`"0.1 M" NH_(4)"OH & 0.01M "NH_(4)OH` are taken. Which is a stronger base

Options

A. `0.1M NH_(4) OH`
B. `"0.01 M "NH_(4)OH`
C. Both equal
D. None

Explanation

To determine which of the two solutions of NH₄OH (ammonium hydroxide) is a stronger base, we need to analyze the concentration of hydroxide ions (OH⁻) produced by each solution.

### Step-by-Step Solution:

1. **Identify the concentrations of the solutions:**
- Solution 1: 0.1 M NH₄OH
- Solution 2: 0.01 M NH₄OH

2. **Dissociation of NH₄OH:**
- NH₄OH dissociates in water to produce NH₄⁺ and OH⁻ ions:
\[ \text{NH}_4\text{OH} \rightleftharpoons \text{NH}_4^+ + \text{OH}^- \]

3. **Calculate the concentration of OH⁻ for both solutions:**
- For Solution 1 (0.1 M NH₄OH):
- The concentration of OH⁻ produced is also 0.1 M.
- For Solution 2 (0.01 M NH₄OH):
- The concentration of OH⁻ produced is also 0.01 M.

4. **Calculate the pOH for both solutions:**
- **For Solution 1:**
\[ \text{pOH} = -\log[0.1] = -\log(10^{-1}) = 1 \]
- **For Solution 2:**
\[ \text{pOH} = -\log[0.01] = -\log(10^{-2}) = 2 \]

5. **Calculate the pH for both solutions:**
- The relationship between pH and pOH is given by:
\[ \text{pH} + \text{pOH} = 14 \]
- **For Solution 1:**
\[ \text{pH} = 14 - \text{pOH} = 14 - 1 = 13 \]
- **For Solution 2:**
\[ \text{pH} = 14 - \text{pOH} = 14 - 2 = 12 \]

6. **Compare the pH values:**
- Solution 1 has a pH of 13.
- Solution 2 has a pH of 12.
- Since a higher pH indicates a stronger base, Solution 1 (0.1 M NH₄OH) is the stronger base.

### Conclusion:
The stronger base is the 0.1 M NH₄OH solution.