Why Molecules Have Shapes

Chapter 2 Counting electrons

Lewis structures

Every valence electron, accounted for. Five steps turn a formula into a Lewis structure, and the Lewis structure tells you how many electron domains decide the shape.

8 min read · 3 interactive figures · 2 questions

Carbon dioxide at step 1: one carbon and two oxygen atoms with their valence electrons drawn as dots, 16 in all. Press Next step (or move the slider) to build the structure; the ledger under the drawing shows where every electron has gone. Choose another molecule or ion from the list to run the same procedure on it.

A Lewis structure accounts for every valence electron in a molecule: shared pairs are drawn as lines between atoms, unshared pairs as dots. Carbon dioxide has 16 valence electrons, and its Lewis structure, O=C=O with two lone pairs on each oxygen, places all 16 so that every atom has eight. Drawing one takes five steps, the first of them a count, and the result tells you how many electron domains sit on the central atom, which is all VSEPR needs to predict the shape.

The stepper at the top of the page runs the procedure on sixteen molecules and ions. This chapter explains each step, the two checks that choose between possible structures (formal charge and resonance), the exceptions, and then the Lewis structures of the molecules people most often look up.

Step 1: count the valence electrons

Only the outermost electrons take part in bonding. For a main-group atom their number is the last digit of its group number: carbon (group 14) has 4, nitrogen 5, oxygen and sulfur 6, the halogens 7, hydrogen 1. Add them up over all the atoms, then subtract one electron for each positive charge or add one for each negative charge[1]. established

  • CO2: 4 + 2 × 6 = 16.
  • SO2: 6 + 2 × 6 = 18.
  • NH4+: 5 + 4 × 1 − 1 = 8.
  • CO32−: 4 + 3 × 6 + 2 = 24.

Every later step only moves these electrons around. If the finished structure has more or fewer dots and lines than the count, something went wrong. The ledger under the stepper keeps the books: each dot is one electron, filled in as it is placed.

Steps 2 to 5: skeleton, outer octets, leftovers, multiple bonds

The procedure in OpenStax's Chemistry 2e[1], which the stepper follows exactly:

  1. Skeleton. Put the least electronegative atom in the centre (never hydrogen, which can form only one bond, nor fluorine) and join each outer atom to it with a single bond. Each bond uses two electrons.
  2. Outer octets. Give each outer atom except hydrogen lone pairs until it has eight electrons, counting the two in its bond.
  3. Leftovers. Any electrons still unplaced go on the central atom, as lone pairs.
  4. Multiple bonds. If the central atom still has fewer than eight electrons, turn a lone pair on an outer atom into a second (or third) shared pair, until it has eight.

For carbon dioxide: two C–O single bonds use 4 electrons; three lone pairs on each oxygen use 12 more; nothing is left for carbon, which so far has only the 4 electrons of its two bonds. Sharing one lone pair from each oxygen makes two double bonds and gives carbon its octet: O=C=O, with two lone pairs on each oxygen. Choose CO2 in the stepper and press Next step to watch the same thing happen.

The octet rule behind steps 3 to 5 is the observation that main-group atoms tend to form bonds until they have eight valence electrons, the count of the noble gas at the end of their row[1]. It is a strong tendency, not a law, and the exceptions are listed below.

Formal charge: choosing between structures

The five steps can produce more than one valid-looking structure. Carbon dioxide could also be drawn O≡C–O, with a triple bond to one oxygen and three lone pairs on the other: 16 electrons, an octet on every atom. To choose, chemists compute a bookkeeping charge for each atom[2]:

formal charge = valence electrons − non-bonding electrons − bonds(2.1)

Here "bonds" counts shared pairs: a double bond is two. In O=C=O every atom comes out at zero. In O≡C–O the triply bonded oxygen is +1 and the singly bonded one −1. OpenStax's guidelines prefer the structure whose formal charges are zero, or as small as possible, with any negative charge on the more electronegative atom[2]. So O=C=O it is. The formal charges always add up to the overall charge of the molecule or ion, which makes them a useful check on the count.

Resonance: when one drawing is not enough

Run the stepper on sulfur dioxide. Its 18 electrons give O=S–O: a double bond to one oxygen, a single bond to the other, a lone pair on sulfur, formal charges of +1 on sulfur and −1 on the singly bonded oxygen. But nothing in the procedure says which oxygen gets the double bond.

