What is a true statement with regard to 0.10 M `H_2 SO_4` solution ?

Options

A. `[HSO_4^(-)] gt [H^+]`
B. `[SO_4^(2-)] [H^+]`
C. `[H^+] gt [HSO_4^(-)]`
D. `[H_2SO_4] gt [H^+]`

Answer

To determine the true statement regarding a 0.10 M \( H_2SO_4 \) solution, we need to analyze the dissociation of sulfuric acid in water.

### Step-by-Step Solution:

1. **Understand the Nature of \( H_2SO_4 \)**:
- Sulfuric acid (\( H_2SO_4 \)) is a strong acid. This means it completely dissociates in water to produce hydrogen ions (\( H^+ \)) and bisulfate ions (\( HSO_4^- \)).

2. **Dissociation Reaction**:
- The first dissociation of \( H_2SO_4 \) can be represented as:
\[ H_2SO_4 \rightarrow H^+ + HSO_4^- \]
- This reaction shows that for every mole of \( H_2SO_4 \) that dissociates, one mole of \( H^+ \) and one mole of \( HSO_4^- \) are produced.

3. **Concentration of Ions**:
- In a 0.10 M \( H_2SO_4 \) solution, the concentration of \( H^+ \) produced from the first dissociation is 0.10 M.
- The \( HSO_4^- \) produced from the first dissociation is also 0.10 M.

4. **Second Dissociation of \( HSO_4^- \)**:
- The \( HSO_4^- \) can further dissociate as follows:
\[ HSO_4^- \rightleftharpoons H^+ + SO_4^{2-} \]
- However, \( HSO_4^- \) is a weak acid and does not completely dissociate. Therefore, the concentration of \( H^+ \) from this second dissociation will be less than 0.10 M.

5. **Total Concentration of \( H^+ \)**:
- The total concentration of \( H^+ \) ions in the solution will be the sum of the \( H^+ \) from the first dissociation and the \( H^+ \) from the second dissociation.
- Let’s denote the amount of \( H^+ \) produced from the second dissociation as \( y \). Thus, the total concentration of \( H^+ \) will be:
\[ [H^+] = 0.10 + y \]
- Since \( y \) is positive (but small), the total concentration of \( H^+ \) will be greater than 0.10 M.

6. **Conclusion**:
- The concentration of \( H^+ \) ions in the solution is greater than the concentration of \( HSO_4^- \) ions. Therefore, the true statement regarding the 0.10 M \( H_2SO_4 \) solution is that the concentration of \( H^+ \) is greater than the concentration of \( HSO_4^- \).

### Final Answer:
The true statement regarding a 0.10 M \( H_2SO_4 \) solution is that the concentration of \( H^+ \) ions is greater than the concentration of \( HSO_4^- \) ions.