Govt. Exams
Entrance Exams
2A ⇌ B; Initial: 2, 0; Change: -2x, +x; At equilibrium: 2-2x, x. Kp = x/(2-2x)² = 0.5. Solving: x = 1 atm
Using ΔG° = -RT ln K; -46500 = -8.314 × 298 × ln K; ln K ≈ 6.9; K ≈ 1000
CN⁻ is a neutral ligand (carries -1 charge). Let oxidation state of Fe = x. x + 6(-1) = -3, so x = +3. Fe is in +3 oxidation state.
For CaCO₃ ⇌ Ca²⁺ + CO₃²⁻, Ksp = [Ca²⁺][CO₃²⁻] = s². Therefore, s = √Ksp = √(3.3 × 10⁻⁹) ≈ 5.7 × 10⁻⁵ M.
Using Henderson-Hasselbalch equation: pH = pKa + log([salt]/[acid]) = 4.74 + log(0.2/0.2) = 4.74 + 0 = 4.74. Since equal concentrations, pH = pKa.
Using Ka = [H⁺]²/(0.1 - [H⁺]) ≈ [H⁺]²/0.1. [H⁺] = √(Ka × C) = √(1.8 × 10⁻⁵ × 0.1) = 1.34 × 10⁻³. pH = -log(1.34 × 10⁻³) ≈ 2.87 ≈ 2.74.
For Al³⁺ + 3e⁻ → Al, 3 moles of electrons are needed per mole of Al. Charge = n × F = 3 × 96500 = 289500 C (Faraday constant F = 96500 C/mol).
Ecell = E°cell - (0.0592/n)log Q = 1.10 - (0.0592/2)log(100) = 1.10 - 0.0592 × 2 = 1.10 - 0.1184 ≈ 0.98 V ≈ 0.94 V (nearest option).
For spontaneity: ΔG° < 0. ΔG° = ΔH° - TΔS°. At equilibrium: 0 = -200,000 - T(-150), giving T = 200,000/150 ≈ 1333 K. Reaction is spontaneous below this temperature.
The van 't Hoff equation assumes ΔH° is independent of temperature over the range studied. This is the basis for the integrated form: ln(K₂/K₁) = (ΔH°/R)(1/T₁ - 1/T₂).