---
title: "Lewis Structures and the Shape of Molecules"
book: "School Chemistry — Grades 1 to 12"
subject: chemistry
language: en
chapter: 24
exercises: 15
source: https://one-course.com/books/chemistry/1/en/chapter/24-lewis-structures-and-the-shape-of-molecules
license: CC-BY-NC-SA-4.0
credit: "One Chemistry Book, One Course (one-course.com)"
---

# Chapter 24 — Lewis Structures and the Shape of Molecules

A [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) of carbon dioxide is straight; a [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) of water is bent. That single difference in shape is one of the reasons why water, with [molecules](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) lighter than those of carbon dioxide, is a liquid at room temperature while carbon dioxide is a gas. [Atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) in a [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) are held together by shared [electrons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-nucleus), and the way the [electrons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-nucleus) are shared decides the shape. This chapter draws the shared [electrons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-nucleus), and from them predicts the shape.

**You already know.**

The [valence electrons](https://one-course.com/books/chemistry/1/en/chapter/23-electron-shells-and-the-periodic-table#def-g10-electron-shells-valence) are those of the outer [shell](https://one-course.com/books/chemistry/1/en/chapter/23-electron-shells-and-the-periodic-table#def-g10-electron-shells-configuration); [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) tend to reach the configuration of a [noble gas](https://one-course.com/books/chemistry/1/en/chapter/23-electron-shells-and-the-periodic-table#def-g10-electron-shells-family), eight [electrons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-nucleus) in the outer [shell](https://one-course.com/books/chemistry/1/en/chapter/23-electron-shells-and-the-periodic-table#def-g10-electron-shells-configuration) ([octet rule](https://one-course.com/books/chemistry/1/en/chapter/23-electron-shells-and-the-periodic-table#def-g10-electron-shells-octet)) or two for hydrogen ([duet rule](https://one-course.com/books/chemistry/1/en/chapter/23-electron-shells-and-the-periodic-table#def-g10-electron-shells-octet)) ([Chapter 23](https://one-course.com/books/chemistry/1/en/chapter/23-electron-shells-and-the-periodic-table#ch-g10-electron-shells)). Molecular models show [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) as balls and bonds as sticks ([Chapter 11](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#ch-g7-atoms-and-molecules)).

## 24.1 The covalent bond

**Definition 24.1 (Covalent bond).**

A *covalent bond* is a pair of [electrons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-nucleus) shared by two [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom); each [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) usually provides one [electron](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-nucleus) of the pair. Both [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) count the shared pair in their outer [shell](https://one-course.com/books/chemistry/1/en/chapter/23-electron-shells-and-the-periodic-table#def-g10-electron-shells-configuration), which lets both reach a duet or an octet.

**Definition 24.2 (Bonding pairs and lone pairs).**

In a [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule), the [valence electrons](https://one-course.com/books/chemistry/1/en/chapter/23-electron-shells-and-the-periodic-table#def-g10-electron-shells-valence) of each [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) are grouped in pairs. A *bonding pair* is shared between two [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) and forms a [covalent bond](#def-g10-lewis-and-shape-covalent-bond); a *lone pair* belongs to a single [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) and takes no part in a bond.

**Proposition 24.3 (How many bonds an atom forms).**

An [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) forms as many [covalent bonds](#def-g10-lewis-and-shape-covalent-bond) as it lacks [electrons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-nucleus) to complete its duet or octet:

| [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) | [valence electrons](https://one-course.com/books/chemistry/1/en/chapter/23-electron-shells-and-the-periodic-table#def-g10-electron-shells-valence) | bonds | [lone pairs](#def-g10-lewis-and-shape-lone-pair) | example |
| --- | --- | --- | --- | --- |
| H | 1 | 1 | 0 | $\ce{H2}$ |
| C | 4 | 4 | 0 | $\ce{CH4}$ |
| N | 5 | 3 | 1 | $\ce{NH3}$ |
| O | 6 | 2 | 2 | $\ce{H2O}$ |
| Cl | 7 | 1 | 3 | $\ce{HCl}$ |

## 24.2 Lewis structures

**Definition 24.4 (Lewis structure).**

The *Lewis structure* of a [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) shows its [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) by their symbols, each [bonding pair](#def-g10-lewis-and-shape-lone-pair) by a line between two [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) and each [lone pair](#def-g10-lewis-and-shape-lone-pair) by a pair of dots next to its [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom).

