Shafieq Ahmad Wagay
B.ed, M.Sc, M.Phil Chemistry
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Topic;- Lattice energy and its calculation.
Class;- Bsc.Ist year chemistry
Lattice energy
The amount of energy released when cations and anions in their gaseous state are brought from infinity to their lattice sites in crystal to form one mole of ionic solid.
A+ (g) + B-(g) -U A+ B-(S)
U = lattice energy with negative sign as energy is released in the process (exothermic reaction)
Lattice energy of an ionic crystal can also be defined as the amount of energy needed to break one mole of the ionic solid into its constituent gaseous ions. Thus
A+ B-(S) +U A+ (g) + B-(g)
U = lattice energy with positive sign as energy is absorbed in the process (endothermic reaction)
Lattice energy is determined by born-lande equation.
U =
Where N0 = avagadro numbe
A = madelung constant
n = born exponent
e = electronic charge
Z+, Z- = charge on ions
ro = inter-ionic distance
Calculation of lattice energy of NaCl by using born-lande equation.
A = 1.74756 Madelung constant
No = 6.022 x 1023 ion per mol-1 Avogadro’s number
Z+ = +1the charge of Na+ ion
Z- = -1 the charge on Cl- ion
e = 1.60218 x 10-19C, the charge on electron
π = 3.14159
ϵo = 8.854 x 10-12C2J-1m-1
ro = 2.814 x 10-10m, the experimental value
n = 8 the average of the value of N
U = 755 KJ mol-1
Since n is always more than 1, U would be negative. Some conclusions of born equation are as under
The higher the charge on cation and anion the greater would be the magnitude of lattice energy and therefore the greater would be the stability of the crystal e.g.
Na+ F- ‹ Mg2+ F2-‹ Mg2+ O2-
Thus lattice energy of Bi-bivalents solids ˃ Bi-univalent solids ˃ Uni-univalent solids.
The lattice energy is inversely proportional to interionic distance. e.g.
Lattice energy of alkali fluorides decreases in the order as given below;
LiF ˃ NaF ˃ KF ˃ RbF ˃ CsF
Size of M+ion Li ˂ Na ˂ K ˂ Rb ˂ Cs ( down the group in a periodic table shell number increases and therefore size of metal ion increases)
Lattice energy of the halides decreases in the order.
LiF ˃ LiCl ˃ LiBr ˃ LiI
For the same anion but different cation the magnitude of lattice energy of ionic solids decreases as the size of cation increases e.g.
LiF ˃ CsF
Lattice energy of the oxides of the oxides of alkaline earth metals also decreases on descending the group.
BeO ˃ MgO ˃CaO ˃ SrO ˃ BaO
Thus in order to get high value of lattice energy, the size of cation or anion should be small electric charge on the cation/anion should be high.
The lattice energy and hence stability of an ionic crystal is directly proportional to the madelung constant which depends upon the coordination number of each ion and the geometric pattern of the ions in the crystal lattice of the crystal.
Table of lattice energy of some ionic solids Uni-Univalent , Uni-Bivalent and Bi-Bivalent
Uni-Univalent / Uni-Bivalent / Bi-BivalentIonic solid / Lattice energy / Ionic solid / Lattice energy / Ionic solid / Lattice energy
LiF / -1033 / CaF2 / 2581 / BeO / 3125
CsF / -748 / CaCl2 / 2254 / MgO / 3932
NaCl / -778 / MgF2 / 2882 / MgS / 3254
NaBr / -752 / MnCl2 / 2525 / ZnO / 4032
LiI / -140
CsI / -795
Madelung constant of some common crystal lattice;
The value of madelung constant is determined by only by the geometry of the lattice and is independent of ionic radius and charge.
