Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN: 9781259696527
Author: J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher: McGraw-Hill Education
bartleby

Videos

Question
Book Icon
Chapter 13, Problem 13.32P

(a)

Interpretation Introduction

Interpretation:

The parameter values for the Margules equation which provide the best fit of GE/RTto the given data are to be determined. Also, a Pxydiagram is to be prepared and compared with the experimental data.

Concept Introduction:

Equation 13.19 to be used for Modified Raoult’s law is:

  yiP=xiγiPisat   ...... (1)

The formula to calculate the value of GE/RTfor a binary system is:

  GERT=x1lnγ1+x2lnγ2   ...... (2)

Margules equation for excess Gibbs energy in terms of the composition of the binary system in VLE is:

  GERT=(A12x1+A21x2)x1x2   ...... (3)

Here, A12 and A21are the temperature dependent parameters, specific for a system.

The equations used to calculate lnγ1 and lnγ2are:

  lnγ1=x22[A12+2(A 21A 12)x1]lnγ2=x12[A21+2(A 12A 21)x2]   ...... (4)

(a)

Expert Solution
Check Mark

Answer to Problem 13.32P

The parameter values for the Margules equation which provide the best fit of GE/RTto the given data are:

  A12=0.6828A21=0.4753

The Pxydiagram for the binary system containing methanol (1)/water (2) at 333.15 Kfor both calculated as well as experimental values are shown below. The values do not deviate by considerable extent from each other.

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  1

Explanation of Solution

Given information:

The set of VLE data for the binary system containing methanol(1)/water(2) at 333.15 Kis:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  2

From the given data, first calculate the value of x2, and y2and tabulating then in excel spreadsheet as shown below:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  3

Now, use equation (1) for the Modifies Raoult’s law and calculate the value of γ1 and γ2using the below mentioned formula and tabulate it in the excel spreadsheet.

  γ1=y1Px1P1satγ2=y2Px2P2sat

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  4

Use the equation (2) to calculate the value of GE/RTfor every value of x1and tabulate it in the excel spreadsheet as shown below:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  5

Rewrite equation (3) so that the equation becomes linear in x1as:

  ( G E/RT x 1 x 2)=(A12x1+A21(1 x 1))( G E/RT x 1 x 2)=(A21A12)x1+A12                                                                                     ...... (5)

Now, calculate the values of (GE/RTx1x2)as shown below:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  6

Plot the graph of (GE/RTx1x2)versus x1and using the excel tool as:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  7

The equation that fits the plot is:

  (GE/RTx1x2)=0.2075x1+0.6828

Compare it with equation (5) so that the values of A12 and A21will be:

  A12=0.6828A21=0.4753

According to the above correlation for GE/RTand the values of A12 and A21, the correlations for lnγ1 and lnγ2using the equation set (4) will be:

  ln(γ1)calc.=x22[0.6828+2(0.47530.6828)x1](γ1)calc.=exp(x22[0.68280.415x1])ln(γ2)calc.=x12[0.4753+2(0.68280.4753)x2](γ2)calc.=exp(x12[0.4753+0.415x2])

Now, using the above relations, calculate the values of γ1 and γ2for each value of x1 and x2and tabulate the data in the excel spreadsheet as:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  8

Again, use the Modified Raoult’s law equation (1) to calculate the pressure at each value of x1 and x2using the calculated values of γ1 and γ2as:

  (P)calc.=x1(γ1)calc.P1sat+x2(γ2)calc.P2sat

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  9

Now, use the below mentioned formula to calculate the value of y1for each of the calculated value of Pas:

  (y1)calc.=x1( γ 1)calc.P1sat(P)calc.

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  10

Using the tools of the excel, plot the graph of (Px)calc.(Py)calc., Px, and Pyand mark labels as shown below:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  11

Calculate the deviation the calculated value of pressure by determining the root mean square (RMS) as shown below:

  RMS= i=1n ( P i ( Pi ) calc. )2nHere, n is number of entries.RMS=0.3989

Since, the RMS value is very small, the experimental and calculated value of pressure do not deviate much from each other.

(b)

Interpretation Introduction

Interpretation:

The parameter values for the van Laar equation which provide the best fit of GE/RTto the given data are to be determined. Also, a Pxydiagram is to be prepared and compared with the experimental data.

