Lattice energy
In
Lattice energy and lattice enthalpy
The concept of lattice energy was originally applied to the formation of compounds with structures like
) where the ions occupy high-symmetry crystal lattice sites. In the case of NaCl, lattice energy is the energy change of the reaction- Na+ (g) + Cl− (g) → NaCl (s)
which amounts to −786 kJ/mol.[2]
Some chemistry textbooks
The relationship between the lattice energy and the lattice enthalpy at pressure is given by the following equation:
- ,
where is the lattice energy (i.e., the molar internal energy change), is the lattice enthalpy, and the change of molar volume due to the formation of the lattice. Since the molar volume of the solid is much smaller than that of the gases, . The formation of a
Theoretical treatments
The lattice energy of an ionic compound depends strongly upon the charges of the ions that comprise the solid, which must attract or repel one another via
Born–Landé equation
In 1918[5] Born and Landé proposed that the lattice energy could be derived from the electric potential of the ionic lattice and a repulsive potential energy term.[2]
where
- NA is the Avogadro constant;
- M is the Madelung constant, relating to the geometry of the crystal;
- z+ is the charge number of the cation;
- z− is the charge number of the anion;
- e is the elementary charge, equal to 1.6022×10−19 C;
- ε0 is the permittivity of free space, equal to 8.854×10−12 C2 J−1 m−1;
- r0 is the nearest-neighbor distance between ions; and
- n is the Born exponent (a number between 5 and 12, determined experimentally by measuring the compressibility of the solid, or derived theoretically).[6]
The Born–Landé equation above shows that the lattice energy of a compound depends principally on two factors:
- as the charges on the ions increase, the lattice energy increases (becomes more negative),
- when ions are closer together the lattice energy increases (becomes more negative)
Barium oxide (BaO), for instance, which has the NaCl structure and therefore the same Madelung constant, has a bond radius of 275 picometers and a lattice energy of −3054 kJ/mol, while sodium chloride (NaCl) has a bond radius of 283 picometers and a lattice energy of −786 kJ/mol. The bond radii are similar but the charge numbers are not, with BaO having charge numbers of (+2,−2) and NaCl having (+1,−1); the Born–Landé equation predicts that the difference in charge numbers is the principal reason for the large difference in lattice energies.
Closely related to this widely used formula is the Kapustinskii equation, which can be used as a simpler way of estimating lattice energies where high precision is not required.[2]
Effect of polarization
For certain ionic compounds, the calculation of the lattice energy requires the explicit inclusion of polarization effects.
Representative lattice energies
The following table presents a list of lattice energies for some common compounds as well as their structure type.
Compound | Experimental Lattice Energy[1] | Structure type | Comment |
---|---|---|---|
LiF | −1030 kJ/mol | NaCl | difference vs. sodium chloride due to greater charge/radius for both cation and anion |
NaCl | −786 kJ/mol | NaCl | reference compound for NaCl lattice |
NaBr | −747 kJ/mol | NaCl | weaker lattice vs. NaCl |
NaI | −704 kJ/mol | NaCl | weaker lattice vs. NaBr, soluble in acetone |
CsCl | −657 kJ/mol | CsCl | reference compound for CsCl lattice |
CsBr | −632 kJ/mol | CsCl | trend vs CsCl like NaCl vs. NaBr |
CsI | −600 kJ/mol | CsCl | trend vs CsCl like NaCl vs. NaI |
MgO | −3795 kJ/mol | NaCl | M2+O2- materials have high lattice energies vs. M+O−. MgO is insoluble in all solvents |
CaO | −3414 kJ/mol | NaCl | M2+O2- materials have high lattice energies vs. M+O−. CaO is insoluble in all solvents |
SrO | −3217 kJ/mol | NaCl | M2+O2- materials have high lattice energies vs. M+O−. SrO is insoluble in all solvents |
MgF2 | −2922 kJ/mol | rutile | contrast with Mg2+O2- |
TiO2 | −12150 kJ/mol | rutile | TiO2 (rutile) and some other M4+(O2-)2 compounds are refractory materials |
See also
- Bond energy
- Born–Haber cycle
- Chemical bond
- Madelung constant
- Ionic conductivity
- Enthalpy of melting
- Enthalpy change of solution
- Heat of dilution
Notes
References
- ^ ISBN 978-1-4292-1820-7.
- ^ ISBN 0-85404-665-8
- ISBN 978-0-669-41794-4.
- ISBN 9781498754293.
- ISBN 0-19-850870-0
- ^ Cotton, F. Albert; Wilkinson, Geoffrey; (1966). Advanced Inorganic Chemistry (2d Edn.) New York:Wiley-Interscience.
- S2CID 122527743.
- S2CID 250815717.