Question

draw the lewis structure for sulfate (so₄²⁻) with minimized formal charges. how many total equivalent likely resonance structures exist for so₄²⁻?

Explanation:

Step1: Calculate the total number of valence electrons

Sulfur (\(S\)) has \(6\) valence electrons. Oxygen (\(O\)) has \(6\) valence electrons. The ion has a charge of \(- 2\).
The total number of valence electrons \(=6+(4\times6)+2=6 + 24+2=32\)

Step2: Determine the central atom

Sulfur is the central atom as it is less electronegative than oxygen.

Step3: Connect atoms and distribute electrons

Connect \(4\) oxygen atoms to sulfur. First, form single bonds (\(S - O\)). Each single bond uses \(2\) electrons. So \(4\) single bonds use \(4\times2 = 8\) electrons. Remaining electrons \(=32 - 8=24\). Distribute these as lone pairs on oxygen atoms (each oxygen gets \(3\) lone pairs initially). But to minimize formal charges, we can form double bonds.
The formal charge formula is \(FC=V - N-\frac{B}{2}\), where \(V\) is the number of valence electrons, \(N\) is the number of non - bonding electrons, and \(B\) is the number of bonding electrons.
For \(S\) in \(SO_{4}^{2-}\) with \(4\) single bonds: \(FC(S)=6-(0)-\frac{8}{2}=6 - 4=2\). For \(O\) with \(3\) lone pairs and \(1\) single bond: \(FC(O)=6 - 6-\frac{2}{2}=- 1\).
If we form \(2\) double bonds (\(S = O\)):
For \(S\): \(FC(S)=6-(0)-\frac{12}{2}=6 - 6 = 0\). For \(O\) with double bond: \(FC(O)=6 - 4-\frac{4}{2}=6-(4 + 2)=0\). For \(O\) with single bond: \(FC(O)=6 - 6-\frac{2}{2}=-1\).
If we form \(4\) double bonds (\(S = O\)):
For \(S\): \(FC(S)=6-(0)-\frac{16}{2}=6 - 8=-2\). Not good.
If we form \(3\) double bonds: \(FC(S)=6-(0)-\frac{14}{2}=6 - 7=-1\).
The best structure has \(2\) double bonds. But due to the symmetry of the sulfate ion, we can move the double bonds around.

Step4: Count resonance structures

The sulfate ion \(SO_{4}^{2-}\) has \(4\) equivalent resonance structures. In each resonance structure, the double bonds are in different positions among the \(4\) oxygen atoms.

Answer:

\(4\)