Which of the following solutions will have `pH = 10` at `298 K`?

Options

A. `1 xx 10^(-10)M HCI` solution
B. `1 xx 10^(-4)M NaOH` solution
C. `1xx10^(-10)M NaOH` solution
D. Both (a) and (b)

Explanation

To determine which of the given solutions will have a pH of 10 at 298 K, we need to understand the relationship between pH, pOH, and the concentration of hydrogen ions \([H^+]\).

### Step-by-Step Solution:

1. **Understanding pH and pOH:**
The pH of a solution is defined as:
\[ \text{pH} = -\log[H^+] \]
At 298 K, the relationship between pH and pOH is:
\[ \text{pH} + \text{pOH} = 14 \]

2. **Calculating pOH:**
Given that the pH is 10, we can calculate the pOH:
\[ \text{pOH} = 14 - \text{pH} = 14 - 10 = 4 \]

3. **Finding the Concentration of Hydrogen Ions:**
Now, we can find the concentration of hydrogen ions \([H^+]\) using the pH:
\[ [H^+] = 10^{-\text{pH}} = 10^{-10} \text{ M} \]

4. **Identifying the Nature of the Solution:**
A pH of 10 indicates that the solution is basic. Therefore, we can also calculate the concentration of hydroxide ions \([OH^-]\) using the pOH:
\[ [OH^-] = 10^{-\text{pOH}} = 10^{-4} \text{ M} \]

5. **Analyzing the Given Solutions:**
We need to check the nature of the solutions provided in the options:
- If a solution is a strong acid (like HCl), it will contribute a high concentration of \([H^+]\) and result in a pH less than 7.
- If a solution is a strong base (like NaOH), it will contribute a high concentration of \([OH^-]\) and result in a pH greater than 7.

6. **Conclusion:**
Since we need a solution with a pH of 10, we are looking for a basic solution. The solution that provides a concentration of \([OH^-]\) equal to \(10^{-4} \text{ M}\) would correspond to a pH of 10. Therefore, the correct option is the one that represents a basic solution with the appropriate concentration.

### Final Answer:
The solution that will have a pH of 10 at 298 K is **Option B** (the one that corresponds to a concentration of \(10^{-4} \text{ M}\) of a strong base).