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Chem 59-
Ionic Bonding
Whereas the term covalent implies sharing of electrons between atoms, theterm ionic indicates that electrons are taken from one atom by another. Thenature of ionic bonding is very different than that of covalent bonding andmust be considered using different approaches. Some aspects to remember: 1. Electronegative atoms will generally gain enough electrons to fill theirvalence shell and more electropositive atoms will lose enough electrons toempty their valence shell. e.g.
Na: [Ne]3s
1
Na
+^ : [Ne]
Ca: [Ar]4s
2
Ca
: [Ar]
Cl: [Ne]3s
2
3p
5
Cl
-^ : [Ar]
O: [He]2s
2
2p
4
O
: [Ne]
2. Ions are considered to be spherical and their size is given by the ionicradii that have been defined for most elements (there is a table in the noteson Atomic Structure). The structures of the salts formed from ions is basedon the close packing of spheres. 3. The cations and anions are held together by electrostatic attraction.
Chem 59-
Ionic Bonding
Because electrostatic attraction is not directional in the same way as is covalentbonding, there are many more possible structural types. However, in the solid state, allionic structures are based on
infinite lattices of cations and anions
. There are some
important classes that are common and that you should be able to identify, including:
CsCl
NaCl
Zinc Blende
Fluorite
Wurtzite
And others…Fortunately, we can use the size of the ions to find out what kind ofstructure an ionic solid should adopt and we will use the structural arrangement todetermine the energy that holds the solid together - the crystal lattice energy,
U
F^ Ca
F
Chem 59-
Ionic Bonding
Some common arrangements for simple ionic salts:
Cesium chloride structure 8:8 coordinationPrimitive Cubic (52% filled)e.g. CsCl, CsBr, CsI, CaS
Rock Salt structure 6:6 coordinationFace-centered cubic (fcc)e.g. NaCl, LiCl, MgO, AgCl
Zinc Blende structure 4:4 coordinationfcce.g. ZnS, CuCl, GaP, InAs
Wurtzite structure 4:4 coordinationhcpe.g. ZnS, AlN, SiC, BeO
Chem 59-
Ionic Bonding
Fluorite structure 8:4 coordinationfcce.g. CaF
, BaCl 2
, UO 2
, SrF 2
2
Anti-fluorite structure 4:8 coordinatione.g. Li
O, Na 2
Se, K 2
S, Na 2
S 2
Rutile structure 6:3 coordinationBody-centered cubic (bcc)(68% filled)e.g. TiO
, GeO 2
, SnO 2
, NiF 2
2
Nickel arsenide structure 6:6 coordinationhcpe.g. NiAs, NiS, FeS, PtSn There are many other common forms of ionic structures but it is more important to beable to understand the reason that a salt adopts the particular structure that it doesand to be able to predict the type structure a salt might have.
You can determine empiricalformula for a structure by countingthe atoms and partial atoms withinthe boundary of the unit cell (thebox). E.g. in the rutile structure,two of the O ions (green) are fullywithin the box and there are fourhalf atoms on the faces for a totalof 4 O ions. Ti (orange) one ion iscompletely in the box and thereare 8 eighth ions at the corners;this gives a total of 2 Ti ions in thecell. This means the empiricalformula is TiO
; the 6:3 ratio is 2
determined by looking at thenumber of closest neighboursaround each cation and anion.
F^ Ca
F
Chem 59-
Ionic Bonding
The energy that holds the arrangement of ions together is called the
lattice energy
,^
U
, o
and this may be determined experimentally or calculated.^ U
o^
is a measure of the energy released as the
gas phase ions
are assembled into a
crystalline lattice. A lattice energy must always be exothermic.E.g.: Na
NaCl
(s)
U
o^
= -788 kJ/mol
NaCl
(s)
Na
(s)
Na
(g)
Na
+(g)
½ Cl
2(g)
Cl
(g)
Cl
H°
ea
H°
d
H°
ie
H°
sub
H°
f
Lattice Energy,
U
o
Lattice energies are determined experimentally using a Born-Haber cyclesuch as this one for NaCl. This approach is based on Hess’ law and can be used todetermine the unknown lattice energy from known thermodynamic values.
