The internal energy change (in J) when 90 g of water undergoes complete evaporation at 100ºC is (Giv — Thermodynamics and Thermochemistry Chemistry Question
Question
The internal energy change (in J) when 90 g of water undergoes complete evaporation at 100ºC is (Given : for water at 373 K = 41 kJ/mol, R = 8.314 JK mol ) –1 –1
💡 Solution & Explanation
**Step 1: Calculate moles of water** Molar mass of water = 18 g/mol Moles = 90 g ÷ 18 g/mol = 5 mol **Step 2: Identify the relationship between ΔH and ΔU** For phase changes at constant temperature and pressure: ΔH = ΔU + Δ(PV) ΔH = ΔU + nRΔT (for gases, assuming ideal behavior) At constant T during evaporation: ΔH = ΔU + nRT **Step 3: Rearrange to find ΔU** ΔU = ΔH - nRT **Step 4: Convert enthalpy of vaporization to joules** ΔH_vap = 41 kJ/mol = 41,000 J/mol Total ΔH = 5 mol × 41,000 J/mol = 205,000 J **Step 5: Calculate nRT term** nRT = 5 mol × 8.314 J/(mol·K) × 373 K nRT = 15,505.61 J **Step 6: Calculate ΔU** ΔU = 205,000 - 15,505.61 ΔU = 189,494.39 J Therefore, the answer is 189494.39.