How do atoms share electrons, and what does a bond look like on paper?
Draw Lewis structures, assign formal charges, and judge resonance, bond order and bond energy.
ExperimentsWhat does a shared pair do?Measure the distance between bonded atoms, and the energy that holds them.
Experiment 1 · Measured today
How far apart are the atoms?
A bond is a shared pair of electrons. What happens to the distance between the nuclei when two atoms share more than one pair?
In 1916 Gilbert Lewis proposed that a chemical bond is a pair of electrons shared between two atoms, and that a double bond is two pairs. It was a bold idea, because nobody could see electrons. But spectroscopy later made it possible to measure the distance between the nuclei of bonded atoms, and that gives a test. If a double bond is really two shared pairs, the nuclei should sit closer together than in a single bond. Predict the distance, drag the atom to where you think it sits, and compare with experiment.
Bond 1 of 3 · C=CThe dashed circle shows the C–C distance in ethane. In ethylene, H₂C=CH₂ the atoms share two pairs. Drag the right-hand atom to where you think it sits: nearer, or farther?
BondC=C
Shared pairs2
Distance shown135.0 pm
Predictions made0 / 3
The maths
Bond length = the distance between the two nuclei, in picometres (1 pm = 10⁻¹² m).
C–C in ethane: 153.6 pm. Now C=C in ethylene, H₂C=CH₂.
Questions you might have (3)Why do more shared electrons bring the nuclei closer?
The shared electrons sit between the two positive nuclei and pull both toward them. With more electron density between the nuclei there is a stronger pull holding them together, so they settle closer. The nuclei repel each other, and they stop approaching where that repulsion balances the pull of the shared electrons: at a shorter distance when more pairs are shared.
Where do the numbers come from?
From the NIST Computational Chemistry Comparison and Benchmark Database, which lists measured geometries (mostly from microwave and infrared spectroscopy). A script reads them: C–C from ethane, C=C from ethylene, C≡C from acetylene, N–N from hydrazine and N≡N from nitrogen.
Is the C–C bond always 153.6 pm?
No: that is the value in ethane, and it is the usual figure for a carbon–carbon single bond. Real bonds change a little with the rest of the molecule. The trend across bond orders is much larger than that variation.
Run the experiment to see what it showed.
Experiment 2 · Hess, 1840
How strong is a bond?
How much energy does it take to pull apart the atoms that a single, double or triple bond is holding?
In 1840 Germain Hess showed that the heat of a reaction depends only on where you start and finish, not on the route. That lets you do something you cannot do directly: you cannot snap one bond and weigh the energy, but you can pull a whole molecule into atoms, measure what that costs by a roundabout route, and share the energy among the bonds. Do the accounting for three hydrocarbons and see whether more shared pairs make a stronger bond as well as a shorter one.
Molecule:
Energy to pull methane into atoms
1663 kJ/mol
1663 left
0 of 4 C–H bonds taken off
Step 1 of 4 · MethaneMethane has four identical C–H bonds. Click each one to take its share of the energy, and see how big a C–H bond is.
Atomization1663 kJ/mol
Taken off0 × 416
Left for the bond1663 kJ/mol
Bond order1
The maths
Hess's law: tearing a molecule into gaseous atoms costs the sum of the atoms' enthalpies of formation, less the molecule's own.
Four identical C–H bonds share it equally: 1663 / 4 = 416 kJ/mol each.
Questions you might have (4)Why does the double bond not give twice the energy?
The first shared pair, the sigma bond, lies right along the line between the nuclei and overlaps well. The second pair, the pi bond, is formed from sideways overlap of p orbitals, which is weaker. In the next unit you will see these as separate parts of the bond.
How accurate are these numbers?
They are bond energies in the average sense. The C–H bond in methane is not exactly the C–H bond in ethane or acetylene, so the energies left over come out a few percent away from tabulated average values (for C–C the usual figure is 347 kJ/mol, and this gives 330). The trend, and the sizes, are right.
Where do the enthalpies come from?
From the NIST CCCBDB, which lists the measured enthalpy of formation of each molecule and each gaseous atom at 298 K. A script reads them; the page does the subtraction.
Why is bond energy useful?
Add up the bonds broken and the bonds made in a reaction, and the difference is a good estimate of how much heat the reaction releases or absorbs. That is the subject of the thermochemistry unit, and it is how chemists see that burning a fuel is mostly the exchange of weaker bonds for stronger ones.
Run the experiment to see what it showed.
TheoryThe bookkeeping of shared electronsCount the electrons, share them, and keep track of who has what.
