Question

Acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) has a tendency to lose two protons \(\left(\mathrm{H}^{+}\right)\) and form the carbide ion \(\left(\mathrm{C}_{2}^{2-}\right),\) which is present in a number of ionic compounds, such as \(\mathrm{CaC}_{2}\) and \(\mathrm{MgC}_{2}\). Describe the bonding scheme in the \(\mathrm{C}_{2}^{2-}\) ion in terms of molecular orbital theory. Compare the bond order in \(\mathrm{C}_{2}^{2-}\) with that in \(\mathrm{C}_{2}\).

Short answer

The bond order increases from 2 in \( \mathrm{C}_{2} \) to 3 in \( \mathrm{C}_{2}^{2-} \).

Step-by-step solution

Identify the Molecular Orbitals

The molecular orbital (MO) configuration of diatomic molecules is determined by the combination of atomic orbitals. For carbon, the relevant orbitals are the 2s and 2p orbitals. The carbon atoms in the \( \mathrm{C}_{2}^{2-} \) ion will form a molecular orbital scheme similar to the typical MO diagram for molecules involving 2nd period elements.

Assign Electrons to Molecular Orbitals for Neutral C2

In a neutral \( \mathrm{C}_{2} \) molecule, each carbon atom contributes 4 valence electrons (total of 8). These electrons are filled into molecular orbitals in the order of increasing energy: \( \sigma_{2s}^2, \sigma^{*}_{2s}^2, \pi_{2px}^2, \pi_{2py}^2 \). The \( \sigma_{2px} \) orbital remains empty.

Calculate Bond Order for Neutral C2

The bond order is calculated using the formula:\[ \text{Bond Order} = \frac{1}{2}(\text{Number of bonding electrons} - \text{Number of antibonding electrons}) \]For \( \mathrm{C}_{2} \), this is \[ \text{Bond Order} = \frac{1}{2}(6 - 2) = 2 \].

Modify Electron Configuration for C2(2-) Ion

In the \( \mathrm{C}_{2}^{2-} \) ion, two additional electrons are added, resulting in a total of 10 electrons. These electrons are added to the next available molecular orbital, which is the \( \sigma_{2px} \) orbital, leading to the configuration:\( \sigma_{2s}^2, \sigma^{*}_{2s}^2, \pi_{2px}^2, \pi_{2py}^2, \sigma_{2px}^2 \).

Calculate Bond Order for C2(2-) Ion

The bond order for \( \mathrm{C}_{2}^{2-} \) is calculated as follows using the formula:\[ \text{Bond Order} = \frac{1}{2}(\text{Number of bonding electrons} - \text{Number of antibonding electrons}) \]For \( \mathrm{C}_{2}^{2-} \), this is \[ \text{Bond Order} = \frac{1}{2}(8 - 2) = 3 \].

Compare Bond Orders

The bond order of \( \mathrm{C}_{2} \) is 2, indicating a double bond, while the bond order of \( \mathrm{C}_{2}^{2-} \) is 3, indicating a triple bond. The additional electrons in the \( \sigma_{2px} \) confer extra bonding strength to \( \mathrm{C}_{2}^{2-} \) compared to neutral \( \mathrm{C}_{2} \).

Key concepts

Bond Order

In molecular orbital theory, the bond order is an important concept for determining the stability of a molecule. It refers to the number of chemical bonds between a pair of atoms. To find the bond order, you use the formula:

• Bond Order = \( \frac{1}{2}(\text{Number of bonding electrons} - \text{Number of antibonding electrons}) \)

When applying this to the carbide ion \( \mathrm{C}_{2}^{2-} \), you find a bond order of 3. This means there is a triple bond between the carbon atoms, suggesting a strong and stable interaction.
In contrast, the neutral \( \mathrm{C}_{2} \) molecule has a bond order of 2, indicating a double bond. This means adding two electrons to the neutral molecule increases the bond strength in the carbide ion. A higher bond order generally indicates a more robust bond, contributing to the molecule's stability and its chemical characteristics.

Carbide Ion

The carbide ion \( \mathrm{C}_{2}^{2-} \) is a negatively charged species formed when acetylene loses two protons. This ion carries a double negative charge due to these additional electrons.
The presence of extra electrons significantly impacts the electronic structure of the carbide ion. For instance, these electrons fill available bonding orbitals in the molecular orbital model, enhancing the bond strength compared to neutral \( \mathrm{C}_{2} \).
The carbide ion is crucial in various compounds like \( \mathrm{CaC}_{2} \) and \( \mathrm{MgC}_{2} \). These compounds have unique properties due to the strong triple bond present in the \( \mathrm{C}_{2}^{2-} \) ion, which can result in interesting physical and chemical behaviors.

Molecular Orbitals

Molecular orbitals are the foundation of molecular orbital theory, where atomic orbitals combine to form these new, hybrid orbitals across a molecule. The electrons in a molecule occupy these molecular orbitals according to their energy levels.
For \( \mathrm{C}_{2}^{2-} \), carbon atoms use their 2s and 2p orbitals to form molecular orbitals. These orbitals are filled according to Hund’s rule and the Pauli exclusion principle, starting from the lowest energy level.

• Bonding molecular orbitals: Electrons in these contribute to bond formation and stability.
• Antibonding molecular orbitals: Electrons here destabilize the molecule, reducing bond strength.

In \( \mathrm{C}_{2}^{2-} \), electrons fill into the \( \sigma_{2s} \), \( \pi_{2p} \), and \( \sigma_{2px} \) orbitals, maximizing bonding interactions and enhancing molecular stability.

Valence Electrons

Valence electrons are the outermost electrons of an atom. They play a pivotal role in chemical bonding and molecular formation. In the context of the carbide ion \( \mathrm{C}_{2}^{2-} \), each carbon atom originally contributes four valence electrons because carbon has four electrons in its outer shell.
For the neutral \( \mathrm{C}_{2} \) molecule, these 8 valence electrons are distributed among the orbitals according to molecular orbital theory. In \( \mathrm{C}_{2}^{2-} \), two extra electrons are added, resulting in a total of 10 valence electrons.
These additional electrons increase bonding interactions by being placed in bonding molecular orbitals, thus strengthening the bond order from 2 to 3. The proper arrangement and occupation of valence electrons within molecular orbitals are key in determining the chemical properties and reactivity of molecules.