Question

1. Calculate AHL of Ag2S using each of the following methods. You will need to look up ionization energies, AHEA, AH and radii for all of the species involved. Cite your sources. AH; (Ag2S) = -31.8 kJ/mol a. Born Haber Cycle b. Born Equation c. Born Mayer Equation d. Kapustinskii Equation e. Compare the values obtained from the three calculation methods (b-d). Which is the most accurate? Which is the easiest calculation to carry out? f. Compare AH (calc) to AH (expt). Is this a case of purely ionic bonding or is there a significant contribution from covalent bonding? How did you come to this conclusion?

Assume that Ag2S forms a rutile structure with A = 2.406

Answer 1

Fig. Born Haber cycle for Ag₂S

-∆H_f⁰ + 2∆H_sub(Ag) + ∆H_{sub(S) +} 2I.E_Ag+ + E.A₁ + E.A₂ +∆H_L = 0

∆H_L = ∆H_f⁰ - 2∆H_sub(Ag) - ∆H_sub(S) - 2I.E_Ag+ - E.A₁ - E.A₂

∆H_L = -31.8 -2(255) -9.8 – 2(731)- 200+ 456

∆H_L = -31.8-510-9.8- 1462- 200-456

∆H_L = -2669.6 KJ/mol

2. From Born-Lande equation we have,

∆G = -ANz2e24πϵor(1- -1n)

∆G = - 2.4 x (6.023 x10+²³) x 1x 2 x(1.6x10^-19)²4 x 3.14 x 8.854x 10-12 x 2.406x 10-10X(1-110)

∆G = - 2489.5 KJ/mol

3. From Born-Mayer equation we have,

∆G = -NMz2e24πϵr(1- -34.5 x 10-12r)

∆G = -6.023 x10+²³x 2.4 x 1x 2 x(1.6x10^-19)²4 x 3.14 x 8.854 x 10-12 x 2.406x 10-10X(1-34.5 x 10-122.406x 10-10)

∆G = - 2370 KJ/mol

4. From Kaputinskii equation we have,

U_L = 1.202X10^-4 nZ₊Z_-r _{1-34.5 x 10-12r}

U_{L =} - 2568 KJ/mol

Method	Lattice energy (KJ/mol)
Born Haber Cycle	-2669.6
Born Lande equation	-2489.5
Born Mayer equation	- 2370
Kaputinskii Equation	-2568

Born Haber cycle is most accurate among these methods because it considers all the possible physical and chemical changes during the formation of the lattice.

Kaputinskii method is the easiest to carry out.

6. Silver sulfide is the inorganic compound with the formula Ag₂S. A dense black solid, it is the only sulfide of silver. It is useful as a photosensitizer in photography. It constitutes the tarnish that forms over time on silverware and other silver objects. Silver sulfide is insoluble in most solvents, but is degraded by strong acids. Silver sulfide is a network solid made up of silver (electronegativity of 1.98) and sulfur (electronegativity of 2.58) where the bonds have low ionic character (approximately 10%).

Sources

Wikipedia

Periodictable.com

Chemlibretexts.org