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 can follow these steps:

### Step 1: Understand the relationship between pH and pOH
The relationship between pH and pOH is given by the equation:
\[ \text{pH} + \text{pOH} = 14 \]

### Step 2: Calculate the pOH for a pH of 12
If we want to find the pOH corresponding to a pH of 12, we can rearrange the equation:
\[ \text{pOH} = 14 - \text{pH} \]
Substituting the value of pH:
\[ \text{pOH} = 14 - 12 = 2 \]

### Step 3: Identify the concentration of OH⁻ ions
To find the concentration of OH⁻ ions that corresponds to a pOH of 2, we use the formula:
\[ \text{pOH} = -\log[\text{OH}^-] \]
Rearranging gives:
\[ [\text{OH}^-] = 10^{-\text{pOH}} \]
Substituting the value of pOH:
\[ [\text{OH}^-] = 10^{-2} = 0.01 \, \text{M} \]

### Step 4: Analyze the options
Now, we need to check the given options to see which one has a concentration of OH⁻ equal to 0.01 M.

1. **0.01 M KOH**:
- KOH dissociates completely to give 0.01 M OH⁻.
- pOH = 2, pH = 12. (This is a match)

2. **1 N KOH**:
- This is equivalent to 1 M KOH, which gives 1 M OH⁻.
- pOH = 0, pH = 14. (Not a match)

3. **1 N NaOH**:
- Similar to KOH, this is also equivalent to 1 M NaOH, giving 1 M OH⁻.
- pOH = 0, pH = 14. (Not a match)

4. **1 N Ca(OH)₂**:
- Ca(OH)₂ dissociates to give 2 moles of OH⁻ per mole of Ca(OH)₂.
- 1 N means 1 M / 2 = 0.5 M Ca(OH)₂, which gives 1 M OH⁻.
- pOH = 0, pH = 14. (Not a match)

### Conclusion
The only solution that has a pH of 12 is **0.01 M KOH**.