Polyatomic Sulfur–Oxygen Species: Resonance, Charge, and Expanded Octets
This calculator compares the structures of \(\mathrm{SO_2}\), \(\mathrm{SO_3}\),
\(\mathrm{SO_3^{2-}}\), \(\mathrm{SO_4^{2-}}\), and \(\mathrm{HSO_4^-}\).
All have sulfur from group 16 as the central atom, bonded to oxygen atoms.
The key ideas are:
valence electron counting, electron-domain geometry,
resonance and average S–O bond order, and
formal charge / charge delocalisation.
1. Valence electrons and total electron count
For a species, the total number of valence electrons is:
\[
N_\mathrm{val} =
\sum (\text{valence of each atom})
\;\pm\; (\text{charge})
\]
- \(\mathrm{SO_2}\): \(6 \text{ (S)} + 2 \times 6 \text{ (O)} = 18\ \mathrm{e^-}\)
- \(\mathrm{SO_3}\): \(6 + 3 \times 6 = 24\ \mathrm{e^-}\)
- \(\mathrm{SO_3^{2-}}\): \(6 + 3 \times 6 + 2 = 26\ \mathrm{e^-}\)
- \(\mathrm{SO_4^{2-}}\): \(6 + 4 \times 6 + 2 = 32\ \mathrm{e^-}\)
- \(\mathrm{HSO_4^-}\): \(1 \text{ (H)} + 6 \text{ (S)} + 4 \times 6 \text{ (O)} + 1 = 32\ \mathrm{e^-}\)
Once the total is fixed, the Lewis structure must use exactly this number of electrons
in bonds and lone pairs.
2. Electron-domain geometry around sulfur
Around sulfur we count electron domains (bonding regions + lone pairs):
-
\(\mathrm{SO_2}\) and \(\mathrm{SO_3}\): 3 domains → trigonal planar
electron-domain geometry.
\(\mathrm{SO_2}\) is bent (one lone pair on S); \(\mathrm{SO_3}\) is trigonal planar.
-
\(\mathrm{SO_3^{2-}}\), \(\mathrm{SO_4^{2-}}\), \(\mathrm{HSO_4^-}\):
4 domains → tetrahedral electron-domain geometry around S.
Sulfite is trigonal pyramidal (one lone pair on S), while sulfate and hydrogen sulfate
are tetrahedral around S.
3. Resonance and average S–O bond order
For these species, a single Lewis structure cannot show the true electron distribution.
Instead, we draw several resonance structures with different choices of S=O
and S–O single bonds. The actual molecule is the resonance hybrid, where all
equivalent S–O bonds have the same length and an average bond order.
-
\(\mathrm{SO_2}\): two main contributors, each with one S=O and one S–O.
Average S–O bond order ≈ \(1.5\).
-
\(\mathrm{SO_3}\): three equivalent contributors; all three S–O bonds are equivalent
in the hybrid.
Average S–O bond order ≈ \( \tfrac{4}{3} \).
-
\(\mathrm{SO_3^{2-}}\): three contributors with one S=O and two S–O⁻ in each.
Average S–O bond order ≈ \( \tfrac{4}{3} \) again, but with overall charge −2.
-
\(\mathrm{SO_4^{2-}}\): several contributors with two S=O and two S–O⁻.
In the hybrid all four S–O bonds are equal.
Average S–O bond order ≈ \(1.5\).
-
\(\mathrm{HSO_4^-}\): similar to sulfate, but one oxygen is protonated (O–H).
Resonance delocalises the negative charge mainly over the three non-protonated
oxygens.
4. Formal charges and charge delocalisation
The formal charge on an atom is:
\[
\text{FC} = (\text{valence electrons}) -
(\text{nonbonding electrons}) -
\frac{1}{2}(\text{bonding electrons})
\]
For these ions:
-
In \(\mathrm{SO_2}\) and \(\mathrm{SO_3}\), some resonance contributors give
formal charge +1 on S and −1 on O, but the sum is always 0.
-
In \(\mathrm{SO_3^{2-}}\), each contributor has two \(\mathrm{O^-}\) atoms
(formal charge −1), the third O and S are formally 0. Resonance spreads
the −2 charge over all three oxygens.
-
In \(\mathrm{SO_4^{2-}}\), each contributor has two \(\mathrm{O^-}\) atoms
and two neutral oxygens; in the resonance hybrid, the −2 charge is
approximately evenly delocalised over four oxygens.
-
In \(\mathrm{HSO_4^-}\), the oxygen bonded to H is neutral in most contributors,
and the −1 charge is delocalised over the remaining three oxygens.
The more widely a negative charge is delocalised over electronegative atoms (like O),
the more stabilised the ion becomes. This is one reason why
\(\mathrm{SO_4^{2-}}\) and \(\mathrm{HSO_4^-}\) are particularly important
and stable oxoanions.
5. Expanded octets on sulfur
Sulfur is in the third period, so simple Lewis structures often show
an expanded octet on sulfur (10 or 12 electrons) to minimise formal charges,
especially in \(\mathrm{SO_3}\), \(\mathrm{SO_3^{2-}}\), \(\mathrm{SO_4^{2-}}\),
and \(\mathrm{HSO_4^-}\).
More advanced bonding models (molecular orbital theory) explain these structures
using delocalised \(\pi\) bonding rather than literal \(d\)-orbital participation,
but at this level it is acceptable to treat sulfur as using an expanded octet
to account for the short, partially multiple S–O bonds in these polyatomic ions.
