Which of the following solutions has `pH = 12 `?

Options

A. `0.01 ` M KOH
B. 1 N KOH
C. 1 N NaOH
D. `1 N Ca (OH)_(2)`

Answer

To determine which of the given solutions has a pH of 12, we need to analyze each option based on the concentration of hydroxide ions (OH⁻) they provide. A pH of 12 indicates a basic solution, and we can use the relationship between pH and pOH to find the concentration of OH⁻ ions.

### Step-by-Step Solution:

1. **Understanding pH and pOH Relationship**:
- The relationship between pH and pOH is given by the equation:
\[ \text{pH} + \text{pOH} = 14 \]
- For a solution with a pH of 12, we can find pOH:
\[ \text{pOH} = 14 - \text{pH} = 14 - 12 = 2 \]

2. **Calculating the Concentration of OH⁻**:
- The pOH is related to the concentration of hydroxide ions by the formula:
\[ \text{pOH} = -\log[\text{OH}⁻] \]
- Rearranging this gives us:
\[ [\text{OH}⁻] = 10^{-\text{pOH}} = 10^{-2} \text{ M} = 0.01 \text{ M} \]

3. **Analyzing Each Solution**:
- **Option 1: 0.01 M KOH**:
- KOH is a strong base and dissociates completely:
\[ \text{KOH} \rightarrow \text{K}^+ + \text{OH}^- \]
- Therefore, the concentration of OH⁻ is 0.01 M, which gives:
\[ \text{pOH} = 2 \quad \text{and} \quad \text{pH} = 12 \]
- This option is correct.

- **Option 2: 1 N KOH**:
- KOH has an n-factor of 1, so 1 N = 1 M.
- The concentration of OH⁻ is 1 M:
\[ \text{pOH} = -\log(1) = 0 \quad \text{and} \quad \text{pH} = 14 \]
- This option does not yield a pH of 12.

- **Option 3: 1 N NaOH**:
- Similar to KOH, NaOH is also a strong base with an n-factor of 1, so 1 N = 1 M.
- The concentration of OH⁻ is 1 M:
\[ \text{pOH} = 0 \quad \text{and} \quad \text{pH} = 14 \]
- This option does not yield a pH of 12.

- **Option 4: 1 N Ca(OH)₂**:
- Ca(OH)₂ has an n-factor of 2, so:
\[ \text{Molarity} = \frac{1 \text{ N}}{2} = 0.5 \text{ M} \]
- The concentration of OH⁻ is 0.5 M:
\[ \text{pOH} = -\log(0.5) \approx 0.301 \quad \text{and} \quad \text{pH} = 14 - 0.301 \approx 13.699 \]
- This option does not yield a pH of 12.

### Conclusion:
The only solution that gives a pH of 12 is **Option 1: 0.01 M KOH**.