Bigger molecules need a method
Lesson 2.2.6 drew Lewis symbols for atoms, and lesson 2.4.2 drew simple molecules such as H₂O and N₂. As molecules get more complicated, guessing stops working: are the bonds in CO₂ single or double? How many electrons does NH₄⁺ have? This lesson gives a method that always works. (Chinese textbooks draw the same structures as electron-dot formulas, with two dots in place of each line; the steps are identical.)
Steps for drawing a Lewis structure
- Count the total valence electrons. Add up the valence electrons of all the atoms. For an anion, add one electron per negative charge; for a cation, subtract one per positive charge.
- Draw the skeleton. Usually the less electronegative atom goes in the center; H and F form only one bond, so they are always on the outside. Connect each outer atom to the central atom with a single bond, which uses 2 electrons.
- Complete the outer atoms first. Use the remaining electrons to give each outer atom an octet (hydrogen needs only 2).
- Put any leftovers on the central atom. Place all remaining electrons on the central atom as lone pairs.
- If the central atom lacks an octet, make multiple bonds. Move a lone pair from an outer atom into the bond, turning a single bond into a double bond; if that isn’t enough, move another to make a triple bond.
- Check. Is the electron total right? Does every atom have an octet (2 for hydrogen)?
Following these steps for CO₂, HCN, and formaldehyde gives:
Exceptions to the octet rule
- Electron-deficient atoms: a central atom with very few valence electrons, such as boron or beryllium, can end up with fewer than 8. Boron in BF₃ has only 6.
- Expanded octets: elements in period 3 and beyond are larger and can hold more than 8 electrons as central atoms: phosphorus has 10 in PCl₅, and sulfur has 12 in SF₆. Period 2 elements (C, N, O, F) never exceed 8.
- Odd-electron molecules: a molecule with an odd number of valence electrons, such as NO (11) or NO₂ (17), always has one atom short of an octet. These are called free radicals and are usually very reactive.
Formal charge
Some molecules can be drawn several ways that all satisfy the octet rule. AP uses formal charge to choose the best one (Chinese textbooks don’t teach it):
Here FC is the formal charge, V is the atom’s number of valence electrons, N is its number of nonbonding electrons (the electrons in its lone pairs), and B is the number of bonds (lines) drawn to it. The best structure is the one where:
- the formal charges are as close to 0 as possible;
- any negative formal charge sits on the more electronegative atom;
- the formal charges add up to the charge of the whole species, as they always must.
For example, CO₂ could also be drawn with one single bond and one triple bond, and every atom would still have an octet, but the two oxygens would have formal charges of −1 and +1. With two double bonds, every formal charge is 0, so that is the best structure:
Now draw some yourself. Choose a molecule and click bonds to switch between single, double, and triple; the lone pairs fill in automatically, following the steps above. Orange atoms don’t have an octet yet:
Click a bond to switch it between single, double, and triple. Orange atoms don't have an octet yet; green atoms do.
Example 1: Carbon dioxide
Draw the Lewis structure of CO₂.
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Count the valence electrons. C has 4 and each O has 6:
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Build the skeleton. The less electronegative atom goes in the center: O–C–O. The two single bonds use 4 electrons, leaving 12.
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Complete the outer atoms first. Each oxygen already has one shared pair; give each 3 lone pairs (6 electrons). That uses all 12, leaving 0.
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Check the central atom. Carbon has only 2 shared pairs (4 electrons), short of 8. Move one lone pair from each oxygen into a bond to make two double bonds: O=C=O, with 2 lone pairs left on each oxygen.
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Check. There are 4 shared pairs and 4 lone pairs, exactly 16 electrons, and all three atoms have 8. Every formal charge is 0; for carbon, 4 − 0 − 4 = 0.
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A common mistake. Drawing a triple bond to one oxygen and a single bond to the other (O≡C–O). The electron count works, but the oxygens get formal charges of +1 and −1, so it’s less favorable than O=C=O.
Example 2: The ammonium ion
Draw the Lewis structure of NH₄⁺.
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Count the valence electrons. For a cation, subtract the charge:
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Build the skeleton. Nitrogen goes in the center, with a single bond to each of four hydrogens. That uses exactly 8 electrons.
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Check every atom. Nitrogen has 8 electrons and each hydrogen has 2 (all hydrogen needs).
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Formal charge. Formal charge = valence electrons − lone-pair electrons − bonds:
This matches the charge of the ion.
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Write it as an ion. Put the whole structure in square brackets with a + at the upper right. A common mistake is forgetting to subtract the electron, which leaves an extra lone pair.
- H₂O
2 × 1 + 6 = 8.
- CO₂
4 + 2 × 6 = 16.
- HCN
1 + 4 + 5 = 10.
- CH₂O
4 + 2 × 1 + 6 = 12.
- NH₄⁺
5 + 4 × 1 − 1 = 8: subtract the positive charge of a cation.
- N₂
2 × 5 = 10.
- CCl₄
4 + 4 × 7 = 32.
- NO₃⁻
5 + 3 × 6 + 1 = 24: add the negative charge of an anion.
- C₂H₄
2 × 4 + 4 × 1 = 12.
Common mistakes
Mistake 1: “A Lewis structure shows the real shape of the molecule.” A Lewis structure shows only which atoms are connected and where the electrons are. Water’s Lewis structure is often drawn in a straight line, but the real molecule is bent, with a 104.5° angle (lesson 2.4.6).
Mistake 2: “An ion’s valence electrons are just the sum for its atoms.” You must also account for the charge: NH₄⁺ has 9 − 1 = 8 and OH⁻ has 7 + 1 = 8. Skip this step and everything after it goes wrong.
Mistake 3: “Hydrogen can go in the center.” Hydrogen has only 1 valence electron and forms only one bond, so it is always on the outside. The skeleton of HCN is H–C–N, never C–H–N.
Quick check
How many valence electrons does CO₃²⁻ have in all?
4 + 3 × 6 + 2 = 24: 4 from carbon, 18 from the three oxygens, and 2 more for the 2− charge.
In which molecule does the central atom have fewer than 8 electrons?
Boron has only 3 valence electrons. In BF₃ it forms three single bonds and has just 6 electrons around it, an exception to the octet rule.
Summary
- To draw a Lewis structure: count the valence electrons (adjusting for any charge), draw the skeleton, complete the outer atoms, put leftovers on the central atom, form multiple bonds if the central atom lacks an octet, and check.
- Exceptions to the octet rule: electron-deficient atoms (BF₃), expanded octets (PCl₅, SF₆; period 3 and beyond only), and odd-electron molecules (NO, NO₂).
- Formal charge = valence electrons − nonbonding electrons − bonds. In the best structure, formal charges are as close to 0 as possible, and any negative formal charge is on the more electronegative atom.
On to AP (for later)
AP U2.5 free-response questions often ask for a “complete Lewis electron-dot diagram”: every valence electron must be shown, including every lone pair, or you lose the point. U2.6 uses formal charge to compare possible structures, and you will need it again for resonance in the next lesson.