Answer key · Unit 2

Bonding and structure.

Each lesson’s practice questions, their correct answers and the mistakes they spot. Answers read off the Scene use the same setting the learner sees.

Misconception catalogue

Answer key 6

Lesson 1 of 6 · About 25 minutes

Ions and ionic bonding

Why atoms give or take electrons, how positive and negative ions form, what sets their charge, and how to write the formula of an ionic compound.

Open the lesson

The 6 steps and their answers

Step 1 of 6
Open this step
A gap and a spare
Practice · Predict, then look
Question
Sodium, 2,8,1, has a spare outer electron, and chlorine, 2,8,7, is one short. What happens when they meet?

Correct answer
- Correct Sodium’s electron moves over to chlorine
Setup, choices and feedback
The Scene at this step
Family
Halogen (group 17)
Period (row)
3
Bring in sodium
On its own
Choices
- Correct Sodium’s electron moves over to chlorine
- Wrong Chlorine gives an electron to sodium
  Misconception: Has the electron moving the wrong way: the non-metal giving electrons to the metal.
  Feedback from the catalogue
  Metals, with few outer electrons, are the ones that give electrons away, and non-metals, close to a full shell, are the ones that take them. Sodium, 2,8,1, easily gives up the single electron in its third shell, and chlorine, 2,8,7, is exactly one short. So Na⁺ and Cl⁻ form, not the other way round.
- Wrong They share a pair of electrons between them
  Feedback
  Sharing a pair is a covalent bond, between two non-metals. Sodium gives up the single electron in its third shell easily, and chlorine gains by taking it, so the electron moves.
Once the prediction is locked in, the Scene changes
Bring in sodium
Meets sodium
The Scene then shows: -1 · Charge of the ion it forms with sodium: −1 for a halogen, 0 for a noble gas (none)/nodes/pair/outputs/ionCharge
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
The electron jumps into the free place in chlorine’s shell. Both atoms now have a full outer shell: sodium becomes Na⁺, 2,8, and chlorine becomes Cl⁻, 2,8,8.

Worked solution
1. Sodium, 2,8,1: the short way to a full shell is to give away one electron.
2. Chlorine, 2,8,7: the short way is to take one electron.
3. The electron moves from sodium to chlorine, making Na⁺ and Cl⁻.
If you predicted chlorine would give an electron, you reversed the direction: chlorine would be left with 2,8,6, further from a full shell.
Step 2 of 6
Open this step
Counting the ions
Practice · Calculate
Question
Chlorine has $17$ ⁠ protons. How many electrons does the chloride ion, Cl⁻, have?

Correct answer
18 ± 0.01
Setup, choices and feedback
The Scene at this step
Family
Halogen (group 17)fixed
Period (row)
3fixed
Bring in sodium
Meets sodium
Accepted within
± 0.01
Computed from the Scene at this step’s setting
Electrons once it has met sodium: Z + 1 for a halide ion, Z for a noble gas/nodes/pair/outputs/ionElectrons
Wrong answers it recognises
- 16 ± 0.01
  Misconception: Thinks a negative ion is one that lost electrons, mixing up the sign.
  Feedback from the catalogue
  Electrons are the negative particles. An atom that takes electrons becomes negative, since it has more electrons than protons, and an atom that gives electrons away becomes positive. The Cl⁻ ion has $17$ ⁠ protons and $18$ ⁠ electrons.
Feedback for a right answer
$18$ ⁠: the atom took one electron, and now has one electron more than protons, so its charge is $-1$ ⁠. It is arranged 2,8,8, like argon.

Hint
A negative charge means more electrons than protons.

Worked solution
1. A neutral chlorine atom: $17$ ⁠ protons and $17$ ⁠ electrons.
2. Cl⁻ has taken one electron: $17 + 1 = 18$ ⁠.
3. A check: the charge is $17 - 18 = -1$ ⁠.
If you answered $16$ ⁠, you thought a negative charge comes from losing an electron. But electrons are the negative ones: whatever takes them becomes negative.
Step 3 of 6
Open this step
A full shell says no
Practice · Predict, then look
Question
Argon has a full outer shell, 2,8,8. What happens when sodium comes close?

Correct answer
- Correct Nothing: sodium drifts away with its electron
Setup, choices and feedback
The Scene at this step
Family
Noble gas (group 18)
Period (row)
3
Bring in sodium
On its own
Choices
- Correct Nothing: sodium drifts away with its electron
- Wrong Argon takes the electron and becomes Ar⁻
  Feedback
  Argon has no free place: an extra electron would have to start a distant fourth shell, and it is not held there.
- Wrong Argon gives an electron to sodium
  Misconception: Has the electron moving the wrong way: the non-metal giving electrons to the metal.
  Feedback from the catalogue
  Metals, with few outer electrons, are the ones that give electrons away, and non-metals, close to a full shell, are the ones that take them. Sodium, 2,8,1, easily gives up the single electron in its third shell, and chlorine, 2,8,7, is exactly one short. So Na⁺ and Cl⁻ form, not the other way round.
Once the prediction is locked in, the Scene changes
Bring in sodium
Meets sodium
The Scene then shows: 0 · Charge of the ion it forms with sodium: −1 for a halogen, 0 for a noble gas (none)/nodes/pair/outputs/ionCharge
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
Sodium bounces off. Argon has no free place in its outer shell and no spare electron, so there is no reaction. That is what makes the noble gases noble.

Worked solution
1. Argon, 2,8,8: the outer shell is full.
2. It has no room for sodium’s electron, and giving one away would break open its full shell.
3. Neither side gains, so no ions form.
Step 4 of 6
Open this step
The charge from the group
Practice · Choose
Question
Oxygen, 2,6, has six outer electrons. Which ion does it form when it meets a metal?

Correct answer
- Correct O²⁻
Setup, choices and feedback
The Scene at this step
Family
Halogen (group 17)
Period (row)
2
Bring in sodium
Meets sodium
Choices
Shown in a random order.
- Correct O²⁻
- Wrong O⁶⁻
  Misconception: Takes an ion’s charge to be its number of outer electrons.
  Feedback from the catalogue
  An ion’s charge is the number of electrons the atom took or gave away to reach a full shell, not its number of outer electrons. Oxygen has six outer electrons, but it is only two short, and it takes those two: O²⁻. For non-metals the charge is eight minus the number of outer electrons, with a minus sign.
- Wrong O⁶⁺
  Misconception: Takes an ion’s charge to be its number of outer electrons.
  Feedback from the catalogue
  An ion’s charge is the number of electrons the atom took or gave away to reach a full shell, not its number of outer electrons. Oxygen has six outer electrons, but it is only two short, and it takes those two: O²⁻. For non-metals the charge is eight minus the number of outer electrons, with a minus sign.
- Wrong O²⁺
  Misconception: Thinks a negative ion is one that lost electrons, mixing up the sign.
  Feedback from the catalogue
  Electrons are the negative particles. An atom that takes electrons becomes negative, since it has more electrons than protons, and an atom that gives electrons away becomes positive. The Cl⁻ ion has $17$ ⁠ protons and $18$ ⁠ electrons.
Feedback for a right answer
O²⁻: oxygen is two electrons short of eight, and takes them. With $8$ ⁠ protons and $10$ ⁠ electrons, its charge is $-2$ ⁠.

Hint
How many electrons is oxygen short of a full shell?

Worked solution
1. Oxygen has $6$ ⁠ outer electrons; a full shell is $8 - 6 = 2$ ⁠ away.
2. Taking $2$ ⁠ is easier than giving away $6$ ⁠.
3. $8$ ⁠ protons and $10$ ⁠ electrons: a charge of $8 - 10 = -2$ ⁠, that is O²⁻.
The charge is not the number of outer electrons: it is the number of electrons the atom took (negative) or gave away (positive).
Step 5 of 6
Open this step
Balancing the charges
Practice · Choose
Question
Magnesium forms an Mg²⁺ ion, and chlorine a Cl⁻ ion. What is the formula of magnesium chloride?

