Which of the following solutions will have pH = 9 at 298 K?

Options

A. `1xx10^(-9)M` HCl solution
B. `1xx10^(-5)M` NaOH solution
C. `1xx10^(-9)M` KOH solution
D. Both (A) and (B)

Explanation

To determine which of the following solutions will have a pH of 9 at 298 K, we need to analyze each option based on the relationship between pH, pOH, and the concentration of hydrogen ions (H⁺) and hydroxide ions (OH⁻) in the solution.

### Step-by-Step Solution:

1. **Understanding pH and pOH**:
- pH is defined as \( \text{pH} = -\log[H^+] \)
- pOH is defined as \( \text{pOH} = -\log[OH^-] \)
- At 298 K, the relationship between pH and pOH is given by \( \text{pH} + \text{pOH} = 14 \).

2. **Option 1: \( 1 \times 10^{-9} \) M HCl Solution**:
- HCl is a strong acid and completely dissociates in solution:
\[ HCl \rightarrow H^+ + Cl^- \]
- The concentration of \( H^+ \) from HCl is \( 1 \times 10^{-9} \) M.
- However, we must also consider the contribution of \( H^+ \) from water, which is \( 1 \times 10^{-7} \) M at 298 K.
- Total \( [H^+] = 1 \times 10^{-9} + 1 \times 10^{-7} \approx 1 \times 10^{-7} \) M.
- Calculate pH:
\[ \text{pH} = -\log(1 \times 10^{-7}) = 7 \]
- Since pH = 7, this option is **not correct**.

3. **Option 2: \( 1 \times 10^{-5} \) M NaOH Solution**:
- NaOH is a strong base and completely dissociates:
\[ NaOH \rightarrow Na^+ + OH^- \]
- The concentration of \( OH^- \) is \( 1 \times 10^{-5} \) M.
- Calculate pOH:
\[ \text{pOH} = -\log(1 \times 10^{-5}) = 5 \]
- Calculate pH:
\[ \text{pH} = 14 - \text{pOH} = 14 - 5 = 9 \]
- Since pH = 9, this option is **correct**.

4. **Option 3: \( 1 \times 10^{-9} \) M KOH Solution**:
- KOH is also a strong base and completely dissociates:
\[ KOH \rightarrow K^+ + OH^- \]
- The concentration of \( OH^- \) is \( 1 \times 10^{-9} \) M.
- Calculate pOH:
\[ \text{pOH} = -\log(1 \times 10^{-9}) = 9 \]
- Calculate pH:
\[ \text{pH} = 14 - \text{pOH} = 14 - 9 = 5 \]
- Since pH = 5, this option is **not correct**.

5. **Option 4: (not provided)**:
- Since we have already determined the outcomes of the first three options, we can conclude that the only solution with a pH of 9 is from Option 2.

### Conclusion:
The solution that will have a pH of 9 at 298 K is the \( 1 \times 10^{-5} \) M NaOH solution.