Which of the following solution contains approximately equal hydrogen ion concentration

Options

A. `100 mL of 0.1 M HCl + 50 mL H_(2) O`
B. `75 mL of 0.1 M HCl + 75 mL H_(2) O`
C. `50 mL of 0.1 M H_(2) SO_(4) + 100 mL H_(2)`
D. `100 mL of 0.1 NH_(2)SO_(4) + 50 mL H_(2) O`

Explanation

To determine which of the given solutions contains approximately equal hydrogen ion concentrations, we will analyze each option step by step.

### Step 1: Analyze Option A
- **Given**: 100 ml of 0.11 M HCl + 50 ml of H2O
- **Total Volume**: 100 ml + 50 ml = 150 ml = 0.15 L
- **Moles of H⁺**:
\[ \text{Moles of H⁺} = \text{Molarity} \times \text{Volume} = 0.11 \, \text{M} \times 0.1 \, \text{L} = 0.011 \, \text{moles} \]
- **Concentration of H⁺**:
\[ \text{Concentration} = \frac{\text{Moles of H⁺}}{\text{Total Volume}} = \frac{0.011}{0.15} \approx 0.0733 \, \text{M} \]

### Step 2: Analyze Option B
- **Given**: 75 ml of 0.1 M HCl + 75 ml of H2O
- **Total Volume**: 75 ml + 75 ml = 150 ml = 0.15 L
- **Moles of H⁺**:
\[ \text{Moles of H⁺} = 0.1 \, \text{M} \times 0.075 \, \text{L} = 0.0075 \, \text{moles} \]
- **Concentration of H⁺**:
\[ \text{Concentration} = \frac{0.0075}{0.15} = 0.05 \, \text{M} \]

### Step 3: Analyze Option C
- **Given**: 50 ml of 0.1 M HCl + 100 ml of H2O
- **Total Volume**: 50 ml + 100 ml = 150 ml = 0.15 L
- **Moles of H⁺**:
\[ \text{Moles of H⁺} = 0.1 \, \text{M} \times 0.05 \, \text{L} = 0.005 \, \text{moles} \]
- **Concentration of H⁺**:
\[ \text{Concentration} = \frac{0.005}{0.15} \approx 0.0333 \, \text{M} \]

### Step 4: Analyze Option D
- **Given**: 100 ml of 0.1 M HCl + 50 ml of H2O
- **Total Volume**: 100 ml + 50 ml = 150 ml = 0.15 L
- **Moles of H⁺**:
\[ \text{Moles of H⁺} = 0.1 \, \text{M} \times 0.1 \, \text{L} = 0.01 \, \text{moles} \]
- **Concentration of H⁺**:
\[ \text{Concentration} = \frac{0.01}{0.15} \approx 0.0667 \, \text{M} \]

### Summary of Concentrations
- **Option A**: 0.0733 M
- **Option B**: 0.05 M
- **Option C**: 0.0333 M
- **Option D**: 0.0667 M

### Conclusion
From the calculations, we find that:
- **Option A**: 0.0733 M
- **Option D**: 0.0667 M

Options A and D have approximately equal hydrogen ion concentrations. Therefore, the correct answer is **Option D**.