Correct answer
- Correct MgCl₂
Setup, choices and feedback
The Scene at this step
Family
Halogen (group 17)
Period (row)
3
Bring in sodium
Meets sodium
Choices
Shown in a random order.
- Correct MgCl₂
- Wrong MgCl
  Misconception: Pairs the ions of an ionic compound one to one whatever their charges.
  Feedback from the catalogue
  An ionic compound is neutral overall, so the ions combine in the ratio that balances the charges. Mg²⁺ needs two Cl⁻: MgCl₂. Al³⁺ and O²⁻ balance only as two against three: Al₂O₃. One to one is right only when the charges are equal in size.
- Wrong Mg₂Cl
  Feedback
  Here the total charge is $2 \times (+2) + (-1) = +3$ ⁠. You need more chloride ions, not more magnesium ions.
Feedback for a right answer
MgCl₂: one magnesium ion, charge $+2$ ⁠, and two chloride ions, $-2$ ⁠ between them. The magnesium gave away two electrons, each to a different chlorine atom.

Hint
How many Cl⁻ ions does it take to balance a charge of +2?

Worked solution
1. The positive ion’s charge: $+2$ ⁠. The negative ion’s: $-1$ ⁠.
2. For the total to be $0$ ⁠ you need two Cl⁻ for each Mg²⁺: $+2 + 2 \times (-1) = 0$ ⁠.
3. The formula: MgCl₂.
If you chose MgCl, a charge of $+1$ ⁠ is left over: ions do not always pair one to one.
Step 6 of 6
Open this step
Small ions hold tighter
Practice · Reach the target
Question
Change Period (row) until you find the halogen whose salt with sodium releases the most energy, then press Check.

Goal
- 577 ± 1
  At the start of the step: 361
Setup, choices and feedback
The Scene at this step
Family
Halogen (group 17)fixed
Period (row)
4
Bring in sodium
Meets sodium
Read from the Scene at
KJ/mol released forming the sodium salt; 0 for a noble gas/nodes/pair/outputs/saltHeat
One setting that reaches it
Period (row)
2
Feedback for a right answer
Fluorine: sodium fluoride releases 577 kJ/mol, against only 288 kJ/mol for sodium iodide. The fluoride ion is the smallest of the halide ions, so the ions get closest and pull hardest.

Feedback for a wrong answer
Not yet. Try the smallest halogen.

Hint
Small ions can get closer.

Worked solution
1. The pull between two ions grows as the distance between their centres shrinks.
2. Down group 17 the ions grow: F⁻ smallest, I⁻ largest.
3. So the most energy is released with fluorine: set Period (row) to $2$ ⁠.

Lesson 2 of 6 · About 25 minutes

Ionic and metallic lattices

Inside a salt crystal and a lump of copper: a lattice of ions each pulled by all its neighbours, and a lattice of positive ions in a sea of electrons, and why salt cracks while a metal bends and conducts.

Open the lesson

The 7 steps and their answers

Step 1 of 7
Open this step
A giant lattice
Practice · Calculate
Question
How many chloride ions touch each sodium ion inside the salt crystal?

Correct answer
6 ± 0.01
Setup, choices and feedback
The Scene at this step
Bond type
Ionic: saltfixed
Slide the top half
0 steps
Zoom to the atoms
Atoms
Accepted within
± 0.01
Computed from the Scene at this step’s setting
Nearest neighbours of each particle: 6 salt, 12 copper, 8 iron, 4 diamond, ice and quartz (Si), 3 graphite, graphene and C₆₀/nodes/solid/outputs/coordination
Wrong answers it recognises
- 1 ± 0.01
  Misconception: Pictures sodium chloride as separate NaCl molecules, each sodium bonded to one chlorine.
  Feedback from the catalogue
  Salt has no molecules. It is a giant ionic lattice, and each ion is pulled equally by all the oppositely charged ions around it: every Na⁺ is surrounded by six Cl⁻, and every Cl⁻ by six Na⁺. The formula NaCl describes only the ratio, one to one.
Feedback for a right answer
$6$ ⁠: one on each side, above and below, left and right, in front and behind. And each chloride ion is surrounded by six sodium ions, so the ratio stays one to one, NaCl.

Hint
Look at a sodium ion in the middle: above and below, left and right, in front and behind.

Worked solution
1. In the salt lattice the ions alternate along three axes.
2. Along each axis a sodium ion has two neighbours, one on each side.
3. $3 \times 2 = 6$ ⁠ chloride ions.
If you answered $1$ ⁠, you thought of NaCl as a molecule, a pair of ions. In the crystal each ion is pulled by all the neighbours around it.
Step 2 of 7
Open this step
Salt shatters
Practice · Predict, then look
Question
Slide the top half of the salt crystal one whole step along the plane. What happens?

Correct answer
- Correct The crystal cracks in two
Setup, choices and feedback
The Scene at this step
Bond type
Ionic: saltfixed
Slide the top half
0 steps
Zoom to the atoms
Atoms
Choices
- Correct The crystal cracks in two
- Wrong The crystal bends and stays whole
  Feedback
  That is how a metal behaves. In salt, half a step already brings ions of the same charge face to face.
- Wrong Nothing: the ions go back to their places
  Feedback
  A whole step would bring every ion opposite an opposite one again, but on the way there the layers have already pushed apart.
Once the prediction is locked in, the Scene changes
Slide the top half
1 steps
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
It cracks. As the layer moves, sodium ions come to face sodium ions and chloride faces chloride. Like charges repel, and the layers part. That is why ionic crystals are hard, but brittle.

Worked solution
1. At rest each ion faces ions of the opposite charge.
2. Half a step on, each ion faces one of the same charge.
3. The repulsion parts the layers: the crystal cracks.
Step 3 of 7
Open this step
When salt conducts
Practice · Choose
Question
When does table salt conduct electricity? Select every right answer.

Correct answer
- Correct When melted by heat
- Correct When dissolved in water
Setup, choices and feedback
The Scene at this step
Bond type
Ionic: salt
Slide the top half
0 steps
Zoom to the atoms
Atoms
Choices
Shown in a random order. More than one choice is correct: every one must be selected.
- Wrong As a solid crystal
  Misconception: Thinks a solid ionic compound conducts because it is made of ions.
  Feedback from the catalogue
  For a current to flow, charged particles have to move. In an ionic solid each ion is locked in place in the lattice, so solid salt does not conduct, although it is made entirely of ions. Only when the lattice comes apart, melted or dissolved in water, are the ions free to move, and then it conducts.
- Correct When melted by heat
- Correct When dissolved in water
Feedback for a right answer
Both melted and dissolved. Either way the lattice comes apart and the ions are free to move towards the electrodes. In a solid crystal the same ions are locked in place.

Hint
For a current to flow, the charged particles must move.

Worked solution
1. A current is a flow of charged particles.
2. In salt the charged particles are the ions.
3. In the solid they are fixed in the lattice: no current.
4. Melted or dissolved, the lattice comes apart and the ions move: a current flows.
Step 4 of 7
Open this step
A sea of electrons
Practice · Calculate
Question
In copper the atoms are packed as tightly as they can be. How many touching neighbours does each copper atom inside the crystal have?

