Enthalpy vs. Composition – Ponchon-Savarit Plot We have begun to employ mass balances, both total and component. We will also need to employ energy balances, based on enthalpy, for certain separation problems. We can use the Enthalpy vs. composition plot to obtain this information. Lecture 5

Enthalpy vs. Composition – Ponchon-Savarit Plot Lecture 5

Enthalpy vs. Composition – Ponchon-Savarit Plot 3 phases are shown on the plot – solid, liquid, and vapor. Temperature is represented by isothermal tie lines between the saturated liquid (boiling) line and the saturated vapor (dew) line. Points between the saturated liquid line and the saturated vapor line represent a two-phase, liquid-vapor system. An azeotrope is indicated by the composition at which the isotherm becomes vertical. Why? Why are the boiling point temperatures of the pure components different than those determined from the y vs. x and T vs. x,y plots for ethanol-water? The azeotrope for ethanol-water is indicated as T = 77.65 oC and a concentration of 0.955. Why is this different than that determined from the y vs. x and T vs. x,y plots for ethanol-water? Lecture 5

Enthalpy vs. Composition – Ponchon-Savarit Plot Note the boiling temperatures of the pure components, water and ethanol, and the temperature of the azeotrope are different due to the pressure at which the data was taken: P = 1 kg/cm2 (0.97 atm) 1 atm Water 99.1 oC 100 oC Ethanol 77.8 78.30 Azeotrope 77.65 78.15 Lecture 5

Mole Fraction vs. Weight Fraction Note that the enthalpy- composition plot is presented in terms of weight fractions – we will typically use mole fractions so one must convert between the two. For ethanol-water, this can be readily done using the molecular weights, MWEtOH =46.07 and MWw = 18.02. Lecture 5

Azetrope Composition – Mole Fraction vs. Weight Fraction Converting from wt fraction of the azeotrope to mole fraction: Thus, the azeotropic mole fraction is greater at P = 1 Kg/cm2 than at 1 atm: 0.902 vs. 0.8943. Although slight, one can begin to see the effect of pressure on the azeotropic point. Lecture 5

Converting Weight Fraction to Mole Fraction In General For a binary mixture: For a mixture of C components: Lecture 5

Enthalpy vs. Composition – Ponchon-Savarit Plot The bubble point temperature and dew point temperatures can be determined from the enthalpy vs. composition plot. The compositions of the 1st bubble formed and the last liquid drop can be determined from the enthalpy vs. composition plot. An auxiliary line is used to assist in these determinations… Lecture 5

Enthalpy vs. Composition – Bubble Point Temperature 82.2 oC Lecture 5

Enthalpy vs. Composition – 1st Bubble Composition Lecture 5

Enthalpy vs. Composition – Dew Point Temperature 94.8 oC Lecture 5

Enthalpy vs. Composition – Last Liquid Drop Composition Lecture 5

Enthalpy vs. Composition – Enthalpy Determination The major purpose of an enthalpy diagram is to determine enthalpies. We will use enthalpies in energy balances later. For example, if one were given a feed mixture of 35% ethanol (weight %) at T = 92oC and P = 1 kg/cm2 and the mixture was allowed to separate into vapor and liquid, what would be the enthalpies of the feed, vapor, and liquid? Lecture 5

Enthalpy vs. Composition – Enthalpy Determination 425 295 90 Lecture 5

Equilibrium Data – How to Handle? Tabular Data Generate graphical plots Generate analytical expressions (curve fit) Graphical y vs. x (P constant) – McCabe-Theile Pot T vs. x,y (P constant) – Saturated Liquid, Vapor Plot Enthalpy vs. composition (P constant, T) – Ponchon-Savarit Plot Analytical expressions Thermodynamics: Equations of state/Gibbs free energy models Distribution coefficients, K values Relative volatility DePreister charts Curve fit of data Lecture 5

Analytical Expressions for Equilibrium To date, we have looked at various ways to represent equilibrium behavior of binary systems graphically. There are several disadvantages to using graphical techniques: One cannot readily plot multi-component systems graphically (maximum is typically three). Separator design often has to be done using numerical methods; thus, analytical expressions for equilibrium behavior are needed. We will now look at other representations for handling equilibrium data analytically… Lecture 5

Other Equilibrium Relationships – Distribution Coefficient Lecture 5

Other Equilibrium Relationships – DePriester Charts One convenient source of K values for hydrocarbons, as a function of temperature and pressure (watch units), are the DePriester charts (Figs. 2-11 and 2-12, pp. 24-25, Wankat). The DePriester plots are presented over two different temperature ranges. Lecture 5

Lecture 5

Lecture 5

Using DePriester Charts – Boiling Temperatures of Pure Components One can determine the boiling point for a given component and pressure directly from the DePriester Charts – one can then determine which component in a mixture is the more volatile – the lower the boiling point, the more volatile a component is. For a pure component, K = 1.0. Assume one wishes to determine the boiling point temperature of ethylene at a pressure of P = 3000 kPa… Lecture 5

Tbp = - 9.5 oC Lecture 5

Question – DePriester Charts What are the equilibrium distribution coefficients, K, for a mixture containing: Ethylene n-Pentane n-Heptane at T = 120 oC and P =1500 kPa? Lecture 5

Lecture 5

Answer – DePriester Charts The equilibrium distribution coefficients, K, are: K Ethylene 8.5 n-Pentane 0.64 n-Heptane 0.17 at T = 120 oC and P =1500 kPa. Lecture 5

Question – Volatility What can one say about the volatility of each component from the K values? K Ethylene 8.5 n-Pentane 0.64 n-Heptane 0.17 Lecture 5

Answer – Volatility What can one say about the volatility of each component from the K values? K T boiling Ethylene 8.5 -35.5 oC n-Pentane 0.64 153 oC n-Heptane 0.17 >200 oC The boiling point temperatures of the pure components at P = 1500 kPa have also been determined from the DePriester charts for K = 1.0 for each component (n-heptane’s is off the chart). From the K values and the boiling point temperature of each pure component, one can say that the volatility follows the trend that ethylene>n-pentane>n-heptane. Lecture 5

Other Equilibrium Relationships – DePriester Equation Lecture 5

Other Equilibrium Relationships – Other Equilibrium Relationships – Mole Fraction – Vapor Pressure Relationship Lecture 5

Other Equilibrium Relationships – Distribution Coefficient – Vapor Pressure Relationship Lecture 5

Other Equilibrium Relationships – Relative Volatility Lecture 5

Other Equilibrium Relationships – Relative Volatility Lecture 5