12.8 g of solid naphthalene ( C₁₀H₈ ) is burnt in a bomb calorimeter at 300 K . The temperature of the calorimeter increases by 4 K . The heat capacity of the bomb calorimeter is 128.5 kJ K ⁻¹ . The magnitude of the molar enthalpy of combustion of naphthalene is _____ kJ mol ⁻¹ . (Given: Molar mass of naphthalene = 128 g mol ⁻¹ , R = 25 3 J K ⁻¹ mol ⁻¹ , assume water formed is in the liquid state)

Step-by-step solution

Heat released at constant volume, q_v = C T = 128.5 4 = 514 kJ . Moles of naphthalene burnt, n = 12.8 128 = 0.1 mol . Molar internal energy of combustion, U = -514 0.1 = -5140 kJ mol ⁻¹ . The balanced chemical equation for the combustion of solid naphthalene is: C₁₀H₈(s) + 12 O₂(g) 10 CO₂(g) + 4 H₂O(l) Change in gaseous moles, n_g = 10 - 12 = -2 . From the thermodynamic relation H = U + n_g RT : H = -5140 + (-2) ( 25 3 10⁻³ kJ K ⁻¹ mol ⁻¹ ) 300 K H = -5140 - 5 = -5145 kJ mol ⁻¹ . The magnitude of the molar enthalpy