Ionic Lattices, Their Properties and Lattice Energy – Formation of Ionic and Metallic Bonds (Senior 4 Chemistry) | Ganzaa

Formation of Ionic and Metallic Bonds

Lessons

Senior 4 · Chemistry

Formation of Ionic and Metallic Bonds

3 lessons

Lesson 2 of 3

Ionic Lattices, Their Properties and Lattice Energy

25 min

Why does salt need 801 °C to melt?

Sugar melts in a pan at about 186 °C. Table salt stays solid in a cooking fire; it melts only at 801 °C. Magnesium oxide does not melt until about 2850 °C, which is why it is used to line furnaces. Yet a crystal of salt shatters if you hit it with a hammer, a piece of solid salt does not conduct electricity, and salt dissolves easily in water. All of these facts follow from one structure, the giant ionic lattice, and one quantity, the lattice energy.

Definition

Giant ionic lattice: a regular three-dimensional arrangement of a very large number of cations and anions, held together by strong electrostatic attraction in all directions. There are no separate molecules.

Coordination number: the number of nearest neighbours of opposite charge around an ion. In sodium chloride it is 6 for both ions (6 : 6).

The sodium chloride structure

In solid sodium chloride each $\mathrm{Na^{+}}$ ion is surrounded by six $\mathrm{Cl^{-}}$ ions at the corners of an octahedron, and each $\mathrm{Cl^{-}}$ by six $\mathrm{Na^{+}}$ . The ions alternate along every row, in all three directions, so every ion is attracted by its nearest neighbours and repelled only by more distant ions of the same charge. The formula NaCl gives only the ratio of ions, 1 : 1.

The coordination number depends on the relative sizes of the ions. Caesium ions are much larger than sodium ions, so eight chloride ions fit around each one: caesium chloride has an 8 : 8 structure.

Physical properties, and why

Property	Explanation
High melting and boiling points (NaCl 801 °C, MgO 2852 °C)	Many strong electrostatic attractions act in all directions; a lot of energy is needed to separate the ions.
Hard but brittle	The ions are held firmly in place, but if one layer is pushed one ion along, ions of the same charge meet and repel, and the crystal splits (Figure 2.2).
Do not conduct when solid; conduct when molten or dissolved in water	In the solid, the ions are fixed in the lattice. When it melts or dissolves, the ions are free to move and carry charge. (The electrons are held on the ions and cannot move through the solid.)
Many are soluble in water, insoluble in non-polar solvents such as hexane	Polar water molecules surround and attract each ion (hydration), releasing energy that helps to break up the lattice. Hexane molecules cannot attract ions. Some ionic solids with very high lattice energies, such as MgO, are almost insoluble.

Definition

Lattice energy (lattice enthalpy of formation), $\Delta H_{\text{latt}}$ : the enthalpy change when one mole of an ionic solid is formed from its gaseous ions under standard conditions. For sodium chloride:

\mathrm{Na^{+}(g)} + \mathrm{Cl^{-}(g)} \longrightarrow \mathrm{NaCl(s)} \qquad \Delta H_{\text{latt}} = -787\,\mathrm{kJ\,mol^{-1}}

It is always exothermic. The larger its magnitude, the stronger the ionic bonding. (Some books use the reverse process, lattice dissociation, with the same number and a positive sign.)

What makes a lattice energy large?

The attraction between two ions follows Coulomb's law: it is proportional to the product of their charges and inversely proportional to the distance between their centres, which is roughly the sum of their radii:

\left|\Delta H_{\text{latt}}\right| \propto \frac{z_{+} \times z_{-}}{r_{+} + r_{-}}

So lattice energy is larger for smaller ions and, above all, for more highly charged ions.

