At equilibrium, the chemical potential of a substance is the same in all phases present. This is the condition for phase equilibrium.
π = MRT, where π = 10 atm, T = 300 K, R = 0.0821 L·atm/(mol·K). M = π/(RT) = 10/(0.0821 × 300) ≈ 0.41 M.
ΔTf = Kf × m, where m = molality = 0.5 mol/1 kg (approximately). ΔTf = 0.93°C, so Kf = 0.93/0.5 = 1.86 K·kg/mol.
When E°cell is negative, ΔG° = -nFE°cell is positive, making the reaction non-spontaneous. Also, negative E°cell indicates Kequilibrium < 1.
For first-order reactions, t₁/₂ = 0.693/k, which is independent of initial concentration. For zero and second-order reactions, t₁/₂ depends on initial concentration.
Relationship: Kp = Kc(RT)^Δn, where Δn = 2 - 1 = 1. Therefore, Kc = Kp/(RT) = 0.5/(RT). But using proper units, Kc = 0.5/(RT)² when pressure is in atm and volume in L.
Using Arrhenius equation: ln(k₂/k₁) = (Ea/R)[1/T₁ - 1/T₂]. With k₂/k₁ = 2, T₁ = 300 K, T₂ = 310 K: ln(2) = (Ea/8.314)[1/300 - 1/310], solving gives Ea ≈ 50 kJ/mol.
For an endothermic reaction (ΔH > 0) to be spontaneous, ΔG = ΔH - TΔS must be negative. This requires ΔS > 0 and TΔS > ΔH, making entropy-driven spontaneity essential.
For spontaneous process: ΔG < 0. Generally also ΔS > 0 for most spontaneous processes. (ΔH < 0 is not always required)
For AgCl: Ksp = [Ag⁺][Cl⁻] = s² = 1.8 × 10⁻¹⁰. s = √(1.8 × 10⁻¹⁰) = 1.34 × 10⁻⁵ mol/L