Introduction to Phase Behavior (9:37) (msu.edu)
Students tend to be distracted with the algorithms for bubble, dew, and flash, and often miss the important concepts of the relation of the calculations to the phase diagram. This screencast discusses the pure component endpoints, the trends in phase behavior at the bubble and dew conditions, and the qualitative relation between the P-x-y and T-x-y diagrams.

Comprehension Questions:

1. Referring to the Txy diagram on slide 3, estimate T, nature (ie. L,V, V+L, L+L), composition(s), and amount of the phase(s) for points: a, b. d, g.
2. Referring to the Txy diagram on slide 3, suppose we had T = 340K and zA = 0.40. Estimate T, nature (ie. L,V, V+L, L+L), composition(s), and amount of the phase(s) for that point.
3. Which component is more volatile, A or B?

Bubble, Dew, Flash Concepts and the Lever Rule (4:01) (msu.edu)

Understanding what is present (known) and not present (unkown) for a given state of a system will help you decide which routine to use. Notation is introduced for liquids, vapor, and overall compositions. Also, the lever rule concept is used throughout the chemical engineering curriculum, but it is important to see how to use compositions for the lever rule.

Comprehension Questions:

1. Which variables are fixed and which do you need to find in each of the following:
a. Bubble temperature
b. Bubble pressure
c. Dew temperature
d. Dew pressure
e. Isothermal flash
f. Adiabatic flash

VLE Routines - General Strategies (4:49) (msu.edu)

Deciding which routine to use is more challenging than it appears. Also understanding the strategy used to solve the problems is extremely helpful in being able to develop the equations to solve instead of trying to memorize them.

Raoult's Law (5:39) (msu.edu)
What type of components make an ideal solution that follows Raoult's Law? What does a diagram look like for a system that follows Raoult's Law? Can you identify the regions? What is the K-ratio for Raoult's Law? What simple principles must be followed for the K-ratios of the components in a binary mixture?

Raoult's Law Calculation Procedures (11:45) (msu.edu)
Details on how to implement bubble, dew, and flash calculations for Raoult's Law. This screencast shows sample calculations for the bubble pressure and dew pressure of methanol+ethanol.

Comprehension Questions: Assume the ideal solution SCVP model (Eqns. 2.47 and 10.8).

1. Estimate the bubble pressure (bars) of 30% acetone + 70% benzene at 333K.
2. Estimate the dew temperature (K) of 30% acetone + 70% benzene at 1 bar.
3. Estimate the fraction vapor and phase compositions ethylamine+ethanol at 298K, 400mmHg and a feed of 60%amine.

This example shows how to use VLookup with the xls Solver to facilitate  multicomponent  VLE calculations for ideal solutions: bubble, dew, and isothermal flash. (15min, uakron.edu) The product xls file serves as a starting point for multicomponent VLE calculations with activity models and for adiabatic flash and stream enthalpy calculations. This video shows sample calculations for the bubble, dew, and flash of propane, isobutane, and n-butane, like Example 10.1.

Note: This is a companion file in a series. You may wish to choose your own order for viewing them. For example, you should implement the first three videos before implementing this one. Also, you might like to see how to quickly visualize the Txy analog of the Pxy phase diagram. If you see a phase diagram like the ones in section 11.8, you might want to learn about LLE phase diagrams. The links on the software tutorial present a summary of the techniques to be implemented throughout Unit3 in a quick access format that is more compact than what is presented elsewhere. Some students may find it helpful to refer to this compact list when they find themselves "not being able to find the forest because of all the trees."

Comprehension Questions - Assume the reboiler composition for the column in Example 10.1 was zi={0.2,0.3,0.5} for n-butane, isopentane, and n-pentane, respectively.

a)  Calculate the temperature at which the boiler must operate in order to boil the bottoms product completely at 8 bars.
b)  Assuming the bottoms product liquid is in equilibrium with the liquid in the boiler, calculate the temperature of boiler and composition of the vapor in the boiler.
c)  Suppose this stream is to be boiled again and the vapor returned to the column with a ratio of 2 parts vapor to 1 product. (FYI: this is known as "boilup ratio.") Find the relevant temperature and compositions.

This example hypothesizes a "pre-quel" to Example 10.1 in the form of a liquid reactor at 20 bars and asks what temperature the reactor must have been in order to result in the flash at 320K and 8 bars if no heat was added. This requires an adiabatic flash calculation. (7min, uakron.edu) The procedure demonstrated here applies the enthalpy pathway of Fig. 2.6c, with Eqn. 2.45 to estimate heats of vaporization. With this approach, you should be able to solve for mass and energy balances of any mixture at any vapor fraction. You should watch the video about Multicomponent VLE for Ideal Solutions before this one (see link above).