Correct answer
12 ± 0.01
Setup, choices and feedback
The Scene at this step
Bond type
Metallic: copperfixed
Slide the top half
0 steps
Zoom to the atoms
Atoms
Accepted within
± 0.01
Computed from the Scene at this step’s setting
Nearest neighbours of each particle: 6 salt, 12 copper, 8 iron, 4 diamond, ice and quartz (Si), 3 graphite, graphene and C₆₀/nodes/solid/outputs/coordination
Feedback for a right answer
$12$ ⁠: six around it in its own layer, three in the layer above and three in the layer below. It is the tightest packing of equal balls, like oranges stacked at a market stall.

Hint
Count the neighbours in the atom’s own layer, then in the layers above and below.

Worked solution
1. In a close-packed layer each ball is surrounded by six.
2. The layer above sits in the hollows: three balls touch it.
3. Below, three more.
4. $6 + 3 + 3 = 12$ ⁠.
Step 5 of 7
Open this step
Metals bend
Practice · Predict, then look
Question
Slide the top half of the copper crystal one whole step, as you did with salt. What happens?

Correct answer
- Correct The layers slide, and the crystal stays whole
Setup, choices and feedback
The Scene at this step
Bond type
Metallic: copperfixed
Slide the top half
0 steps
Zoom to the atoms
Atoms
Choices
- Correct The layers slide, and the crystal stays whole
- Wrong The crystal cracks, like the salt
  Feedback
  A metal has no negative ions: all its ions are positive, and the sea of electrons keeps holding them wherever they go.
- Wrong The bonds tear all at once
  Feedback
  The metallic bond is not a bond between two particular atoms, so there is no bond to tear: the electrons belong to the whole crystal.
Once the prediction is locked in, the Scene changes
Slide the top half
1 steps
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
The layers slide and the crystal stays whole. The positive ions move within the sea of electrons, and each new place is as good as the last. That is why metals can be hammered flat and drawn into wires.

Worked solution
1. In a metal all the ions are positive, so no ions of opposite charge can come face to face.
2. The electrons belong to no particular atom, and keep holding the ions after the move.
3. So the layer slides without cracking.
Step 6 of 7
Open this step
Why metals conduct
Practice · Choose
Question
A copper wire carries a current. Which particles move along it?

Correct answer
- Correct The electrons of the sea of electrons
Setup, choices and feedback
The Scene at this step
Bond type
Metallic: copper
Slide the top half
0 steps
Zoom to the atoms
Atoms
Choices
Shown in a random order.
- Correct The electrons of the sea of electrons
- Wrong The positive copper ions
  Misconception: Thinks the current in a metal (or in graphite) is carried by moving ions.
  Feedback from the catalogue
  In a metal the positive ions are fixed in place in the lattice. The current is a flow of electrons: the electrons of the sea belong to no particular atom and move freely through the whole crystal. So too in graphite, where one electron from each atom moves along the sheet.
- Wrong Whole copper atoms
  Feedback
  If atoms flowed along the wire, it would wear away at one end and thicken at the other. The wire stays as it is.
Feedback for a right answer
The electrons. They are bound to no particular atom, so a small voltage is enough to move them along the whole wire. The ions stay in their places in the lattice.

Hint
What in a metal crystal is free to move?

Worked solution
1. In the metallic lattice the positive ions are fixed in place.
2. The electrons of the sea are free to move through the whole crystal.
3. So a current in a metal is a flow of electrons.
Step 7 of 7
Open this step
The copper cell
Practice · Calculate
Question
Bond type: Metallic: copper. Copper’s unit cell has an atom at each corner and in the middle of each face, and the atoms touch along each face’s diagonal. A copper atom’s radius is 128 pm. How long is the cell’s edge?

Correct answer
361.5 pm ± 1%
Setup, choices and feedback
The Scene at this step
Bond type
Metallic: copperfixed
Slide the top half
0 steps
Zoom to the atoms
Atoms
Accepted within
± 1%
Computed from the Scene at this step’s setting
Edge a of the repeating cell the view outlines (the base of a hexagonal one); NaN for C₆₀, a single molecule/nodes/solid/outputs/cellEdge
Any unit of the same quantity is accepted; it is converted before checking.
Wrong answers it recognises
- 256 pm ± 1%
  Misconception: Takes the distance between two neighbouring particles for the edge of the repeating unit cell.
  Feedback from the catalogue
  The unit cell is the smallest box that repeats through the whole crystal. The particles at its corners are identical, so along the edge there is usually more than one neighbour-to-neighbour distance: in salt two sodium–chloride distances, and in copper the atoms touch along the diagonal, not the edge.
Feedback for a right answer
About 362 pm: along the edge itself the atoms do not touch.

Hint
Along a face diagonal: a radius, the whole diameter of the atom in the middle of the face, and another radius. And a square’s diagonal is $\sqrt{2}$ ⁠ times its side.

Worked solution
1. The face diagonal: $4r = 4 \times 128 = 512$ ⁠ picometres.
2. The diagonal of a square of side $a$ ⁠ is $a\sqrt{2}$ ⁠, so $a = \dfrac{512}{\sqrt{2}} \approx 362$ ⁠ picometres.
If you answered 256 pm, you assumed the atoms touch along the edge. In copper they touch along the diagonal, which packs them as tightly as possible.

Lesson 3 of 6 · About 25 minutes

Molecules and covalent bonds

When non-metals meet they share electrons: a shared pair, double and triple bonds, and lone pairs, and how the repulsion between electron pairs sets a molecule’s shape and its bond angles.

Open the lesson

The 6 steps and their answers

Step 1 of 6
Open this step
Sharing a pair
Practice · Choose
Question
Oxygen has six outer electrons. How many covalent bonds does an oxygen atom make?

Correct answer
- Correct $2$ ⁠
Setup, choices and feedback
The Scene at this step
Molecule
Water (H₂O)
Temperature
300 K
Fill the space
Ball and stick
Choices
Shown in a random order.
- Correct $2$ ⁠
- Wrong $6$ ⁠
  Misconception: Takes the number of covalent bonds an atom makes to be its number of outer electrons.
  Feedback from the catalogue
  Each covalent bond adds one shared electron to the atom, so an atom makes as many bonds as it is short of a full shell: hydrogen $1$ ⁠, oxygen $2$ ⁠, nitrogen $3$ ⁠, carbon $4$ ⁠. The number of bonds is eight minus the number of outer electrons (for hydrogen, two minus one).
- Wrong $1$ ⁠
  Feedback
  One bond gives oxygen only one shared electron, leaving it another free place.
Feedback for a right answer
$2$ ⁠: oxygen is two electrons short, and each bond adds one shared electron. So in water the oxygen is bonded to two hydrogens, and in carbon dioxide to the carbon by a double bond.

Hint
How many electrons is oxygen short of a full shell?

Worked solution
1. Oxygen has $6$ ⁠ outer electrons; it is $2$ ⁠ short of a full shell.
2. Each covalent bond gives it one more shared electron.
3. So it makes $2$ ⁠ bonds.
If you answered $6$ ⁠, you counted the outer electrons. The number of bonds is the number of electrons missing.
Step 2 of 6
Open this step
Double and triple bonds
Practice · Calculate
Question
Each nitrogen atom has five outer electrons. How many pairs of electrons do the two atoms in an N₂ molecule share?

Correct answer
3 ± 0.01
Setup, choices and feedback
The Scene at this step
Molecule
Nitrogen (N₂)fixed
Temperature
300 K
Fill the space
Ball and stick
Accepted within
± 0.01
Computed from the Scene at this step’s setting
Electron pairs shared in the whole molecule/nodes/mol/outputs/sharedPairs
Wrong answers it recognises
- 5 ± 0.01
  Misconception: Takes the number of covalent bonds an atom makes to be its number of outer electrons.
  Feedback from the catalogue
  Each covalent bond adds one shared electron to the atom, so an atom makes as many bonds as it is short of a full shell: hydrogen $1$ ⁠, oxygen $2$ ⁠, nitrogen $3$ ⁠, carbon $4$ ⁠. The number of bonds is eight minus the number of outer electrons (for hydrogen, two minus one).
Feedback for a right answer
$3$ ⁠: a triple bond. Each nitrogen is three electrons short, and each gives three to share. The triple bond is very strong, which is why the nitrogen in air hardly reacts.

