Consider the Gibbs energies at 25 ∘ C. Substance Î" G ∘ f (kJ â‹ ... mol âˆ' 1) Ag + (aq) 77.1 Cl âˆ' (aq) âˆ' 131.2 AgCl (s) âˆ' 109.8 Br âˆ' (aq) âˆ' 104.0 AgBr (s) âˆ' 96.9 (a) Calculate Î" G ∘ rxn for the dissolution

(a) + 55.7 KJ/mol

(b) 1.74 x 10-10

(c) + 70 KJ/mol

(d) 5.44 x 10-13

Explanation:

(a) ∆G reaction = n ∆Gproducts - m ∆Greactants

Where, = sigma = sum of,

∆ = delta = change in,

n and m = stoichiometric coefficients of the products and reactants from the balanced equation respectively.

For AgCl, it ionizes in the form:

AgCl (s) ↔ Ag + (aq) + Cl - (aq)

∆G reaction = [ {1 x ∆Gf (Ag + (aq)) } + { 1 x ∆Gf (Cl - (aq) } ] - [ { 1 x ∆Gf (AgCl (s)) } ]

∆G reaction = [ { 1 x 77.1 } + { 1 x (-131.2) } ] - [ 1 x (-109.8) ]

∆G reaction = [ 77.1 - 131.2 ] - [ - 109.8 ]

∆G reaction = - 54.1 + 109.8

∆G reaction = + 55.7 KJ/mol

(b) Ksp = [Ag+] [Cl-]

At equilibrium,

∆G = - RT InK

Ksp = e (-∆G/RT)

Where, ∆G = 55.7 KJ/mol = 55.7 x 1000 J/mol = 55,700 J/mol,

R = 8.314 J/mol. K,

T = 25oC = 25 + 273.15 = 298.15 K

Ksp = e [ - 55,700 J/mol / 8.314 J/mol. K x 298.15 K ]

Ksp = e [ - 22.470 ]

Ksp = 1.74 x 10-10

(c) For AgBr, ionizing in the form:

AgBr (s) ↔ Ag + (aq) + Br - (aq)

∆G reaction = [ {1 x ∆Gf (Ag + (aq)) } + { 1 x ∆GfBr - (aq) } ] - [ { 1 x ∆Gf (AgBr (s)) } ]

∆G reaction = [ { 1 x 77.1 } + { 1 x (-104) } ] - [ 1 x (-96.9) ]

∆G reaction = [ 77.1 - 104 ] - [ - 96.9 ]

∆G reaction = - 26.9 + 96.9

∆G reaction = + 70 KJ/mol

(d) Ksp = [Ag+] [Br-]

At equilibrium,

∆G = - RT InK

Ksp = e (-∆G/RT)

Where, ∆G = 70 KJ/mol = 70 x 1000 J/mol = 70,000 J/mol,

R = 8.314 J/mol. K,

T = 25oC = 25 + 273.15 = 298.15 K

Ksp = e [ - 70,000 J/mol / 8.314 J/mol. K x 298.15 K ]

Ksp = e [ - 28.2393 ]

Ksp = 5.44 x 10-13