Lattice Energy Formula And Sample Sums

Lattice Energy Formula :

Equilibrium value of the lattice energy UL (µl) in milliliter is equal to the product of Avogadro’s constant NA(6.022 × 1022) , Madelung constant ∝(r/s2) in radius per second square, Cation and anion charge Z2 (cl) in  ions charge, Electron charge e2 is divided by Permittivity of free space  ∈o(8.8541878128(13)×10−12 F⋅m−1 ) in farad per meter, Closest ion distance r 2o (m/s)  in meter per second and multiply by Born Exponent n. Hence lattice energy formula has been written as,

UL (µl) = (NA(6.022 × 1022)(r/s2)Z2 (cl)  e2 /

4π∈o(8.8541878128(13)×10−12 F⋅m−1) r 2o(m/s)) (1-1/n)

NA →Avogadro’s constant (6.022 × 1022)

α → Madelung constant in  r/s2

e →Electron charge in (1.6022 × 10-19C)

Zand Z– →Cation and anion charge in cl  and Na+

ϵo → Permittivity of free space  in  8.8541878128(13)×10−12 F⋅m−1

n → Born Exponent

r0 →Closest ion distance in cm

U→equilibrium value of the lattice energy  in (µl),

Sample Examples :

Example 1:

Calculate the Lattice energy of NaCl by using

Born-Landed equation

Given :

α = 1.74756
Z = -1 (the Cl ions charge)
Z= +1 (the charge of the Na+ ion)
NA = 6.022 × 1023 ion pairs mol-1

C = 1.60210 × 10-19C (the charge on the electron)
π = 3.14159
εo  = 8.854185 × 10-12 C2 J-1 m-1
ro = 2.82× 10-12 m, the sum of radii of  Born-Landed equation.

Na+ and Cl
n = 9.1 the average of the values for Na+ and Cl.

Solution :

Using the Born –Landed equation



4×3.14159 (8.854×10−10)(2.82×10−12)(1–1/9.1)

UL = –756   kJ per mol

Therefore lattice energy for NaCl is 756 KJ per mol.

Example 2 :

The lattice energy of AgBr is 795 KJ mol-1. Predict the Lattice energy of the isomorphous Agl using Born-Landed equation . the numeric of rc+ra is 221 pm for AgBr and 242 pm for Agl.


if the only variance between AgBr and Agl were in the size of the anion, one would expect the lattice energies to be relational to the inverse ratio of rc+ra. hence forth we expect the lattice energy of Agl to be,

=(795) (221/242)

=425 J mole-1.

Leave a Comment