Chem 59-
NaCl
(s)
Na
(s)
Na
(g)
Na
+(g)
½ Cl
2(g)
Cl
(g)
Cl
H°
ea
H°
d
H°
ie
H°
sub
H°
f
Lattice Energy,
U
o
Born-Haber cycle
Ionic Bonding
H°
f^
H°
sub
H°
ie
H°
d^
H°
ea
U
o
U
o
U
o^
= -788 kJ/mol
You must use the correct stoichiometry and signs to obtain the correct lattice energy. Practice Born-Haber cycle analyses at: http://chemistry2.csudh.edu/lecture_help/bornhaber.html
Chem 59-
Born-Mayer Equation: U
0
= (e
2
N
z
A
z
B
/ d
A
* (1 – (d
*^
/ d
U
0
= 1390 (z
A
z
B
/ d
A
* (1 – (d
*****^
/ d
in kJ/mol
Kapustinskii equation : U
0
= (1210 kJ Å / mol) * (
n
z
A
z
B
/ d
) * (1 – (d 0
*****^
/ d
Where:e is the charge of the electron,
ε
0
is the permittivity of a vacuum
N
is Avogadro’s number z
A^
is the charge on ion “A”, z
B^
is the charge on ion “B”
d
0
is the distance between the cations and anions (in Å) = r
+^
A
is a Madelung constant d
*^
= exponential scaling factor for the repulsive term = 0.345 Å n
= the number of ions in the formula unit
The equations that we will use to predict lattice energies for crystalline solids arethe Born-Mayer equation and the Kapustinskii equation, which are very similar toone another. These equations are simple models that calculate the attraction andrepulsion for a given arrangement of ions.
Ionic Bonding
Chem 59-
In this case the energy of coulombic forces (electrostatic attraction and repulsion) are:E
coul
= (e
2
π ε
) * (z 0
A^
z
B^
/ d) * [+2(1/1) - 2(1/2) + 2(1/3) - 2(1/4) + ....]
because for any given ion, the two adjacent ions are each a distance of d away, the next two ions are 2
×
d, then 3
×
d, then 4
×
d etc. The series in the square brackets can
be summarized to give the expression:E
coul
= (e
2
π ε
) * (z 0
A^
z
B^
/ d) * (2 ln 2)
where (2 ln 2) is a
geometric factor
that is adeqate for describing the 1-D nature of the
For an Infinite Chain of Alternating Cations and Anions:infinite alternating chain of cations and anions.
Ionic Bonding
The origin of the equations for lattice energies.
The lattice energy
U
0
is composed of both coulombic (electrostatic) energies and an
additional close-range repulsion term - there is some repulsion even between cationsand anions because of the electrons on these ions. Let us first consider the coulombicenergy term:
U
0
= E
coul
+ E
rep
Chem 59-
The numerical values of Madelung constants for a variety of different structures arelisted in the following table. CN is the coordination number (cation,anion) and
n
is the
total number of ions in the empirical formula e.g. in fluorite (CaF
) there is one cation 2
and two anions so
n
= 1 + 2 = 3. lattice
Ionic Bonding
A
CN
stoich
A
/^
n
CsCl
(8,8)
AB
NaCl
(6,6)
AB
Zinc blende
(4,4)
AB
wurtzite
(4,4)
AB
fluorite
(8,4)
AB
2
rutile
(6,3)
AB
2
CdI
2
(6,3)
AB
2
Al
O 2
3
(6,4)
A
B 2
3
Notice that the value of A is fairly constant for each given stoichiometry and that thevalue of A/
n
is very similar regardless of the type of lattice.
Chem 59-
Ionic Bonding
This is the Born-Mayer equation, when the constants are evaluatedwe get the form of the equation that we will use:
U
0
= 1390 (z
A^
z
B
/ d
A
*** (1 - (d**
*****^
/ d
in kJ/mol
Note: d
*^
is the exponential scaling factor for the repulsive term and a
value that we will use for this is
0.345 Å
If only the point charge model for coulombic energy is used to estimate the lattice energy (i.e. if U
0
= E
coul
) the calculated values are much higher than the experimentally measured lattice
energies.E.g. for NaCl (r
Na+
= 0.97Å, r
Cl-
= 1.81Å):
U
0
= 1390 (z
A^
z
B^
/ d
A
= 1390 ((1)(-1)/2.78) * (1.748) kJ/mol = - 874 kJ/mol
But the experimental energy is -788 kJ/mol. The difference in energy is caused by the repulsionbetween the electron clouds on each ion as they are forced close together. A correction factor,E
rep
, was derived to account for this.
E
rep
= - (e
2
π ε
) * (z 0
A^
z
B^
d*/ d
2 ) * A
and since
E
coul
= (e
2
π ε
) * (z 0
A^
z
B^
/ d) *
A
the total is given by
U
0
= (e
2
π ε
) * (z 0
A^
z
B^
/ d
A
