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Section: 12 | Lattice Energies |
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John R. Rumble, ed., CRC Handbook of Chemistry and Physics, 103rd Edition (Internet Version 2022), CRC Press/Taylor & Francis, Boca Raton, FL.
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LATTICE ENERGIES

H. D. B. Jenkins and H. K. Roobottom

THERMOCHEMICAL CYCLE AND CALCULATED VALUES

Table 1 contains calculated values of the lattice energies (total lattice potential energies), UPOT, of crystalline salts, MaXb. UPOT is expressed in units of kilojoules per mole, kJ mol–1. M and X can be either simple or complex ions. Substances are arranged by chemical class.

Also listed in the table is the lattice energy, UPOTBFHC, obtained from the application of the Born–Fajans–Haber cycle (BFHC) described below, using the “Standard Thermochemical Properties of Chemical Substances” table in Section 5 of this Handbook, References 1 through 4, and certain other data that are given in Table 3 below.

The lattice enthalpy, ∆HL, is given by the cycle:

thermochemical cycle

where (ss) is the standard state of the element concerned.

The lattice enthalpy, ∆HL, is obtained using the equation:

ΔHL = aΔfH°(Mb+,g)+bΔfH°(Xa–,g) –ΔfH°(MaXb,c)

and is further related to the total lattice potential energy, UPOT, by the relationship:

ΔHL=UPOT+[a(nM2 −2)+b(nX2 −2)]RT

where nM and nX equal 3 for monatomic ions, 5 for linear polyatomic ions and 6 for polyatomic non-linear ions.

METHOD OF ESTIMATION OF VALUES NOT TABULATED

In cases where the lattice energy is not tabulated and we want to furnish an estimate, then the Kapustinskii equation (Ref. 5) can be used to obtain a value (in kJ mol–1):

UPOT=121.4zazbv(ra+rb)(1−0.0345(ra+rb))

where za and zb are the moduli of the charges on the v ions in the lattice and ra and rb (in nm) are the thermochemical radii given in Table 2. The ra for metal ions is taken to be the Goldschmidt radius (Ref. 6).

To cite an example, if we wish to estimate the lattice energy of the salt [NH4+][HF2–] using the above procedure, we see that Table 2 gives the thermochemical radius (ra) for NH4+ to be 0.136 nm and that for HF2– (rb) to be 0.172 nm. The lattice potential energy is then estimated to be 700 kJ mol–1 compared with the calculated value of 705 kJ mol–1 and the Born–Fajans–Haber cycle value of 658 kJ mol–1.

References

  1. Wagman, D. D., Evans, W. H., Parker, V. B., Schumm, R. H., Halow, I., Bailey, S. M., Churney, K. L., and Nuttall, R. L., The NBS Tables of Chemical Thermodynamic Properties, J. Phys. Chem. Ref. Data, Vol. 11, Suppl. 2, 1982.
  2. Chase, M. W., Davies, C. A., Downey, J. R., Frurip, D. J., McDonald, R. A., and Syverud, A. N., JANAF Thermochemical Tables, Third Edition, J. Phys. Chem. Ref. Data, Vol. 14, Suppl. 1, 1985.
  3. Lias, S. G., Bartmess, J. E., Liebman, J. F., Holmes, J. L., Levin, R. D., and Mallard, W. G., Gas-Phase Ion and Neutral Thermochemistry, J. Phys. Chem. Ref. Data, Vol. 17, Suppl. 1, 1988.
  4. Jenkins, H. D. B., and Pratt, K. F., Adv. Inorg. Chem. Radiochem. 22, 1, 1978. [https://doi.org/10.1016/S0065-2792(08)60079-5]
  5. Kapustinskii, A. F., Quart. Rev. 10, 283, 1956. [https://doi.org/10.1039/qr9561000283]
  6. Goldschmidt, V. M., Skrifter Norske Videnskaps-Akad. Oslo, I, Mat.-Naturn. Kl, 1926. See also Dasent, W. E., Inorganic Energetics, 2nd ed., Cambridge University Press, 1982.
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TABLE 1. Lattice Energies of Crystalline Salts



SubstanceCalc. UPOT/kJ mol-1UPOTBHFC/kJ mol-1
Continued on next page...
Acetates
Li(CH3COO)843
Na(CH3COO)828807
K(CH3COO)749726
Rb(CH3COO)715
Cs(CH3COO)682
Acetylides
CaC229112902
SrC227882782
BaC226472652
Azides
LiN3861875
NaN3770784
KN3697
RbN3674691
CsN3665674
AgN3854910
TlN3689742
Ca(N3)221862316
Sr(N3)220562187
Ba(N3)22021
Mn(N3)224082348

  • aEstimated


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