1.2
Born–Haber cycles
ASSIGNMENT 1: BORN–HABER CYCLES AND NONEXISTENT COMPOUNDS (PS 1.1, 3.2, MS 0.0, 2.1)
(a) (b) Figure A1 (a) Powdered magnesium chloride; (b) crystals of magnesium chloride hexahydrate
Anhydrous magnesium chloride (Figure A1) has the formula MgCl2(s). No other chlorides of magnesium such as MgCl(s) or MgCl3(s) are known. Why? Born–Haber cycles may be used to work out the enthalpy of formation of unknown ionic compounds. The data required are:
›› the standard enthalpies of atomisation of the elements
›› successive ionisation energies for the metal ›› successive electron affinities for the nonmetal ›› the lattice enthalpy, estimated from models, of the hypothetical compound.
The sign and magnitude of the calculated enthalpy of formation are a good indication of the stability of a compound. Stable compounds usually have high negative values. For example, Mg(s) + Cl2(g) → MgCl2(s) ΔfHϴ[MgCl2(s)] = −642 kJ mol−1 In other words, stable compounds have enthalpies of formation that are highly exothermic.
Mg(s) → Mg(g)
ΔatHϴ = +148 kJ mol−1
Mg(g) → Mg+(g) + e−
1st Ei = +738 kJ mol−1
Mg+(g) → Mg2+(g) + e−
1st Ei = +1451 kJ mol−1
Mg2+(g) → Mg3+(g) + e−
1st Ei = +7733 kJ mol−1
½Cl2(g) → Cl(g)
ΔatHϴ = +121 kJ mol−1
Cl(g) + e− → Cl−(g)
1st Eea = −349 kJ mol−1
Mg+(g) + Cl−(g) → MgCl(s)
ΔlattHϴ = −815 kJ mol−1 (estimated from models)
Mg+(g) + 3Cl−(g) → MgCl3(s)
ΔlattHϴ = −5540 kJ mol−1 (estimated from models)
Table A1
Questions A1. Using the thermodynamic data provided, calculate the standard enthalpy of formation of these two hypothetical compounds:
(a) MgCl(s)
(b) MgCl3(s).
A2. Explain why MgCl3(s) has never been made. A3. During the reaction of magnesium with chlorine it seems likely that MgCl may form, but immediately disproportionate to MgCl2 and Mg: 2MgCl(s) → MgCl2(s) + Mg(s)
Use Hess’s law to determine the enthalpy change for this reaction.
Unstable compounds have enthalpies that are highly endothermic.
KEY IDEAS
›› The formation of compounds involves endothermic and exothermic reactions.
›› An endothermic change occurs when forces must
be overcome, e.g. during atomisation, ionisation or breaking up a lattice.
›› An exothermic change occurs when forces of attraction operate, e.g. in the case of electron affinity or forming an ionic lattice.
›› Born–Haber cycles can be used to calculate an unknown enthalpy; usually this is the lattice enthalpy.
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