Theory 1 · G. N. Lewis, 1916
Build the Lewis structure
Where do the valence electrons go when atoms join up?
In 1916 Gilbert Lewis, at Berkeley, drew atoms with dots for their outer electrons and a bond as a shared pair; Irving Langmuir developed the idea into the octet rule a few years later. A century on, every chemistry student still draws them. The bench counts the electrons and rings each atom by how many it has, and it refuses anything that breaks the rules. Draw the molecules yourself, and find the places where the rules give way.
Molecule:
Select an atom to give it lone pairs.
Task 1 of 6 · waterSelect H₂O above. Count the valence electrons first: 6 from oxygen and 1 from each hydrogen. Two bonds use 4. Where do the other 4 go?4 electrons still to place (2 pairs). Select an atom and give it lone pairs, or click a bond to share more.
Electrons to place8
Drawn4
Left4
Total formal charge4
The maths
Count first: valence electrons of each atom, plus 1 for each negative charge, minus 1 for each positive charge.
H₂O: 1 × 6 (O) + 2 × 1 (H) = 8 electrons
Drawn so far: 4 (bonds 4 + lone pairs 0). Left: 4
Questions you might have (4)Why the octet?
The s and three p orbitals of the outer shell hold eight electrons in all. Filling them gives a configuration like a noble gas, which you saw is especially stable. Hydrogen has only the 1s orbital, which holds two.
What is formal charge, and is it real?
It is the charge an atom would have if every bond were shared exactly equally: valence electrons minus lone-pair electrons minus the number of bonds. It is a bookkeeping tool for choosing between drawings, not a measured charge. Real charges lie between the formal charge and the polarity of the bond.
Why can phosphorus and sulfur have more than eight?
The usual explanation is that atoms of period 3 and below have d orbitals available. Modern calculations suggest the d orbitals play a smaller part than once thought, and that the bonding in molecules like SF₆ is highly polar. For the purposes of drawing, the rule stands: period 3 and below may exceed an octet, period 2 may not.
How do I place the atoms to start?
The central atom is usually the one that makes the most bonds and is the least electronegative (never hydrogen). Here the skeletons are given, so you can concentrate on the electrons.
Work through it to see what it shows.
Theory 2 · Lewis and Langmuir, 1916 to 1919
Which drawing is better?
Several Lewis structures obey the octet rule. How do you choose between them?
The octet rule alone does not always pick one structure: for a given set of atoms it can allow several. Chemists needed a tie-breaker, and the one they use is formal charge, a bookkeeping of which atom has how many of the shared electrons. Look at every drawing the octet rule allows for a few ions and molecules, and choose the best.
Species:
Three drawings give every atom an octet. Formal charges are shown in colour: red positive, blue negative.
Species 1 of 3Choose the best drawing of CO₂. Add up the size of the formal charges on each, and prefer the smallest.
SpeciesCO₂
Octet drawings3
Best total |charge|?
Judged0 / 3
The maths
Formal charge = valence electrons − (lone-pair electrons + bonds). Prefer: (1) the smallest charges; (2) a negative charge on the more electronegative atom.
Questions you might have (3)Why do small formal charges make a drawing better?
Charges that cost energy to separate are signs of a poor distribution of the electrons. If a drawing puts +1 and −1 on neighbouring atoms, the atoms have to hold on to electrons unevenly, and bonds do not usually work that way unless the atoms differ a lot in electronegativity.
Why put the negative charge on the more electronegative atom?
Electronegativity is how strongly an atom holds electrons. An atom that grips electrons hard is happier carrying the extra one. Oxygen holds electrons better than nitrogen, which holds them better than carbon.
Is a drawing with the lowest formal charge always the true structure?
No. It is the best single guess, and often it is right. But it is a guide for the choice, and real molecules can be a mixture of drawings, as the next two sections show.
Work through it to see what it shows.
ExperimentsDo the drawings tell the truth?Measure the bonds in two molecules whose drawings offer a choice.
Experiment 3 · Kekulé, 1865, and spectroscopy today
The bonds you cannot draw
The Lewis drawing of ozone has one double bond and one single bond. Does the molecule?
In 1865 August Kekulé proposed that benzene is a ring of six carbon atoms with alternating single and double bonds. Chemists argued about it for decades, because benzene did not behave like a molecule with three double bonds. Today the bonds can simply be measured. A Lewis drawing makes a testable claim: its single bonds should be longer than its double bonds. Predict what the measurement will show for ozone and for benzene, and then look.
one Lewis drawing of ozone
Predicted from the drawing, against measured (pm):
O–O single bond
147.5
O=O double bond
120.8
measured, every bond
?
