Chemistry 401

Measuring Lattice Energies

Direct measurement is possible but experimentally difficult and low accuracy:

M⁺(g) + X^–(g)→ ← MX(s)      ΔH^o

Better to use a thermodynamic cycle; a Born-Haber cycle:

ΔH^o_{atom M} + ΔH^o_{atom X} + IP_M – EA_X – E_lat – ΔH_f^o = 0

solve for E_lat by measuring all the other parameters

NaCl:

S + 0.5D + IP – EA – E_lat – ΔH_f^o = 0 so E_lat = S + 0.5D + IP – EA – ΔH_f^o

E_lat = (+108.4) + 0.5(+241.8) + (+495.4) - (+348.5) - (-410.9) = 787.1 kJ/mol

 

What do we mean by ionic size?

We can only measure the distance between ions experimentally; however, this distance should equal the sum of the cation size and the anion size, so

d_o = r₊ + r_–

r₊ = cation radius, r_– = anion radius

How is the sum apportioned?

Landé used LiI as the starting point: rock salt lattice. Iodides form lattice and are "touching" because of their large size and the small size of Li⁺ which fits completely in the O_h holes (an assumption). For a lattice constant = a, then √2a = 4r_– and a = 2r₊ + 2r_– so that each ionic radius can be found.

Now do the same experiment for other ionic salts without making the "touching" assumption. A whole set of self-consistent ionic radii can then be found.

Results are reasonable but not perfect. Ionic radii depend on coordination number: ions in T_d holes have different radii than ions in O_h holes. When using ionic radii, always need to use a self-consistent set of values and to know the coordination number.