Hint
How many electrons is each nitrogen atom short?

Worked solution
1. Nitrogen has $5$ ⁠ outer electrons; it is $8 - 5 = 3$ ⁠ short.
2. Each shared pair gives each atom one more electron.
3. So it takes $3$ ⁠ pairs: a triple bond.
4. Each atom keeps one lone pair besides: $3 + 2 = 5$ ⁠.
Step 3 of 6
Open this step
As far apart as possible
Practice · Calculate
Question
What is the angle between two bonds in a methane molecule?

Correct answer
109.5 ° ± 0.5 °
Setup, choices and feedback
The Scene at this step
Molecule
Methane (CH₄)fixed
Temperature
300 K
Fill the space
Ball and stick
Accepted within
± 0.5 °
Computed from the Scene at this step’s setting
Angle between two bonds at the central atom; NaN for two atoms/nodes/mol/outputs/bondAngle
Any unit of the same quantity is accepted; it is converted before checking.
Wrong answers it recognises
- 90 ° ± 1 °
  Misconception: Reads a molecule’s shape from its flat drawing, such as 90° between the bonds of methane.
  Feedback from the catalogue
  The drawing on the page is flat, but the molecule is three-dimensional. Electron pairs spread as far apart as they can in three dimensions: four pairs point to the corners of a tetrahedron, at 109.5°, not to the ends of a cross, at 90°. Turn the molecule in the Scene to see it.
Feedback for a right answer
109.5°, the tetrahedral angle. In three dimensions four pairs can spread further apart than the 90° of a flat cross.

Hint
The four bonds point to the corners of a tetrahedron.

Worked solution
1. Four bonding pairs surround the carbon, and they repel each other.
2. In a plane they would be 90° apart; in three dimensions they spread to the corners of a tetrahedron.
3. The angle between any two bonds: 109.5°.
If you answered 90°, you read the flat drawing on the page. The molecule itself is three-dimensional.
Step 4 of 6
Open this step
Is water straight?
Practice · Predict, then look
Question
CO₂ and H₂O each have a central atom with two atoms bonded to it. CO₂ is straight. What shape is a water molecule?

Correct answer
- Correct Bent
Setup, choices and feedback
The Scene at this step
Molecule
Carbon dioxide (CO₂)
Temperature
300 K
Fill the space
Ball and stick
Choices
- Correct Bent
- Wrong Straight, like carbon dioxide
  Misconception: Counts only the bonds when working out a molecule’s shape, leaving out the lone pairs.
  Feedback from the catalogue
  Lone pairs do not show in a ball-and-stick drawing, but they take up room and push on the bonding pairs, even harder. The oxygen in water has two bonding pairs and two lone pairs: four pairs, so the molecule is bent, at 104.5°, not straight like CO₂, whose carbon has no lone pairs.
Once the prediction is locked in, the Scene changes
Molecule
Water (H₂O)
The Scene then shows: 104.5 ° · Angle between two bonds at the central atom; NaN for two atoms/nodes/mol/outputs/bondAngle
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
Bent, at an angle of 104.5°. The oxygen also carries two lone pairs, and the four pairs arrange themselves almost as in methane.

Worked solution
1. In carbon dioxide all of the carbon’s outer electrons are in bonds: two double bonds, on opposite sides.
2. The oxygen in water has two bonding pairs and two lone pairs.
3. Four pairs spread like a tetrahedron, so the two bonds make an angle: the molecule is bent.
Step 5 of 6
Open this step
The pairs you cannot see
Practice · Calculate
Question
How many lone pairs are there on the oxygen atom in a water molecule?

Correct answer
2 ± 0.01
Setup, choices and feedback
The Scene at this step
Molecule
Water (H₂O)fixed
Temperature
300 K
Fill the space
Ball and stick
Accepted within
± 0.01
Computed from the Scene at this step’s setting
Unshared electron pairs on the central atom (either atom of a pair)/nodes/mol/outputs/lonePairs
Wrong answers it recognises
- 0 ± 0.01
  Misconception: Counts only the bonds when working out a molecule’s shape, leaving out the lone pairs.
  Feedback from the catalogue
  Lone pairs do not show in a ball-and-stick drawing, but they take up room and push on the bonding pairs, even harder. The oxygen in water has two bonding pairs and two lone pairs: four pairs, so the molecule is bent, at 104.5°, not straight like CO₂, whose carbon has no lone pairs.
Feedback for a right answer
$2$ ⁠: two of oxygen’s six electrons are in bonds, and the other four make two lone pairs. They do not show in the Scene, but they are what bends the molecule.

Hint
Of six outer electrons, how many are in bonds?

Worked solution
1. Oxygen has $6$ ⁠ outer electrons.
2. $2$ ⁠ of them are in the two bonds to the hydrogens.
3. $4$ ⁠ electrons are left: $2$ ⁠ lone pairs.
Step 6 of 6
Open this step
A pyramid
Practice · Reach the target
Question
Choose in Molecule the molecule whose bond angle is about 107°, with three bonding pairs and one lone pair, then press Check.

Goal
- 106.8 ° ± 0.5 °
  At the start of the step: 104.5 °
Setup, choices and feedback
The Scene at this step
Molecule
Water (H₂O)
Temperature
300 K
Fill the space
Ball and stick
Read from the Scene at
Angle between two bonds at the central atom; NaN for two atoms/nodes/mol/outputs/bondAngle
One setting that reaches it
Molecule
Ammonia (NH₃)
Temperature
50 K
Feedback for a right answer
Ammonia, NH₃: nitrogen has three bonds to hydrogens and one lone pair. Four pairs as in methane, but only three atoms: a shallow pyramid with an angle of about 107°.

Feedback for a wrong answer
Not yet. Look for a central atom with three bonds.

Hint
Which atom makes three bonds?

Worked solution
1. Three bonding pairs and one lone pair: a central atom with five outer electrons, that is nitrogen.
2. Nitrogen and three hydrogens: ammonia, NH₃.
3. Choose ammonia; the angle is a little under 109.5°, because the lone pair pushes harder.

Lesson 4 of 6 · About 25 minutes

Giant structures and small molecules

One carbon, four solids: diamond, graphite, graphene and buckyballs. Giant covalent structures against molecular substances, and how structure explains melting point, hardness and conduction.

Open the lesson

The 7 steps and their answers

Step 1 of 7
Open this step
One element, four solids
Practice · Calculate
Question
How many carbon atoms is each carbon atom in diamond bonded to?

Correct answer
4 ± 0.01
Setup, choices and feedback
The Scene at this step
Form of carbon
Diamondfixed
Slide the top layers
0 steps
Zoom to the atoms
Atoms
Accepted within
± 0.01
Computed from the Scene at this step’s setting
Nearest neighbours of each particle: 6 salt, 12 copper, 8 iron, 4 diamond, ice and quartz (Si), 3 graphite, graphene and C₆₀/nodes/carbon/outputs/coordination
Feedback for a right answer
$4$ ⁠, arranged as a tetrahedron, like the bonds in methane. Each of those neighbours is bonded to three more, so the network runs in three dimensions through the whole crystal.

Hint
Carbon has four outer electrons, and is four short.

