Predict IR absorption count and vibrations for simple molecules

Linear CO₂ has four normal-mode coordinates: symmetric stretch, asymmetric stretch and two perpendicular bends.

GCE A-Level H3 Chemistry 9813-2027

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Learning objectives

Predict IR absorption count and vibrations for simple molecules

Count frequencies, not arrows

Linear CO₂ has four normal-mode coordinates: symmetric stretch, asymmetric stretch and two perpendicular bends.

The two bends are degenerate and the symmetric stretch is IR inactive, so ideal CO₂ gives two fundamental IR absorption frequencies.

Normal modes and IR-active absorptions

A non-linear molecule with N atoms has 3N−6 normal modes; a linear molecule has 3N−5. The syllabus task is to identify modes for supplied simple molecules, not merely quote the formula.

A mode produces an IR absorption only if it changes dipole moment; degenerate modes share one frequency.

CO₂ compared with SO₂

CO₂: symmetric stretch inactive; asymmetric stretch active near 2350 cm⁻¹; doubly degenerate bend active near 667 cm⁻¹. Therefore two distinct absorptions arise from three active coordinates.

Bent SO₂ is non-linear and has three fundamentals—symmetric stretch, bend and asymmetric stretch—which are all IR active and non-degenerate.

Account for CO₂'s two bands

Do not count the two perpendicular bends twice in a frequency list; label them as a degenerate pair.

Do not count the symmetric stretch because its dipole derivative is zero in ideal CO₂.

Try this

Predict the number and origins of ideal CO₂ fundamental absorptions.

Check your answer

Two: one degenerate bending frequency near 667 cm⁻¹ and one asymmetric-stretch frequency near 2350 cm⁻¹.

Build the SO₂ mode table

SO₂ is bent (N = 3), so first count its fundamental modes with 3N − 6, then give each mode its own row.

For each row, decide from the motion whether the dipole changes; do not copy CO₂'s linear result.

Try this

Complete the SO₂ table with three modes and three distinct absorptions.

Check your answer

3N − 6 = 3 modes: symmetric stretch, bend and asymmetric stretch. All three change the dipole of bent SO₂, so all are IR active with three distinct absorptions; CO₂'s inactive symmetric stretch does not transfer because CO₂ is linear.

Transfer to H₂O and HCN

H₂O is bent; HCN is linear (H–C≡N). Choose 3N − 6 or 3N − 5 from the geometry.

Then use symmetry and dipole change, not atom count alone, to decide how many distinct IR frequencies each gives.

Try this

Predict the fundamental mode pattern for H₂O, then explain why linear HCN needs a degeneracy check.

Check your answer

H₂O: 3N − 6 = 3 modes (symmetric stretch, bend, asymmetric stretch), all changing the dipole, so three active frequencies. HCN: 3N − 5 = 4 modes, but its two perpendicular bends are degenerate and share one frequency, while the C–H and C≡N stretches are distinct, so three frequencies.

Normal-mode count is not peak count

The 3N−5 or 3N−6 result counts coordinates, not necessarily observed absorption frequencies.

IR inactivity, degeneracy and coincident bands can reduce the number of distinct observed fundamentals.

Try this

Better reasoning: “CO₂ has four normal modes, so it must show four IR bands.”

Check your answer

State that the symmetric stretch is inactive and the two bends are degenerate, leaving two fundamental frequencies.

From motion inventory to spectral evidence

After the check questions, try the CS₂ example without notes. Return later for a different H₂S question.

Try this next: identify functional-group bands.

Try this

Produce a mode/activity table for CO₂ and SO₂.

Check your answer

Every row must specify geometry, motion, degeneracy and dipole-change activity; totals are CO₂ two and SO₂ three.