Note: This is a companion file in a series. You may wish to choose your own order for viewing them. For example, you should implement the first three videos before implementing this one. Also, you might like to see how to quickly visualize the Txy analog of the Pxy phase diagram. If you see a phase diagram like the ones in section 11.8, you might want to learn about LLE phase diagrams. The links on the software tutorial present a summary of the techniques to be implemented throughout Unit3 in a quick access format that is more compact than what is presented elsewhere. Some students may find it helpful to refer to this compact list when they find themselves "not being able to find the forest because of all the trees."

Comprehension Questions
1. Make a spreadsheet like the one in the video. Modify the compositions  to make a binary system like Example 10.2. Can you reproduce the results of Example 10.2?
2. Suppose a reactor was at 380K and 2MPa with a composition of {0.115, 0.335, 0.15, 0.15, 0.25} for {propane, isobutane, nbutane, isopentane, npentane}. What would be the adiabatic T&q of this stream exiting a valve at 8 bars?

Distillation is the primary choice for separations in the petrochemical industry. Because the majority of chemical processing involves separations/purifications, that makes distillation the biggest economic driver in all of chemical production. Therefore, it is very important for chemical engineers to understand how distillation works (21min, uakron.edu) and how VLE plays the major role. This video is a bit long, but it puts into context how phase diagrams and thermodynamic properties relate to very important practical applications. You may find it helpful to reinforce the conceptual video with some sample calculations.(12min) At the end of the video, you should be able to answer the following:

Consider the acetone+ethanol system. Use SCVP (Eqn 2.47) to answer the following.

1. Sketch a Txy diagram for acetone+ethanol at 1 bar with accurate Tsat's. Label completely.
2. Which component pertaining to #1 would have enhanced concentration in the distillate?
3. Accurately sketch the yx diagram pertaining to #1
4. Use Raoult's Law to estimate α_LH pertaining to #1.
5. Use your sketch from 3 to estimate N_min  to go from x1=0.1 to 0.9.
6. Use the Fenske equation to estimate N_min  with splits of 0.9 and 0.1.

This screencast shows how to quickly visualize Pxy phase diagrams for nonideal systems using Excel (5min, uakron.edu). These sample calculations for methanol+benzene apply the simplest nonideal solution model: ΔH_mix = A₁₂*x₁*x₂. Rigors of this model are discussed in Chapter 11. Nevertheless, its basic elements are simple enough that they can be understood in Chapter 10. When x1=0 or x2=0, a pure fluid is indicated, corresponding to no mixing and zero heat of mixing. When A12=0, the ideal solution approximation is recovered. When A12>0, the model indicates an endothermic interaction (like 2-propanol+water, Fig. 10.8c), giving rise to "positive deviations from Raoult's Law." When A12<0, the model indicates an exothermic interaction (like acetone+chloroform, Fig. 10.9c), giving rise to "negative deviations from Raoult's Law." With this spreadsheet, you can quickly change your components and A12 values to see how the phase diagram changes and gain "hands-on" familiarity with the principles discussed in Section 10.7. 

Note: This is a companion file in a series. You may wish to choose your own order for viewing them. For example, you should implement the first three videos before implementing this one. Also, you might like to see how to quickly visualize the Txy analog of the Pxy phase diagram. If you see a phase diagram like the ones in section 11.8, you might want to learn about LLE phase diagrams. The links on the software tutorial present a summary of the techniques to be implemented throughout Unit3 in a quick access format that is more compact than what is presented elsewhere. Some students may find it helpful to refer to this compact list when they find themselves "not being able to find the forest because of all the trees."

Comprehension Questions:
1. Make a Pxy diagram for cyclohexane+toluene at 80C and A12=200. What kind of system is this?
2. Make a Pxy diagram for cyclohexane+benzene at 80C and A12=200. What kind of system is this?
3. Why does the system's qualitative behavior change so much when the components and model parameters are changed so little?

Txy phase diagrams are basically the mirror image of Pxy diagrams for VLE because a high pressure indicates a liquid but a high temperature leads to a vapor. We can visualize Txy diagrams for VLE (uakron, 7min) in much the same way as for Pxy diagrams. Txy diagrams have the additional advantage of illustrating the onset of liquid-liquid equilibrium (uakron, 6min) at low temperatures. We discuss liquid-liquid equilibria (LLE) calculations in Chapter 14, but it is useful to learn your way around a complete phase diagram (uakron, 10min) properly from the beginning, instead of learning bits and pieces here and there.The first two videos illustrate sample calculations for methanol+benzene. Both of these are revisited in later chapters. The last video illustrates a sample quiz/test question about interpreting a phase diagram.