Worked solution
1. Carbon has $4$ ⁠ outer electrons, and is $4$ ⁠ short.
2. In diamond every outer electron is in a bond with a different neighbour.
3. So each atom is bonded to $4$ ⁠ neighbours, at angles of 109.5°.
Step 2 of 7
Open this step
Sheets
Practice · Predict, then look
Question
Slide graphite’s top layers one whole step. What happens?

Correct answer
- Correct The layers glide over each other
Setup, choices and feedback
The Scene at this step
Form of carbon
Graphitefixed
Slide the top layers
0 steps
Zoom to the atoms
Atoms
Choices
- Correct The layers glide over each other
- Wrong Bonds tear, as in diamond
  Feedback
  In diamond the covalent bonds run between the layers. In graphite only weak forces act between the layers, and there are no bonds to tear.
- Wrong The crystal cracks, like salt
  Feedback
  Graphite has no ions, so there are no like charges to come face to face.
Once the prediction is locked in, the Scene changes
Slide the top layers
1 steps
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
The layers glide. Within each layer the bonds are strong, but between layers the forces are weak. When you write with a pencil, layers of graphite stay behind on the paper.

Worked solution
1. In graphite each layer is a network of strong covalent bonds.
2. Only weak forces act between the layers.
3. So the layers slide over each other without breaking a single bond.
Step 3 of 7
Open this step
A non-metal that conducts
Practice · Choose
Question
Carbon is a non-metal, and diamond does not conduct. Why does graphite conduct electricity?

Correct answer
- Correct Each atom is bonded to only three neighbours, and one of its electrons is free to move along the sheet
Setup, choices and feedback
The Scene at this step
Form of carbon
Graphite
Slide the top layers
0 steps
Zoom to the atoms
Atoms
Choices
Shown in a random order.
- Correct Each atom is bonded to only three neighbours, and one of its electrons is free to move along the sheet
- Wrong Graphite has ions that move between the layers
  Misconception: Thinks the current in a metal (or in graphite) is carried by moving ions.
  Feedback from the catalogue
  In a metal the positive ions are fixed in place in the lattice. The current is a flow of electrons: the electrons of the sea belong to no particular atom and move freely through the whole crystal. So too in graphite, where one electron from each atom moves along the sheet.
- Wrong Graphite is really a metal
  Feedback
  Graphite is not a metal: it has no lattice of positive ions, and it is brittle and cannot be hammered out. But like metals it has free electrons.
Feedback for a right answer
In diamond all four outer electrons are locked in bonds. In graphite only three, and the fourth from each atom joins a cloud of electrons that moves along the sheet. So graphite conducts along its layers.

Hint
Compare an atom’s number of neighbours in diamond and in graphite.

Worked solution
1. Carbon has $4$ ⁠ outer electrons.
2. In graphite each atom is bonded to only $3$ ⁠ neighbours, so one electron per atom is not in a bond.
3. These electrons move freely along the sheet and carry a current.
Step 4 of 7
Open this step
A molecule of carbon
Practice · Choose
Question
Water boils at 100 °C. What breaks when water boils?

Correct answer
- Correct The weak forces between the water molecules
Setup, choices and feedback
The Scene at this step
Form of carbon
Buckyball (C₆₀)
Slide the top layers
0 steps
Zoom to the atoms
Atoms
Choices
Shown in a random order.
- Correct The weak forces between the water molecules
- Wrong The bonds between the oxygen and the hydrogens, so the water splits into oxygen and hydrogen
  Misconception: Thinks melting or boiling a molecular substance breaks the covalent bonds inside its molecules.
  Feedback from the catalogue
  A molecular substance has two kinds of pull: strong covalent bonds within each molecule, and weak forces between molecules. Melting and boiling break only the weak forces: the molecules move apart but stay whole. Steam is still H₂O. That is why molecular substances have low boiling points.
- Wrong Nothing: the water only gets hotter
  Feedback
  Something does break: in the liquid the molecules cling together, and in the steam they are far apart. The forces that held them together have broken.
Feedback for a right answer
The forces between the molecules. Steam is made of the same whole H₂O molecules, only far apart. Splitting a water molecule into oxygen and hydrogen takes tens of times more energy.

Hint
What is in the steam rising from a kettle?

Worked solution
1. Water is a molecular substance: strong covalent bonds inside each molecule, weak forces between molecules.
2. On boiling the molecules move apart and become a gas.
3. Only the weak forces break; the steam is still H₂O.
Step 5 of 7
Open this step
Structure decides
Practice · Choose
Question
Which of these solids are giant structures, with no separate molecules? Select every right answer.

Correct answer
- Correct Diamond
- Correct Table salt, NaCl
- Correct Quartz, SiO₂
- Correct Copper
Setup, choices and feedback
The Scene at this step
Form of carbon
Diamond
Slide the top layers
0 steps
Zoom to the atoms
Material
Choices
Shown in a random order. More than one choice is correct: every one must be selected.
- Correct Diamond
- Correct Table salt, NaCl
- Correct Quartz, SiO₂
- Correct Copper
- Wrong Ice, H₂O
  Feedback
  Ice is built of whole water molecules arranged in a crystal. That is why it melts at just 0 °C.
- Wrong A crystal of buckyballs, C₆₀
  Feedback
  Each ball is a separate molecule of $60$ ⁠ atoms. It is large, but finite, and only weak forces act between the balls.
Feedback for a right answer
Diamond and quartz are giant covalent structures, salt is an ionic lattice, and copper a metallic lattice. In all of them the bonds run through the whole crystal, so all have high melting points. Ice and buckyballs are built of separate molecules.

Hint
In a giant structure the bonds, of whatever kind, run through the whole crystal.

Worked solution
1. Check each solid: can you mark out one whole “molecule” in it?
2. In diamond, quartz, salt and copper you cannot: the bonds go on and on.
3. Ice has H₂O molecules, and the buckyball crystal C₆₀ molecules: these are molecular substances.
Step 6 of 7
Open this step
One sheet
Practice · Calculate
Question
How many neighbours is each carbon atom bonded to in a sheet of graphene?

Correct answer
3 ± 0.01
Setup, choices and feedback
The Scene at this step
Form of carbon
Graphenefixed
Slide the top layers
0 steps
Zoom to the atoms
Atoms
Accepted within
± 0.01
Computed from the Scene at this step’s setting
Nearest neighbours of each particle: 6 salt, 12 copper, 8 iron, 4 diamond, ice and quartz (Si), 3 graphite, graphene and C₆₀/nodes/carbon/outputs/coordination
Feedback for a right answer
$3$ ⁠, at angles of 120° in the plane. And a fourth electron from each atom is free to move, so graphene conducts electricity very well along the sheet.

Hint
The sheet is made of hexagons.

Worked solution
1. Graphene is a single sheet of graphite.
2. In the hexagons each corner is shared by three edges.
3. So each atom is bonded to $3$ ⁠ neighbours, which is also what leaves it a free electron.
Step 7 of 7
Open this step
The repeat
Practice · Calculate
Question
Form of carbon: Graphene. Each carbon–carbon bond is 0.142 nm long. The pattern repeats over the distance between the centres of two neighbouring hexagons, $\sqrt{3}$ ⁠ times the bond length. What is that distance?

