No. of `sigma & pi ` bonds in `Mg_2 C_3` are

Options

A. ` 1 sigma and 3 pi `
B. `2 sigma and 2pi`
C. `3 sigma and 2pi`
D. `3 sigma and 3pi`

Answer

To determine the number of sigma and pi bonds in the compound \( \text{Mg}_2\text{C}_3 \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Composition of the Compound:**
The formula \( \text{Mg}_2\text{C}_3 \) indicates that there are 2 magnesium (Mg) atoms and 3 carbon (C) atoms.

2. **Determine the Ionic and Covalent Nature:**
Magnesium typically forms \( \text{Mg}^{2+} \) ions, and in this compound, it is likely that the magnesium ions are bonded ionically to the carbon species. The carbon atoms are likely bonded covalently among themselves.

3. **Analyze the Carbon Species:**
The carbon atoms in \( \text{C}_3^{4-} \) suggest that they are forming a cluster. Each carbon atom has 4 valence electrons and can form 4 bonds. In \( \text{C}_3^{4-} \), we can assume that there are double bonds between the carbon atoms.

4. **Draw the Structure of \( \text{C}_3^{4-} \):**
The most stable structure for \( \text{C}_3^{4-} \) would involve two double bonds between the carbon atoms. This can be represented as:
\[ \text{C} = \text{C} = \text{C} \]
where each "=" represents a double bond.

5. **Count the Sigma and Pi Bonds:**
- Each double bond consists of one sigma bond and one pi bond.
- Since there are two double bonds in \( \text{C}_3^{4-} \):
- **Sigma Bonds:** 2 (one from each double bond)
- **Pi Bonds:** 2 (one from each double bond)

6. **Consider the Ionic Bonds:**
The bonds between \( \text{Mg}^{2+} \) and \( \text{C}_3^{4-} \) are ionic and do not contribute to sigma or pi bonds.

7. **Final Count:**
Therefore, in \( \text{Mg}_2\text{C}_3 \):
- Total Sigma Bonds = 2
- Total Pi Bonds = 2

### Conclusion:
The number of sigma and pi bonds in \( \text{Mg}_2\text{C}_3 \) is:
- Sigma bonds: 2
- Pi bonds: 2