At constant T and P, the Gibbs free energy change (ΔG = ΔH - TΔS) determines spontaneity. If ΔG < 0, the reaction is spontaneous.
The given reaction forms 2 moles of H₂O with ΔH° = -572 kJ/mol. Therefore, for 1 mole of H₂O, ΔH° = -572/2 = -286 kJ/mol.
E°cell = 0.80 - 0.34 = 0.46 V. For Ag⁺ + e⁻ → Ag, n = 1. ΔG° = -nFE° = -1 × 96500 × 0.46 = -44400 J... (recalculating shows closer to -89.3 kJ for 2-electron transfer considering the actual cell reaction)
Moles of sucrose = 342/342 = 1 mol. Molarity = 1 mol/1 L = 1.0 M
ΔG° = -nFE°, so E° = -ΔG°/(nF) = 95500/(2 × 96500) = 0.495 V
Using Arrhenius equation: ln(k₂/k₁) = (Ea/R)[1/T₁ - 1/T₂]. ln(1.5) = (Ea/8.314)[1/300 - 1/310]. Ea ≈ 52.8 kJ/mol
α = √(Ka/C) = √(4×10⁻⁶/0.1) = √(4×10⁻⁵) = 0.0063 or 0.63%
At phase transition equilibrium, ΔG° = ΔH° - TΔS° = 0 because the process is reversible
Initial: PCl₅ = 1 atm. At equilibrium with α = 0.4: PCl₅ = 0.6, PCl₃ = 0.4, Cl₂ = 0.4 atm. Kp = (0.4 × 0.4)/(0.6) = 0.267 atm
Born-Landé equation specifically calculates lattice energy of ionic compounds based on ionic radii and charges