Which of the following solutions has the same concentration of `H^(+)` ions as 0.1 N HCl ?

Options

A. 0.1 N `H_(2)SO_(4)`
B. 0.3 N `H_(3)PO_(4)`
C. 0.2 N `HNO_(3)`
D. All of these

Answer

To determine which solution has the same concentration of \( H^+ \) ions as 0.1 N HCl, we need to follow these steps:

### Step 1: Understand Normality and Molarity
Normality (N) is a measure of concentration equivalent to molarity (M) multiplied by the number of equivalents of the solute. For acids, the number of equivalents is equal to the number of \( H^+ \) ions that the acid can donate.

### Step 2: Calculate Molarity of 0.1 N HCl
Since hydrochloric acid (HCl) is a strong acid that dissociates completely in solution, it donates one \( H^+ \) ion per molecule. Therefore, for HCl:
- Number of \( H^+ \) ions = 1

Using the formula:
\[ \text{Normality (N)} = \text{Molarity (M)} \times \text{Number of \( H^+ \) ions} \]
We can rearrange this to find molarity:
\[ \text{Molarity (M)} = \frac{\text{Normality (N)}}{\text{Number of \( H^+ \) ions}} = \frac{0.1 \, N}{1} = 0.1 \, M \]

### Step 3: Identify Solutions with the Same \( H^+ \) Concentration
Now, we need to find other solutions that have a molarity of \( 0.1 \, M \) in terms of \( H^+ \) ions.

1. **HCl**: 0.1 M HCl will also yield 0.1 M \( H^+ \).
2. **HNO₃**: 0.1 M HNO₃ will yield 0.1 M \( H^+ \) since it also dissociates completely.
3. **CH₃COOH (Acetic Acid)**: This is a weak acid and does not dissociate completely, so its \( H^+ \) concentration will be less than 0.1 M.
4. **H₂SO₄ (Sulfuric Acid)**: The first dissociation of sulfuric acid is strong, yielding 1 \( H^+ \) ion, but the second dissociation is weak.

### Step 4: Conclusion
The solutions that have the same concentration of \( H^+ \) ions as 0.1 N HCl are:
- 0.1 M HCl
- 0.1 M HNO₃