Ionic Bonding (6) More on Lattice Energy

Ionic Bonding (6) More on Lattice Energy

Let’s look at some Lattice Energy data and see what we can learn from it.

First, let’s look at how lattice energy changes down a group of the periodic table

Let’s keep the anion the same and change the cation as in this data for the Group 1 chlorides and the Group 2 chlorides:

Group 1 chlorides             Group 2 Chlorides

LiCl                848                BeCl₂              3020

NaCl               780                MgCl₂            2526

KCl                 711                CaCl₂             2258

RbCl               685                SrCl₂              2156

CsCl               661                BaCl₂             2056

Two trends stand out:

First, the Lattice Energy for the chlorides within each group decreases as the cation size, as measured by its ionic radius, increases. 

This decrease occurs, even though the structure of these chlorides changes, as we go down the group e.g. sodium chloride (NaCl) has a face centred cubic lattice with 6:6 coordination.

 Whereas caesium chloride (CsCl) has a body centred cubic lattice structure with 8:8 coordination. 

So despite the structure of the halides changing it is the change in ionic radii of the cations that is significantly affecting the experimentally determined lattice energy. 

The change is likely to give rise to a greater distance between ions. 

Furthermore the charge density of the cation is decreasing and reducing the attractive force between cation and anion.

The polarising effect of the cation on the softer anion is not that significant since the difference between the experimentally determined lattice energy and the corresponding theoretical value is very small.

We also note a second trend that is shown from this data.

The charge on a Group 1 metal ion is 1+ and on Group 2 metal ions 2+ and this accounts for the much larger values for the Group 2 chloride lattice energies. 

Let’s look now at changes to the lattice energy of the halides of Group 1:

Lattice energies of the Sodium Halides (kJ.mol^-1)

NaF                918

NaCl               780

NaBr              742

NaI                 705

Again we observe that the lattice energy falls as we go down the group.

The cation radius remains constant but the anion increases in size.

The anion’s charge density is decreasing as each has the same charge ‘spread’ over a greater surface area. 

The effect is to reduce the force of attraction between ions of opposite charge. 

The other effect that can be seen is that the Iodide has the largest difference between experimental and theoretical lattice energies. 

As predicted the softest lowest charge density ion, in this case Iodide I^-, is the most polarisable by a small highly charge dense cation Na+. 

There is a 28kJmol^-1 difference between the two values for the iodide’s lattice energy.

Here is a typical question from a recent British Advanced level examination paper covering some of the ideas discussed in these blogs on lattice energy (they call lattice energy the lattice enthalpy of dissociation.)

1 (a) Define the term lattice enthalpy of dissociation. ...................................................................................................................................... ....................................................................................................................................... (2 marks) 1 (b) Lattice enthalpy can be calculated theoretically using a perfect ionic model. Explain the meaning of the term perfect ionic model. ...................................................................................................................................... ....................................................................................................................................... 1(c) Suggest two properties of ions that influence the value of a lattice enthalpy calculated using a perfect ionic model. Property 1 .......................................................................................................................... ...................................................................................................................................... Property 2 .......................................................................................................................... .......................................................................................................................................

1 (d)

Use the data in the table below to calculate a value for the lattice enthalpy of dissociation for silver chloride.

Enthalpy of atomisation for silver	+289
First ionisation energy for silver	+732
Enthalpy of atomisation for chlorine	+121
Electron affinity for chlorine	– 364
Enthalpy of formation for silver chloride	–127

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 (3 marks)

1 (e) Predict whether the magnitude of the lattice enthalpy of dissociation that you have calculated in part (d) will be less than, equal to or greater than the value that is obtained from a perfect ionic model. Explain your answer.

Prediction compared with ionic model ...............................................................................

Explanation .

The ionic radius of Ag+ is 0.065nm and of the chloride ion Cl^- 0.180nm.

Ionic Bonding (5) Ions and Polarisation

So here is a question for you if you have been following this blog recently.

When the experimentally determined value for the lattice energy is compared with the theoretically calculated values of lattice energy, for some ionic compounds there is a significant difference between the two values.

Why the significant difference?

Let’s first have a look at some data and see if there are any patterns to observe.

Here are the lithium halides

Name	Formula	Theoretical Lattice energy (kJ.mol—1)	Experimental Lattice energy (kJ.mol—1)	Difference (kJ.mol—1)
Lithium Fluoride	LiF	1031	1031	0
Lithium Chloride	LiCl	845	848	3
Lithium Bromide	LiBr	799	803	4
Lithium Iodide	LiI	738	759	21

Here are the silver halides

Name	Formula	Theoretical Lattice energy (kJ.mol—1)	Experimental Lattice energy (kJ.mol—1)	Difference (kJ.mol—1)
Silver Fluoride	AgF	920	958	38
Silver Chloride	AgCl	833	905	72
Silver Bromide	AgBr	816	891	75
Silver Iodide	AgI	778	889	111

The first thing we see is that as the anion increases in size the lattice energy decreases. 

Assuming that these compounds all have the same structure then the influence of the positive ion on the negative ion is decreasing with anion size.

Another thing to note is that these binary compounds all have lattice energies in a similar range around 800 to 900 (kJ.mol^—1)

Thirdly and most importantly, the difference between theoretical and experimental lattice energies increases as the anion increases in size. 

Why is this?

The way the theoretical lattice energy is calculated begins to become less valid as the anion size increases.

Clearly, in the case of the iodides what we assume is being measured is not quite what is being measured at all.

Theoretical values of lattice energy rely on the assumption that ions are either point charges or spherical in shape. 

This spherical model for the shape of the ions is not valid.

Furthermore we find that the properties of the iodides does not fit the ionic model.

For example, the iodides have a significant degree of solubility in organic solvents which would suggest that there is a degree of covalent bonding in these compounds.

How can that be?

One suggestion is that the small, positively charged ions e.g. lithium or silver  polarize the electron clouds of the significantly larger iodide ion. 

Here is a very crude representation of this effect:

Most other diagrams are not much better.

But the point is significant, a region of covalency is created between the ions.

For the first time we see that the “pure” ionic bond or the “pure” covalent bond is a misnomer. 

We have to ask whether they actually exist.

We are going to have to think in terms of partial covalency or partial ionic character.

The ionic or covalent character of a bond will depend on the two atoms in it.

In my next post I’ll discuss this phenomena from the standpoint of a covalent bond that takes on a degree of ionic character.