(5 \times 10^{-4}) \]

Using the logarithmic property:
\[ \text{pOH} = -\log(5) - \log(10^{-4}) = -\log(5) + 4 \]

### Step 3: Find the value of log(5)
Using a calculator or logarithm table:
\[ \log(5) \approx 0.69897 \]
Now substituting this value back into the pOH equation:
\[ \text{pOH} = 4 - 0.69897 = 3.30103 \]

### Step 4: Calculate the pH
Finally, we can find the pH using the relationship between pH and pOH:
\[ \text{pH} = 14 - \text{pOH} \]
Substituting the pOH value:
\[ \text{pH} = 14 - 3.30103 = 10.69897 \]

### Final Answer
Thus, the pH of the 0.01 M ammonia solution that is 5% ionized is approximately **10.70**.

---