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Lattice enthalpy can be estimated using Born-Mayer equation given below.
H_L = [(N_A |Z_AZ_B| e²) / (4_od)] {[1 - (d^o/d)]A}
H_L is lattice enthalpy;N_A = 6.022 *10²³ mol^-1 is avogadro number;Z_A and Z_B are charges on cation and anion respectively;
e = fundamental charge = 1.602 * 10^-19C
_o = permittivity of free space = 8.854 * 10^-12 J^-1C²m^-1
d = distance between centres of nearest cation and anion or sum of radii of cation and anion
d^o is constant that depends on compressibility of crystal; for alkali metal halide d^o =34.5 pm =34.5*10^-12m    (1pm=10^-12m)
A = Madelung constant; for NaCl, A = 1.748
For NaCl, |Z_AZ_B| = |+1*-1| =1;
Given, d = 283pm = 283 * 10^-12m;   A = 1.748 (1 pm = 10^-12m)
H_L = [(N_A |Z_AZ_B| e²) / (4_od)] {[1 - (d^o/d)]A}
={[6.022*10²³ *1*(1.602*10^-19)²] / (4 * 3.14* 8.854 * 10^-12 * 283 * 10^-12)}{[1-(34.5*10^-12/283*10^-12)]*1.748}
H_L = 7.53 * 10⁵Jmol^-1
Hence, lattice enthalpy of NaCl is 7.53 * 10⁵Jmol^-1
Answer: (b) 7.53 * 10⁵Jmol^-1 

queen_honey_blossom answered 2 years ago

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