Born-Haber cycles,
and lattice energy
• Mr Michael (Hamzah) Allan (019 254 7120)
KYUEM
5. Chemical energetics (p23)
b) explain and use the term:
iii) lattice energy
(ΔH negative, i.e. gaseous ions to solid lattice)
Definition:
Lattice energy (enthalpy) is the
enthalpy change when
one mole of an ionic crystal (lattice) is
formed from its
constituent gaseous ions
under standard conditions ...
(Ionic) Bond
forming
Crystal
(lattice)
forms
(Ionic) Bond
forming
DHLE = -’ve
DHLE = -x kJmol-1
(Ionic) Bond
--breaking--
DH = +’ve
DH = +x kJmol-1
i.e. DH = - LE
Examples (1/4)….
Na+(g) + Cl-(g)  NaCl(s) DHLE = -781 kJmol-1
gaseous
ions
sign
Standard
state for
the product
Remember
to state the
units
Examples (2/4)….
Potassium superoxide
K+(g) + O2-(g)  KO2(s) DHLE = -1540 kJmol-1
gaseous
ions
sign
Standard
state for
the product
Remember
to state the
units
Examples (3/4) – D.I.Y.
Write a thermochemcial equation for the lattice
energy of barium chloride given that the 0.1
moles of the salt formed (in the appropriate
manner) liberates 235.2 kJ of energy
Answer =
Ba2+(g) + 2 Cl-(g)  BaCl2(s) DHLE = -2352 kJmol-1
Examples (4/4)
Potassium peroxide
2K+(g) + O22-(g)  K2O2(s) DHLE = -1980 kJmol-1
gaseous
ions
sign
Standard
state for
the product
Remember
to state the
units
Points of significance about
Lattice energy
• It assumes a purely IONIC
MODEL
• Can be expressed as an equation
(based on Coulombs law):
𝐿. 𝐸. = 𝑘
𝑄1
𝑄2
𝑑2
k is a constant 8.9875×109 N·m2/C2
Q1 and Q2 are the charges on the ions in coulombs
(each charge = 1.602 × 10-19 C, (can include -ve for anions, + for cations)
d = distance between charges in metres.
5. (e) (iv) Born-Haber cycles (P23)
(including ionization energy and
electron affinity)
Uses of Lattice energy.
• Born-Haber cycles, which shows the step-wise
process of lattice formation from elements.
• Born-Haber cycles have numerous uses, e.g.
predicting the stability of an ionic compound.
Other definitions to learn (1/3)…
• Enthalpy of formation (DHf): 1 mole of a
compound is formed from its elements in
their standard states under standard
conditions.
• Enthalpy of atomization (DHat):
1 mole of gaseous atoms is formed from its
element under standard conditions.
Other definitions to learn (2/3)…
• Ionization energy (DHIE): 1 mole of electrons is
removed from 1 mole of gaseous atoms
under standard conditions.
NOTE: Removing e- from atoms is always an
endothermic process. Energy must be supplied
to overcome the attraction of the e- to the
nucleus. The more e- that are removed, the
more endothermic the process will be.
Other definitions to learn (3/3)…
• Electron affinity enthalpy (DHea):
One mole of electrons is added to one mole
of gaseous atoms under standard conditions.
Note: The first ea’s are almost always negative.
(noble gasses excepted). 2nd and later ea’s are
ALWAYS positive (adding an electron to an
already negative ion = repulsion to overcome)
Standard conditions (1/2).
• To keep all data comparable (therefore easy to
use and easily transferable), measurements
are usually taken under standard conditions.
• 1 atmosphere (101 kPa, 760mmHg, 1 barr)
• 298K (25oC – but must use K temperatures in
equations)
• 1 Molar solution (see electrochemistry etc)
Standard conditions (2/2).
• The symbol DH is accompanied with a
“  ” symbol to donate standard conditions,

i.e. DH
If no symbol is present, assume standard
conditions are used, unless stated otherwise
(and mention them in definitions, e.g. “Standard
enthalpy of atomization”)
Born-Haber cycle for NaCl (step by step)
Na+(g) + Cl (g)
½ Cl2(g)  Cl(g) DHat = +122 kJ mol-1
Cl (g)  Cl -(g) DHea = - 349 kJ mol-1
Na(g) + ½ Cl2(g)
Na+(g) + Cl - (g)
Na(g)  Na+(g) DHIE = +496 kJ mol-1
Na(g) + ½ Cl2(g)
Na+(g) + Cl -(g)  NaCl(s) DHLE = - 787 kJ mol-1
Na(s)  Na(g) DHat = +107 kJ mol-1
Datum line
(zero energy line)
Na(s) + ½ Cl2(g)
Lattice
energy
<<< Elements
Na(s) + ½ Cl2(g)  NaCl(s) DHf = - 411 kJ mol-1
NaCl(s) product
<< Lattice
Practice (revision guide)
Born-Haber cycle for AgCl (step by step)
Ag+(g) + Cl (g)
½ Cl2(g)  Cl(g) DHat = +121 kJ mol-1
Cl (g)  Cl -(g) DHea = - 349 kJ mol-1
Ag(g) + ½ Cl2(g)
Ag+(g) + Cl - (g)
Ag(g)  Ag+(g) DHIE = +731 kJ mol-1
Ag(g) + ½ Cl2(g)
Ag+(g) + Cl -(g)  AgCl(s) DHLE = - 915 kJ mol-1
Ag(s)  Ag(g) DHat = +285 kJ mol-1
Datum line
(zero energy line)
Ag(s) + ½ Cl2(g)
Lattice
energy
<<< Elements
Ag(s) + ½ Cl2(g)  AgCl(s) DHf = - 127 kJ mol-1
AgCl(s) product
<< Lattice
References:
1) Formation of crystal lattice from ions:
http://www.everystockphoto.com/photo.php?imageId=1717296
2) NaHalide LE’s figure:
http://www.chemhume.co.uk/A2CHEM/Unit%202b/9%20Lattice%20enthalpy/Ch9
Latticec.htm
3) The LiF Born Haber cycle :
http://en.wikipedia.org/wiki/Born%E2%80%93Haber_cycle
4) Scaled Born-Haber diagram for NaCl and practice question:
CAMBRIDGE INTERNATIONAL AS AND A LEVEL CHEMISTRY REVISION GUIDE - David
Bevan. Pub: Hodder. ISBN 978 1 4441 1268 9