Ignoring the precise
details of the lattice structure, the Coulombic force of attraction
(F) between two
ions is proportional to the charge on the cation (c+)
x charge on the anion (c–)
divided by the distance between the centres of the ions (r)
squared, so
F
c+ x c–
/ d2
Known as Coulomb's inverse–square
law.
Note that
d = r+ + r–
(total of the two ionic radii)
The factors affecting the values of
lattice enthalpies were briefly discussed in
section 2.1c.
BUT, here I want to quote
and discuss a
comparison between experimental lattice enthalpies and theoretically
calculated lattice enthalpies.
By comparing
experimental lattice
enthalpies calculated from Born–Haber cycles with those from theoretical calculations based on a
perfect ionic model, the
difference in values provide evidence for some covalent character in
ionic compounds.
Despite the evidence of a 'little'
covalent character, most 'ionic compounds' have sufficient ionic
character to produce a crystal lattice where the ions are
essentially in the same positions in the lattice as they would be if it
was perfectly ionic (as in the diagram of sodium chloride above right).
I've collected some data from my
textbook library and come up with some good sets of data to make the
point. I've quoted the difference in ΔHθLE
and then quoted the theoretically calculated value as a percentage of
the experimentally derived value from a Born – Haber cycle (like those
on this page). I'm afraid data varies from book to book, so I've tried
to judge a consensus!
Considering differences in
electronegativity also fit in with the idea that covalent character
influences the lattice enthalpy.
Generally speaking the
experimental lattice enthalpies are greater than the theoretical
lattice enthalpies, the latter are calculated from the accurately
known crystal structures.
The
differences tend to increase with an increase in the small, but
influential contribution of covalent character to the metal -
non-metal bond.
The
increase experimental lattice enthalpies is attributed to the
covalent character contributing an extra component to the total bond
strength.
(compiled from various
data sources, which can vary!)
|
Ionic compound |
formula |
ΔHθLE
Born – Haber experimental |
ΔHθLE
theoretical
calculation |
ΔHθLE
Difference (theoretical as a % of the experimental) |
Electronegativity difference,
non–metal – metal, from the Pauling scale |
Comments on whether, or not, the ΔHθLE
data indicates covalent character in the crystal |
|
lithium
fluoride |
LiF |
1037 |
1033 |
4 (99.6%) |
4.0 –1.0 =
3.0 |
Little
evidence of covalent character until LiBr and LiI with the
larger anion. BUT clear trend of increasing covalent character,
however small, in covalent character down the group 7/17 halides,
note the decrease in electronegativity difference too. |
|
lithium
chloride |
LiCl |
852 |
845 |
7 (99.2%) |
3.0 – 1.0 =
2.0 |
|
lithium
bromide |
LiBr |
815 |
798 |
17 (97.9%) |
2.8 – 1.0 =
1.8 |
|
lithium
iodide |
LiI |
761 |
740 |
21 (97.2%) |
2.5 – 1.0 =
1.5 |
|
caesium
fluoride |
CsF |
750 |
748 |
2 (99.7%) |
4.0 – 0.7 =
3.3 |
Not a clear
trend, CsF highly ionic, the rest showing a trace of covalent
character with a significantly smaller electronegativity
difference. |
|
caesium
chloride |
CsCl |
676 |
652 |
24 (96.4%) |
3.0 – 0.7 =
2.3 |
|
caesium
bromide |
CsBr |
654 |
632 |
22 (96.6%) |
2.8 – 0.7 =
2.1 |
|
caesium
iodide |
CsI |
620 |
601 |
19 (96.9%) |
2.5 – 0.7 =
1.8 |
|
silver
fluoride |
AgF |
953 |
920 |
33 (96.5%) |
4.0 – 1.9 =
2.1 |
All the
silver halides show some covalent character. A clear trend of
increasing covalent character down group 7/17 as the halide ion
radius increases and can be more easily polarised by the Ag+
ion drawing the electron cloud of the anion towards itself, thus
creating the covalent character. The decreasing
electronegativity difference fits the trend too |
|
silver
chloride |
AgCl |
903 |
832 |
71 (92.1%) |
3.0 – 1.9 =
1.1 |
|
silver
bromide |
AgBr |
895 |
815 |
80 (91.1%) |
2.8 – 1.9 =
0.9 |
|
silver
iodide |
AgI |
882 |
777 |
105 (88.1%) |
2.5 – 1.9 =
0.6 |
|
sodium chloride |
NaCl |
781 |
777 |
4 (99.5%) |
3.0 – 0.9 = 2.1 |
Very highly ionic, big difference in
electronegativity. |
|
potassium bromide |
KBr |
679 |
667 |
12 (98.2%) |
2.8 – 0.8 = 2.0 |
A trace of covalent character, but pretty
ionic, big difference in electronegativity. |
|
calcium oxide |
CaO |
3607 |
3519 |
88 (97.6%) |
3.5 – 1.0 = 2.5 |
Little covalent character, perhaps more
than sodium chloride because of more highly charged cation?, but
pretty ionic with a large electronegativity difference |
|
calcium fluoride |
CaF2 |
2611 |
2586 |
25 (99.0%) |
4.0 – 1.0 = 3.0 |
A big electronegativity difference, very
ionic, little evidence of covalent character |
|
cadmium iodide |
CdI2 |
2435 |
1986 |
449 (81.6%) |
2.5 – 1.7 = 0.8 |
Large discrepancy suggesting a fair
degree of covalent character in the bonding and note the small
difference in electronegativity, from which you should predict
some covalent character anyway. |
