Metallic bonding

1. Overview

Metals are held together by metallic bonding: positive metal ions held in a lattice by electrons that belong to no single atom. This section has one outcome, the definition, but the model behind it explains a great deal: why metals conduct electricity, why most have high melting and boiling points, and why the melting point rises from sodium to aluminium. Knowing exactly which particles attract which also keeps metallic, ionic and covalent bonding apart in your answers.

Key Definitions

• Metallic bonding: the electrostatic attraction between positive metal ions and delocalised electrons.
• Delocalised electrons: electrons that do not belong to any single atom or ion; in a metal such as sodium or magnesium they are the outer-shell electrons, shared by the whole lattice and able to move through it.
• Positive metal ion: the particle left when a metal atom's outer-shell electrons join the delocalised electrons; for example, each magnesium atom becomes an Mg²⁺ ion in the lattice.
• Giant metallic lattice: a regular three-dimensional arrangement of a very large number of positive metal ions, held together by their attraction to the delocalised electrons that move between them.
• Electrostatic attraction: the force of attraction between opposite charges; metallic, ionic and covalent bonding are all electrostatic attractions, each between different kinds of particle.
• Non-directional bonding: bonding in which the attraction acts in all directions around each particle, not along a line to one particular neighbour; metallic bonding is non-directional, a covalent bond is not.
• Outer-shell electrons: the electrons in the highest occupied shell of an atom; in metals such as sodium, magnesium and aluminium they become the delocalised electrons, so their number equals the charge on the ion.

Content

The definition, phrase by phrase

This is the definition you are expected to give. Learn it as it stands:

Metallic bonding is the electrostatic attraction between positive metal ions and delocalised electrons.

Each phrase does a job:

Phrase	What it means
electrostatic attraction	the force between opposite charges: here, positive ions and negative electrons
positive metal ions	what is left of each metal atom once its outer-shell electrons have become delocalised, for example Mg²⁺ in magnesium
delocalised electrons	electrons that belong to no single ion; they are shared by the whole lattice and can move through it

So the attraction is between ions and electrons. It is not between metal atoms, and not between the ions themselves, which repel each other. It is not between molecules either: a metal contains no molecules.

Where the delocalised electrons come from

A metal atom has only a few outer-shell electrons, and they are held relatively weakly (metals have relatively low ionisation energies). When a very large number of metal atoms pack closely together, these outer-shell electrons are no longer tied to their own atom. They spread out through the whole structure. The inner-shell electrons stay around the nucleus, and together they make up the positive ion.

For sodium, magnesium and aluminium, each atom gives all its outer-shell electrons, so the number of delocalised electrons per atom equals the charge on the ion:

Metal	Electron configuration	Ion in the lattice	Delocalised electrons per atom
sodium	1s² 2s² 2p⁶ 3s¹	Na⁺	1
magnesium	1s² 2s² 2p⁶ 3s²	Mg²⁺	2
aluminium	1s² 2s² 2p⁶ 3s² 3p¹	Al³⁺	3

All three ions keep the 1s² 2s² 2p⁶ arrangement, so in each of these metals most of the electrons stay on the ions and are not delocalised. For a d-block metal such as copper the count is less simple, so describe its lattice as positive copper ions and delocalised electrons.

How the lattice holds together

In a solid metal, the positive ions sit in a regular arrangement called a giant metallic lattice. The delocalised electrons move through the spaces between them. A useful picture is "positive ions in a sea of delocalised electrons", but the picture is not the definition: the bond is the attraction.

• Each ion is attracted to the delocalised electrons all around it. The ions repel one another, and so do the electrons, but overall the attraction between ions and electrons wins, so the lattice holds together.
• The attraction acts in all directions. Metallic bonding is non-directional: no ion is bonded to one particular neighbour, unlike two atoms joined by a covalent bond.
• The bonding runs through the whole piece of metal, so a metal is a giant structure, never a collection of separate molecules.
• The metal is electrically neutral overall. The total positive charge on the ions equals the total negative charge on the delocalised electrons.

Metallic bonding is still present in a liquid metal. On melting, the ions are no longer held in fixed positions and can move past one another, but they are still surrounded by delocalised electrons. That is why molten metals still conduct electricity. Only on boiling does the metal separate into gaseous atoms, with the metallic bonding fully overcome.

