To solve the question, we need to analyze the given statements about the concentrations of H⁺ ions and the dissociation constant of water (K_w) at 298 K. Let's go through the statements step by step.
### Step-by-Step Solution:
1. **Understanding Neutral Aqueous Solution**:
- In a neutral aqueous solution at 298 K, the concentration of H⁺ ions ([H⁺]) is equal to the concentration of OH⁻ ions ([OH⁻]).
- The dissociation constant of water (K_w) at this temperature is \(1.0 \times 10^{-14}\) M².
2. **Finding [H⁺] in Neutral Solution**:
- Since [H⁺] = [OH⁻], we can express K_w as:
\[
K_w = [H^+][OH^-] = [H^+]^2
\]
- Therefore, we can find [H⁺] by taking the square root of K_w:
\[
[H^+] = \sqrt{K_w} = \sqrt{1.0 \times 10^{-14}} = 1.0 \times 10^{-7} \text{ M}
\]
3. **Evaluating Statement 1**:
- The first statement claims that in a neutral aqueous solution, the concentration of H⁺ is equal to \(\sqrt{K_w}\).
- From our calculation, this statement is **correct**.
4. **Evaluating Statement 2**:
- The second statement claims that in an acidic aqueous solution, the concentration of H⁺ is less than \(\sqrt{K_w}\).
- In acidic solutions, the pH ranges from 0 to 6.9, which means:
\[
[H^+] = 10^{-pH} \text{ ranges from } 10^0 \text{ to } 10^{-6.9}
\]
- This means [H⁺] is greater than \(1.0 \times 10^{-7}\) M (which is \(\sqrt{K_w}\)), making this statement **incorrect**.
5. **Evaluating Statement 3**:
- The third statement claims that in a basic aqueous solution, the concentration of H⁺ is greater than \(\sqrt{K_w}\).
- In basic solutions, the pH is greater than 7, thus:
\[
[H^+] < 10^{-7} \text{ M}
\]
- Therefore, this statement is also **incorrect**.
6. **Evaluating Statement 4**:
- The fourth statement claims that in a basic aqueous solution, pH is less than pOH.
- In basic solutions, [OH⁻] > [H⁺], which implies:
\[
pOH < pH
\]
- Thus, this statement is **incorrect**.
### Conclusion:
After evaluating all the statements, we find that only **Statement 1** is correct. Therefore, the correct option is **Option 1**.