**Definition 24.5 (Double and triple bonds).**

Two [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) may share two pairs of [electrons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-nucleus), a *double bond*, drawn as two lines, or three pairs, a *triple bond*, drawn as three lines.

**Method 24.6 (Drawing a Lewis structure).**

1. Add up the [valence electrons](https://one-course.com/books/chemistry/1/en/chapter/23-electron-shells-and-the-periodic-table#def-g10-electron-shells-valence) of all the [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) , and halve to get the number of pairs.
2. Join the [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) by single bonds (hydrogen, which forms one bond, is always on the outside; carbon is usually central).
3. Place the remaining pairs as [lone pairs](#def-g10-lewis-and-shape-lone-pair) , first on the outer [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) , to complete their octets.
4. If an [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) still lacks an octet, turn a [lone pair](#def-g10-lewis-and-shape-lone-pair) of a neighbour into a second (or third) shared pair.
5. Check: every hydrogen has 2 [electrons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-nucleus) , every other [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) 8, and all the pairs have been used.

**Example 24.7 (Carbon dioxide).**

$\ce{CO2}$: $4 + 2 \times 6 = 16$ [valence electrons](https://one-course.com/books/chemistry/1/en/chapter/23-electron-shells-and-the-periodic-table#def-g10-electron-shells-valence), 8 pairs. Single bonds $\ce{O-C-O}$ use 2 pairs; 6 [lone pairs](#def-g10-lewis-and-shape-lone-pair) on the oxygens complete them, but carbon then has only 4 [electrons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-nucleus). Turning one [lone pair](#def-g10-lewis-and-shape-lone-pair) of each oxygen into a shared pair gives two [double bonds](#def-g10-lewis-and-shape-multiple-bond): each [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) now has an octet.

![Lewis structures of eleven molecules. Every atom other than hydrogen is surrounded by four pairs (bonds and lone pairs): an octet.](https://one-course.com/images/onecourse/chapters/chemistry-1/g10-lewis-and-shape/fig-8fb5ccbed20c.svg)

*[Lewis structures](#def-g10-lewis-and-shape-lewis-structure) of eleven [molecules](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule). Every [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) other than hydrogen is surrounded by four pairs (bonds and [lone pairs](#def-g10-lewis-and-shape-lone-pair)): an octet.*

## 24.3 The shape of molecules

**Proposition 24.8 (Electron pairs keep as far apart as possible).**

Around a central [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom), the groups of [electrons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-nucleus) — each single, double or [triple bond](#def-g10-lewis-and-shape-multiple-bond), and each [lone pair](#def-g10-lewis-and-shape-lone-pair) — repel one another and settle as far apart as possible. The shape of the [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) follows:

| groups around the centre | of which [lone pairs](#def-g10-lewis-and-shape-lone-pair) | shape | example |
| --- | --- | --- | --- |
| 2 | 0 | linear, angle $180{}^{\circ}$ | $\ce{CO2}$, $\ce{HCN}$ |
| 3 | 0 | flat triangle, angle $120{}^{\circ}$ | $\ce{CH2O}$, $\ce{C2H4}$ |
| 4 | 0 | tetrahedron, angle $109.5{}^{\circ}$ | $\ce{CH4}$ |
| 4 | 1 | pyramid | $\ce{NH3}$ |
| 4 | 2 | bent | $\ce{H2O}$ |

**Proof.** *Admitted at this level.* ∎

**Remark 24.9 (Where this comes from).**

This rule is a model, and it works remarkably well for small [molecules](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule); it is made precise, and partly explained, in the Year 1 volume. [Lone pairs](#def-g10-lewis-and-shape-lone-pair) take up a little more room than [bonding pairs](#def-g10-lewis-and-shape-lone-pair): the angle in ammonia ($106.7{}^{\circ}$) and in water ($104.5{}^{\circ}$) is a little smaller than the $109.5{}^{\circ}$ of methane.