Correct answer
0.246 nm ± 1%
Setup, choices and feedback
The Scene at this step
Form of carbon
Graphenefixed
Slide the top layers
0 steps
Zoom to the atoms
Atoms
Accepted within
± 1%
Computed from the Scene at this step’s setting
Edge a of the repeating cell the view outlines (the base of a hexagonal one); NaN for C₆₀, a single molecule/nodes/carbon/outputs/cellEdge
Any unit of the same quantity is accepted; it is converted before checking.
Wrong answers it recognises
- 0.142 nm ± 1%
  Misconception: Takes the distance between two neighbouring particles for the edge of the repeating unit cell.
  Feedback from the catalogue
  The unit cell is the smallest box that repeats through the whole crystal. The particles at its corners are identical, so along the edge there is usually more than one neighbour-to-neighbour distance: in salt two sodium–chloride distances, and in copper the atoms touch along the diagonal, not the edge.
Feedback for a right answer
About 0.246 nm: in graphite too, which is a stack of graphene sheets.

Hint
$\sqrt{3} \approx 1.732$ ⁠.

Worked solution
1. $a = \sqrt{3} \times 0.142 \approx 1.732 \times 0.142$ ⁠.
2. $a \approx 0.246$ ⁠ nanometres.
If you answered 0.142 nm, you gave the bond length. A bond joins two neighbouring atoms, but two neighbouring atoms do not look the same: the pattern repeats only over a longer distance.

Lesson 5 of 6 · About 25 minutes

Crystals

Why a grain of salt is a cube and a snowflake has six sides: a unit cell that repeats, and the shape it gives the crystal. Seeds and growth, and why slow cooling grows big crystals and fast cooling a crowd of tiny ones.

Open the lesson

The 7 steps and their answers

Step 1 of 7
Open this step
One small box
Practice · Calculate
Question
Salt’s unit cell is a cube 0.564 nm along each edge. How many such cells are there across a grain of salt 1 mm wide?

Correct answer
1770000 ± 3%
Setup, choices and feedback
The Scene at this step
Crystal
Saltfixed
Cooling rate
4 × slowest
Show unit cell
on
Zoom to the atoms
Atoms
Accepted within
± 3%
A fixed value in the question
Feedback for a right answer
About 1.8 million cells, 1.77 × 10⁶, all identical and lined up the same way. That is why a grain’s faces are so flat.

Hint
1 mm = 10⁶ nm. Divide the grain’s width by the cell’s edge.

Worked solution
1. Given: the grain is 1 mm = 1 000 000 nm wide, the cell’s edge 0.564 nm.
2. Cells across the grain: $\dfrac{1\,000\,000}{0.564} \approx 1.77 \times 10^{6}$ ⁠.
3. Nearly two million cells across one millimetre.
Step 2 of 7
Open this step
Six-sided snowflakes
Practice · Choose
Question
Why does every snowflake have six arms?

Correct answer
- Correct Ice’s water molecules are hydrogen-bonded into hexagonal rings, and that pattern repeats through the crystal
Setup, choices and feedback
The Scene at this step
Crystal
Ice
Cooling rate
4 × slowest
Show unit cell
on
Zoom to the atoms
Atoms
Choices
Shown in a random order.
- Correct Ice’s water molecules are hydrogen-bonded into hexagonal rings, and that pattern repeats through the crystal
- Wrong The wind in the cloud shapes each flake into a hexagon
  Misconception: Thinks a crystal’s shape is given from outside, by cutting, a mould or the weather, rather than by its repeating cell.
  Feedback from the catalogue
  A crystal’s shape is set by the pattern inside it. The particles are arranged in a unit cell repeated billions of times in the same direction, and the crystal grows along its planes: salt, with a cubic cell, comes out as cubes, and ice, with a hexagonal cell, as six-armed flakes. Conditions outside change only details, such as how branched the arms are.
- Wrong A water molecule has six atoms
  Feedback
  A water molecule has three atoms, H₂O. The six comes from the rings: six molecules in each.
Feedback for a right answer
The shape comes from inside. Ice’s cell is hexagonal, like quartz’s, and so is the crystal: six-sided plates and six-armed flakes. Salt’s cell is a cube, so its grains are cubes.

Worked solution
1. In ice each water molecule is hydrogen-bonded to its neighbours, and they form rings of six molecules.
2. The unit cell is hexagonal, and it repeats billions of times in the same direction.
3. The crystal grows along the cell’s planes, so it is hexagonal too.
The weather in the cloud decides how branched the arms are, but not how many there are.
Step 3 of 7
Open this step
Neighbours in ice
Practice · Calculate
Question
How many water molecules is each water molecule in ice hydrogen-bonded to?

Correct answer
4 ± 0.01
Setup, choices and feedback
The Scene at this step
Crystal
Icefixed
Cooling rate
4 × slowest
Show unit cell
off
Zoom to the atoms
Atoms
Accepted within
± 0.01
Computed from the Scene at this step’s setting
Nearest neighbours of each particle: 6 salt, 12 copper, 8 iron, 4 diamond, ice and quartz (Si), 3 graphite, graphene and C₆₀/nodes/crystal/outputs/coordination
Wrong answers it recognises
- 6 ± 0.01
  Misconception: Counts six neighbours for a water molecule in ice because its rings are hexagons.
  Feedback from the catalogue
  The rings in ice are hexagons, but each molecule is bonded to only four neighbours: two through its hydrogen atoms and two through the oxygen’s lone pairs. Each molecule belongs to several rings at once, so its number of neighbours is not the number of molecules in a ring.
Feedback for a right answer
Four: two through its two hydrogen atoms, and two through the oxygen’s lone pairs. They point to the corners of a tetrahedron, which is why the rings are puckered, not flat.

Hint
Turn the crystal and look at one molecule in the middle: count the dashed lines leaving it.

Worked solution
1. A water molecule has two hydrogen atoms, and each makes a hydrogen bond to a neighbour’s oxygen.
2. The oxygen has two lone pairs, and each takes a hydrogen bond from a neighbour.
3. $2 + 2 = 4$ ⁠.
If you answered $6$ ⁠, you counted the molecules in a ring. Each molecule belongs to several rings, but is bonded to only four neighbours.
Step 4 of 7
Open this step
Slow cooling
Practice · Calculate
Question
With Cooling rate at 1, the slowest, how many crystals have grown on the rock?

Correct answer
3 ± 0.01
Setup, choices and feedback
The Scene at this step
Crystal
Salt
Cooling rate
1 × slowestfixed
Show unit cell
on
Zoom to the atoms
Crystals
Accepted within
± 0.01
Computed from the Scene at this step’s setting
Crystals in the crust grown at this cooling rate; 1 for a single crystal (cooling rate 0)/nodes/crystal/outputs/crystals
Feedback for a right answer
Three large crystals. In slow cooling the first seeds have time to grow across all the liquid before more seeds appear.

Hint
Turn the rock: each crystal has its own flat faces, and crystals meet along straight lines.

Worked solution
1. Count the blocks that each have their own faces: three.
2. Each crystal started from one seed.
3. Slow cooling makes few seeds, so few, large crystals.
Step 5 of 7
Open this step
Fast cooling
Practice · Predict, then look
Question
Move Cooling rate from 1 up to 100. What happens to the crystals?

Correct answer
- Correct There are many more crystals, each smaller
Setup, choices and feedback
The Scene at this step
Crystal
Salt
Cooling rate
1 × slowestfixed
Show unit cell
on
Zoom to the atoms
Crystals
Choices
- Correct There are many more crystals, each smaller
- Wrong There are fewer, bigger crystals
  Misconception: Expects fast cooling to give bigger crystals, or slow cooling small ones.
  Feedback from the catalogue
  The cooling rate decides how many seeds appear. In fast cooling the liquid falls far below its freezing point, seeds appear everywhere, and they share the material: a crowd of tiny crystals, and at the extreme a glass. In slow cooling a few seeds grow through everything: large crystals, as in granite.
- Wrong The same three crystals, only grown faster
  Feedback
  Growth is faster too, but the liquid cools far below its freezing point while it is still mostly liquid, and new seeds appear everywhere.
Once the prediction is locked in, the Scene changes
Cooling rate
100 × slowestfixed
The Scene then shows: 165 · Crystals in the crust grown at this cooling rate; 1 for a single crystal (cooling rate 0)/nodes/crystal/outputs/crystals
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
More than a hundred and fifty tiny crystals, from the same amount of material. Seeds appeared almost everywhere at once and crowded each other out before any could grow large.

