9.3 Bonding in crystalline solids  (Page 3/9)

The energy per ion pair needed to separate the crystal into ions is therefore

This is the dissociation energy    of the solid. The dissociation energy can also be used to describe the total energy needed to break a mole of a solid into its constituent ions, often expressed in kJ/mole. The dissociation energy can be determined experimentally using the latent heat of vaporization. Sample values are given in the following table.

Thus, we can determine the Madelung constant from the crystal structure and n from the lattice energy. For NaCl, we have $r_0=2.81\text{Å}$ , $n\approx 8$ , and $U_{\text{diss}}=7.84\text{eV/ion pair}\text{.}$ This dissociation energy is relatively large. The most energetic photon from the visible spectrum, for example, has an energy of approximately

Because the ions in crystals are so tightly bound, ionic crystals have the following general characteristics:

1. They are fairly hard and stable.
2. They vaporize at relatively high temperatures (1000 to 2000 K).
3. They are transparent to visible radiation, because photons in the visible portion of the spectrum are not energetic enough to excite an electron from its ground state to an excited state.
4. They are poor electrical conductors, because they contain effectively no free electrons.
5. They are usually soluble in water, because the water molecule has a large dipole moment whose electric field is strong enough to break the electrostatic bonds between the ions.

The dissociation energy of salt

Strategy

Solution

where M is the mass of one mole of salt, $N_{\text{A}}$ is Avogadro’s number, and $r_0$ is the equilibrium separation distance. The factor 2 is needed since both the sodium and chloride ions represent a cubic volume $r_0^3$ . Solving for the distance, we get

or

The potential energy of one ion pair $\left({\text{Na}}^{+}{\text{Cl}}^{\text{–}}\right)$ is

where $\alpha$ is the Madelung constant, $r_0$ is the equilibrium separation distance, and n is the repulsion constant. NaCl is FCC, so the Madelung constant is $\alpha =1.7476.$ Substituting these values, we get