Ionic bonds and lattice enthalpy

Kossel's picture: electrons move

Sodium has one electron in its outer shell. Chlorine has seven. When sodium gives its outer electron to chlorine, both reach a noble gas arrangement.

The ions attract each other strongly. This attraction is the ionic bond. The number of electrons an atom gives or takes is its electrovalence. Sodium and chlorine have an electrovalence of 1. Calcium in $\text{CaCl}_2$ has 2.

When does an ionic bond form?

Three things favour it.

• The metal has a low ionisation enthalpy, so it gives up electrons easily. The metals of groups 1 and 2 are the best examples.
• The non-metal has a negative electron gain enthalpy, so it takes electrons readily. The halogens and oxygen are good examples.
• The ions pack into a crystal with a large lattice enthalpy.

Making the ions costs energy

Look at the numbers for sodium chloride, in kJ/mol.

• Removing an electron from a gaseous sodium atom costs $+495.8$.
• Adding an electron to a gaseous chlorine atom gives out $348.7$, so its value is $-348.7$.

Together, $495.8 - 348.7 = +147.1$ kJ/mol. Making a pair of gaseous ions is uphill. If that were the whole story, sodium chloride would never form. Something else must give out a lot of energy.

Lattice enthalpy

The ions do not stay apart. They pack into a crystal in which every ion is surrounded by ions of the other charge.

The lattice enthalpy is the energy needed to separate one mole of a solid ionic compound completely into its gaseous ions.

For sodium chloride it is $788$ kJ/mol. The same amount is given out when the gaseous ions come together to form the crystal. That is far more than the $147.1$ kJ/mol the ions cost, so the solid forms.

Two things decide the size of the lattice enthalpy.

• Charge. Ions with larger charges attract more strongly. Magnesium oxide, $\text{Mg}^{2+}\text{O}^{2-}$, has a lattice enthalpy of about $3890$ kJ/mol.
• Size. Small ions sit close together and attract more strongly. A large distance between their centres weakens the lattice.

Start from sodium chloride, as set. Then make both charges 2 and shrink the cation. How many times larger does the lattice enthalpy become?

The Born-Haber idea

The lattice enthalpy cannot be measured directly. By Hess's law, the enthalpy change of a reaction is the same whichever path it takes. So we can go from the elements to the solid in small steps, and add them up. This path is a Born-Haber cycle.

For sodium chloride, all in kJ/mol:

1. Sublimation of sodium, $\text{Na(s)} \rightarrow \text{Na(g)}$: $+108.4$.
2. Half the bond enthalpy of chlorine, $\tfrac{1}{2}\text{Cl}_2\text{(g)} \rightarrow \text{Cl(g)}$: $+121$.
3. Ionisation of sodium: $+495.8$.
4. Electron gain of chlorine: $-348.7$.
5. Lattice forming: $-788$.

This matches the measured enthalpy of formation of sodium chloride. When the enthalpy of formation is known, the same cycle gives the lattice enthalpy instead.

Properties of ionic compounds

The strong pull between ions in every direction explains how ionic solids behave.

• They have high melting and boiling points.
• They are hard but brittle. A blow pushes ions of the same charge next to each other, and the crystal splits.
• They conduct electricity when molten or dissolved in water, because the ions can then move. The solid does not conduct.
• Many dissolve in water, whose polar molecules pull the ions apart.

Practise with new numbers

Try it in Python

The program walks through the Born-Haber cycle of sodium chloride and adds up the steps. Then it shows what the ions alone cost.

Common mistakes

• Thinking the ions form because they are stable alone. Making $\text{Na}^+$ and $\text{Cl}^-$ in the gas costs energy. The lattice pays for it.
• Getting the sign of the lattice step wrong. The lattice enthalpy is positive for breaking the solid apart. Forming the solid gives it out.
• Using the whole bond enthalpy of chlorine. One mole of NaCl needs only half a mole of $\text{Cl}_2$.
• Saying ionic solids conduct. Only the melt or a solution conducts.

Remember these

• Ionic bonds form between a metal of low ionisation enthalpy and a non-metal of negative electron gain enthalpy.
• Lattice enthalpy: the energy to separate one mole of an ionic solid into gaseous ions. Larger for higher charges and smaller ions.
• Born-Haber: sublimation + half bond + ionisation + electron gain $-$ lattice $=$ enthalpy of formation.
• Ionic solids: high melting points, brittle, conduct only when molten or in solution.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. What is the electrovalence of aluminium in $\text{AlF}_3$?

2. Making $\text{Na}^+$ and $\text{Cl}^-$ in the gas costs energy. Why does sodium chloride form at all?

3. Which has the larger lattice enthalpy, NaF or NaI, and why?

4. Why does solid sodium chloride not conduct electricity, while molten sodium chloride does?

5. In a Born-Haber cycle, why is half the bond enthalpy of chlorine used?