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 following ions does not liberate hydrogen gas when reacting with dilute acids, we need to analyze the standard reduction potentials (E°) of the given ions. The ions provided are Ti²⁺, V²⁺, Cr²⁺, and Mn²⁺.

### Step-by-Step Solution:

1. **Understand the Reaction**: When a metal ion reacts with a dilute acid, it can either liberate hydrogen gas (H₂) or not, depending on its standard reduction potential (E°). If the E° value of the metal ion is more negative than that of hydrogen (0 V), it will liberate hydrogen gas.

2. **List the E° Values**:
- For Ti²⁺: E° = -0.37 V
- For V²⁺: E° = -0.26 V
- For Cr²⁺: E° = -0.41 V
- For Mn²⁺: E° = +1.57 V

3. **Analyze the E° Values**:
- E° values less than 0 V indicate that the ion can reduce and liberate hydrogen gas.
- E° values greater than 0 V indicate that the ion is a strong oxidizing agent and will not liberate hydrogen gas.

4. **Determine Which Ion Does Not Liberate Hydrogen**:
- Ti²⁺, V²⁺, and Cr²⁺ all have negative E° values, meaning they can liberate hydrogen gas.
- Mn²⁺ has a positive E° value (+1.57 V), indicating that it will not liberate hydrogen gas when reacting with dilute acids.

5. **Conclusion**: The ion that does not liberate hydrogen gas on reaction with dilute acids is **Mn²⁺**.

### Final Answer:
**Mn²⁺ (Manganese ion)** does not liberate hydrogen gas on reaction with dilute acids.