Which of the following ions does not liberate hydrogen gas on reaction with dilute acids ?

Options

A. `Ti^(2+)`
B. `V^(2+)`
C. `Cr^(2+)`
D. `Mn^(2+)`

Explanation

To determine which of the given ions does not liberate hydrogen gas when reacted with dilute acids, we need to analyze the standard reduction potentials (E°) of each ion. The ions in question are Ti²⁺, V²⁺, Cr²⁺, and Mn²⁺.

### Step-by-Step Solution:

1. **Understand the Reaction**: When a metal ion reacts with dilute acids, it can either reduce the hydrogen ions (H⁺) to hydrogen gas (H₂) or not. The ability to do this is determined by the standard reduction potential (E°) of the metal ion.

2. **Standard Reduction Potentials**: The standard reduction potentials for the given ions are as follows:
- Ti²⁺ + 2e⁻ → Ti; E° = -0.37 V
- V²⁺ + 2e⁻ → V; E° = -0.26 V
- Cr²⁺ + 2e⁻ → Cr; E° = -0.41 V
- Mn²⁺ + 2e⁻ → Mn; E° = +1.57 V

3. **Analyzing the Potentials**: In the electrochemical series, a more negative E° value indicates a stronger reducing agent, which means it is more likely to donate electrons and thus reduce H⁺ to H₂. Conversely, a positive E° value indicates a weaker reducing agent.

4. **Determine Which Ion Does Not Liberate H₂**:
- Ti²⁺, V²⁺, and Cr²⁺ all have negative E° values, indicating they can reduce H⁺ and liberate hydrogen gas.
- Mn²⁺ has a positive E° value (+1.57 V), indicating it is a strong oxidizing agent and will not reduce H⁺ to liberate hydrogen gas.

5. **Conclusion**: Therefore, the ion that does not liberate hydrogen gas when reacted with dilute acids is **Mn²⁺**.

### Final Answer:
The ion that does not liberate hydrogen gas on reaction with dilute acids is **Mn²⁺**.