Linear and Trigonal Planar Shapes

Introduction

Two or three electron domains around a central atom give some of the clearest shape predictions. Two domains can point in opposite directions; three spread around a plane. The examples CO₂, HCN, BF₃ and formaldehyde show why bond multiplicity and electron-domain number must be kept separate.

Core explanation

With two central domains and no central lone pair, the simplest arrangement places the regions opposite each other. The ideal bond angle is 180°, so a three-atom molecule such as CO₂ is linear. Carbon's ordinary Lewis structure O=C=O has two double bonds, but each C=O direction is one domain; carbon has no lone pair. Both the electron-domain arrangement and the molecular shape are linear. The two oxygen atoms are equivalent in this molecule, allowing their equal bond dipoles to cancel.

HCN offers a different two-domain example. Its common structure is H–C≡N: with carbon at the center of H and N. The C–H single bond is one domain and the C≡N triple bond is one, so the H–C–N nuclei are predicted to be linear. Unlike CO₂, its terminal atoms differ; its bond contributions do not cancel by identical opposite ends. The shape category alone does not decide polarity without considering bond dipoles and atom identity.

With three central domains and no central lone pair, the simplest arrangement spreads them in one plane, ideally 120° apart. BF₃ has three B–F bond directions and no B lone pair in the common electron-deficient Lewis diagram. Boron counts only six valence electrons in that diagram, yet VSEPR still predicts a trigonal-planar arrangement of the three domains. The shape model does not require boron to have an octet before it can count directions.

Formaldehyde, H₂C=O, also has three domains around carbon: two C–H single-bond directions and one C=O double-bond direction. Its local arrangement is approximately trigonal planar, though the exact H–C–H and H–C–O angles need not all be precisely 120° because the domains are not identical. This is a useful reminder that “trigonal planar” describes a broad geometry category, not a claim that every angle is mathematically equal in every substituted molecule.

Nitrate, NO₃⁻, has three N–O directions around central N in its resonance description and no central lone pair in the usual contributors. Its idealized local arrangement is trigonal planar. One contributor draws a double bond, but that still counts as one direction. Resonance helps explain equivalent N–O links, while VSEPR describes the arrangement of the three oxygen nuclei. The two models answer related but distinct questions.

For a molecule with two atoms, such as HCl, calling it linear is geometrically trivial because two points define a line. A bond angle requires three nuclei, so one should not invent an H–Cl–? angle. Domain-count tables are most informative when there is a central atom bonded to at least two others.

Step-by-step reasoning

1. Choose the central atom and draw a correct Lewis structure. 2. Count each attached atom as one direction, including multiple bonds once. 3. Add any central lone pairs; the simple examples here have none. 4. Map two domains to linear or three to trigonal planar and state ideal angles. 5. Check symmetry and atom identity separately before inferring molecular polarity.

Visual explanation

Draw CO₂ as O←C→O on one straight axis and HCN as H–C≡N on another. Write “two domains, ideal 180°” beneath both. Draw BF₃ as three spokes separated equally in a plane, then H₂C=O as three spokes with one thicker C=O direction. Label “three domains, ideal 120°” and add “actual substituted angles may differ.”

Real-world analogy

Two people standing around a central post can occupy opposite sides for maximum separation; three can stand at the corners of a broad flat triangle. The arrangement analogy captures directions, but actual electron-density interactions are not people on fixed marks and molecules need not be perfectly ideal.

Real-world example

BF₃ is electron-deficient yet trigonal planar in a simple molecular model. Its planar three-direction arrangement leaves the boron center accessible to an electron-pair donor such as NH₃. Formation of an adduct changes the number of connections at boron, so the local geometry changes too. The geometry prediction and Lewis acid-base behavior reinforce one another.

Why?

Why is HCN linear despite the three lines in C≡N? The triple bond is one C-to-N direction. Carbon has only two neighboring-atom directions, toward H and toward N, and they are approximately opposite.

Common misconception

“A double bond counts twice when naming shape.” It contains two shared electron pairs but one directional domain. Counting the two strokes separately would misclassify CO₂ or formaldehyde.

Worked example

Compare CO₂ and H₂CO. CO₂ has carbon linked to two O atoms by double bonds, yielding two central domains and linear geometry. H₂CO has carbon linked to two H atoms and one O by a double bond, yielding three domains and approximately trigonal-planar geometry. Both carbon atoms count four bond-line shares for octets, but their domain numbers differ. Therefore octet count does not by itself determine shape; connectivity and the number of distinct electron-density directions do.

Quick check

1. How many central domains are in H₂CO, and what broad shape follows? Answer: Three domains around carbon, giving an approximately trigonal-planar local arrangement.

Exam focus

State ideal 180° for two domains and ideal 120° for three, then qualify real angles when domains differ. Multiple bonds count once. Do not infer molecular polarity from “linear” or “planar” without checking terminal identities and dipole directions.

Advanced insight

Measured bond angles in substituted trigonal centers can deviate from 120° because electron-density regions differ in size, polarity and interaction. More detailed energy calculations predict the optimized geometry. VSEPR remains a quick local classifier, especially when a Lewis structure clearly gives two or three domains.

Summary

Two central electron domains give a linear arrangement; three give a trigonal-planar one when no lone pair changes the molecular-shape name. CO₂ and HCN illustrate two-domain linearity, while BF₃, H₂CO and nitrate illustrate three-domain planarity. Bond order affects the electron ledger but a multiple bond is one domain.

Practice questions

1. What is the ideal angle for two domains around a central atom? Answer: 180°, placing the directions opposite each other. 2. How many domains are around boron in ordinary BF₃? Answer: Three B–F bonding directions and no boron lone pair. 3. Why can HCN be polar although it is linear? Answer: Its different terminal atoms do not give equal opposing bond-dipole contributions. 4. Does a carbon octet guarantee a linear molecule? Answer: No. H₂CO has a carbon octet but three domains and an approximately planar arrangement.