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 (σ) and pi (π) bonds in the compound \( \text{Mg}_2\text{C}_3 \), we can follow these steps:

### Step-by-step Solution:

1. **Identify the Structure of \( \text{Mg}_2\text{C}_3 \)**:
- The compound consists of 2 magnesium (Mg) atoms and 3 carbon (C) atoms.
- In \( \text{Mg}_2\text{C}_3 \), each magnesium atom donates two electrons to the carbon atoms, forming ionic bonds.

2. **Determine the Bonding Between Carbon Atoms**:
- The carbon atoms in \( \text{Mg}_2\text{C}_3 \) are arranged such that there are two carbon-carbon double bonds.
- Each carbon-carbon double bond consists of one sigma bond and one pi bond.

3. **Count the Sigma and Pi Bonds**:
- For each carbon-carbon double bond:
- 1 sigma bond
- 1 pi bond
- Since there are 2 carbon-carbon double bonds, we can calculate:
- Total sigma bonds from C-C: \( 2 \times 1 = 2 \)
- Total pi bonds from C-C: \( 2 \times 1 = 2 \)

4. **Consider the Sigma Bonds Involving Magnesium**:
- Each magnesium atom forms a single bond with a carbon atom (since the carbon atoms are bonded to magnesium).
- Each Mg-C bond is a sigma bond. Since there are 2 magnesium atoms and each is bonded to a carbon atom, we have:
- Total sigma bonds from Mg-C: \( 2 \)

5. **Final Count of Sigma and Pi Bonds**:
- Total sigma bonds: \( 2 \) (from C-C) + \( 2 \) (from Mg-C) = \( 4 \)
- Total pi bonds: \( 2 \) (from C-C)

### Conclusion:
- The number of sigma bonds in \( \text{Mg}_2\text{C}_3 \) is \( 4 \).
- The number of pi bonds in \( \text{Mg}_2\text{C}_3 \) is \( 2 \).

### Final Answer:
- **Number of Sigma Bonds**: 4
- **Number of Pi Bonds**: 2

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