A fish swimming in water body when taken out from the water body is covered with a film of water of — Thermodynamics and Thermochemistry Chemistry Question
Question
A fish swimming in water body when taken out from the water body is covered with a film of water of weight 36 g. When it is subjected to cooking at 100°C, then the internal energy for vaporization in kJ mol is ____. [nearest integer] [Assume steam to be an ideal gas. Given for water at 373 K and 1 bar is 41.1 kJ mol ; R = 8.31 J K mol ] –1 –1 –1 –1
💡 Solution & Explanation
**Step 1: Identify the given information** - Mass of water film: 36 g - Temperature: 373 K (100°C) - Pressure: 1 bar - Enthalpy of vaporization (ΔH_vap): 41.1 kJ/mol - Gas constant R: 8.31 J/(K·mol) - Molar mass of water: 18 g/mol **Step 2: Use the relationship between ΔH_vap and ΔU_vap** The internal energy change for vaporization is related to enthalpy by: $$\Delta U_{vap} = \Delta H_{vap} - \Delta(PV)$$ For an ideal gas at constant temperature and pressure: $$\Delta(PV) = nRT = \Delta n_{gas} \times RT$$ where Δn_gas = moles of gas produced - moles of liquid (≈ 1 for vaporization) **Step 3: Calculate the correction term** $$\Delta(PV) = 1 \times 8.31 \times 373 = 3101.63 \text{ J/mol}$$ Converting to kJ/mol: $$\Delta(PV) = 3.10 \text{ kJ/mol}$$ **Step 4: Calculate ΔU_vap** $$\Delta U_{vap} = \Delta H_{vap} - \Delta(PV)$$ $$\Delta U_{vap} = 41.1 - 3.10 = 38.0 \text{ kJ/mol}$$ Therefore, the answer is **38.00**.