Lecture 5 1

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 2

Enthalpy vs. Composition – Ponchon-Savarit Plot

Lecture 5 3

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 4

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 oCEthanol 77.8 78.30Azeotrope 77.65 78.15

Lecture 5 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 6

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.

ethanolfraction mole 902.0

waterg/gmole 02.18ethanolfraction wt 96.01

ethanol g/gmole 07.46ethanolfraction wt 96.0

ethanol g/gmole 07.46ethanolfraction wt 96.0

Lecture 5 7

Converting Weight Fraction to Mole Fraction In General

For a binary mixture:

For a mixture of C components:

2

2

1

1

1

1

1

mww

mwwmww

x

C

j j

j

i

i

i

mw

wmww

x

1

Lecture 5 8

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 9

Enthalpy vs. Composition – Bubble Point Temperature

82.2 oC

Lecture 5 10

Enthalpy vs. Composition – 1st Bubble Composition

Lecture 5 11

Enthalpy vs. Composition – Dew Point Temperature

94.8 oC

Lecture 5 12

Enthalpy vs. Composition – Last Liquid Drop Composition

Lecture 5 13

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 14

Enthalpy vs. Composition – Enthalpy Determination

425

295

90

Lecture 5 15

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 16

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 17

Other Equilibrium Relationships – Distribution Coefficient

Another method of representing equilibrium data is to define a distribution coefficient or K value as:

AAA/ xyK Eq. (2-10)

KA is typically a function of temperature, pressure, and composition. The distribution coefficient K is dependent upon temperature, pressure, and composition. However, for a few systems K is independent of composition, to a good approximation, which greatly simplifies the problem. p)K(T,K

A Eq. (2-11)

Lecture 5 18

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 19

Lecture 5 20

Lecture 5 21

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 22

Tbp = - 9.5 oC

Lecture 5 23

Question – DePriester Charts What are the equilibrium distribution

coefficients, K, for a mixture containing:

Ethylenen-Pentanen-Heptane

at T = 120 oC and P =1500 kPa?

Lecture 5 24

Lecture 5 25

Answer – DePriester Charts The equilibrium distribution

coefficients, K, are: K

Ethylene 8.5n-Pentane 0.64n-Heptane 0.17

at T = 120 oC and P =1500 kPa.

Lecture 5 26

Question – Volatility

What can one say about the volatility of each component from the K values?

K Ethylene 8.5n-Pentane 0.64n-Heptane 0.17

Lecture 5 27

Answer – Volatility What can one say about the volatility of each component from the

K values? K T boiling

Ethylene 8.5 -35.5 oCn-Pentane 0.64 153 oCn-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.

AAA / xyK

Lecture 5 28

Other Equilibrium Relationships – DePriester Equation

While the DePreister charts may be used directly, they have been conveniently fit as a function of temperature and pressure:

p

a

p

aaa

T

a

T

a2

p3

2

p2p1T6

T22

T1 plnKln Eq. (2-12)

where T is in oR and p is in psia. Table 2.4 (p. 26, Wankat) contains the K fit constants along with their mean errors (again, watch units!). Eq. (2-12) provides an analytical expression which can be used in numerical analyses. We will use this later for bubble and dew-point temperature calculations.

Lecture 5 29

Other Equilibrium Relationships –Mole Fraction – Vapor Pressure Relationship

If one does not have equilibrium data, K can be approximated using other more common thermodynamic data quantities such as vapor pressures. From Raoult’s law for ideal systems: AAA (VP)xp Eq. (2-14) where pA is the pressure due to component A in the mixture and (VP)A is the vapor pressure of pure component A, which is temperature dependent. From Dalton’s law of partial pressures:

p

py A

A Eq. (2-15)

Combining Eqs. (2-15) and (2-14) and rearranging yields:

p

(VP)

x

y A

A

A Eq. (2-16)

Lecture 5 30

Other Equilibrium Relationships – Distribution Coefficient – Vapor Pressure Relationship

The left-hand side of Eq. (2-16) is the definition of the distribution coefficient K; thus,

p

(VP)K A

A Eq. (2-17)

Eq. (2-17) allows one to obtain K’s from the vapor pressures of the pure components, which can be readily found for many chemical species using the Antoine equation:

CT

BAln(VP)A

Eq. (2-18)

where A, B, and C are constants, which can be found in many thermodynamic texts for many chemical species. Vapor pressure correlations can also be found in “The Properties of Gases and Liquids” (5th Ed. Poling, Prausnitz, O’Connell) Caution must be used when applying this K relationship since many systems are non-ideal. Actually, systems are often less ideal in the liquid phase because of the intimate contact of the chemical species, and these are handled by the liquid-phase activity coefficient, γA:

p

(VP)K AA

A

Eq. (2-19)

The activity coefficient can be obtained from correlations, e.g, Van Laar, Wilson, etc. (see thermodynamic texts).

Lecture 5 31

Other Equilibrium Relationships –Relative Volatility

K values are strongly dependent on temperature; however, this temperature behavior maybe somewhat similar, especially for similar chemical species, over certain temperature ranges. Consequently, if one takes the ratio of the K’s for two components, the temperature dependence will be less (see HW problem 2-D5). This ratio, defined as the relative volatility, αAB, for a binary system is:

BB

AA

B

AAB /xy

/xy

K

K Eq. (2-20)

If the temperature dependence for the K values is identical, then αAB will be independent of temperature. However, for all but the most ideal situations, αAB will have some temperature dependence. Why is it termed relative volatility? Because, if Raoult’s law is valid:

B

AAB (VP)

(VP) Eq. (2-21)

Thus, if (VP)A > (VP)B, component A is the more volatile and αAB > 1. Likewise, KA > KB; thus, one can determine the more volatile component by comparing K’s. If A is more volatile, its K value will be greater than B’s K value.

Lecture 5 32

Other Equilibrium Relationships –Relative Volatility

It will be convenient later on in separation problems to express the relative volatility in terms of the mole fractions and vice-versa For binary systems, the mole fractions are related by AB y1y and AB x1x Eq. (2-4) and substituting these into Eq. (2-20) yields:

AA

AAAB )xy(1

)x(1y

Eq. (2-22)

or A

AAAB y1

x1K

Solving Eq. (2-22) for yA and xA yields:

AAB

AABA x)1(1

xy

Eq. (2-23)

and

AABAB

AA y)1(

yx