When 1.4 g of ethylene ( C ₂ H ₄ ) undergoes combustion in a bomb calorimeter at 300 K , the temperature of the calorimeter system rises by 5 K . The heat capacity of the calorimeter system is 14.1 kJ K ⁻¹ . Given the standard enthalpies of formation of CO ₂( g ) and H ₂ O ( l ) are -393.5 kJ mol ⁻¹ and -286 kJ mol ⁻¹ respectively. The standard enthalpy of formation of ethylene is ________ kJ mol ⁻¹ . (Nearest intege

Step-by-step solution

The heat released in the bomb calorimeter at constant volume is: q_v = C_v T = 14.1 5 = 70.5 kJ Molar mass of C ₂ H ₄ = 2(12) + 4(1) = 28 g mol ⁻¹ Moles of ethylene burnt = 1.4 28 = 0.05 mol Molar internal energy of combustion ( U_ comb ) is: U_ comb = - 70.5 0.05 = -1410 kJ mol ⁻¹ The combustion reaction of ethylene is: C ₂ H ₄( g ) + 3 O ₂( g ) 2 CO ₂( g ) + 2 H ₂ O ( l ) Change in gaseous moles: n_g = 2 - (1 + 3) = -2 Enthalpy of combustion ( H_ comb ) is: H_ comb = U_ comb + n_g RT H_ comb = -1410 + -2 8.3 300