Q.Explain the structure of the $CO_2$ molecule.

The key idea is resonance: a single Lewis structure cannot correctly represent

$CO_2$'s real, experimentally measured bond length, so we describe its structure as a hybrid of

several canonical (contributing) forms — exactly as we did for $O_3$ and $CO_3^{2-}$.

A simple Lewis structure gives $CO_2$ as $O=C=O$ (Form I), with two ordinary C=O double bonds.

But the C–O bond length actually measured in $CO_2$ is $115$ pm — shorter than a pure C=O double

bond ($121$ pm) but longer than a pure C≡O triple bond ($110$ pm). A structure of only double

bonds can't explain this intermediate length on its own.

To account for it, $CO_2$'s structure is described as a resonance hybrid of three canonical

forms (Fig. 4.5 of the textbook):

• Form I: $O=C=O$
• Form II: $^+O-C\equiv O^-$
• Form III: $^-O\equiv C-O^+$

The true structure is the hybrid of all three — none of them alone is the real molecule. This

hybrid character is exactly why the observed C–O bond length (115 pm) sits between the double- …

Why a single Lewis structure isn't enough

A straightforward Lewis-structure treatment of $CO_2$ gives one clean answer: carbon, with 4

valence electrons, forms a double bond with each of the two oxygens, using all 16 valence

electrons ($4 + 2\times 6$) and leaving no lone pairs on carbon. This structure — $O=C=O$ — is

perfectly valid on its own, is linear, and correctly predicts a $180°$ bond angle and a nonpolar

molecule.

But a single structure like this makes a specific, checkable prediction: if both C–O bonds are

plain double bonds, they should both have the normal C=O bond length, $121$ pm. Experiment

says otherwise — the C–O bond length actually measured in $CO_2$ is $115$ pm, noticeably shorter

than $121$ pm. Something in the simple picture is incomplete.

Bringing in resonance

This is the same situation we already saw for ozone ($O_3$) and the carbonate ion ($CO_3^{2-}$):

whenever a molecule's real, experimentally measured bond length falls between the values

expected for two different bond orders, a single Lewis structure cannot be the whole truth, and

we turn to resonance.

For $CO_2$, the textbook gives three canonical (contributing) structures, shown together in Fig.

4.5:

• Form I: $O=C=O$ — the ordinary double-bond structure, with no formal charges.
• Form II: $^+O-C\equiv O^-$ — one oxygen forms a single bond and carries a formal positive charge; the other forms a triple bond and carries a formal negative charge.
• Form III: $^-O\equiv C-O^+$ — the mirror image of Form II, with the triple bond and single bond swapped between the two oxygens.

None of these three forms is the actual structure of $CO_2$ on its own. The real molecule is a

resonance hybrid of all three — a single, stable structure whose true bonding character is

an average of the three canonical forms, not a molecule flipping between them.

Why the hybrid explains the bond length

Averaging across the three forms, each C–O bond has some triple-bond character (from whichever

form puts a triple bond on that side) mixed with mostly double-bond character (since Form I,

the pure double-bond form, contributes most heavily and is the lowest-energy, most stable of the

three canonical structures). This gives each C–O bond a bond order between 2 (pure double) and 3

(pure triple) — and a bond length correspondingly between the double-bond value (121 pm) and the

triple-bond value (110 pm).

The measured value, 115 pm, sits neatly in that intermediate range — shorter and stronger than a …