Which of the following statements is definitely accurate?

Question

The reaction A + B ? C occurs in the vapor phase. It is an endothermic reaction. It is beneficial to carry out the reaction in the presence of liquid water, because C is somewhat soluble in water while A and B are effectively insoluble. The Henry’s Law constant for C in water increases as the temperature increases. We are interested in maximizing the total number of moles of C in the system, regardless of whether the C is in the liquid or vapor phase.
A system initially contains 10 moles each of A and B (vapor) and 100 moles of liquid water. The system is allowed to reach equilibrium at T= 298.15 K and 0.1 MPa. In a separate experiment, the system initially contains 10 moles each of A and B (vapor) and 100 moles of liquid water, and is allowed to reach equilibrium at T= 423.15 K and 0.1 MPa.
A. The system at 298.15 K will have more total moles of C.
B. The system at 423.15 K will have more total moles of C.
C. The system at 298.15 K will have a higher mole fraction of C in the vapor phase and a lower mole fraction of C in the liquid phase than the one at 423.15 K. But it is unclear which will have a larger total number of moles of C.
D. The system at 298.15 K will have a lower mole fraction of C in the vapor phase and a higher mole fraction of C in the liquid phase than the one at 423.15 K. But it is unclear which will have a larger total number of moles of C.
E. None of these is definitely accurate.

Answer 1

A. Incorrect. Consider the effect of increasing the Henry’s Law constant on x, and consider the effect of temperature on K for an endothermic reaction. Then try again.
B. Incorrect. Consider the effect of increasing the Henry’s Law constant on x, and consider the effect of temperature on K for an endothermic reaction. Then try again.
C. Incorrect. Consider the effect of increasing the Henry’s Law constant on x, and consider the effect of temperature on K for an endothermic reaction. Then try again.
D. Incorrect. Lower T means a lower Henry’s Law constant H, which by itself means a higher x (mole fraction of C in the liquid phase).But lower T, for an endothermic reaction, also means a lower equilibrium constant K, and consequently a lower y (mole fraction of C in the vapor phase). Based on all that, D sounds like the correct answer. Is there one more cause-effect relationship you are missing?
E. Correct. For an endothermic reaction, it is clear K will increase as temperature increases, so the value of y will increase at T increases. The effect of changing T on x is less clear. Lower H (at 423.15 K) means higher x, but higher y (at 423.15 K) also means higher x, according to Henry’s Law. Thus it is impossible to say, from the given information, which system has a higher mole fraction of C in the liquid phase. Without knowing the specific values of Henry’s Law constant and K at 423.15 K and 423.15 K, one cannot say A, B, C or D is absolutely true.
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