Given the tabulated data, what is the lattice energy of crystalline calcium chloride? heat of sublimation for calcium +178 kJ/mol
First ionization energy for calcium +590 kJ/mol
Second ionization energy for calcium +1145 kJ/mol
Heat of dissociation for chlorine +122 kJ/mol(Cl)
Electron affinity for chlorine -349 kJ/mol
Heat of formation for calcium chloride -796 kJ/mol

Question

Quizplus · Accepted Answer

The lattice energy formula is:
Lattice energy = k(Q1Q2)/d
where k is Coulomb's constant, Q1 and Q2 are the charges of the ions (in multiples of e, the electron charge), and d is the distance between the ions in the crystal lattice. We need to find the charges of Ca and Cl ions.

Ca has lost two electrons, so its charge is +2e.
Cl has gained one electron, so its charge is -e.

The distance between the ions is not given, so we need to use the Born-Haber cycle to relate the lattice energy to other thermodynamic quantities. The Born-Haber cycle for CaCl2 is:

Ca(s) + Cl2(g) -> CaCl2(s) ΔHf = -796 kJ/mol (formation)
Ca(s) -> Ca(g) ΔHsub = +178 kJ/mol (sublimation)
Ca(g) -> Ca+(g) + e- ΔH1 = +590 kJ/mol (first ionization)
Ca+(g) -> Ca2+(g) + e- ΔH2 = +1145 kJ/mol (second ionization)
Cl2(g) -> 2 Cl(g) ΔHdissoc = +244 kJ/mol (dissociation)
Cl(g) + e- -> Cl-(g) ΔH = -349 kJ/mol (electron affinity)

Using these values, we can calculate the lattice energy via the cycle:

ΔHf = ΔHsub + ΔH1 + ΔH2 + ΔHdissoc + k(Q1Q2)/d - ΔH
where k = 8.987 x 109 N m2/C2 and e = 1.602 x 10-19 C.

Substituting the values given, we get:

-796 = 178 + 590 + 1145 + 244 + 8.987E9(2e)(-e)/d - (-349)
-796 = 2150 + 1.794E10/d
d = 4.34 x 10-10 m

Then we can calculate the lattice energy:

Lattice energy = k(Q1Q2)/d = 8.987E9(2e)(-e)/(4.34E-10) = -2255 kJ/mol.

Therefore, the answer is C, -2255 kJ/mol.

Given the Tabulated Data, What Is the Lattice Energy of Crystalline