Concept Introduction:

Equation 13.19 to be used for Modified Raoult’s law is:

  yiP=xiγiPisat   ...... (1)

The formula to calculate the value of GE/RTfor a binary system is:

  GERT=x1lnγ1+x2lnγ2   ...... (2)

Van Laar equation for excess Gibbs energy in terms of the composition of the binary system in VLE is:

  GERT=x1x2A12A21(A12x1+A21x2)   ...... (6)

Here, A12 and A21are the temperature dependent parameters, specific for a system.

The equations used to calculate lnγ1 and lnγ2from van Laar equation are:

  lnγ1=A12(1+ A12 x1 A21 x2 )2lnγ2=A21(1+ A21 x2 A12 x1 )2   ...... (7)

(b)

Expert Solution
Check Mark

Answer to Problem 13.32P

The parameter values for the van Laar equation which provide the best fit of GE/RTto the given data are:

  A12=0.705A21=0.485

The Pxydiagram for the binary system containing methanol(1)/water(2) at 333.15 Kfor both calculated as well as experimental values are shown below. The values do not deviate by considerable extent from each other.

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  12

Explanation of Solution

Given information:

The set of VLE data for the binary system containing methanol(1)/water(2) at 333.15 Kis:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  13

From the given data, first calculate the value of x2, and y2and tabulating then in excel spreadsheet as shown below:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  14

Now, use equation (1) for the Modifies Raoult’s law and calculate the value of γ1 and γ2using the below mentioned formula and tabulate it in the excel spreadsheet.

  γ1=y1Px1P1satγ2=y2Px2P2sat

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  15

Use the equation (2) to calculate the value of GE/RTfor every value of x1and tabulate it in the excel spreadsheet as shown below:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  16

Rewrite equation (6) so that the equation becomes linear in x1as:

  ( G E/RT x 1 x 2)=A12A21( A 12 x 1+ A 21 x 2)( x 1 x 2 G E/RT)=( A 12 x 1+ A 21 x 2)A12A21=A12x1A12A21+A21x2A12A21( x 1 x 2 G E/RT)=x1A21+1x1A12( x 1 x 2 G E/RT)=(1 A 211 A 12)x1+1A12                                                                             ...... (8)

Now, calculate the values of (x1x2GE/RT)as shown below:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  17

Plot the graph of (x1x2GE/RT)versus x1and using the excel tool as:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  18

The equation that fits the plot is:

  (x1x2GE/RT)=0.6414x1+1.4185

Compare it with equation (8) so that the values of A12 and A21will be:

  intercept=1.4185=1A12A12=11.4185=0.705slope=0.6414=1A211A120.6414=1A2110.705A21=10.6414+10.705=0.485

According to the above correlation for GE/RTand the values of A12 and A21, the correlations for lnγ1 and lnγ2using the equation set (7) will be:

  ln(γ1)calc.=A12(1+ A12 x1 A21 x2 )2(γ1)calc.=exp[0.705( 1+0.705 x 10.485 x 2 )2](γ1)calc.=exp[0.705( 1+1.454 x 1 x 2 )2]ln(γ2)calc.=A21(1+ A21 x2 A12 x1 )2(γ2)calc.=exp[0.485( 1+0.485 x 20.705 x 1 )2](γ2)calc.=exp[0.485( 1+0.688 x 2 x 1 )2]

Now, using the above relations, calculate the values of γ1 and γ2for each value of x1 and x2and tabulate the data in the excel spreadsheet as:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  19

Again, use the Modified Raoult’s law equation (1) to calculate the pressure at each value of x1 and x2using the calculated values of γ1 and γ2as:

  (P)calc.=x1(γ1)calc.P1sat+x2(γ2)calc.P2sat

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  20

Now, use the below mentioned formula to calculate the value of y1for each of the calculated value of Pas:

  (y1)calc.=x1( γ 1)calc.P1sat(P)calc.

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  21

Using the tools of the excel, plot the graph of (Px)calc.(Py)calc., Px, and Pyand mark labels as shown below:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  22

Calculate the deviation the calculated value of pressure by determining the root mean square (RMS) as shown below:

  RMS= i=1n ( P i ( Pi ) calc. )2nHere, n is number of entries.RMS=0.454

Since, the RMS value is very small, the experimental and calculated value of pressure do not deviate much from each other.