Table 2.1: Lattice energies and melting points (lattice energies rounded)

Compound	Ions (radius / pm)	$\Delta H_{\text{latt}}$ / $\mathrm{kJ\,mol^{-1}}$	Melting point / °C
NaF	$\mathrm{Na^{+}}$ 102, $\mathrm{F^{-}}$ 133	about −920	996
NaCl	$\mathrm{Na^{+}}$ 102, $\mathrm{Cl^{-}}$ 181	about −790	801
NaBr	$\mathrm{Na^{+}}$ 102, $\mathrm{Br^{-}}$ 196	about −750	747
NaI	$\mathrm{Na^{+}}$ 102, $\mathrm{I^{-}}$ 220	about −700	661
KCl	$\mathrm{K^{+}}$ 138, $\mathrm{Cl^{-}}$ 181	about −720	771
CaO	$\mathrm{Ca^{2+}}$ 100, $\mathrm{O^{2-}}$ 140	about −3400	2613
MgO	$\mathrm{Mg^{2+}}$ 72, $\mathrm{O^{2-}}$ 140	about −3800	2852

Worked example 1: why is MgO so much stronger than NaCl?

Use the charges and radii in Table 2.1 to predict roughly how many times larger the lattice energy of MgO is than that of NaCl. Compare with the data.

Solution.

\text{NaCl: } \frac{1 \times 1}{102 + 181} = \frac{1}{283} \qquad \text{MgO: } \frac{2 \times 2}{72 + 140} = \frac{4}{212}

\text{ratio} = \frac{4}{212} \times \frac{283}{1} = 5.3

Answer: the simple model predicts about 5 times; the data give $\frac{3800}{790} \approx 4.8$ . The doubled charges on both ions (a factor of 4) matter more than the smaller distance (a factor of 1.3). That is why MgO melts at 2852 °C and is used in furnace linings.

Finding a lattice energy: the Born–Haber cycle

A lattice energy cannot be measured directly, because gaseous ions cannot be collected and combined. It is calculated with Hess's law: the enthalpy change for going from the elements to the ionic solid is the same whether it happens in one step or by a series of steps. The steps for sodium chloride are drawn as an energy-level diagram called a Born–Haber cycle.

Worked example 2: the lattice energy of sodium chloride

Use the cycle in Figure 2.3: enthalpy of formation of NaCl(s) −411; atomisation of sodium +107; atomisation of chlorine (half the Cl–Cl bond energy) +122; first ionisation energy of sodium +496; first electron affinity of chlorine −349 (all in $\mathrm{kJ\,mol^{-1}}$ ).

Solution. By Hess's law, the direct route equals the sum of the steps:

\Delta H_f = \Delta H_{\text{at}}(\mathrm{Na}) + \Delta H_{\text{at}}(\mathrm{Cl}) + IE(\mathrm{Na}) + EA(\mathrm{Cl}) + \Delta H_{\text{latt}}

-411 = 107 + 122 + 496 + (-349) + \Delta H_{\text{latt}}

\Delta H_{\text{latt}} = -411 - 376 = -787\,\mathrm{kJ\,mol^{-1}}

Answer: $-787\,\mathrm{kJ\,mol^{-1}}$ . Notice the large uphill steps (+725 in total to make gaseous $\mathrm{Na^{+}}$ and Cl): only the lattice energy brings the total below zero.

Warning

Common mistakes. (1) Saying ionic solids conduct because "electrons move": in the melt or solution it is the ions that move. (2) Comparing lattice energies by size alone when the charges differ: charge usually wins. (3) Mixing up the signs: lattice energy as defined here (formation) is negative; check which definition a question uses. (4) Forgetting that the atomisation of chlorine is half the bond energy, because one mole of Cl atoms comes from half a mole of $\mathrm{Cl_2}$ .

Safety. If you test the conductivity of molten salts, use a fume cupboard and a crucible on a pipeclay triangle, wear goggles and heat-resistant gloves, and never touch the electrodes while the supply is on.

Tip

In any comparison of ionic compounds, say three things in this order: the charges of the ions, the sizes of the ions, and so the strength of attraction (lattice energy), then link to the property asked about, usually melting point or solubility.

Chemistry Student: Lattice Enthalpies (A-Level Chemistry) (12 min). Watch the sections on lattice enthalpy of formation and dissociation and on how the size and charge of the ions change the strength of the lattice.