Worked example 1: counting ions and delocalised electrons

Question: A strip of pure aluminium has a mass of 0.648 g. Calculate (a) the number of aluminium ions in the strip, (b) the number of delocalised electrons in the strip, and (c) the percentage of all the electrons in the strip that are delocalised. ($A_{\text{r}}$: Al = 27.0; Avogadro constant $L = 6.022 \times 10^{23}$ mol⁻¹; the atomic number of Al is 13.)

Step 1: amount of aluminium. $$n(\text{Al}) = \frac{m}{M} = \frac{0.648}{27.0} = 0.0240\ \text{mol}$$

Step 2: number of ions. Every atom becomes one Al³⁺ ion in the lattice. $$N(\text{Al}^{3+}) = 0.0240 \times 6.022 \times 10^{23} = 1.445 \times 10^{22}$$

Step 3: delocalised electrons. Each atom gives its three outer-shell electrons (3s² 3p¹). $$n(\text{e}^-) = 3 \times 0.0240 = 0.0720\ \text{mol} \qquad N(\text{e}^-) = 0.0720 \times 6.022 \times 10^{23} = 4.336 \times 10^{22}$$

Step 4: check the charges. Each Al³⁺ ion carries three positive charges, so the ions carry $3 \times 1.445 \times 10^{22} = 4.336 \times 10^{22}$ positive charges in total. That equals the number of delocalised electrons, each with one negative charge, so the strip is neutral overall.

Step 5: percentage delocalised. Each atom has 13 electrons. It gives 3 to the delocalised electrons and keeps 10 in the ion (1s² 2s² 2p⁶). Every atom is the same, so the percentage does not depend on the mass of the strip. $$\frac{3}{13} \times 100 = 23.1\%$$

Answer: (a) $1.45 \times 10^{22}$ Al³⁺ ions; (b) $4.34 \times 10^{22}$ delocalised electrons; (c) 23.1% (all to 3 s.f.). Fewer than a quarter of the electrons in aluminium are delocalised; the rest stay on the ions.

Metallic, ionic and covalent bonding compared

All three strong types of bonding are electrostatic attractions. What differs is which particles attract each other:

Bonding	Electrostatic attraction between	Usually found in
metallic	positive metal ions and delocalised electrons	metal elements, solid or liquid
ionic	oppositely charged ions (cations and anions)	compounds of a metal with a non-metal, such as NaCl
covalent	the nuclei of two atoms and a shared pair of electrons	non-metal elements and compounds, such as Cl₂ and CO₂

Metallic, ionic and covalent bonding are, in general, stronger than intermolecular forces. Sodium, held together by metallic bonding, boils at 883 °C. Chlorine, whose molecules are attracted to one another only by intermolecular forces, boils at −34 °C. The words "in general" matter: they describe the usual pattern, not a rule for every pair of substances.

What makes metallic bonding stronger

The attraction between the ions and the delocalised electrons is stronger when:

1. the ions have a larger charge, so each ion attracts the electrons around it more strongly;
2. there are more delocalised electrons per ion, so there is more negative charge around each ion;
3. the ions are smaller, so the delocalised electrons can be closer to the nucleus of each ion.

For sodium, magnesium and aluminium, points 1 and 2 go together: the charge on each ion equals the number of electrons its atom gave to the lattice. Stronger attraction means more energy is needed to overcome it, so the melting and boiling points are higher.

Metal	Ion	Delocalised electrons per ion	Melting point / °C	Boiling point / °C
sodium	Na⁺	1	98	883
magnesium	Mg²⁺	2	650	1090
aluminium	Al³⁺	3	660	2519

From sodium to aluminium, all three factors change in the same direction: the ion charge rises, the number of delocalised electrons per ion rises and the ions get smaller (all three have 10 electrons, but 11, 12 and 13 protons; topic 1.1 explains ion sizes). So the model predicts stronger metallic bonding from sodium to aluminium, and the data agree.

The boiling points show this more clearly than the melting points. Magnesium and aluminium melt only 10 °C apart, but aluminium boils over 1400 °C higher. That fits the point above: melting only loosens the lattice, while boiling overcomes the metallic bonding completely. In an exam, explain a melting-point difference in the same way: stronger attraction, so more energy is needed to overcome it.

