Which of the following solutions has `pH =11` ?

Options

A. `10^(-11) M NaOH
B. `10^(-3)M `HCl
C. `10^(-3)` M NaOH
D. `10^(3)` M NaOH

Explanation

To determine which solution has a pH of 11, we can analyze each option provided in the question.

### Step-by-Step Solution:

1. **Understanding pH and pOH:**
The pH scale ranges from 0 to 14, where:
- pH < 7 indicates an acidic solution,
- pH = 7 indicates a neutral solution,
- pH > 7 indicates a basic (alkaline) solution.
The relationship between pH and pOH is given by the equation:
\[ \text{pH} + \text{pOH} = 14 \]
Therefore, if the pH is 11, the pOH can be calculated as:
\[ \text{pOH} = 14 - \text{pH} = 14 - 11 = 3 \]

2. **Analyzing the First Option: \(10^{-11} \, \text{M NaOH}\):**
- For NaOH, a strong base, it completely dissociates in solution:
\[ \text{NaOH} \rightarrow \text{Na}^+ + \text{OH}^- \]
- The concentration of OH⁻ ions will be \(10^{-11} \, \text{M}\).
- To find the pOH:
\[ \text{pOH} = -\log(10^{-11}) = 11 \]
- Therefore, pH:
\[ \text{pH} = 14 - \text{pOH} = 14 - 11 = 3 \]
- This option does not have a pH of 11.

3. **Analyzing the Second Option: \(10^{-3} \, \text{M HCl}\):**
- HCl is a strong acid and completely dissociates:
\[ \text{HCl} \rightarrow \text{H}^+ + \text{Cl}^- \]
- The concentration of H⁺ ions will be \(10^{-3} \, \text{M}\).
- To find the pH:
\[ \text{pH} = -\log(10^{-3}) = 3 \]
- This option also does not have a pH of 11.

4. **Analyzing the Third Option: \(10^{-3} \, \text{M NaOH}\):**
- Again, NaOH is a strong base and completely dissociates:
\[ \text{NaOH} \rightarrow \text{Na}^+ + \text{OH}^- \]
- The concentration of OH⁻ ions will be \(10^{-3} \, \text{M}\).
- To find the pOH:
\[ \text{pOH} = -\log(10^{-3}) = 3 \]
- Therefore, pH:
\[ \text{pH} = 14 - \text{pOH} = 14 - 3 = 11 \]
- This option has a pH of 11.

5. **Analyzing the Fourth Option: \(10^{3} \, \text{M NaOH}\):**
- This is a highly concentrated solution, and while NaOH is a strong base, at such high concentrations, the activity of ions must be considered.
- The concentration of OH⁻ ions is \(10^{3} \, \text{M}\), which means:
\[ \text{pOH} = -\log(10^{3}) = -3 \]
- Since pOH cannot be negative, the pH will be very high (greater than 14), indicating a very basic solution.
- This option does not have a pH of 11.

### Conclusion:
The solution that has a pH of 11 is the **third option: \(10^{-3} \, \text{M NaOH}\)**.