SME
General Chemistry I · Problem type
Lattice energy from a Born–Haber cycle
Use this for “Find the lattice energy of NaCl from these values in kJ/mol: sublimation of Na 107, first ionization energy of Na 496, half the Cl–Cl bond energy 121, electron affinity of Cl −349 and ΔH°f of NaCl −411.”
Diagram
ΔHsub: M(s) + ½X₂ → M(g) + ½X₂, +107 kJ/mol
½D: M(g) + ½X₂ → M(g) + X(g), +121 kJ/mol
IE: M(g) + X(g) → M⁺(g) + X(g), +496 kJ/mol
EA: M⁺(g) + X(g) → M⁺(g) + X⁻(g), −349 kJ/mol
U: M⁺(g) + X⁻(g) → MX(s), −786 kJ/mol
ΔH°f
=
ΔHsub
+
1
2
D
+
IE
+
EA
+
U
ΔH°f = 107 + 121 + 496 + (−349) + (−786)
ΔH°f = −411 kJ/mol
Down the ladder: heat is given off (exothermic).
This is an example. Type your own values to start a new problem.
ΔH°f (kJ/mol)
=
ΔHsub (kJ/mol)
+
IE (kJ/mol)
+
½D (kJ/mol)
+
(
EA (kJ/mol)
)
+
(
U (kJ/mol)
)
Formulas
ΔH°f
=
ΔHsub
+
IE
+
1
2
D
+
EA
+
U
−411 = 107 + 496 + 121 + (−349) + (−786)
Assumptions
•
The salt MX is a metal M with a 1+ charge and a halogen X with a 1− charge, each from its element in its standard state. The cycle makes one mole of MX, each step in kJ/mol.
•
Hess’s law: the path through gaseous atoms and gaseous ions has the same ΔH as forming the salt in one step.
•
U is the energy given off when the gaseous ions come together as the solid, so it is negative. Some books quote the reverse, a positive number.
•
An electron affinity here is the energy change when the atom takes an electron: −349 kJ/mol for Cl, energy given off.
Step-by-step
WE KNOW
ΔHsub = 107 kJ/mol, IE = 496 kJ/mol, ½D = 121 kJ/mol, EA = −349 kJ/mol, ΔH°f = −411 kJ/mol
FIND
lattice energy (U)
Step 1 · Find lattice energy (U)
Use ΔH°f = ΔHsub + IE + ½D + EA + U
Hess’s law: the five steps add to ΔH°f, so take the other four off it. What is left is the ions coming together.
U
=
ΔH°f
−
ΔHsub
−
IE
−
1
2
D
−
EA
U
=
−411
−
107
−
496
−
121
−
(−349)
U
=
−786
kJ/mol
Check
Put the numbers back in. Both sides should match.
−411 = 107 + 496 + 121 + (−349) + (−786) ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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Bonding and molecular geometry
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