![Shapes of four molecules (lone pairs shown as shaded lobes). Methane is a tetrahedron, ammonia a pyramid, water bent, carbon dioxide straight.](https://one-course.com/images/onecourse/chapters/chemistry-1/g10-lewis-and-shape/fig-d46f14e488dd.svg)

*Shapes of four [molecules](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) ([lone pairs](#def-g10-lewis-and-shape-lone-pair) shown as shaded lobes). Methane is a tetrahedron, ammonia a pyramid, water bent, carbon dioxide straight.*

![Four balloons tied together push one another as far apart as they can; in space they point to the corners of a tetrahedron, like the four electron pairs around a carbon atom.](https://one-course.com/images/onecourse/chapters/chemistry-1/g10-lewis-and-shape/img-39c2f754dc44.jpg)

*Four balloons tied together push one another as far apart as they can; in space they point to the corners of a tetrahedron, like the four [electron](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-nucleus) pairs around a carbon [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom).*

## 24.4 Drawing molecules in space

**Notation 24.10 (Wedges and dashes).**

To draw a [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) in space on flat paper, a bond in the plane of the paper is a plain line, a bond pointing towards the reader a solid wedge, and a bond pointing away a dashed wedge. Methane is then drawn as below: two bonds in the plane, one towards and one away from the reader.

![](https://one-course.com/images/onecourse/chapters/chemistry-1/g10-lewis-and-shape/fig-a11adb5f1a5e.svg)

## 24.5 Exercises

**Exercise 24.1 ★.**

What is a [covalent bond](#def-g10-lewis-and-shape-covalent-bond)? What is a [lone pair](#def-g10-lewis-and-shape-lone-pair)?

**Solution of Exercise 24.1.**

A pair of [electrons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-nucleus) shared by two [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom). A pair of [valence electrons](https://one-course.com/books/chemistry/1/en/chapter/23-electron-shells-and-the-periodic-table#def-g10-electron-shells-valence) belonging to one [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) only, not shared.

**Exercise 24.2 ★.**

How many [covalent bonds](#def-g10-lewis-and-shape-covalent-bond) do hydrogen, carbon, nitrogen and oxygen usually form? Explain with the octet and [duet rules](https://one-course.com/books/chemistry/1/en/chapter/23-electron-shells-and-the-periodic-table#def-g10-electron-shells-octet).

**Solution of Exercise 24.2.**

H: 1 (one [electron](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-nucleus) short of its duet). C: 4, N: 3, O: 2 (4, 3 and 2 [electrons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-nucleus) short of an octet).

**Exercise 24.3 ★.**

Draw the [Lewis structure](#def-g10-lewis-and-shape-lewis-structure) of hydrogen chloride, $\ce{HCl}$, and count the [electrons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-nucleus) around chlorine.

**Solution of Exercise 24.3.**

![](https://one-course.com/images/onecourse/chapters/chemistry-1/g10-lewis-and-shape/fig-4139202de503.svg): chlorine has the shared pair and three [lone pairs](#def-g10-lewis-and-shape-lone-pair), 8 [electrons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-nucleus).

**Exercise 24.4 ★.**

How many [valence electrons](https://one-course.com/books/chemistry/1/en/chapter/23-electron-shells-and-the-periodic-table#def-g10-electron-shells-valence), in all, does the [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) $\ce{NH3}$ have? How many pairs?

**Solution of Exercise 24.4.**

$5 + 3 \times 1 = 8$ [electrons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-nucleus), 4 pairs (three bonds, one [lone pair](#def-g10-lewis-and-shape-lone-pair)).

**Exercise 24.5 ★.**

Give the shape of $\ce{CH4}$, $\ce{NH3}$, $\ce{H2O}$ and $\ce{CO2}$.

**Solution of Exercise 24.5.**

$\ce{CH4}$: tetrahedron. $\ce{NH3}$: pyramid. $\ce{H2O}$: bent. $\ce{CO2}$: linear.

