Which of the following statements is true?

Question

A rigid vessel with known volume initially contains 10 moles of A and 10 moles of B at 298.15 K, and nothing else. The reaction A+B?C+D occurs in the liquid phase, but not in the vapor phase. When the vessel reaches equilibrium, at 298.15 K, both a liquid and a vapor phase are present. The equilibrium constant for the reaction is 0.4. 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. You are trying to calculate the eight unknown values of number of moles (N), one for each compound in each phase that will be present at equilibrium.
A. Assuming the liquid is an ideal solution and the vapor is an ideal gas, Raoult’s Law represents four equations that contain no additional unknowns, since the mole fractions can be expressed in terms of the eight values of N.
B. The total number of moles of A at equilibrium, in both phases combined, must be equal to the total number of moles of B at equilibrium in both phases combined. However, they can be distributed differently between the two phases.
C. An additional equation can be gained by setting the vapor phase volume equal to the vessel volume, since the liquid phase volume will be insignificant compared to the vapor phase volume.
D. All of the above are true.
E. None of the above are true.

Answer 1

A. Incorrect. Raoult’s Law requires the system pressure, which we do not have, and therefore represents an additional unknown. Review Section 10.2 and especially Equations 10.4 through 10.8.
B. Correct. Because they were fed in equal molar amounts and only one reaction occurs—said reaction consuming and generating A and B in equal amounts— the two amounts must be the same. The distribution between the phases, however, needn’t be the same and probably isn’t.
C. Incorrect. We do not know the pressure of the system or the volume of the system, so we cannot say that the vapor phase is so much larger than the liquid phase that this is true. While vapor molar volumes are typically orders of magnitude larger than liquid molar volumes, this may be a small container in which only a tiny fraction of the material is in the vapor phase.
D. Incorrect. You should review your analysis of the three statements because at least one is not an accurate statement.
E. Incorrect. At least one statement is accurate.