Structure / Coordination number / Geomaterical factor A / Conventional factor AaSodium Chloride / 6:6 / 1.74756 / 1.74756
Cesium Chloride / 8:8 / 1.76267 / 1.76267
Zinic blende / 4:4 / 1.63806 / 1.63806
Wurtizite / 4:4 / 1.64132 / 1.64132
Fluorite / 8:4 / 2.51939 / 5.03878
Rutile / 6:3 / 2.408 / 4.816
Β-Cristobalite / 4:2 / 2.298 / 4.597
Corundum / 6:4 / 4.1719 / 25.0312
B. Experimental determination of lattice energy. The Born Haber cycle. Since direct experimental determination of lattice energy is not so easy, these are determined indirectly with the help of a thermo-chemical cyclic process known as Born Habber Cycle. Calculation of lattice energy of NaCl by Born Haber Cycle.
The various steps involved in the formation of NaCl (s) in crystalline state are as follows:
Conversion of metallic sodium into gaseous sodium atom: the amount of energy required for the conversion of one mole of metallic sodium ion into gaseous sodium metal atom is called sublimation energy and is represented by S.
Na(s) + S Na(g)
1 mol S = sublimation energy
Dissosiation of gaseous chlorine molecule into gaseous chlorine atoms; the amount of energy required for the dissociation ofone mole of gaseous chlorine molecule into one mole of gaseous chlorine atoms is called dissociation energy and is represented by D.
Cl2(g) + D 2Cl (g)
1 mol D = dissociation energy
Evidently the energy required to produce one mole of gaseous chlorine atom would be D/2.
Conversion of gaseous sodium atom into gaseous sodium ion; the amount of energy required for the conversion of one mole of gaseous sodium atom into one mole of gaseous sodium ion is called Ionisation energy. this is represented by IE.
Na(g) + IE Na+(g) + e-
1 mol IE = ionization energy
Conversion of gaseous chlorine atom into chloride ions; the amount of energy required for the conversion of one mole of gaseous chlorine atom into one mole of gaseous chloride ion is called electron affinity. It is represented by EA.
Cl (g) + e- Cl-(g) + EA
EA = electron affinity
Combination of gaseous ions to form a solid crystal: this step involves the combination of gaseous sodium and chloride ions to give one mole of sodium chloride crystal. The amount of energy released when one mole of solid crystalline compound is formed from gaseous ions of opposite charges is called lattice energy. it is denoted by U;
Na+(g) + Cl-(g) NaCl(s) + U
The overall change may be represented as;
Na+(g) + 1/2Cl2-(g) NaCl(s) + U
Enthalpy change for this reaction is called enthalpy of formation of sodium chloride and may be denoted by ∆Hf
The various steps may be represented in the form of Born haber cycle as shown below;
According to Hess’s law , the enthalpy of formation of sodium chloride should be the same irrespective of the fact weather it takes place directly in one step or through a number of steps as illustrated above; Hence
∆Hf = S + (1/2)D + IE + EA + U
Using positive signs for energy absorbed and negative signs for energy released. We have Heat of sublimation of sodium (S) = 108.5 KJ mol-1
Dissociation energy of Cl2 (D) = 243.0 KJ mol-1
Ionization energy of sodium (IE) = 495.2 KJ mol-1
Electron affinity of chlorine (EA) = -348.3 KJ mol-1
Enthalpy of formation of NaCl (∆Hf ) = -381.8 KJ mol-1
Substituting the various value in the above equation we get,
-381.8 KJ mol-1 = 108.5 KJ mol-1 +1/2 (243.0) KJ mol-1+495.2 KJ mol-1 - -348.3 KJ mol-1 + U
Lattice energy of sodium chloride, U = - 758.7 KJ mol-1
- Calculation of lattice energy by Kapustinskii equation;
The Kapustinskii equation calculates the lattice energy for an ionic crystal . which is experimentally difficult to determine. It is named after Anatoli-Fedorovich Kapustinskii who gave the formula in 1956 for calculation of lattice energy.
U = K
K= 1.2025 x 10-4j m mol
d = 3.45 x 10-11m
v = the number of ions in empirical formula
Z+ and Z- are the numbers of elementary charge on the cation and anion respectively
r+ and r- are the radii of the cation and respectively.