Question

Identify the correct statement describing the characteristics of \(C_2\) molecule.

• A. Bond order = 2.0; Paramagnetic in nature; One sigma and one pi bond forme(D)
• B. Bond order = 0; \(C_2\) molecule is non-existent.
• C. Bond order = 2.0; Diamagnetic in nature; Both bonds formed are pi bonds.
• D. Bond order = 1.5; Paramagnetic in nature; Both bonds formed are sigma bonds (\(\sigma\)).

Hint:

For molecules like \(C_2\), always calculate the bond order using Molecular Orbital Theory to determine its stability, magnetic properties, and bonding characteristics.

Answer 1

The Correct Option is C

The \(C_2\) molecule is composed of two carbon atoms and has 12 valence electrons. According to Molecular Orbital Theory, we can fill the molecular orbitals (MO) based on these 12 electrons: 1. The 12 valence electrons of \(C_2\) molecule will fill the following molecular orbitals: - 2 electrons in the \( \sigma_{1s} \) orbital. - 2 electrons in the \( \sigma^*_{1s} \) orbital. - 4 electrons in the \( \sigma_{2s} \) orbital. - 4 electrons in the \( \pi_{2p_x} \) and \( \pi_{2p_y} \) orbitals. 2. The bonding in \(C_2\) includes: - A sigma bond formed by the \( \sigma_{2s} \) molecular orbital. - A pi bond formed by the degenerate \( \pi_{2p_x} \) and \( \pi_{2p_y} \) molecular orbitals. 3. The bond order is calculated using the formula: \[ \text{Bond order} = \frac{1}{2} \left( \text{Number of bonding electrons} - \text{Number of antibonding electrons} \right) \] For \(C_2\), this gives: \[ \text{Bond order} = \frac{1}{2} \left( 8 \, \text{(bonding electrons)} - 4 \, \text{(antibonding electrons)} \right) = 2.0 \] 4. Since all electrons are paired in the molecular orbitals, the \(C_2\) molecule is diamagnetic in nature. 5. Both the bonds in \(C_2\) molecule are pi bonds formed by the overlap of the p-orbitals, not sigma bonds. Thus, the correct option is C: Bond order = 2.0; Diamagnetic in nature; Both bonds formed are pi bonds.