Question

Estimate the lattice energy, ?U, for NaF if the ionic radii for K+ and F– are 138.0 pm and 133.0 pm, respectively.

Use the Kapustinskii equation.

Answer 1

Kapustinskii equation : U = K v [z⁺] [z^-] /r⁺ + r^- (1-(d/r⁺ + r^-))

r⁺ = 138 pm and r^- = 133 pm

[z⁺] and [z^-] = +1 and -1

v = number of ions = 2

K = 1.202 x 10^-4 J.m/mol

d = 3.45 x 10^-11 m

U = 1.202 x 10^-4 J.m/mol x 2 x 1 x 1(/138 + 133) ) 10^-12 m² ( 1-(3.45 x 10^-11 m/138 + 133 ) 10^-12 m²)

U = 2.404x 10⁸/271) (1- (34.5/271 )

U = 0.00887 X 10⁸ (1-0.127)

U = 887000 x 0.873 = 774351 J/mol