Problem Set #29: Chemical Potential and Phase Equilibrium

Problem Set #29 Assigned: March 18, 2024 Due: March 20, 2024 at 2:30 pm 1. What is the physical explanation for the decrease in the chemical potential of a pure substance as the temperature is increased? 2. What is the physical explanation for the increase in the chemical potential of a pure substance as the pressure is increased? 3. The standard molar entropy (i.e., at 1 bar) of liquid water at 273.15 K is 65 J/K mol. By contrast, the value for ice at the same temperature and pressure is 43 J/K mol. Find the change in the chemical potential for both ice and liquid water upon increasing the temperature by 1 K at constant pressure. Explain which phase is more thermodynamically stable at the new temperature (274.15 K). What does your answer mean? 4. Consider heating 1 mol of water from 25 °C to 35 °C at 1 bar. How much does the chemical potential change? The standard molar entropy of liquid water at 25 °C 69.9 J/K mol. 5. By how much does the chemical potential of copper change when the pressure exerted on a sample is increased from 100 kPa to 10 MPa? The density of copper is 8960 kg/m3 and its molecular mas is 63.546 g/mol. 6. Consider water inside a closed system at 20 °C, such that there is both liquid water and a vapor phase above it. The initial total pressure is 1.0 bar. Of that, the vapor pressure of water is 2.34 x 10-2 bar, and the rest is air. Find the vapor pressure if 200,000 bar of external pressure is applied by introducing an inert gas. The molar volume of water is 18.1 cm3 at 20 °C. For the purpose of this problem, you can treat water in the vapor phase like an ideal gas. 7. Do you have any concerns about your answer to question #6? Please explain your answer. 1. The decrease in chemical potential as the temperature rises is due to an increase in entropy which leads to move favorable condition for spontaneous processes 2. The chemical potential increases with pressure because of the work done to compress the substance and the increased interactions between particles at higher pressures 3 Sm 65 J k.no water Δµ 41 435k.mu ice Δµ 43Ymo 654m01 The phase of solid ice is thermodynamically more stable than the liquid water phase 4 Δµ DH TLS ΔH 9 MCLT ΔH I mol 418J k 10K ΔS Δ5 RIn 05 69.9 8.314 in 3 Δ8 70 17 J k Mol OH 41.8J Δµ ΔH TDS 41.8 10K 70 17 Δµ 659.9 5 Δµ M Y Δp 10MPa 100kpa 9.90 106Pa Δµ M Y 63.546 Δµ 7 02 6 p 9 104 8 06 J mol 7 px.ec Δp Pf Pi 20MPa 1 89 Δp 1.99 107Pa D 2.34 103 p 2711.6 Pa 1bar 10 8 29 103 This number means that the introduction of the inert gas causes the vapor pressure of water to be increased to 2711 Pa