Worked solution
1. In fast cooling the liquid falls far below its freezing point while it is still almost all liquid.
2. The further below its freezing point, the faster new seeds appear.
3. A great many seeds share the same material, so each crystal is small.
Step 6 of 7
Open this step
Rocks remember
Practice · Choose
Question
Obsidian, a volcanic glass, has almost no crystals at all. How did it form?

Correct answer
- Correct Lava that cooled very fast, too fast for seeds to grow
Setup, choices and feedback
The Scene at this step
Crystal
Quartz
Cooling rate
15 × slowest
Show unit cell
on
Zoom to the atoms
Crystals
Choices
Shown in a random order.
- Correct Lava that cooled very fast, too fast for seeds to grow
- Wrong Molten rock that cooled very slowly, deep underground
  Misconception: Expects fast cooling to give bigger crystals, or slow cooling small ones.
  Feedback from the catalogue
  The cooling rate decides how many seeds appear. In fast cooling the liquid falls far below its freezing point, seeds appear everywhere, and they share the material: a crowd of tiny crystals, and at the extreme a glass. In slow cooling a few seeds grow through everything: large crystals, as in granite.
- Wrong Large crystals ground to a fine powder
  Feedback
  A powder of crystals is still crystalline, every grain ordered. In a glass the particles are not ordered at all.
Feedback for a right answer
Lava poured into water or cold air cooled within minutes. Its particles froze in place before they could settle into a pattern, and the result is a glass. Granite, which cooled slowly deep down, is full of large crystals.

Worked solution
1. The faster the cooling, the smaller the crystals: granite, basalt, obsidian.
2. At the extreme, cooling is so fast that the particles never get to line up.
3. A solid with no such order is a glass.
Step 7 of 7
Open this step
Ions that touch
Practice · Calculate
Question
Crystal: Salt. Along each edge of the unit cell, sodium and chloride ions touch in turn: $\mathrm{Cl^-}$ ⁠, $\mathrm{Na^+}$ ⁠, $\mathrm{Cl^-}$ ⁠. The radius of $\mathrm{Na^+}$ ⁠ is 102 pm, and of $\mathrm{Cl^-}$ ⁠ 181 pm. How long is the unit cell’s edge?

Correct answer
564 pm ± 1%
Setup, choices and feedback
The Scene at this step
Crystal
Saltfixed
Cooling rate
4 × slowest
Show unit cell
on
Zoom to the atoms
Atoms
Accepted within
± 1%
Computed from the Scene at this step’s setting
Edge a of the repeating cell the view outlines (the base of a hexagonal one); NaN for C₆₀, a single molecule/nodes/crystal/outputs/cellEdge
Any unit of the same quantity is accepted; it is converted before checking.
Wrong answers it recognises
- 283 pm ± 1%
  Misconception: Takes the distance between two neighbouring particles for the edge of the repeating unit cell.
  Feedback from the catalogue
  The unit cell is the smallest box that repeats through the whole crystal. The particles at its corners are identical, so along the edge there is usually more than one neighbour-to-neighbour distance: in salt two sodium–chloride distances, and in copper the atoms touch along the diagonal, not the edge.
Feedback for a right answer
About 566 pm, close to the 564 pm measured: the ions really do touch.

Hint
From corner to corner the edge passes through two chloride radii and one whole sodium diameter.

Worked solution
1. Along the edge: a radius of $\mathrm{Cl^-}$ ⁠, a diameter of $\mathrm{Na^+}$ ⁠, and another radius of $\mathrm{Cl^-}$ ⁠.
2. $a = 2(r_+ + r_-) = 2(102 + 181) = 566$ ⁠ picometres.
3. X-ray measurement gives 564 pm, 0.564 nm.
If you answered 283 pm, you worked out the distance from a sodium ion to a chloride ion, half the edge.

Lesson 6 of 6 · About 25 minutes

Alloys

Why an 18-carat gold ring is harder than pure gold: layers of atoms that slip over each other, the yield strength, and odd-sized atoms that buckle the slip plane. And why silver hardly helps.

Open the lesson

The 6 steps and their answers

Step 1 of 6
Open this step
Metals bend by slipping
Practice · Predict, then look
Question
Push the top half of a block of pure gold with a gentle Push, 50 MPa. What happens?

Correct answer
- Correct The top half slides along a plane, and does not come back
Setup, choices and feedback
The Scene at this step
Gold content
24 ctfixed
Push
0 MPafixed
Mixed with
Copper
Slip the layers
Crystal
Choices
- Correct The top half slides along a plane, and does not come back
- Wrong The block holds: pure gold is the strongest
  Misconception: Thinks a pure metal is stronger than an alloy of it, as if purity meant strength.
  Feedback from the catalogue
  In a pure metal every atom is the same size, and the slip plane is smooth: layers slide over each other easily, and the metal is soft. Foreign atoms of another size buckle the layers and stop the slipping. That is why 18-carat gold is about ten times stronger than pure gold, and steel far stronger than pure iron.
- Wrong The block cracks in two, like salt
  Feedback
  In salt, slipping puts like-charged ions face to face, and they repel. In a metal the sea of electrons keeps holding the layers, and they just slide.
Once the prediction is locked in, the Scene changes
Push
50 MPafixed
The Scene then shows: 2 · Whole atom spacings the top half has slipped, 0–3/nodes/gold/outputs/steps
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
The top half slipped by two atom spacings. Even a gentle push is enough to move pure gold, which is why it is so soft.

Worked solution
1. In pure gold every atom is the same size, and the slip plane is smooth.
2. A sliding layer meets the same hollows and bumps everywhere, and nothing stops it.
3. A small push, 50 MPa, is already past the yield strength, and the block slips.
Step 2 of 6
Open this step
The yield strength
Practice · Reach the target
Question
Find the largest Push at which the block of pure gold still only leans and does not slip, then press Check.

Goal
- 30 MPa ± 2.5 MPa
  At the start of the step: 0 MPa
- 0 ± 0.01
  At the start of the step: 0
Setup, choices and feedback
The Scene at this step
Gold content
24 ctfixed
Push
0 MPa
Mixed with
Copper
Slip the layers
Crystal
Read from the Scene at
Push/nodes/gold/props/push
Read from the Scene at
Whole atom spacings the top half has slipped, 0–3/nodes/gold/outputs/steps
One setting that reaches it
Push
30 MPa
Mixed with
Copper
Feedback for a right answer
30 MPa: the yield strength of soft pure gold in this model. At 35 MPa the block slips.

Feedback for a wrong answer
Not yet. If the block slips, lower the push; if it only leans, try one step more.

Hint
Raise the push in steps of 5 MPa, and watch for the moment the reading changes from “Holds” to “Slips”.

Worked solution
1. From zero up to 30 MPa the block only leans, and springs back when released.
2. At 35 MPa the top half slips.
3. Pure gold’s yield strength is about 30 MPa.
Step 3 of 6
Open this step
Odd-sized atoms
Practice · Predict, then look
Question
Pure gold slipped under a firm push, 150 MPa. Set Gold content to 18 carat, with copper. What happens under the same push?

