Which of the following has highest pH ?

Options

A. `(M)/(4)KOH`
B. `(M)/(4)NaOH`
C. `(M)/(4)NH_(4)OH`
D. `(M)/(4)Ca(OH)_(2)`

Explanation

To determine which of the given options has the highest pH, we need to analyze the hydroxide ion (OH⁻) concentrations of each solution. The relationship between pH and pOH is given by the equation:

\[ \text{pH} + \text{pOH} = 14 \]

From this, we can derive that:

\[ \text{pH} = 14 - \text{pOH} \]

To have the highest pH, we need the pOH to be the lowest, which means we need the concentration of OH⁻ ions to be the highest.

### Step-by-step Solution:

1. **Identify the compounds and their dissociations:**
- For each compound, we need to find out how many OH⁻ ions are produced when they dissociate in water.

2. **Analyze the options:**
- **Option A: Sodium Hydroxide (NaOH)**
- NaOH is a strong base and dissociates completely in water:
\[ \text{NaOH} \rightarrow \text{Na}^+ + \text{OH}^- \]
- If the concentration of NaOH is 0.25 M, then the concentration of OH⁻ ions will also be 0.25 M.

- **Option B: Ammonium Hydroxide (NH₄OH)**
- NH₄OH is a weak base and does not dissociate completely. For simplicity, we can assume it dissociates to a concentration slightly less than 0.25 M, say approximately 0.25 M.

- **Option C: Calcium Hydroxide (Ca(OH)₂)**
- Ca(OH)₂ is a strong base and dissociates as follows:
\[ \text{Ca(OH)}_2 \rightarrow \text{Ca}^{2+} + 2 \text{OH}^- \]
- If the concentration of Ca(OH)₂ is 0.25 M, it produces 2 moles of OH⁻ ions for every mole of Ca(OH)₂. Therefore, the concentration of OH⁻ ions will be:
\[ 0.25 \, \text{M} \times 2 = 0.50 \, \text{M} \]

3. **Calculate pOH for each option:**
- **Option A (NaOH):**
\[ \text{pOH} = -\log(0.25) \approx 0.60 \]
\[ \text{pH} = 14 - 0.60 = 13.40 \]

- **Option B (NH₄OH):**
- Assuming it is approximately 0.25 M:
\[ \text{pOH} \approx -\log(0.25) \approx 0.60 \]
\[ \text{pH} \approx 14 - 0.60 = 13.40 \]

- **Option C (Ca(OH)₂):**
\[ \text{pOH} = -\log(0.50) \approx 0.30 \]
\[ \text{pH} = 14 - 0.30 = 13.70 \]

4. **Conclusion:**
- Comparing the pH values:
- NaOH: pH ≈ 13.40
- NH₄OH: pH ≈ 13.40
- Ca(OH)₂: pH ≈ 13.70
- The highest pH is from Calcium Hydroxide (Ca(OH)₂).

### Final Answer:
The compound with the highest pH is **Calcium Hydroxide (Ca(OH)₂)**.