Which of the following statements is true?

Question

A rigid, adiabatic vessel is initially evacuated. 10 moles of liquid A and 10 moles of liquid B at 298.15 K are injected into the vessel, and this 20 moles of liquid is regarded as the “initial state” of the system. When the vessel reaches equilibrium, both a liquid and a vapor phase are present, and the entire equilibrium VLE mixture inside the vessel is regarded as the “final state” of the system. The reaction A+B?C+D occurs in the liquid phase, but not in the vapor phase. The equilibrium constant for the reaction is 0.4 and the reaction is exothermic. The vapor pressures are 0.12 MPa for compound A, 80kPa for compound B, 0.15 MPa for compound C and 70kPa for compound D. The vapor phase can be modeled as an ideal gas, but the liquid phase can NOT be modeled as an ideal solution.
A. The “final state” temperature is definitely below 298.15 K, because the formation of the vapor phase will lead to evaporative cooling.
B. The energy balance will contain a significant “expansion work” term, because the initial state of the system (20 moles of liquid) is much smaller in volume than the final state of the system (in which the system has partially evaporated and expanded to fill the entire vessel).
C. The modified Raoult’s Law can be written for each of the four compounds, and each of these equations will contain an activity coefficient. The equation for chemical reaction equilibrium will contain the fifth activity coefficient.
D. Because this is an adiabatic reversible process, Sgen= 0 and Q/T = 0 in an entropy balance.
E. None of the above are true.

Answer 1

A. Incorrect. The reaction is exothermic. It is possible that the energy released by the reaction exceeds the energy required for the phase change, and that the final temperature is higher than 298.15 K.
B. Incorrect. The vessel is initially evacuated. The expansion occurs against no opposing pressure.
C. Incorrect. The mixture fugacity of each compound is equal to ?xf. This same mixture fugacity appears in modified Raoult’s Law and the reaction equilibrium expression. There are only four activity coefficients.
D. Incorrect. While the vessel is adiabatic, the addition of A and B to the vacuum will cause a rapid irreversible change in the system pressure. This will cause Sgen> 0.
E. Correct. Each is false.