Potassium chloride is used as a pet-safe deicer. When investigating such applications, it is useful to understand the thermodynamic properties of the materials you are using. Devise and use a Born–Haber cycle to calculate the lattice enthalpy of potassium chloride.

ANTICIPATE A glance at Table 4E.1 shows that typical lattice enthalpies of ionic solids are close to 1000 kJ · mol^–1, so you should expect a similar result for KCl.

PLAN Find the enthalpy change for each step, starting with the pure elements: atomize them to form gaseous atoms (steps a and b), ionize the atoms to form gaseous ions (steps c and d), allow the ions to form an ionic solid (this is the negative of the lattice enthalpy, –ΔH_L), and then convert the solid back into the pure elements (step e). Steps c and d require ionization enthalpies for cation formation and electron-gain enthalpies for anion formation. Provided you are not seeking high precision, use ionization energies and electron affinities, being careful with the sign of the latter. Solve for the lattice enthalpy, ΔH_L, on the basis that the sum of the enthalpy changes for the complete cycle is zero.