The model is a guide, not a law. Magnesium, for example, melts and boils at lower temperatures than calcium (650 °C and 1090 °C, against 842 °C and 1484 °C), although Mg²⁺ is smaller and has the same charge. Factors outside this course also play a part, so ion size alone does not decide every comparison.

Worked example 2: why potassium melts at a lower temperature than sodium

Question: Sodium and potassium are both in Group 1. Use the data to (a) calculate the amount, in mol, of delocalised electrons in 1.00 cm³ of each metal, and (b) explain why potassium has the lower melting point.

Metal	Density / g cm⁻³	$A_{\text{r}}$	Melting point / °C
sodium	0.968	23.0	97.8
potassium	0.862	39.1	63.5

Step 1: mass of 1.00 cm³. Mass = density × volume, so 1.00 cm³ of sodium has a mass of 0.968 g and 1.00 cm³ of potassium has a mass of 0.862 g.

Step 2: amount of atoms. $$n(\text{Na}) = \frac{0.968}{23.0} = 0.04209\ \text{mol} \qquad n(\text{K}) = \frac{0.862}{39.1} = 0.02205\ \text{mol}$$

Step 3: delocalised electrons. Both atoms have one outer-shell electron (3s¹ and 4s¹). Each atom gives one delocalised electron and becomes a 1+ ion, so the amount of delocalised electrons equals the amount of atoms.

Step 4: compare. $$\frac{0.04209}{0.02205} = 1.91$$

Answer (a): 1.00 cm³ of sodium contains 0.0421 mol of delocalised electrons and 1.00 cm³ of potassium contains 0.0220 mol (3 s.f.). Sodium has about 1.9 times as many in each cm³.

Answer (b):

• Both metals have 1+ ions and one delocalised electron per ion, so the ion charge is not the difference.
• The K⁺ ion is larger than the Na⁺ ion because it has one more occupied electron shell (K⁺ is 1s² 2s² 2p⁶ 3s² 3p⁶; Na⁺ is 1s² 2s² 2p⁶).
• In potassium, the delocalised electrons are further from the nucleus of each ion, and there are fewer of them in each cm³, as part (a) shows.
• So the electrostatic attraction between the positive ions and the delocalised electrons is weaker in potassium. Less energy is needed to overcome it enough for the ions to move past one another, so potassium melts at a lower temperature.

Using the model to explain conductivity

The delocalised electrons can move through the lattice. When a potential difference is applied, they drift towards the positive terminal and carry charge, in the solid and in the liquid. In a metal, electrons carry the current; in a molten ionic compound such as NaCl(l), it is the ions that move. Topic 4.2 compares the properties of all the structure types.

Drawing metallic bonding

You may be asked for a labelled diagram. Draw it to this checklist:

• At least two rows of identical circles in a regular arrangement, close together.
• A + sign, or the ion's symbol and charge (for example Mg²⁺), inside each circle, with a label: "positive ions" or "cations".
• Electrons (e⁻ or small dots) spread through the spaces between the circles, with a label: "delocalised electrons". If you draw individual electrons, keep the ratio right: two for each Mg²⁺ ion.
• Never label the circles "atoms", "nuclei" or "protons", and never scatter the ions at random.

Worked example 3: describing the bonding in rubidium

Question: Rubidium, Rb, is in Group 1. Its electron configuration is [Kr] 5s¹ and it melts at 39 °C. (a) Describe the bonding in solid rubidium. (b) Explain why rubidium conducts electricity both as a solid and when it has melted.

Answer (a):

• Rubidium has metallic bonding in a giant metallic lattice.
• Each atom gives its one 5s electron to the delocalised electrons, leaving Rb⁺ ions in a regular arrangement.
• Metallic bonding is the electrostatic attraction between these positive Rb⁺ ions and the delocalised electrons.
• A diagram would show regular rows of Rb⁺ ions with one delocalised electron for each ion, both labelled.

Answer (b):

• The delocalised electrons can move through the whole lattice, so they carry charge when a potential difference is applied.
• Above 39 °C the ions can move past one another, but the delocalised electrons and the metallic bonding are still there, so liquid rubidium conducts too.