✦

Practice

Describe the structure of solid sodium chloride and state the coordination number of each ion.
Explain why sodium chloride (a) has a high melting point, (b) conducts electricity when molten but not when solid, (c) shatters when hit with a hammer.
Write the equation, with state symbols, that represents the lattice energy of magnesium chloride.
Put these in order of increasing magnitude of lattice energy and explain: KCl, NaCl, MgCl₂? (Hint: compare charges and radii.)
Explain why the melting point of NaI (661 °C) is lower than that of NaF (996 °C).
Calculate the lattice energy of potassium chloride from: $\Delta H_f(\mathrm{KCl}) = -437$ ; $\Delta H_{\text{at}}(\mathrm{K}) = +89$ ; $\Delta H_{\text{at}}(\mathrm{Cl}) = +122$ ; $IE(\mathrm{K}) = +419$ ; $EA(\mathrm{Cl}) = -349$ (all $\mathrm{kJ\,mol^{-1}}$ ).
Magnesium oxide is used to line steel furnaces. Explain, using the idea of lattice energy, why it is suitable.

Show answersHide answers

A giant ionic lattice: $\mathrm{Na^{+}}$ and $\mathrm{Cl^{-}}$ ions alternate in all three directions in a cubic arrangement; each ion has six nearest neighbours of opposite charge (6 : 6).
(a) Many strong electrostatic attractions between oppositely charged ions in all directions need a lot of energy to overcome. (b) In the solid the ions are fixed; when molten they can move and carry charge. (c) A blow moves one layer of ions relative to the next, bringing like charges together; they repel and the crystal splits.
$\mathrm{Mg^{2+}(g)} + 2\mathrm{Cl^{-}(g)} \rightarrow \mathrm{MgCl_2(s)}$ .
KCl < NaCl < $\mathrm{MgCl_2}$ . $\mathrm{K^{+}}$ is larger than $\mathrm{Na^{+}}$ , so the ions are further apart in KCl; $\mathrm{Mg^{2+}}$ has twice the charge and is smaller still, so $\mathrm{MgCl_2}$ has much the largest lattice energy.
Both contain $\mathrm{Na^{+}}$ , but $\mathrm{I^{-}}$ (220 pm) is much larger than $\mathrm{F^{-}}$ (133 pm). The ions are further apart in NaI, the attraction is weaker, the lattice energy smaller, and less energy is needed to melt it.
$-437 = 89 + 122 + 419 - 349 + \Delta H_{\text{latt}}$ , so $\Delta H_{\text{latt}} = -437 - 281 = -718\,\mathrm{kJ\,mol^{-1}}$ .
$\mathrm{Mg^{2+}}$ and $\mathrm{O^{2-}}$ are small and doubly charged, so the lattice energy is very large (about $-3800\,\mathrm{kJ\,mol^{-1}}$ ). The lattice stays solid up to about 2850 °C, well above the temperature of molten steel, and it does not easily react or decompose.

Quick check

Why does solid sodium chloride not conduct electricity, although molten sodium chloride does?

Key points

An ionic solid is a giant lattice; in NaCl each ion has six neighbours of opposite charge.
Ionic solids have high melting points, are hard but brittle, conduct only when molten or dissolved, and are often soluble in water but not in non-polar solvents.
Lattice energy is the enthalpy change when one mole of solid forms from gaseous ions; it is larger for smaller, more highly charged ions: $|\Delta H_{\text{latt}}| \propto \frac{z_{+} z_{-}}{r_{+} + r_{-}}$ .
A Born–Haber cycle uses Hess's law to calculate lattice energy: for NaCl, $-787\,\mathrm{kJ\,mol^{-1}}$ .

Sources and credits

Written by Ganzaa. Melting points, ionic radii (Shannon, six-coordinate) and the thermochemical data are standard reference values, as listed in the CRC Handbook of Chemistry and Physics; lattice energies are rounded.
Video: Lattice Enthalpies (A-Level Chemistry), Chemistry Student, embedded from YouTube.
The lattice drawing, diagrams, tables, worked examples and Practice items were written and drawn by Ganzaa.

1Why does salt need 801 °C to melt?

2The sodium chloride structure

3Physical properties, and why

4What makes a lattice energy large?

5Finding a lattice energy: the Born–Haber cycle

Why does salt need 801 °C to melt?

The sodium chloride structure

Physical properties, and why

What makes a lattice energy large?

Finding a lattice energy: the Born–Haber cycle