Correct answer
- Correct The block holds, and only leans
Setup, choices and feedback
The Scene at this step
Gold content
24 ctfixed
Push
150 MPafixed
Mixed with
Copperfixed
Slip the layers
Crystal
Choices
- Correct The block holds, and only leans
- Wrong It slips as before: copper is as soft as gold
  Misconception: Thinks mixing two soft metals must give a soft alloy, its strength an average of theirs.
  Feedback from the catalogue
  An alloy’s strength is not an average of its parts’. What matters is whether the atoms fit each other in size. Copper atoms are smaller than gold atoms, buckle the layers and stop the slipping, so two soft metals together make a hard alloy: 18-carat gold with copper is about five times stronger than copper alone.
- Wrong It slips even more: the gold is less pure
  Misconception: Thinks a pure metal is stronger than an alloy of it, as if purity meant strength.
  Feedback from the catalogue
  In a pure metal every atom is the same size, and the slip plane is smooth: layers slide over each other easily, and the metal is soft. Foreign atoms of another size buckle the layers and stop the slipping. That is why 18-carat gold is about ten times stronger than pure gold, and steel far stronger than pure iron.
Once the prediction is locked in, the Scene changes
Gold content
18 ctfixed
The Scene then shows: 295 · The alloy's yield strength, MPa (rough)/nodes/gold/outputs/yieldStrength
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
The block holds. The yield strength of 18-carat gold with copper is about 295 MPa, roughly ten times pure gold’s, though copper on its own is only twice as strong as gold.

Worked solution
1. Copper atoms are about 11% smaller than gold atoms, and the layers around them buckle.
2. A sliding layer snags on every odd-sized atom, and a much bigger push is needed to move it.
3. The yield strength rises to about 295 MPa, well above 150 MPa, and the block holds.
Step 4 of 6
Open this step
By weight and by atoms
Practice · Calculate
Question
18-carat gold with copper: 18 g of gold and 6 g of copper. The molar masses: gold 197 g/mol, copper 63.5 g/mol. How many copper atoms are there in every 100 atoms?

Correct answer
50.8 ± 1
Setup, choices and feedback
The Scene at this step
Gold content
18 ctfixed
Push
150 MPa
Mixed with
Copperfixed
Slip the layers
Slip plane
Accepted within
± 1
Computed from the Scene at this step’s setting
Added atoms per 100 atoms/nodes/gold/outputs/atomShare
Wrong answers it recognises
- 25 ± 1
  Misconception: Takes the share of atoms in an alloy to be its share by weight.
  Feedback from the catalogue
  Per cent by weight is not per cent by atoms when the atoms weigh differently. A copper atom weighs less than a third as much as a gold atom, so the quarter of 18-carat gold’s weight that is copper holds about half the atoms. To go from weight to atoms, turn each mass into moles.
Feedback for a right answer
About 51: more than half the atoms are copper, though it is only a quarter of the weight. That is why the Scene rings the gold atoms: in a mix this even, each kind is the odd one out among the other.

Hint
Turn each mass into moles, then work out what share of all the moles is copper.

Worked solution
1. Gold: $\dfrac{18}{197} \approx 0.0914$ ⁠ mol.
2. Copper: $\dfrac{6}{63.5} \approx 0.0945$ ⁠ mol.
3. Copper’s share: $\dfrac{0.0945}{0.0914 + 0.0945} \approx 0.51$ ⁠, about 51 in every 100 atoms.
If you answered 25, you took the share by weight. But a copper atom weighs less than a third as much as a gold atom, so each gram holds more copper atoms.
Step 5 of 6
Open this step
Why silver hardly helps
Practice · Predict, then look
Question
Switch Mixed with from Copper to Silver, at the same 18 carat and under the same 150 MPa push. What happens?

Correct answer
- Correct The block slips, almost like pure gold
Setup, choices and feedback
The Scene at this step
Gold content
18 ctfixed
Push
150 MPafixed
Mixed with
Copperfixed
Slip the layers
Crystal
Choices
- Correct The block slips, almost like pure gold
- Wrong The block holds, as with copper
  Feedback
  Copper hardens because its atoms are smaller and buckle the layers. Silver atoms are gold’s size, and the layers stay flat.
- Wrong The block holds even better: silver is heavier than copper
  Feedback
  What matters is the atoms’ size, not their weight. A silver atom is heavier than a copper atom, but the size of a gold atom.
Once the prediction is locked in, the Scene changes
Mixed with
Silverfixed
The Scene then shows: 75 · The alloy's yield strength, MPa (rough)/nodes/gold/outputs/yieldStrength
A prediction is never marked as a failure: the learner sees the outcome and the explanation either way.
Feedback for a right answer
The block slips. The yield strength of 18-carat gold with silver is only about 75 MPa: silver atoms slot into the crystal without buckling it, and the slip plane stays smooth.

Worked solution
1. A silver atom’s radius is 144.5 pm, almost exactly gold’s 144 pm.
2. Silver atoms do not buckle the layers, and there are no bumps on the slip plane.
3. The yield strength rises only to about 75 MPa, below 150 MPa, and the block slips.
Step 6 of 6
Open this step
Steel and bronze
Practice · Choose
Question
Carbon atoms are far smaller than iron atoms. Where do they sit in steel?

Correct answer
- Correct In the gaps between the iron atoms, where they push the neighbours apart and strain the crystal
Setup, choices and feedback
The Scene at this step
Gold content
18 ct
Push
150 MPa
Mixed with
Copper
Slip the layers
Slip plane
Choices
Shown in a random order.
- Correct In the gaps between the iron atoms, where they push the neighbours apart and strain the crystal
- Wrong In the places of iron atoms, like copper in gold
  Feedback
  An atom that replaces the host’s needs to be close to it in size, like copper and gold. Carbon is so small that it fits into the gaps.
- Wrong In separate grains of charcoal between the iron crystals
  Feedback
  In steel the carbon is spread through the iron crystals themselves, atom by atom, and that is what strengthens them.
Feedback for a right answer
The carbon squeezes into the gaps between the iron atoms and strains the crystal even more than a replacing atom does. That is why a few tenths of a per cent of carbon turn soft iron into strong steel.

Worked solution
1. In bronze, brass and carat gold the foreign atoms are close in size to the host’s, and sit in their places.
2. A carbon atom is far smaller than an iron atom, and fits into a gap between the iron atoms.
3. There it pushes its neighbours aside, the layers buckle, and slipping gets harder.

Across the unit · 18 misconceptions

Misconception catalogue

Each common mistake this unit recognises, in a few words. Open one for what the learner reads when an answer matches it, and where it is asked.

Index

Ions and ionic bonding

A gap and a spare

Question

Correct answer

The Scene at this step

Choices

Once the prediction is locked in, the Scene changes

Worked solution

Counting the ions

Question

Correct answer

The Scene at this step

Wrong answers it recognises

Hint

Worked solution

A full shell says no

Question

Correct answer

The Scene at this step

Choices

Once the prediction is locked in, the Scene changes

Worked solution

The charge from the group

Question

Correct answer

The Scene at this step

Choices

Hint

Worked solution

Balancing the charges

Question

Correct answer

The Scene at this step

Choices

Hint

Worked solution

Small ions hold tighter

Question

Goal

The Scene at this step

One setting that reaches it

Hint

Worked solution

Ionic and metallic lattices

A giant lattice

Question

Correct answer

The Scene at this step

Wrong answers it recognises

Hint

Worked solution

Salt shatters

Question

Correct answer

The Scene at this step

Choices

Once the prediction is locked in, the Scene changes

Worked solution

When salt conducts

Question

Correct answer

The Scene at this step

Choices

Hint

Worked solution

A sea of electrons

Question

Correct answer

The Scene at this step

Hint

Worked solution

Metals bend

Question

Correct answer

The Scene at this step

Choices

Once the prediction is locked in, the Scene changes

Worked solution

Why metals conduct

Question