M+(g) + X–(g) MX(s) H ~ –Elat
This is a difficult measurement - hard to get enough gas phase ions
to achieve big enough heats
Thermochemical cycles: Born-Haber cycles
The sum of the known reactions gives the desired reaction; summing the energies gives the lattice energy. Born-Haber cycles must be set up for each compound to account for the correct states of matter, stoichiometry, etc.
|Na(s)Na(g)||Hsublimation = +107.8 kJ/mole (M atomization)|
|½Br2(l) ½Br2(g)||½Hvaporization = ½(+53.4) = +26.7 kJ/mole|
|½Br2(g) Br(g)||½Hdissociation = ½(+190.2) = +95.1 kJ/mole|
|(Xatomization = ½ Hvaporization + ½Hdissociation)|
|Na(g)Na+(g) + e–||IP = +495.4 kJ/mole|
|Br(g) + e– Br–(g)||–EA = –324.6 kJ/mole|
|Na+(g) + Br–(g) NaBr(s)||–Elat|
|NaBr(s) Na(s) + ½Br2(l)||–Hf = –(–361.4) = 361.4 kJ/mole|
Summing all of these reactions gives nothing so that summing the energies must add to zero:
Hsublimation + ½Hvaporization + ½Hdissociation + IP – EA – Elat – Hf = 0
Elat = +107.8 + 26.7 + 95.1 + 495.4 – 324.6 + 361.4 = 761.8 kJ/mole
Compares to 712.4 kJ/mole from Born-Lande equation
With such large lattice energies, why do ionic compounds dissolve?
Consider another Born-Haber cycle:
|Na+(aq) + Cl–(aq) NaCl(s)||–Hsolvation|
|NaCl(s) Na+(g) + Cl–(g)||Elat|
So that –Hsolvation + Elat + Esolv+ + Esolv– = 0
Hsolvation is usually pretty small - a few 10s of kJ/mol; clearly much different from Elat
This says that Esolv+ + Esolv– ~ Elat
but with opposite signs
Find Esolv in a manner similar to finding Elat. This gives:
r = ionic radius
Z = ionic charge
= solvent dielectric constant
+ or – refers to either cation or anion Z or r
1. Cations are smaller than anions so that r is much smaller for cations than for anions. This means that Esolv for cations is much larger than for anions, i.e., solvation is caused primarily by the cations and not the anions.
2. Solvation energy increases with the square of ionic charge.
3. Solvents with high dielectric constants solvate ionic compounds better;
a dielectric constant near 1 will give near zero solvation energy (water
has ~ 87 at room T)
Deviations from ionic character:
Consider AgCl: has NaCl structure, r0 = 2.77 Å (compared to 2.81 Å for NaCl) yet AgCl is only sparingly soluble in water, mp is ~350 oC lower than NaCl (801 vs 455 oC), Lattice energy is Elat = 907.4 kJ/mol (compared to 786.8 kJ/mol for NaCl).
Why so different?
Polarization effects (covalency): AgCl has more covalent character than NaCl so has less classical ionic character. Consider the limits of bonding: the difference between polarized ionic and polar covalent is merely one of degree. Polarization of "ionic" compounds occurs when the cation is very small and the anion is very large and polarizable. This also can occur in transition metal ions where the d shell electrons are more polarizable than s or p electrons. Transition metals are also more polarizing to anions because of a larger Z*.