A number of processes with salts and crystals can be understood by estimating the energies involved — Analytical Chemistry Chemistry Question
Bonding and bond energies
A number of processes with salts and crystals can be understood by estimating the energies involved with a simple ionic model in which the ions have a specific radius and a change equal to an integer number times by elementary charge. This model is used to describe the dissociation of ionic molecules in the gas phase. Such dissociations usually lead directly to neutral atoms, but the dissociation energy can be calculated by assuming a hypothetical reaction path which involves dissociation to free ions, followed by neutralization of the ions. This is the Born-Haber cycle.
The bonding energies, electron affinity and ionization energies of the following diatomic species have been measured:
Bonding energy NaCl = – 464 kJ mol– 1 Electron affinity Cl = – 360 kJ mol– 1
Bonding energy KCl = – 423 kJ mol– 1
Ionization energy Na = 496 kJ mol– 1
Bonding energy MgCl = – 406 kJ mol– 1 1st ionization energy Ca = 592 kJ mol– 1
Bonding energy CaCl = – 429 kJ mol– 1 2nd ionization energy Ca = 1148 kJ mol– 1
Design a Born-Haber cycle for the dissociation of NaCl into neutral atoms and calculate the dissociation energy of NaCl. Assume that the bonding is completely (100 %) ionic in nature.
Model Answer
Born-Haber cycle for the dissociation of NaCl into Na + Cl:
NaCl Na+ + Cl–
Na+ + Cl– Na + Cl
The energy loss in the first step is 464 kJ mol–1.
The energy gain in the second step is – (I.E. of Na + E.A. of Cl) = – 136 kJ mol–1
Overall loss = dissociation energy = 328 kJ mol–1
Design a Born-Haber cycle for the dissociation of CaCl2 into three neutral atoms and calculate the dissociation energy of CaCl2 assuming that the bond length in the triatomic species is 9 % shorter than in the diatomic species.
Model Answer
Born-Haber cycle for the dissociation of CaCl2 into Ca + 2 Cl :
CaCl2 Ca2+ + 2 Cl–
Ca2+ + 2 Cl– Ca + 2 Cl
The (ionic) bond energy of Ca2+Cl– = – 429 × 2 / 0.91 = – 943 kJ mol–1
(The measured value for CaCl is – 429, but the change of Ca is now +2 and the bond length has decreased by a factor of 0.91).
The energy loss in the first step = – (bond energy of CaCl2) = 2 × 942 minus the Cl–Cl repulsion.
The Cl–Cl repulsion is (429 / 2) × (1 / 0.91) = 236 kJ mol-1, so the energy loss in the first step = 1650 kJ mol-1.
The energy gain in the second step is:
– (2 × E.A. of Cl + total I.E. of Ca) = –1020 kJ mol–1.
Dissociation energy into atoms = 630 kJ mol–1.