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

UL=(NA∝Z2e2/4π∈or2o)(1-1/n)

UL=(6.022×1023/mol)(1.74756)(1.6022×10−19)2(1.747558)/

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.

Answer:

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.

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