How many electrons should `X_(2)H_(4)` liberate so that in the new compound X shows oxidation number of `-1//2`(E.N. X gt H)

Options

A. 10
B. 4
C. 3
D. 2

Explanation

To solve the question, we need to determine how many electrons should be liberated by the compound \( X_2H_4 \) so that in the new compound, the element \( X \) shows an oxidation number of \( -\frac{1}{2} \).

### Step-by-Step Solution:

1. **Identify the Initial Oxidation State of \( X \)**:
- In the compound \( X_2H_4 \), the oxidation state of hydrogen (H) is \( +1 \).
- Let the oxidation state of \( X \) be \( x \).
- The overall charge of the compound is neutral (0), so we can set up the equation:
\[ 2x + 4(+1) = 0 \]
- Simplifying this gives:
\[ 2x + 4 = 0 \implies 2x = -4 \implies x = -2 \]
- Thus, the oxidation state of \( X \) in \( X_2H_4 \) is \( -2 \).

2. **Determine the Final Oxidation State of \( X \)**:
- We want the oxidation state of \( X \) in the new compound to be \( -\frac{1}{2} \).

3. **Calculate the Change in Oxidation State**:
- The change in oxidation state for one atom of \( X \) can be calculated as:
\[ \text{Change} = \text{Final state} - \text{Initial state} = -\frac{1}{2} - (-2) \]
- Simplifying this gives:
\[ \text{Change} = -\frac{1}{2} + 2 = -\frac{1}{2} + \frac{4}{2} = \frac{3}{2} \]

4. **Determine the Total Electrons Liberated**:
- Since there are 2 atoms of \( X \) in \( X_2H_4 \), the total change in oxidation state for both atoms is:
\[ 2 \times \frac{3}{2} = 3 \]
- Therefore, a total of 3 electrons should be liberated.

### Conclusion:
The number of electrons that should be liberated by \( X_2H_4 \) so that in the new compound \( X \) shows an oxidation number of \( -\frac{1}{2} \) is **3 electrons**.