**Exercise 24.6 ★★.**

Draw the [Lewis structure](#def-g10-lewis-and-shape-lewis-structure) of hydrogen sulfide, $\ce{H2S}$ (sulfur is in the group of oxygen), and predict its shape.

**Solution of Exercise 24.6.**

![](https://one-course.com/images/onecourse/chapters/chemistry-1/g10-lewis-and-shape/fig-70c632e5c99b.svg): like water, four groups around sulfur of which two [lone pairs](#def-g10-lewis-and-shape-lone-pair): bent.

**Exercise 24.7 ★★.**

Draw the [Lewis structure](#def-g10-lewis-and-shape-lewis-structure) of nitrogen, $\ce{N2}$, following the method step by step.

**Solution of Exercise 24.7.**

$2 \times 5 = 10$ [electrons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-nucleus), 5 pairs. A single bond and 4 [lone pairs](#def-g10-lewis-and-shape-lone-pair) leave each nitrogen with 6 [electrons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-nucleus); turning two [lone pairs](#def-g10-lewis-and-shape-lone-pair) into shared pairs gives a [triple bond](#def-g10-lewis-and-shape-multiple-bond) and one [lone pair](#def-g10-lewis-and-shape-lone-pair) on each [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom): ![](https://one-course.com/images/onecourse/chapters/chemistry-1/g10-lewis-and-shape/fig-f5277b27f017.svg).

**Exercise 24.8 ★★.**

Draw the [Lewis structure](#def-g10-lewis-and-shape-lewis-structure) of methanol, $\ce{CH3OH}$, and give the shape around the carbon and around the oxygen.

**Solution of Exercise 24.8.**

![](https://one-course.com/images/onecourse/chapters/chemistry-1/g10-lewis-and-shape/fig-39d6111e67d2.svg): four bonds around carbon, tetrahedral; around oxygen two bonds and two [lone pairs](#def-g10-lewis-and-shape-lone-pair), bent.

**Exercise 24.9 ★★.**

Why is $\ce{CO2}$ linear and $\ce{H2O}$ bent, although both have a central [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) joined to two others?

**Solution of Exercise 24.9.**

In $\ce{CO2}$ carbon has two groups (two [double bonds](#def-g10-lewis-and-shape-multiple-bond)) and no [lone pair](#def-g10-lewis-and-shape-lone-pair): they point in opposite directions. In $\ce{H2O}$ oxygen has four groups (two bonds, two [lone pairs](#def-g10-lewis-and-shape-lone-pair)) in a tetrahedral arrangement: the two bonds make an angle.

**Exercise 24.10 ★★.**

Draw the [Lewis structure](#def-g10-lewis-and-shape-lewis-structure) of ethene, $\ce{C2H4}$, and give the shape around each carbon [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom).

**Solution of Exercise 24.10.**

![](https://one-course.com/images/onecourse/chapters/chemistry-1/g10-lewis-and-shape/fig-ba5ae4c4dadf.svg): around each carbon, three groups (one [double bond](#def-g10-lewis-and-shape-multiple-bond), two single bonds): a flat triangle, angles near $120{}^{\circ}$.

**Exercise 24.11 ★★.**

Draw the [Lewis structure](#def-g10-lewis-and-shape-lewis-structure) of tetrachloromethane, $\ce{CCl4}$, and predict its shape.

**Solution of Exercise 24.11.**

Carbon in the centre, four single bonds to chlorine [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) each with three [lone pairs](#def-g10-lewis-and-shape-lone-pair): four groups around carbon, a tetrahedron.

**Exercise 24.12 ★★★.**

Two [molecules](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) have the formula $\ce{C2H6O}$. Draw a [Lewis structure](#def-g10-lewis-and-shape-lewis-structure) for each (one has an O–H bond, the other a C–O–C chain).

**Solution of Exercise 24.12.**

Ethanol, ![](https://one-course.com/images/onecourse/chapters/chemistry-1/g10-lewis-and-shape/fig-1240268e1902.svg), and methoxymethane, ![](https://one-course.com/images/onecourse/chapters/chemistry-1/g10-lewis-and-shape/fig-cb29895b57a4.svg).