Question 1 Prediction: the two bonds of SO₂#

Both bonds in sulfur dioxide measure 1.432 Å, and both bonds in ozone 1.278 Å[3]. The two drawings, double bond on the left or double bond on the right, are called resonance structures, and the real molecule is a resonance hybrid of them, with each bond of order one and a half. OpenStax is emphatic that the molecule never actually has either structure; the drawings are a way of writing down a single structure that one Lewis drawing cannot show[2]. established

Figure 1 Sulfur dioxide, the first of its two resonance structures, with formal charges circled. Move the Structure slider to see the other one, then tick Show the hybrid: each bond is drawn as a full line plus a dashed half bond. Choose ozone, the nitrite ion or the carbonate ion to compare. For SO₂, Expanded-octet structure shows the drawing many textbooks use instead.#

The carbonate ion, CO32−, has three resonance structures, because the double bond can sit on any of three oxygens; each C–O bond is a third of the way from single to double. For VSEPR, resonance changes nothing that matters: every structure of SO2 has two bonded atoms and one lone pair on sulfur, three domains, a bent shape.

The Expanded-octet structure option shows the drawing for SO2 that follows the formal-charge guideline to the letter: O=S=O, every formal charge zero, ten electrons around sulfur. Many textbooks prefer it. It also has three domains on sulfur and also predicts a bent molecule, so the shape does not depend on which drawing you use. contested

Exceptions to the octet rule

Three kinds of molecule cannot give every atom eight electrons[1]:

  • Odd numbers of electrons. Nitrogen dioxide has 17 valence electrons, so one is unpaired and the molecule is a radical. In its Lewis structure nitrogen ends with seven.
  • Too few electrons. Boron trifluoride gives boron only six: fluorine keeps its lone pairs rather than share them in a double bond. Boron's unfilled octet is why BF3 readily accepts a lone pair from ammonia.
  • Too many. Atoms from the third period on can hold more than eight valence electrons: PCl5 has ten around phosphorus, SF6 twelve around sulfur, and ClF3 ten around chlorine, including two lone pairs. The stepper puts these on the central atom at step 4 and makes no multiple bonds.

None of these breaks VSEPR. It counts domains, not octets: NO2 has three (two bonds and one unpaired electron), BF3 three, ClF3 five.

From Lewis structure to shape

Once the Lewis structure is drawn, the shape is a count away. Bonded atoms on the central atom plus lone pairs on the central atom give the steric number; the steric number gives the electron geometry; the lone pairs give the shape (chapter 1). Lone pairs on the outer atoms play no part.

Question 2 Prediction: xenon tetrafluoride#
Figure 2 Water: its Lewis structure (two bonds and two lone pairs on oxygen) together with the molecule in its measured geometry, 104.5°. Choose another molecule to see the same translation from a flat drawing to a three-dimensional shape. Formal charges other than zero are circled in the Lewis structure. Drag the model to turn it.#

A flat Lewis drawing never shows angles. Water's is often drawn with the hydrogens at 180° and the lone pairs above and below, which looks linear; the bent shape comes only from counting. Read a Lewis structure as an electron count, never as a picture of the molecule.

Lewis structures of common molecules

Carbon dioxide, CO2

16 valence electrons. O=C=O, two lone pairs on each oxygen, all formal charges zero. Two domains on carbon: linear, 180°[3]. Nonpolar despite its two polar bonds, because they point in opposite directions.

Sulfur dioxide, SO2

18 valence electrons. O=S–O with a lone pair on sulfur, two resonance structures; sulfur +1, single-bonded oxygen −1. Three domains on sulfur: bent, measured 119.5°, both S–O bonds 1.432 Å[3]. The expanded-octet drawing O=S=O gives the same shape.

Water, H2O

8 valence electrons. Two O–H bonds and two lone pairs on oxygen. Four domains: tetrahedral electron geometry, bent shape, measured 104.5°[3].

Ammonia, NH3

8 valence electrons. Three N–H bonds and one lone pair on nitrogen. Four domains: trigonal pyramidal, measured 106.7°[3].

Methane, CH4

8 valence electrons. Four C–H bonds, no lone pairs. Four domains: tetrahedral, 109.5° by symmetry.

Hydrogen cyanide, HCN

10 valence electrons. Carbon is central: H–C≡N, one lone pair on nitrogen. Hydrogen cannot form a double bond, so both of carbon's missing electron pairs come from nitrogen, making a triple bond[1]. Two domains on carbon: linear, 180°[3].

Nitrite, NO2−, and nitrogen dioxide, NO2

The nitrite ion has 18 valence electrons: O=N–O− with a lone pair on nitrogen and two resonance structures, like SO2[2]. Three domains: bent. The neutral molecule NO2 has one electron fewer, 17, so nitrogen carries a single unpaired electron instead of a lone pair. It is still bent, but wider: 134.1°[3], because one electron takes less room than two.

Where Lewis structures came from

G. N. Lewis proposed in 1916, in "The atom and the molecule", that a chemical bond is a pair of electrons shared between two atoms[4]. documented The dot diagrams still named after him are a bookkeeping device built on that idea. They are excellent at counting electrons and poor at showing where electrons are; OpenStax calls resonance forms "convenient, imaginary images"[2]. Used for what it is good at, a Lewis structure gives you the one number VSEPR needs.