Chapter 22: Problem 95

Describe the bonding in the \(\mathrm{C}_{2}^{2-}\) ion in terms of the molecular orbital theory.

Short Answer

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The \(\mathrm{C}_{2}^{2-}\) ion has a bond order of 3, consisting of one sigma bond and two pi bonds, according to the molecular orbital theory.

Step by step solution

Electron Configuration

First, the electron configuration of a Carbon atom must be established. A Carbon atom, with an atomic number of 6, has an electron configuration of 1s² 2s² 2p². However, considering the \(\mathrm{C}_{2}^{2-}\) ion, each Carbon atom would contribute 6 electrons and the negative charge would contribute an additional 2 electrons, leading to a total of 14 electrons for consideration in the molecular orbital theory.

Order of Energy Levels

Next, the energy order of molecular orbitals must be considered. In the case of the \(\mathrm{C}_{2}^{2-}\) ion, the ordering is as follows: \(\sigma_{1s} < \sigma_{1s}^* < \sigma_{2s} < \sigma_{2s}^* < \pi_{2p} < \sigma_{2p} < \pi_{2p}^* < \sigma_{2p}^*\). Where \(\sigma\) and \(\pi\) denote the type of bond (sigma or pi) and the asterisk indicates an antibonding orbital.

Filling the Molecular Orbitals

The molecular orbitals are filled according to the Aufbau principle, that is, the orbitals are filled from lowest energy to highest energy. Applying this to the \(\mathrm{C}_{2}^{2-}\) ion, with its 14 electrons, one can fill up the molecular orbitals as follows: \(\sigma_{1s} < \sigma_{1s}^* < \sigma_{2s} < \sigma_{2s}^* < \pi_{2p} < \sigma_{2p}\). It's important to note that \(\sigma_{1s}^*\) and \(\sigma_{2s}^*\) are antibonding orbitals that each accommodate 2 electrons and the \(\pi_{2p} < \sigma_{2p}\) energy level corresponds to a degenerate state accommodating four electrons in total. The remaining two electrons fill up the \(\sigma_{2p}\) orbital.

Bond Order and Description

Bond order can be determined by subtracting the number of electrons in the antibonding orbitals from the number of electrons in the bonding orbitals, and then dividing by 2. In this case, there are 10 electrons in bonding orbitals and 4 in antibonding, therefore the bond order is 3. As such, the \(\mathrm{C}_{2}^{2-}\) ion has a triple bond that consists of one \(\sigma\) bond from the \(\sigma_{2p}\) and two \(\pi\) bonds from the \(\pi_{2p}\) orbitals.

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Describe the bonding in the \(\mathrm{C}_{2}^{2-}\) ion in terms of the molecular orbital theory.

Short Answer

Step by step solution

Electron Configuration

Order of Energy Levels

Filling the Molecular Orbitals

Bond Order and Description

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