The two O–O bonds in ozone will be:
Step 1 of 2 · OzoneHere is the Lewis structure of ozone, with a double bond and a single bond. Predict whether the measured bonds will differ, then look.
MoleculeO₃
Drawing predicts147.5 and 120.8 pm
Measured?
Measured, in between??
The maths
The Lewis drawing says: some bonds are single (long) and some are double (short). Reference lengths: O–O in hydrogen peroxide 147.5 pm, O=O in oxygen 120.8 pm.
Prediction from the drawing: 147.5 pm and 120.8 pm (one of each).
Questions you might have (3)Isn't the molecule flipping between the two drawings?
That is a natural guess and a wrong one. The molecule is not switching: at every moment all the bonds are the same. Neither drawing describes it, and the pair of drawings together does. The next section will make this precise.
Where does the benzene structure come from?
August Kekulé proposed the ring with alternating double bonds in 1865. If it were right, benzene would have two different dibromo compounds with the bromines on neighbouring carbons (one across a single bond, one across a double). Only one exists. Equal bonds explain that.
Where are the lengths from?
From NIST's CCCBDB, which gives the experimental geometry of ozone (rOO = 1.278 Å, from rotational spectroscopy) and benzene (rCC = 1.397 Å). The references for single and double bonds are O–O in hydrogen peroxide, O=O in oxygen, C–C in ethane and C=C in ethylene.
Run the experiment to see what it showed.
TheoryWhen no drawing is rightDraw both, and say the molecule is neither and both.
Theory 3 · Pauling, 1931
Two drawings, one molecule
No Lewis structure of ozone has two equal bonds. What does the molecule look like, then?
By 1931 Linus Pauling had an answer to Kekulé's puzzle. When no single drawing is right, the molecule is neither drawing and both: a blend, which he called a resonance hybrid. The measurement says the bonds in ozone and benzene are all equal and in between single and double. Slide between the drawings, and find the blend that makes every bond equal.
drawing A · 90 %
−0.9+1.0−0.1
the blend
drawing B · 10 %
Step 1 of 2 · OzoneStart with ozone. Drawing A has a double bond on the left and a single on the right, drawing B the reverse. Drag the slider until the two bonds come out equal.The bonds differ by 21.4 pm at this blend. The measured bonds do not differ at all: keep moving.
Blend90 % A
Bond orders1.10 and 1.90
Longest − shortest21.4 pm
Measured0 pm (all equal)
The maths
Bond order of the blend = (weight of A) × (order in A) + (weight of B) × (order in B).
A 90 %, B 10 %: bond orders 1.10, 1.90
Estimated lengths (straight line between 147.5 pm at order 1 and 120.8 pm at order 2): 144.8, 123.5 pm. Measured: all 127.8 pm.
Charges on the three oxygens: -0.90, +1.00, -0.10. At 50 : 50 the ends are −½ each and the middle is +1.
Questions you might have (4)Is the molecule flipping between the two structures?
No. This is the most common misunderstanding. The two drawings are not states the molecule switches between, like a coin flipping. The molecule is one thing, with electrons spread over the whole group of atoms, and the drawings are two imperfect snapshots of that one thing. A better comparison is a mule: it is not sometimes a horse and sometimes a donkey, it is a mule.
Why does the blend come out more stable?
Electrons spread over more atoms have more room, which lowers their energy. This is the same principle that lowers the energy of an electron in a bigger box or standing wave: you saw it in the quantum unit. The extra stability this gives benzene is large, which is why it resists reactions that ordinary double bonds undergo easily.
How do I know when to draw resonance structures?
When you can draw more than one acceptable Lewis structure that differ only in where the electrons (not the atoms) are. Ozone, nitrate (NO₃⁻, three structures), carbonate, benzene and the cyanate ion in the last section are all examples. The resonance forms must all have the same atoms in the same places.
Why does the estimated length not exactly match?
Bond length does not change in a straight line with bond order. At order 1.5 the length estimated by interpolation is a bit longer than measured in both molecules. It is the right region: between a single and a double bond, and the same for every bond, which is the point.
Work through it to see what it shows.
PracticeProblemsNumbers from this unit, in the style of a college problem set.
Practice
Practice
Numbers from the experiments, in the style of a college problem set. Every problem has a hint and a worked solution.
Lewis structures0 right of 0 · streak 0
How many valence electrons must be shown in the Lewis structure of NH4⁺?