When 0.01 moles of the following acids are dissolved in `1 L "of" H_(2)O`, the `[H^(+)]` will be greatest in:-

Options

A. `HNO_(2) , pka = 3.0`
B. `HCOOH , pka = 3.75`
C. `HCN , pka = 9.4`
D. `CH_(3)COOH , pka = 4.75`

Answer

To solve the problem of determining which acid will produce the greatest concentration of hydrogen ions \([H^+]\) when 0.01 moles of each acid are dissolved in 1 L of water, we need to consider the dissociation of each acid in water.

### Step-by-Step Solution:

1. **Identify the Acids**: First, we need to know which acids are being compared. Common acids include strong acids (like HCl, HNO3) and weak acids (like CH3COOH, H2CO3).

2. **Understand Acid Dissociation**: Strong acids completely dissociate in water, while weak acids only partially dissociate. The dissociation of a strong acid can be represented as:
\[ HA \rightarrow H^+ + A^- \]
For a weak acid, the dissociation is represented as:
\[ HA \rightleftharpoons H^+ + A^- \]

3. **Calculate Molarity**: Since we are dissolving 0.01 moles of each acid in 1 L of water, the molarity of each acid solution is:
\[ \text{Molarity} = \frac{\text{moles of acid}}{\text{volume of solution in L}} = \frac{0.01 \text{ moles}}{1 \text{ L}} = 0.01 \text{ M} \]

4. **Determine \([H^+]\) Concentration**:
- For **strong acids**: The concentration of \([H^+]\) will be equal to the molarity of the acid, which is 0.01 M.
- For **weak acids**: We need to use the dissociation constant \(K_a\) to find the degree of dissociation (\(\alpha\)). The formula for the concentration of \([H^+]\) for a weak acid is:
\[ [H^+] = C \cdot \alpha \]
where \(C\) is the initial concentration of the acid and \(\alpha\) is the degree of dissociation.

5. **Compare \(K_a\) Values**: The greater the \(K_a\) value, the stronger the acid and the larger the degree of dissociation \(\alpha\). Therefore, the acid with the highest \(K_a\) will produce the highest concentration of \([H^+]\).

6. **Conclusion**: After comparing the \(K_a\) values of the acids in question, the acid with the highest \(K_a\) will yield the greatest concentration of \([H^+]\) ions in solution.

### Final Answer:
The acid that produces the greatest concentration of \([H^+]\) when 0.01 moles are dissolved in 1 L of water is the one with the highest \(K_a\) value.