The standard electrode potential `(M^(3+)//M^(2+))` for `V, Cr , Mn & Co` are `-0.26V,-0.41V,+1.57V` and `1.97V,` respectively.The metal ions which can liberate `H_(2)` from a dilute acid are

Options

A. `V^(2+)` abd `Mn^(2+)` and `Co^(2+)`
B. `Mn^(2+)` and `Co^(2+)`
C. `Cr^(2+)` and `Co^(2+)`
D. `V^(2+)` and `Cr^(2+)`

Answer

To determine which metal ions can liberate hydrogen gas (H₂) from a dilute acid, we need to analyze the standard electrode potentials provided for each metal ion. The standard electrode potentials for the metal ions are as follows:

- Vanadium (V³⁺/V²⁺): -0.26 V
- Chromium (Cr³⁺/Cr²⁺): -0.41 V
- Manganese (Mn³⁺/Mn²⁺): +1.57 V
- Cobalt (Co³⁺/Co²⁺): +1.97 V

### Step-by-Step Solution:

1. **Understanding the Reaction**:
To liberate hydrogen gas from a dilute acid, the metal ion must be able to reduce H⁺ ions to H₂. The half-reaction for the reduction of hydrogen ions is:
\[ 2H^+ + 2e^- \rightarrow H_2 \quad (E^\circ = 0 \, V) \]

2. **Identifying Oxidation Potentials**:
The standard electrode potential given is for the reduction of the metal ions. To find the oxidation potential, we can use the relation:
\[ E^\circ_{\text{oxidation}} = -E^\circ_{\text{reduction}} \]
Therefore, we can calculate the oxidation potentials for each metal ion:
- For Vanadium: \(E^\circ_{\text{oxidation}} = -(-0.26) = +0.26 \, V\)
- For Chromium: \(E^\circ_{\text{oxidation}} = -(-0.41) = +0.41 \, V\)
- For Manganese: \(E^\circ_{\text{oxidation}} = -(+1.57) = -1.57 \, V\)
- For Cobalt: \(E^\circ_{\text{oxidation}} = -(+1.97) = -1.97 \, V\)

3. **Comparing Oxidation Potentials**:
The metal ions that can liberate hydrogen from dilute acid must have a higher oxidation potential than the reduction potential of hydrogen (0 V). Thus, we compare:
- Vanadium: +0.26 V > 0 V (can liberate H₂)
- Chromium: +0.41 V > 0 V (can liberate H₂)
- Manganese: -1.57 V < 0 V (cannot liberate H₂)
- Cobalt: -1.97 V < 0 V (cannot liberate H₂)

4. **Conclusion**:
Based on the comparison, the metal ions that can liberate hydrogen from a dilute acid are Vanadium (V) and Chromium (Cr).

### Final Answer:
The metal ions which can liberate H₂ from a dilute acid are **Vanadium (V) and Chromium (Cr)**.