The heat of combustion of ethanol into carbon dioxide and water is –327 kcal at constant pressure. T — Thermodynamics and Thermochemistry Chemistry Question
Question
The heat of combustion of ethanol into carbon dioxide and water is –327 kcal at constant pressure. The heat evolved (in cal) at constant volume and 27ºC (if all gases behave ideally) is (R = 2 cal mol K ) ………… . –1 –1
💡 Solution & Explanation
**Step 1: Write the balanced combustion equation for ethanol** C₂H₅OH(l) + 3O₂(g) → 2CO₂(g) + 3H₂O(l) **Step 2: Identify the relationship between Qₚ and Qᵥ** Use the formula: Qᵥ = Qₚ - ΔnRT Where Δn = moles of gaseous products - moles of gaseous reactants **Step 3: Calculate Δn** Δn = (2 + 0) - (3 + 0) = 2 - 3 = -1 mol (CO₂ and O₂ are gases; H₂O is liquid at 27°C; C₂H₅OH is liquid) **Step 4: Convert given heat to calories** Qₚ = -327 kcal = -327,000 cal **Step 5: Calculate Qᵥ** Qᵥ = Qₚ - ΔnRT Qᵥ = -327,000 - (-1)(2)(27 + 273) Qᵥ = -327,000 - (-1)(2)(300) Qᵥ = -327,000 + 600 Qᵥ = -326,400 cal Therefore, the answer is -326400.00.