12 g of a gaseous mixture of ethene ( C ₂ H ₄ ) and methane ( CH ₄ ) produces 35.2 g of CO ₂ gas on complete combustion. If this mixture is combusted in a rigid bomb calorimeter at 300 K , the magnitude of heat evolved is ________ kJ . (Nearest integer) Given: H_c^ ( C ₂ H ₄, g ) = -1400 kJ mol ⁻¹ H_c^ ( CH ₄, g ) = -900 kJ mol ⁻¹ R = 25 3 J K ⁻¹ mol ⁻¹

Step-by-step solution

Let the moles of C ₂ H ₄ be x and CH ₄ be y . Mass of the mixture: 28x + 16y = 12 Moles of CO ₂ produced = 35.2 44 = 0.8 mol From the stoichiometry of combustion, 1 mole of C ₂ H ₄ gives 2 moles of CO ₂ , and 1 mole of CH ₄ gives 1 mole of CO ₂ . 2x + y = 0.8 y = 0.8 - 2x Substituting y into the mass equation: 28x + 16(0.8 - 2x) = 12 28x + 12.8 - 32x = 12 4x = 0.8 x = 0.2 mol y = 0.8 - 2(0.2) = 0.4 mol Total enthalpy of combustion ( H ): H = 0.2(-1400) + 0.4(-900) = -280 - 360 = -640 kJ The combustion reactions are