Lecture Notes Week 1 ChE 1008 Spring Term (03-2)

Lecture 3

y vs. x – McCabe-Thiele Plot

Question Where does the equilibrium curve intersect x = y and what are the equilibrium vapor and liquid ethanol mole fractions at this point?

y vs. x – McCabe-Thiele Plot 0.89 0.89

Azeotropes The equilibrium curve is, in general, above the x = y line when the more volatile component is plotted, in this case ethanol. The point where the liquid and vapor mole fractions touch the x = y line indicates that they are equal – this is termed the azeotropic point or azeotrope. The initially more volatile component is no longer the more volatile component at the azeotrope. For an ethanol-water mixture at P = 1 atm, this point is xEtOH = yEtOH = 0.8943, which from Table 2-1 occurs at T = 78.15oC.

y vs. x – McCabe-Thiele Plot Azeotrope

Azeotropes – The Problem Azeotropes often present problems in equilibrium vapor-liquid phase separations since their presence means that one will not obtain enrichment between the vapor phase and the liquid phase above the azeotrope – one cannot obtain separation greater than the azeotropic point for a given set of conditions. For example, this limit is 0.8943 mole fraction of ethanol for an ethanol-water mixture at P = 1 atm. If one wished to separate a mixture containing 0.9 ethanol liquid mole fraction at 1 atm, one would not obtain a greater concentration in the vapor phase than in the liquid phase.

Azeotropes – Circumventing the Problem Azeotropes are dependent upon pressures and one way to circumvent this problem is to vary the pressure. For example, under a vacuum (P = 70 mmHg), no azeotrope exists for the ethanol-water mixture. This is one reason that vacuum distillation is often done for many separations. Azetropes are often also very component dependent. For example, the addition of a 3rd component to a binary system, may change or “break” the azeotrope. We will discuss how to break the azeotrope later by varying the pressure and also adding additional components to the system.

Minimum Boiling Point Azeotropes An azeotrope that occurs at a temperature that is less than either of the boiling points of the pure components is termed a “minimum boiling point” azeotrope. For example, the azeotrope for ethanol-water is a minimum boiling azeotrope since it occurs at a temperature (T = 78.15oC) which is less than the boiling point of either ethanol or water (T =78.30oC and 100oC, respectively) – see Table 2-1, which indicates this more clearly. Maximum boiling azeotropes also occur where the azeotrope occurs at a temperature above both the boiling points of the pure components – we’ll look at these a little later.

Vapor-Liquid Equilibrium – Component Effect One must remember that the equilibrium behavior is often very different for different systems of components. The following are examples of binary mixtures of ethanol and other components. Comment on the relative ease of separation for each and identify the azeotrope. What does it mean when the equilibrium curve drops below x = y?

Vapor-Liquid Equilibrium – Component Effect

Question From the y vs. x plot, what is temperature at P =1 atm and xEtOH = 0.6?

Answer From the ethanol-water y vs. x plot, what is the temperature at P =1 atm and xEtOH = 0.6 at equilibrium? One cannot tell from the plot. One must have additional data. The temperature is different at each point on the equilibrium curve – although without the corresponding temperature data, one cannot tell directly what the temperature is from the plot alone. One can say that temperature decreases from left to right along the curve or decreases from bottom to top when one plots the more volatile component. There is another way to plot the data that indicates equilibrium temperature behavior…

T vs x,y – Saturated Liquid and Vapor Plot The T vs x,y plot presents the temperature equilibrium relationship for x and y. Pressure is constant. One normally plots the more volatile component.

T vs x,y – Saturated Liquid and Vapor Plot

What can the T vs. x,y plot tell one? One now has two equilibrium curves – a saturated liquid line and saturated vapor line. Any point below the saturated liquid line is a single-phase composition of a subcooled liquid – no vapor exists. Any point above the saturated vapor line is a single-phase composition of a superheated vapor – no liquid exists. Any point between the saturated liquid and saturated vapor lines is a two- phase composition – both vapor and liquid exist in equilibrium. Thus, one can obtain a lot more information from the T vs. x,y plot than from the y vs. x…

Question What are the boiling point temperatures of the pure components from the T vs. x,y plot?

T vs x,y – Saturated Liquid and Vapor Plot

Answer What are the boiling point temperatures of the pure components, ethanol and water, from the T vs. x,y plot? If one has pure ethanol in the system, xEtOH = yEtOH = 1.0; thus, at xEtOH = 1.0, the boiling point of ethanol is 78.3oC at 1 atm from the plot. If one has pure water in the system, xEtOH = yEtOH = 0.0 or xW = yW = 1.0 ; thus, at xEtOH = 0.0 the boiling point of water is 100oC at 1 atm from the plot.

