The molar heat capacity for an ideal gas at constant pressure is 20.785 J K mol . The change in inte — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

**Step 1: Find the molar heat capacity at constant volume (Cv)** Using the relationship: Cp - Cv = R Cv = Cp - R = 20.785 - 8.314 = 12.471 J K⁻¹ mol⁻¹ **Step 2: Calculate the temperature change** ΔT = T₂ - T₁ = 500 - 300 = 200 K **Step 3: Use the internal energy change formula** For an ideal gas: ΔU = n·Cv·ΔT Where: - ΔU = 5000 J - Cv = 12.471 J K⁻¹ mol⁻¹ - ΔT = 200 K - n = number of moles (unknown) **Step 4: Solve for number of moles** 5000 = n × 12.471 × 200 5000 = n × 2494.2 n = 5000/2494.2 = 2.0046 mol **Step 5: Round to nearest integer** n ≈ 2 mol Therefore, the answer is 2.