Use the data given below to construct a Born-Haber cycle to determine the electron affinity of Br. A) -885 kJ mol^-1 B) -325 kJ mol^-1 C) +367 kJ mol^-1 D) -464 kJ mol^-1 E) +246 kJ mol^-1

Question

Quizplus · Accepted Answer

The Born-Haber cycle for the formation of Br- is as follows:

1. Br (g) → Br (s) ΔHsub = +72 kJ/mol
2. Br (s) → Br• (g) First ionization energy = +1142 kJ/mol
3. Br• (g) → Br- (g) Electron affinity = x kJ/mol (what we're trying to find)
4. Br (s) + 1/2 Cl2 (g) → BrCl (s) ΔHf = -92 kJ/mol
5. Na (s) → Na+ (g) + e- First ionization energy = +496 kJ/mol
6. Na+ (g) + Cl- (g) → NaCl (s) Lattice energy = -787 kJ/mol

The sum of these steps must equal the energy released in the formation of Br- from its constituent elements:

Br (g) + e- + 1/2 Cl2 (g) + Na (s) → Na+ (g) + Br- (s) + Cl- (g) ΔHf = -364 kJ/mol

Using Hess's Law, we can write:

ΔHf = -364 kJ/mol = ΔH1 + ΔH2 + x + ΔH4 + ΔH5 + ΔH6
ΔH1 = +72 kJ/mol (sublimation)
ΔH2 = +1142 kJ/mol (ionization of Br)
ΔH4 = -92 kJ/mol (formation of BrCl)
ΔH5 = +496 kJ/mol (ionization of Na)
ΔH6 = -787 kJ/mol (lattice energy of NaCl)

Simplifying this equation, we get:

-364 kJ/mol = +621 kJ/mol + x - 879 kJ/mol
x = -325 kJ/mol

Therefore, the electron affinity of Br is -325 kJ/mol, which corresponds to choice B.

Use the Data Given Below to Construct a Born-Haber Cycle