The answer never says that ions carry the current, and never calls the electrons "free".

Key Equations

Amount of a metal ($m$ = mass in g; $M$ = molar mass in g mol⁻¹, numerically equal to $A_{\text{r}}$; $n$ in mol): $$n = \frac{m}{M}$$

Number of particles ($N$ = number of atoms, ions or electrons; $L$ = Avogadro constant, $6.022 \times 10^{23}$ mol⁻¹): $$N = nL$$

Amount of delocalised electrons ($z$ = charge on the metal ion, equal to the number of outer-shell electrons for sodium, magnesium and aluminium): $$n(\text{e}^-) = z \times n(\text{metal})$$

Amount of delocalised electrons in each cm³ of metal ($\rho$ = density in g cm⁻³; $M$ in g mol⁻¹; the answer is in mol cm⁻³): $$n(\text{e}^-) = \frac{z\rho}{M}$$

Charge balance (a metal is neutral overall): $$z \times N(\text{ions}) = N(\text{delocalised electrons})$$

Common Mistakes to Avoid

• Mistake: writing only "a sea of electrons", or "positive ions surrounded by electrons", as the definition. Fix: name the force and both particles: "the electrostatic attraction between positive metal ions and delocalised electrons". The sea is a picture; the attraction is the bond.
• Mistake: calling them "free electrons". Fix: write "delocalised electrons". They move through the lattice, but they stay attracted to the ions, and that attraction is the bond. In aluminium, the delocalised electrons are the 3s² 3p¹ electrons of every atom, shared by all the Al³⁺ ions.
• Mistake: saying the electrons are attracted to metal atoms, nuclei or protons, or that the ions attract each other. Fix: the electrons are attracted to positive ions, and the ions repel each other. In magnesium the particles are Mg²⁺ ions, each with 10 electrons still around its nucleus.
• Mistake: a diagram with unlabelled circles, ions scattered at random, or electrons drawn as minus signs with no label. Fix: regular rows of ions labelled "positive ions" (for example Na⁺), and electrons between them labelled "delocalised electrons".
• Mistake: calling the forces in a metal "intermolecular forces", or describing the structure as metallic without saying it is giant. Fix: a metal has no molecules. For sodium, write "strong metallic bonding between Na⁺ ions and delocalised electrons throughout a giant metallic lattice".
• Mistake: saying that a compound containing a metal, such as magnesium oxide, has metallic bonding. Fix: metallic bonding needs positive metal ions surrounded by delocalised electrons, as in magnesium metal. Magnesium oxide is made of Mg²⁺ and O²⁻ ions held by ionic bonding; it has no delocalised electrons, which is why solid MgO does not conduct.
• Mistake: explaining conductivity with "it has delocalised electrons" and stopping there. Fix: say that the delocalised electrons can move through the structure and carry charge: "in aluminium, the delocalised electrons move through the lattice, so they carry charge".
• Mistake: explaining a melting-point difference with "more delocalised electrons" alone. Fix: finish the chain. For aluminium against sodium: Al³⁺ has a larger charge and is smaller than Na⁺, and there are three delocalised electrons per ion, not one, so the electrostatic attraction is stronger and more energy is needed to overcome it.

Exam Tips

• Define: write the full sentence, "the electrostatic attraction between positive metal ions and delocalised electrons". Keep the words "electrostatic", "positive ions" and "delocalised"; each one counts.
• Describe the bonding in a named metal: give the type (metallic), the structure (giant metallic lattice), the ion with its charge (for example Ca²⁺), where the delocalised electrons come from, and the definition.
• Draw a labelled diagram: at least two regular rows of ions, with two labels, "positive ions" and "delocalised electrons". An unlabelled drawing shows very little.
• Explain a difference in melting or boiling point: name the bonding, compare ion charge, delocalised electrons per ion and ion size, then finish with "stronger attraction, so more energy is needed to overcome it".
• Explain conductivity: delocalised electrons that move through the structure carry the charge, in the solid and in the liquid.
• In multiple-choice questions, check which particles each option says are attracted to each other. An option that says "atoms" or "ions only" names the wrong particles.