Which solution contains maximum number of `H^(+)` ion

Options

A. 0.1 M HCl
B. `0.1 M NH_(4)Cl`
C. `0.1 M NaHCO_(3)`
D. `0.1 M CH_(3)COOH`

Explanation

To determine which solution contains the maximum number of \( H^+ \) ions, we will analyze each option given in the question step by step.

### Step 1: Analyze HCl
- **Concentration**: 0.1 M (molar)
- **Dissociation**: HCl is a strong acid and dissociates completely in water.
- **Calculation of \( H^+ \) ions**:
\[ \text{Moles of } H^+ = \text{Concentration of HCl} = 0.1 \, \text{mol/L} \]
Therefore, in 1 liter of 0.1 M HCl, there are 0.1 moles of \( H^+ \) ions.

### Step 2: Analyze NH4Cl
- **Concentration**: Not specified, but it is a salt of a weak acid (NH4OH) and a strong base (NaOH).
- **Dissociation**: NH4Cl dissociates into \( NH_4^+ \) and \( Cl^- \) ions.
- **Calculation of \( H^+ \) ions**:
- \( NH_4^+ \) can release \( H^+ \) ions, but it is not a strong acid, and the amount released will be significantly less than 0.1 moles in 1 liter.
- Thus, the contribution of \( H^+ \) ions from NH4Cl is negligible.

### Step 3: Analyze NaHCO3
- **Concentration**: Not specified, but it is a weak acid salt.
- **Dissociation**: NaHCO3 dissociates into \( Na^+ \) and \( HCO_3^- \).
- **Calculation of \( H^+ \) ions**:
- \( HCO_3^- \) can act as a weak acid, but it does not release \( H^+ \) ions in significant amounts.
- Therefore, the contribution of \( H^+ \) ions from NaHCO3 is also negligible.

### Step 4: Analyze Acetic Acid
- **Concentration**: 0.1 M (molar)
- **Dissociation**: Acetic acid is a weak acid and does not dissociate completely.
- **Calculation of \( H^+ \) ions**:
- The dissociation can be represented as:
\[ CH_3COOH \rightleftharpoons CH_3COO^- + H^+ \]
- Since it is a weak acid, the amount of \( H^+ \) produced will be less than the initial concentration of acetic acid (0.1 M). Therefore, the moles of \( H^+ \) will be less than 0.1 moles in 1 liter.

### Conclusion
After analyzing all options:
- **HCl** has 0.1 moles of \( H^+ \) ions.
- **NH4Cl** and **NaHCO3** contribute negligible \( H^+ \) ions.
- **Acetic Acid** contributes less than 0.1 moles of \( H^+ \) ions.

Thus, the solution that contains the maximum number of \( H^+ \) ions is **HCl**.

### Summary of Steps:
1. Analyze the concentration and dissociation of HCl.
2. Analyze NH4Cl and note its negligible contribution of \( H^+ \) ions.
3. Analyze NaHCO3 and note its negligible contribution of \( H^+ \) ions.
4. Analyze acetic acid and note that it contributes less than 0.1 moles of \( H^+ \) ions.
5. Conclude that HCl has the maximum \( H^+ \) ions.