Describe the bonding in the \(\mathrm{CO}_{3}^{2-}\) ion using the localized electron model. How would the molecular orbital model describe the \(\pi\) bonding in this species?

In the carbonate ion, the central atom is carbon (C) surrounded by three oxygen (O) atoms. We can draw its Lewis structure to better understand its structure and bonding. Count the total number of valence electrons: Carbon has 4 valence electrons, each oxygen has 6 valence electrons, and there are two extra electrons due to the 2- charge. So, there are a total of 4 + 3×6 + 2 = 24 valence electrons.

As per the octet rule, each atom must be surrounded by a total of 8 electrons to achieve stability. In the carbonate ion, carbon is double-bonded with one oxygen atom, and the other two oxygen atoms are single-bonded with carbon and have an additional non-bonding electron pair. In this way, the structure obeys the octet rule as every atom has 8 electrons. We can represent the resonance structures of the CO3^2- ion as follows: \[ \Large \begin{array}{cc} - [C \equiv O – O –]^{-} \rightarrow [C = O – O \equiv]^{-} \\ \uparrow \hspace{1cm} \downarrow \\ [C = O – O^{.-}]^{-} \end{array} \]

In the localized electron model (also known as the valence bond theory), the bonding in molecules is described by the overlapping of atomic orbitals. For the carbonate ion, we can describe the π bonding as follows. In each resonance structure, there is a carbon-oxygen double bond. This means that there is a σ bond formed by the overlap of one of the carbon's sp2 hybrid orbitals with an oxygen atom's sp hybrid orbital, and a π bond formed by the side-by-side overlap of carbon's unhybridized 2pz orbital and the oxygen's 2pz orbital.

The molecular orbital model describes bonding in terms of the combination of atomic orbitals to form molecular orbitals. For the carbonate ion, the three sp2 orbitals of carbon and the three sp2 orbitals of oxygen combine to form six sp2 molecular orbitals. Three of these molecular orbitals are bonding, and three are antibonding. The π bond is formed by the combination of the carbon's 2pz orbital with the 2pz orbitals of each oxygen atom. The π molecular orbitals for the carbonate ion are delocalized over the entire structure, which means they are shared by all the atoms in the ion. This delocalization explains why there is resonance in the structure of the carbonate ion. In conclusion, the π bonding in the carbonate ion can be described using both the localized electron model, involving the side-by-side overlap of atomic orbitals, and the molecular orbital model, involving the formation of delocalized molecular orbitals.