Question

Estimate the composition of the liquid and vapor phases when ethylene reacts with water to form ethanol at 474.15K and 3.45x10° Pa, conditions which assure the presence of both liquid and vapor phases. The reaction vessel is maintained at 3.45x10 Pa by connection to a source of ethylene at this pressure. Assume no other reactions, and assume that ethylene, due to its high volatility, is not present in the liquid phase and assume that the vapor phase is an ideal solution of gasses. Neglect the Poynting factor. Assume K2=1. Also consider that you have proper models for the activity coefficients of the components of the liquid mixture, in function of the liquid composition.:

C₂H₄(g) + H₂O(g) —>C₂H₅OHg)

Clearly describe (draw) the system, its variables and the mathematical relations between the variables

Answer 1

To estimate the composition of the liquid and vapor phases in the ethylene-water-ethanol system at 474.15 K and 3.45x10⁵ Pa, we consider the ideal behavior of gases and the activity coefficients of the liquid phase. The system consists of a reaction where ethylene reacts with water to produce ethanol, and the vapor phase is an ideal solution of these gases, while the liquid phase contains mainly ethanol and water.

Step-by-step explanation:

To estimate the composition of the liquid and vapor phases when ethylene reacts with water to form ethanol at a temperature of 474.15 K and a pressure of 3.45x105 Pa, we must assume that the vapor phase behaves as an ideal mixture of gases, and we will use models for activity coefficients for the liquid phase's composition. The reaction is as follows: C2H4(g) + H2O(g) → C2H5OH(g).

We are given that K2=1, which implies that for every mole of ethylene reacting, one mole of ethanol is produced. Since we neglect the Poynting factor and since ethylene is highly volatile and not present in the liquid phase, the liquid phase will primarily contain ethanol and water. The vapor phase will contain ethylene, water vapor, and ethanol vapor, assuming it to be an ideal solution.

Next, we would calculate the mole fraction of ethanol in the liquid phase using the provided models for activity coefficients, which takes into account non-ideality of mixtures. The vapor pressure of each component in the vapor phase can be estimated using Raoult's law, which relates the vapor pressure of a component in a mixture to the vapor pressure of the pure component and its mole fraction in the mixture.