Bubble and Dew Point Temperatures Any point on the saturated liquid line is the point at which the liquid just begins to boil – the first bubble of vapor is formed. This temperature, for a given composition and pressure, is the bubble-point temperature. Any point on the saturated vapor line is the point at which the vapor just begins to condense – the first drop of liquid is formed. This temperature, for a given composition and pressure, is the dew-point temperature.

T vs x,y – Saturated Liquid and Vapor Plot

Example using the T vs. x,y Saturated Liquid and Vapor Plot Assume one is given an ethanol-water mixture with a concentration of 20% ethanol at P = 1 atm and T = 75oC. Explain what happens as one heats the system to 80oC using the T vs. x,y plot. By convention for a feed, designate the mole fraction as zEtOH on the diagram at 75oC and indicate heating to 80oC. What is the phase of this mixture at 75oC and what is the phase at 80oC?

Saturated Liquid and Vapor Plot – Heating, zEtOH = 0.2

Saturated Liquid and Vapor Plot – Heating, zEtOH = 0.2 Starting with zEtOH = 0.2 at T = 75oC, one has a subcooled liquid. As it is heated, this mixture remains a single-phase liquid until the saturated liquid line is reached. Once one reaches the saturated liquid line, the first vapor bubble appears. This is known as the Bubble Point Temperature – the temperature at which the mixture begins to boil. What is the Bubble Point Temperature for a mixture containing mole fraction zEtOH = 0.2? Indicate the isotherm line on the plot.

Saturated Liquid and Vapor Plot – Bubble Point Temperature

Saturated Liquid and Vapor Plot – 1st Vapor Bubble Composition What will be the vapor composition of this first bubble at equilibrium? Indicate the method of determination on the plot. Remember that the temperature of the vapor and liquid phase are the same at equilibrium…

Saturated Liquid and Vapor Plot – 1st Vapor Bubble Composition

Saturated Liquid and Vapor Plot – Heating, zEtOH = 0.2 Assume that the mixture is heated further to T = 89oC. What is the phase of the mixture at T = 89oC? What are the liquid and vapor phase compositions of the mixture at T = 89oC? Indicate your method of determination on the plot.

Saturated Liquid and Vapor Plot – Heating, zEtOH = 0.2

Saturated Liquid and Vapor Plot – Heating, zEtOH = 0.2 Assume that the mixture is heated further through the two phase region. Once one reaches the saturated vapor line, the last liquid drop disappears. This is known as the Dew Point Temperature. Why Dew Point? – because the system is reversible. If one started in the superheated vapor region and cooled, this would be the temperature at which the mixture begins to condense and the first liquid drop would form. What is the Dew Point Temperature, and what will be the liquid composition of the last liquid drop before it disappears? Indicate your method of determination on the plot.

Saturated Liquid and Vapor Plot – Last Liquid Drop Composition

Additional Problem Using the equilibrium data for ethanol-water at P =1 atm (Table 2-1 Wankat), estimate the bubble point temperature and composition of the 1st vapor bubble formed for a feed mixture containing zEtOH = 0.508. Estimate the dew point temperature and composition of the last liquid drop. Use only the data table, do not plot.

T vs x,y – Azeotrope The point where the saturated liquid line and the saturated vapor line touch is the azeotrope (x = y), which can be read directly from the T vs. x,y plot at T = 78.15oC. Compare this to the azeotrope on the y vs. x plot of Figure 2-2, p. 15 in Wankat. This is a minimum boiling azeotrope as we previously determined – the azeotrope occurs at a temperature (T = 78.15oC) which is less than the boiling point of either ethanol or water (T = 78.30 and 100oC, respectively). One can also see this minimum boiling point behavior more clearly in Figure 2-3, p. 16 in Wankat. The azeotrope is the point where the saturated liquid line and the saturated vapor line touch. Note that the equilibrium curves “sweep up” slightly past the azeotrope before reaching the boiling point of pure ethanol since this is a minimum boiling azeotrope.

T vs x,y – Saturated Liquid and Vapor Plot Azeotrope 78.15

T vs x,y – Minimum and Maximum Boiling Azeotropes Figure 2-7, p. 20 in Wankat, exhibits a maximum boiling point azeotrope – what does the y vs. x plot look like for this system (HW problem 2-D1)? Compare a maximum boiling azeotrope to a minimum boiling azeotrope – how is the volatility with respect to concentration different?

End of Lecture 3