The correct order of increasing `[H_(3)O^(o+)]` in the following aqueous solution is

Options

A. `0.01M H_(2)S lt 0.01M H_(2)SO_(4) lt 0.01 M NaC1 lt 0.01M NaNO_(3)`
B. `0.01M NaC1 = 0.01 M NaNO_(3) lt 0.01 M H_(2)S lt 0.01M H_(2)SO_(4)`
C. `0.01M H_(2)S lt 0.01M NaNO_(3) = 0.01 M NaC1 lt 0.01M H_(2)SO_(4)`
D. `0.01M H_(2)S lt 0.01M NaNO_(3) lt 0.01M NaC1 lt 0.01M H_(2)SO_(4)`

Explanation

To determine the correct order of increasing \([H_3O^+]\) in the given aqueous solutions of \(H_2S\), \(H_2SO_4\), \(NaCl\), and \(NaNO_3\), we need to analyze the acidic strength of each compound.

### Step-by-Step Solution:

1. **Identify the Acids and Their Strengths**:
- \(H_2SO_4\) (sulfuric acid) is a strong acid and will dissociate completely in solution, producing a high concentration of \([H_3O^+]\).
- \(H_2S\) (hydrosulfuric acid) is a weak acid and will dissociate to a much lesser extent compared to \(H_2SO_4\), resulting in a lower concentration of \([H_3O^+]\).
- \(NaCl\) (sodium chloride) and \(NaNO_3\) (sodium nitrate) are salts derived from strong acids and strong bases. They do not hydrolyze in water and thus do not contribute to \([H_3O^+]\).

2. **Determine the Relative Concentrations**:
- Since \(H_2SO_4\) is a strong acid, it will produce the highest concentration of \([H_3O^+]\).
- Next is \(H_2S\), which, being a weak acid, will produce a lower concentration of \([H_3O^+]\) than \(H_2SO_4\).
- \(NaCl\) and \(NaNO_3\) do not contribute to \([H_3O^+]\) in solution, so their concentrations will be equal and lower than both acids.

3. **Order of Increasing \([H_3O^+]\)**:
- Therefore, the order of increasing \([H_3O^+]\) is:
\[ [NaCl] \approx [NaNO_3] < [H_2S] < [H_2SO_4] \]

4. **Final Answer**:
- The correct order of increasing \([H_3O^+]\) is:
\[ [NaCl] \approx [NaNO_3] < [H_2S] < [H_2SO_4] \]