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. **Understanding the Dissociation of \( H_2SO_4 \)**:
Sulfuric acid (\( H_2SO_4 \)) is a strong acid that dissociates in two steps:
- The first dissociation is complete:
\[ H_2SO_4 \rightarrow H^+ + HSO_4^- \]
- The second dissociation is also significant, but not complete:
\[ HSO_4^- \rightleftharpoons H^+ + SO_4^{2-} \]

2. **Calculating Ion Concentrations**:
Given the concentration of \( H_2SO_4 \) is 0.10 M:
- From the first dissociation, for every mole of \( H_2SO_4 \), we get 1 mole of \( H^+ \) and 1 mole of \( HSO_4^- \). Therefore, from 0.10 M \( H_2SO_4 \):
- Concentration of \( H^+ \) from the first dissociation = 0.10 M
- Concentration of \( HSO_4^- \) from the first dissociation = 0.10 M

3. **Considering the Second Dissociation**:
- The \( HSO_4^- \) can further dissociate to produce additional \( H^+ \):
- The extent of this dissociation is not complete, but we assume it contributes some additional \( H^+ \) ions.
- For simplicity, let's assume that the second dissociation contributes a small amount of \( H^+ \) ions, which we can denote as \( x \).

4. **Total Concentration of \( H^+ \)**:
- Therefore, the total concentration of \( H^+ \) ions will be:
\[ [H^+]_{total} = [H^+]_{from \, H_2SO_4} + [H^+]_{from \, HSO_4^-} = 0.10 + x \]
- Since \( x \) is positive, we can conclude that:
\[ [H^+]_{total} > 0.10 \, M \]

5. **Final Concentration Comparison**:
- The concentration of \( HSO_4^- \) remains at 0.10 M (from the first dissociation).
- Therefore, the concentration of \( H^+ \) ions is greater than the concentration of \( HSO_4^- \):
\[ [H^+]_{total} > [HSO_4^-] = 0.10 \, M \]

### Conclusion:
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 \( HSO_4^- \).