The diamonds are formed from graphite under very high pressure. Given that the densities of graphite — Chemical Equilibrium Chemistry Question
Question
The diamonds are formed from graphite under very high pressure. Given that the densities of graphite and diamond are, respectively, 2.4 and 3.6 g/cm³ and are independent of pressure. ΔfG° values for graphite and diamond are zero and 3.0 kJ/mol, respectively. If the equilibrium pressure at which graphite is converted into diamond at 25°C is P bar, then the value of 0.01P is
💡 Solution & Explanation
At equilibrium, ΔG = 0. We know ΔG = ΔG° + ∫ΔV dP. ΔG° for C(graphite) → C(diamond) is 3.0 kJ/mol = 3000 J/mol. Molar volumes: V_graphite = 12 / 2.4 = 5.0 cm³/mol, V_diamond = 12 / 3.6 = 3.333 cm³/mol. ΔV = 3.333 - 5.0 = -1.667 cm³/mol = -1.667 × 10⁻⁶ m³/mol. 3000 + (-1.667 × 10⁻⁶ m³/mol) × (P - 1) × 10⁵ Pa/bar = 0. 3000 = 0.1667(P - 1) => P - 1 = 3000 / 0.1667 ≈ 18000 bar. Thus P ≈ 18000 bar. The value of 0.01P is 180. Therefore, correct answer is 0180.