Chemical Engineering Thermodynamics
Instructor: Kamarza Mulia, PhD, Chemical Engineering Department Problem 4: Vapor-liquid equilibria (activity-coefficient approach)
May 15, 2023
Assignment 1. The Raoult’s law [15]
a) The following picture shows a system consisting of two phases ( and ) in equilibrium with each other. In the case of ELPIJI, is vapor and is liquid, and you could assume that the system reached a vapor-liquid equilibrium (VLE) state.
State all of the measurable variables.
b) What are the two terms, and f, shown in the picture?.
c) If a multicomponent vapor and liquid phases are in an equilibrium it means that the following equations apply. Could you explain this statement in terms of the three modes of transport phenomena (momentum, heat, and mass)?
d) Derive the Raoult’s law used to describe the ideal system behavior system in VLE.
e) Apply Raoult’s law to a pure fluid. What do you get?
Assignment 2. The case of ELPJI [10]
Consider the 12 kg LPG produced by PERTAMINA. This product is marketed as ELPIJI and contains equal mass of propane and n-butane (50:50 weight-%).
(a) If we assume that the ELPIJI tank is full of liquid and temperature is constant at 25 C, what is the pressure indicated on the pressure gage?
(b) Kimi-Yong sent you an sms that read: “The ELPIJI tank is very heavy and it is full of liquid. The pressure gauge shows pressure of 55.7 psia, therefore, I could estimate the temperature of gas inside the tank to be 10 C”. Do you agree with his estimation? Carry out calculations to support your argument.
(c) Calculate the temperature and composition of a liquid in equilibrium with a gas mixture consisting of propane and n- butane in 50:50 vol-% at pressure of 7 bar.
(d) Calculate the temperature and composition of a liquid in equilibrium with a gas mixture consisting of propane (40 vol-
%), n-butane (40 vol-%), and air (20 vol-%) at pressure of 7 bar.
(e) You ran out of ELPIJI gas yesterday and you could hear a splashing sound when you shake the tank. You remember reading a newspaper article stating that a significant amount of n-pentane is present in the ELPIJI. Do you think what you observed is related to the article? Explain. Temperature is constant at 25 C.
For questions (a)-(e), assume that vapor-liquid equilibrium is always maintained in the tank, and, the propane and n-butane mixture behaves ideally.
Assignment 3. Vapor-liquid phase diagrams of binary system [20]
(a) The following Pxy and Txy diagram were taken from Smith and van Ness’s book. Read the explanation in the book, then, summarize with your words what happens when the binary mixture changes from state d→c→b→a. Prepare a table with columns (state, phase, degree of freedom, P, T, quality, x1, y1) for both diagrams.
(b) Explain the BUBL P, DEW P, BUBL T, DEW T, and P-T flash calculations in terms of known and unknown variables by refering to the given phase diagram.
(c) Derive the working equations used in the BUBL P, DEW P, BUBL T, DEW T, and P-T flash calculations based on the ideal mixture assumption.
(d) The components of a binary system is cyclohexane+cyclohexanone and their 3-D phase diagram is shown here. Prepare qualitative P-x-y and T-x-y diagrams by examining the 3-D diagram.
Assignment 4. Deviation from ideal VLE [20]
Amir were assigned to design a distillation column to separate binary mixture of methanol and ethyl acetate. The only information available was that the distillation column will operate at 1 bar. From the internet he found the following diagram:
Amir knew that the first thing he had to do was to reproduce the T-x/y diagram above. He tried to use the Raoult’s law but the result was not very good (of course, you say!). Fortunately, he obtained a much better fit using the Margules equation.
(a) Give a definition for activity coefficient of component i (i) using your own words (b) Explain the physical meaning of i in the modified Raoult’s law.
(c) Repeat what Amir has done
(d) Comments on the shape of the phase envelope shown above and based your explanation on the molecular structure and molecular interaction between the molecules.
Assignment 5. Deviation from ideal VLE [20]
A binary gas mixture of CO2 and C3H8 flows inside a transmission pipe at a temperature of -28.9 °C. The composition of the gas is CO2 (70%-mol) and C3H8 (30%-mol). What is the highest pressure in the transmission pipe allowed so that the gas can flow without experiencing condensation? You can use plot P as a function x1 and y1 from the following binary mixture of CO2 (component 1) and propane (component 2):
Determine the parameters of the Margules equation (A12 and A21) for CO2 and C3H8 binary mixture at -28.9 °C using the phase diagram shown above. Use the bubble point pressure data.
Assignment 7. Flash calculation [15]
A saturated liquid mixture consisting of 75-mol% water and 25-mol% acetone at 85 C enters a flash drum. In the flash drum, new equilibrium is reached where 50% of the mixture is vaporized at 85 C. Questions:
a) What is the pressure of the saturated liquid feed?
b) What is the operating pressure of the flash drum?
c) What is the mole fraction of water in the liquid product?
Assume that the mixture behaves ideally and Raoult’s law can be applied.