When 6.4 g of solid naphthalene ( C ₁₀ H ₈ ) is completely burned in a bomb calorimeter at 300 K , the temperature of the calorimeter system increases by 17 K . If the heat capacity of the calorimeter system is 15 kJ K ⁻¹ , the magnitude of the standard enthalpy of combustion of naphthalene at 300 K is ________ kJ mol ⁻¹ . (Given: R = 25 3 J K ⁻¹ mol ⁻¹ , Molar mass of C = 12 g mol ⁻¹ , H = 1 g mol ⁻¹ )

Step-by-step solution

The molar mass of naphthalene ( C ₁₀ H ₈ ) is 10 12 + 8 1 = 128 g mol ⁻¹ . Number of moles of naphthalene burned: n = 6.4 128 = 0.05 mol The heat released at constant volume ( q_v ) in the bomb calorimeter is: q_v = C T = 15 17 = 255 kJ The molar internal energy change of combustion ( U ) is: U = - 255 0.05 = -5100 kJ mol ⁻¹ The balanced chemical equation for the combustion of naphthalene is: C ₁₀ H ₈( s ) + 12 O ₂( g ) 10 CO ₂( g ) + 4 H ₂ O ( l ) The change in the number of moles of gaseous species is: n_g = 10 -