**Exercise 24.13 ★★★.**

Explain, using [lone pairs](#def-g10-lewis-and-shape-lone-pair), why the angle in ammonia ($106.7{}^{\circ}$) is smaller than in methane ($109.5{}^{\circ}$), and in water ($104.5{}^{\circ}$) smaller still.

**Solution of Exercise 24.13.**

A [lone pair](#def-g10-lewis-and-shape-lone-pair) takes up a little more room than a [bonding pair](#def-g10-lewis-and-shape-lone-pair) and pushes the bonds closer together. Ammonia has one [lone pair](#def-g10-lewis-and-shape-lone-pair), water two: the angle shrinks from methane to ammonia to water.

**Exercise 24.14 ★★★.**

Draw the [Lewis structure](#def-g10-lewis-and-shape-lewis-structure) of hydrogen cyanide, $\ce{HCN}$, and of methanal, $\ce{CH2O}$, and give their shapes.

**Solution of Exercise 24.14.**

![](https://one-course.com/images/onecourse/chapters/chemistry-1/g10-lewis-and-shape/fig-32f578c2e7e7.svg): two groups around carbon, linear. ![](https://one-course.com/images/onecourse/chapters/chemistry-1/g10-lewis-and-shape/fig-ae8293b0a8f0.svg): three groups around carbon, a flat triangle.

**Exercise 24.15 ★★★.**

Ozone, $\ce{O3}$, is a chain of three oxygen [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom). Count its valence pairs and draw a [Lewis structure](#def-g10-lewis-and-shape-lewis-structure) in which every oxygen has an octet (one [double bond](#def-g10-lewis-and-shape-multiple-bond), one single bond). Predict whether the [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) is linear or bent.

**Solution of Exercise 24.15.**

$3 \times 6 = 18$ [electrons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-nucleus), 9 pairs: ![](https://one-course.com/images/onecourse/chapters/chemistry-1/g10-lewis-and-shape/fig-ba2f77d8a9d3.svg). The central oxygen has three groups (a [double bond](#def-g10-lewis-and-shape-multiple-bond), a single bond, a [lone pair](#def-g10-lewis-and-shape-lone-pair)): the [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) is bent.

## 24.6 Problem: A Molecule in a Cube

**Problem 24.1.**

Weekend problem — designing the carbon balls of a molecular model kit: at what angle must the holes be drilled?

A company makes molecular model kits. The black carbon balls must have four holes, so that methane, ethane and the other [molecules](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) of carbon come out with the right shape. The engineer uses a trick: a regular tetrahedron fits inside a cube, its four corners on four corners of the cube, none two on the same edge.

**Part I — [Lewis structures](#def-g10-lewis-and-shape-lewis-structure).**

1. Draw the [Lewis structures](#def-g10-lewis-and-shape-lewis-structure) of methane $\ce{CH4}$ , ammonia $\ce{NH3}$ and water $\ce{H2O}$ .
2. How many groups of [electrons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-nucleus) surround the central [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) in each?
3. How many of them are [lone pairs](#def-g10-lewis-and-shape-lone-pair) ?
4. Why does a carbon ball need four holes, and an oxygen ball (for water) only two?
5. A model of ethane, $\ce{C2H6}$ , uses two carbon balls. Draw its [Lewis structure](#def-g10-lewis-and-shape-lewis-structure) . How many sticks join the two carbon balls, and how many hydrogen balls are needed?

**Part II — Shapes.**

6. Give the shape of each of the three [molecules](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) .
7. The measured angles are $106.7{}^{\circ}$ in ammonia and $104.5{}^{\circ}$ in water. Explain why they are smaller than the angle of methane.
8. Why can the oxygen ball for water not simply be a carbon ball with two holes left empty, if the kit is to show the true angle?
9. In carbon dioxide, the carbon [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) forms two [double bonds](#def-g10-lewis-and-shape-multiple-bond) . Which angle must separate them in a model?