Comprehension Questions:

Referring to the phase diagram for ethyl acetate+water (cf. Figure 14.4) identify the phase nature (V, L, V+L, or L+L), phase composition(s), and phase amount(s) for the following points:
A. T = 360, x_E = 0.7
B. T = 360, x_E = 0.3
C. T = 340, x_E = 0.7
D. T = 340, x_E = 0.9

The concept behind multicomponent equilibrium is practically the same as that for pure component equilibrium: minimize the total Gibbs energy by setting the derivative equal to zero. The notation involved in taking that derivative is more complicated than in Chapter 6 because we have a new partial derivative in our chain rule for every component that is added to the mixture. This live video (10min, uakron.edu) portrays students wrestling with why the derivatives must be expressed with respect to constant mole number instead of mole fraction, leading to a better appreciation of each term in the expansion. 

When expressing the derivative of the total Gibbs energy by chain rule, there is one particular partial derivative that relates to each component in the mixture: the "chemical potential." By adapting the derivation from Chapter 9 of the equilibrium constraint for pure fluids, we can show that the equilibrium constraint for mixtures is that the chemical potential of each component in each phase must be equal. That is fine mathematically but it is not very intuitive. By translating the chemical potential into a rigorous definition of fugacity of a component in a mixture, we recognize that an equivalent equilibrium constraint is that the fugacity of each component in each phase must be equal. (8min, Live, uakron.edu) This offers the intuitive perspective of, say, molecules from the liquid escaping to the vapor and molecules from the vapor escaping to the liquid; when the "escaping tendencies" are equal, the phases experience no net change and we call that equilibrium. 

What is the entropy of a "mixture" that is unmixed? (ie. What is the entropy of the overall system when two separate beakers are considered as one total system?) At first glance it may seem like an impossible riddle, but the simple answer to this puzzle holds the key to all of phase equilibria. This video breaks down the entropy calculation for an ideal mixture (20min, uakron.edu) into a series of simple questions (below). By answering these questions, we build an approach for formulating mixture properties in general, not just ideal solutions, and not just for entropy, but for any property (FYI, G is of particular interest.)

Quickly estimate the entropy (J/molK) of a stream that is equimolar in ethane and propane at 25°C and 26 bars relative the ideal gas elements at 25°C and 1 bar.(a) Quickly estimate ΔS for a component going from ideal gas to liquid.(b) Develop a formula for the S of a "mixture" that is NOT mixed (ie. total S of separate beakers). (c) Develop a general formula for the S of a "mixture" that IS mixed.(d) BTW, develop a general formula for the H of a "mixture" that IS mixed.(e) Perform the numerical calculation.

Comprehension Questions:
1. Prepare a graph of G vs. x_E  for ethane+propane at 298K and sufficient pressure to remain liquid at all compositions. 
2. Suppose you had two beakers, one that was 75mol% ethane and another that was 75%propane. Develop a formula to describe the G of this overall system as the size of the ethane-rich beaker goes from overwhelmingly dominant to negligible relative to the propane-rich beaker. Plot this result on the graph from part 1. 

10.9 - 10.12 Mixture Properties Overview (6:53) (msu.edu)

This section of the text is thick with lots of equations. It may help to filter out the most important equations and results so that you have the perspective of the overall objectives of this section. There are a lot of equations in this section to show that the component fugacity in an ideal gas is simply the partial pressure! This screencast goes on to preview the most important results of the next sections to help you see the overall story.

10.9 - 10.12 Mixture Properties Overview (6:53) (msu.edu)

Why does Raoult's law work sometimes? Why does it fail sometimes? How can we hope to understand why it fails?

This section of the text is thick with lots of equations. It may help to filter out the most important equations and results so that you have the perspective of the overall objectives of this section. There are a lot of equations in this section to show that Raoult's law is a equlity of an ideal gas component fugacity with an ideal solution liquid fugacity! By understanding the assumptions used in the development of the equation, we can begin to understand the limitations of Raoult's law. This screencast goes on to preview the methods developed in the next sections of the textbook to deal with deviations in fugacities from ideal solutions and the ideal gas law.

10.9 - 10.12 Mixture Properties Overview (6:53) (msu.edu)

So, what do we do when Raoult's law fails? We use one of two approaches, activity coefficients or fugacity coefficients.

This screencast provides an overview of the most important results from sections 10.9-10.11 for perspective and motivation for improved models.