15.1  ENERGY CYCLES
THE BORN-HABER CYCLE AND ENTHALPY OF FORMATION
DEFINITIONS:
i) Born-Haber Cycle  a series of reactions that can be combined to determine the standard enthalpy of
_______________of an______________ compound; an application of ____________ law
ii) Standard conditions  reactants and products in their normal state at _________ kPa and ______ K.
iii) Lattice enthalpy (ΔH°lat)  the standard enthalpy change that occurs on the formation of ______ mole of
_____________ ions from the ________________ ionic lattice; this is an ______________ process. Lattice enthalpy
values can be found in Section 18 of the Data Booklet. [MX(s)  M+(g) + X-(g) ΔH°lat > 0]
iv) Enthalpy of atomization (ΔH°at) the standard enthalpy change that occurs on the formation of _____ mol of
separate gaseous ___________ of an element in its __________________ state.
M(s)  M(g) ΔH°at > 0
½X2(g)  X(g) ΔH°at > 0
**ΔH°at for diatomic element is ½ the average bond enthalpy value for that bond.
e.g., B.E(O=O bond) = 498 kJ mol-1 (from Data booklet) ; ΔH°at = 249 kJ mol-1
O2(g) + 498 kJ  O(g) + O(g) ΔH°BE = ________ kJ mol-1
½ O2(g) + 249 kJ  O(g)
ΔH°at = _________ kJ mol-1
v) Ionization energy ΔH°IE  the standard enthalpy change that occurs on the removal of 1 mol of ______________
from 1 mol of atoms or positively charged _______ in the _____________ phase.
M(g)  M+(g) + eΔH°IE#1 > 0
M+(g)  M2+(g) + e- ΔH°IE#2 > 0
vi) Electron affinity ΔH°EA  the standard enthalpy change that occurs on the _______________ of 1 mol of electrons
to 1 mol of atoms in the __________ phase
M(g) + e-  M-(g) +
ΔH°EA < 0
*ΔH°EA is typically negative, but there are exceptions.
PRACTICE: CONSTRUCTING AND APPLYING BORN-HABER CYCLES
1. Construct a Born-Haber cycle (on a separate sheet of paper) for each of the following:
(i) potassium bromide, KBr
(ii) magnesium oxide, MgO
2. Illustrate how the Born-Haber cycle for potassium bromide is an application of Hess’s Law.
3. Construct a Born-Haber cycle for barium chloride, BaCl2, then, use the data below to calculate a value of the electron
affinity of the chlorine atom.
Data:
Enthalpy of atomization of barium ----------------- +175 kJ mol-1
Enthalpy of atomization of chlorine --------------- +121 kJ mol-1
First ionization energy of Ba -----------------------+502 kJ mol-1
Second ionization energy of Ba -------------------+966 kJ mol-1
Lattice enthalpy of BaCl2 --------------------------+2018 kJ mol-1
Enthalpy of formation of BaCl2 --------------------860 kJ mol-1
MAIN FACTORS AFFECTING THE MAGNITUDE OF LATTICE ENTHALPY VALUES:
FACTOR #1: ________________of ions making up the ionic lattice:
 ____________ charge on the ions = ↑ electrostatic attraction between them
FACTOR #2: _________of the ions involved:
 _______________ ionic radius = ↓ distance between ions = ↑ electrostatic attraction between them
Examples:
Compound ΔH°lat /
kJ mol-1
MgO
3795
NaCl
KBr
Variation in charge and ionic
radius compared with NaCl
ionic charge
769
671
ionic radius
ENTHALPY CYCLES/CHANGES INVOLVING SOLUTIONS
Definitions:
(i) Standard enthalpy of solution, ΔH°sol  the change in enthalpy when 1 mol of substance is _______________ in a
large exess of pure solvent; Enthalpies of solution can have positive OR negative values.
e.g.,
NH4Cl(s)  NH4+(aq) + Cl-(aq)
LiBr(s)  Li+(aq) + Br-(aq)
ΔH°sol = +14.78 kJ mol-1
ΔH°sol = -48.83 kJ mol-1
(ii) Enthalpy change hydration, ΔH°hyd  enthalpy change of hydration for an ______ is the enthalpy change when 1
mol of the ______________ ion is added to _____________ to form a dilute solution; Enthalpies of hydration are
ALWAYS _______________ values.
*Use the term “solvation” in place of hydration when the solvent isn’t water.
e.g.,
Na+(g)  Na+(aq)
OH-(g)  OH-(aq)
ΔH°hyd = -424 kJ mol-1
ΔH°hyd = -519 kJ mol-1
PRACTICE:
1. Construct an enthalpy cycle (on a separate sheet of paper) representing the dissolution of sodium hydroxide, NaOH.
2. Construct an enthalpy cycle representing the dissolution of barium chloride, BaCl2, and then use the following data to
calculate the enthalpy of solution of barium chloride.
BaCl2(s)  Ba2+(g) + 2Cl-(g)
Ba2+(g)  Ba2+(aq)
Cl-(g)  Cl-(aq)
ΔH°lat = +2069 kJ mol-1
ΔH°hyd = -1346 kJ mol-1
ΔH°hyd = -359 kJ mol-1