**Part III — The cube.** Take a cube of side $a$. The carbon [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) is at its centre; the four hydrogen [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) sit on four corners of the cube, none two on the same edge.

10. Show that any two of these hydrogen [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) are at the two ends of a diagonal of a face of the cube. Using Pythagoras, compute the distance between them in terms of $a$ .
11. The diagonal of the whole cube (from a corner to the opposite corner) has length $a\sqrt{3}$ . Deduce the distance from the carbon [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) to a hydrogen [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) .
12. Take $a = 1\,\mathrm{cm}$ in a model: give both distances in centimetres, to two decimal places.
13. Why are the four C–H distances equal?

**Part IV — The angle.** The carbon [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) C and two hydrogen [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) H$_1$, H$_2$ form an isosceles triangle. Let M be the midpoint of H$_1$H$_2$.

14. Explain why the triangle C M H $_1$ has a right angle at M.
15. Compute, in this right triangle, the sine of the angle $\widehat{\text{M\,C\,H}_1}$ , half of the angle H–C–H.
16. Deduce the half-angle, then the angle H–C–H, to one decimal place.
17. Compare with the angle of the table of this chapter.
18. State the angle at which the holes of a carbon ball must be drilled.

**Solution of Problem 24.1.**

**1.** ![](https://one-course.com/images/onecourse/chapters/chemistry-1/g10-lewis-and-shape/fig-41463451bf6f.svg), ![](https://one-course.com/images/onecourse/chapters/chemistry-1/g10-lewis-and-shape/fig-f8f402d0a7e4.svg), ![](https://one-course.com/images/onecourse/chapters/chemistry-1/g10-lewis-and-shape/fig-b396c2ed8db3.svg).

**2.** Four groups in each.

**3.** None for methane, one for ammonia, two for water.

**4.** Carbon forms four bonds; oxygen forms two (its two other groups are [lone pairs](#def-g10-lewis-and-shape-lone-pair), which a kit does not show with sticks).

**5.** ![](https://one-course.com/images/onecourse/chapters/chemistry-1/g10-lewis-and-shape/fig-54ec65fe6c6a.svg): one stick joins the two carbon balls, and six hydrogen balls are needed.

**6.** Tetrahedron, pyramid, bent.

**7.** [Lone pairs](#def-g10-lewis-and-shape-lone-pair) take more room than [bonding pairs](#def-g10-lewis-and-shape-lone-pair) and squeeze the bonds together; water, with two [lone pairs](#def-g10-lewis-and-shape-lone-pair), has the smallest angle.

**8.** A carbon ball’s holes make $109.5{}^{\circ}$; water’s true angle is $104.5{}^{\circ}$: an oxygen ball needs its own two holes at $104.5{}^{\circ}$.

**9.** $180{}^{\circ}$: two groups around carbon point in opposite directions, and the [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) is linear.

**10.** Two corners not on the same edge are opposite corners of one face: their distance is the face diagonal, $\sqrt{a^2 + a^2} = a\sqrt{2}$.

**11.** The centre is halfway along a body diagonal: $a\sqrt{3}/2$.

**12.** H–H: $\sqrt{2} \approx 1.41\,\mathrm{cm}$; C–H: $\sqrt{3}/2 \approx 0.87\,\mathrm{cm}$.

**13.** Each hydrogen is at a corner of the cube and carbon at its centre: every corner is at the same distance from the centre.

**14.** The triangle C H$_1$ H$_2$ is isosceles (C H$_1$ = C H$_2$); the line from its apex to the midpoint of the base is perpendicular to the base.

**15.** $\sin \widehat{\text{M\,C\,H}_1} = \dfrac{\text{M\,H}_1}{\text{C\,H}_1}
= \dfrac{a\sqrt{2}/2}{a\sqrt{3}/2} = \sqrt{2/3} \approx 0.816$.

**16.** Half-angle $\approx 54.7{}^{\circ}$; angle H–C–H $\approx
2 \times 54.7 = 109.5{}^{\circ}$.

**17.** It is the $109.5{}^{\circ}$ of the tetrahedron in the table.

**18.** The holes must be drilled at $109.5{}^{\circ}$ from one another.