(c)

Interpretation Introduction

Interpretation:

The parameter values for the Wilson equation which provide the best fit of GE/RTto the given data are to be determined. Also, a Pxydiagram is to be prepared and compared with the experimental data.

Concept Introduction:

Equation 13.19 to be used for Modified Raoult’s law is:

  yiP=xiγiPisat   ...... (1)

The formula to calculate the value of GE/RTfor a binary system is:

  GERT=x1lnγ1+x2lnγ2   ...... (2)

Wilson equation for excess Gibbs energy in terms of the composition of the binary system in VLE is:

  GERT=x1ln(x1+x2Λ12)x2ln(x2x1Λ21)   ...... (9)

Here, Λ12 and Λ21are the temperature dependent parameters, specific for a system.

The equations used to calculate lnγ1 and lnγ2from Wilson equation are:

  lnγ1=ln(x1+x2Λ12)+x2( Λ 12 x 1+ x 2 Λ 12 Λ 21 x 2+ x 1 Λ 21)lnγ2=ln(x2+x1Λ21)+x1( Λ 12 x 1+ x 2 Λ 12 Λ 21 x 2+ x 1 Λ 21)   ...... (10)

(c)

Expert Solution
Check Mark

Answer to Problem 13.32P

The parameter values for the Wilson equation which provide the best fit of GE/RTto the given data are:

  Λ12=0.476Λ21=1.026

The Pxydiagram for the binary system containing methanol(1)/water(2) at 333.15 Kfor both calculated as well as experimental values are shown below. The values deviate by considerable extent from each other.

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  23

Explanation of Solution

Given information:

The set of VLE data for the binary system containing methanol(1)/water(2) at 333.15 Kis:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  24

From the given data, first calculate the value of x2, and y2and tabulating then in excel spreadsheet as shown below:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  25

Now, use equation (1) for the Modifies Raoult’s law and calculate the value of γ1 and γ2using the below mentioned formula and tabulate it in the excel spreadsheet.

  γ1=y1Px1P1satγ2=y2Px2P2sat

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  26

Use the equation (2) to calculate the value of GE/RTfor every value of x1and tabulate it in the excel spreadsheet as shown below:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  27

Now, use the method of the non-linear least square and fit the GE/RTdata into equation (9). First guess a value for Λ12 and Λ21 as 0.5 and 1.0respectively, then use it to calculate GE/RTfor each value of x1 . Then find the sum of the squared errors and minimize this value to get the value of the parameters Λ12 and Λ21as:

  Λ12=0.476Λ21=1.026

Use the values of Λ12 and Λ21and the correlations in equation set (10) to calculate the values of γ1 and γ2 as:

Now, using the above relations, calculate the values of γ1 and γ2for each value of x1 and x2and tabulate the data in the excel spreadsheet as:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  28

Again, use the Modified Raoult’s law equation (1) to calculate the pressure at each value of x1 and x2using the calculated values of γ1 and γ2as:

  (P)calc.=x1(γ1)calc.P1sat+x2(γ2)calc.P2sat

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  29

Now, use the below mentioned formula to calculate the value of y1for each of the calculated value of Pas:

  (y1)calc.=x1( γ 1)calc.P1sat(P)calc.

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  30

Using the tools of the excel, plot the graph of (Px)calc.(Py)calc., Px, and Pyand mark labels as shown below:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  31

Calculate the deviation the calculated value of pressure by determining the root mean square (RMS) as shown below:

  RMS= i=1n ( P i ( Pi ) calc. )2nHere, n is number of entries.RMS=2.86

Since, the RMS value is considerable, the experimental and calculated value of pressure deviate from each other by a considerable measure.

(d)

Interpretation Introduction

Interpretation:

The parameter values for the Margules equation which provide the best fit of Px1data using Barker’s method data are to be determined. Also, a diagram is to be prepared to show the residuals δP and δy1which are plotted versus x1 .

Concept Introduction:

Equation 13.19 to be used for Modified Raoult’s law is:

  yiP=xiγiPisat   ...... (1)

Margules equation for excess Gibbs energy in terms of the composition of the binary system in VLE is:

  GERT=(A12x1+A21x2)x1x2   ...... (3)

Here, A12 and A21are the temperature dependent parameters, specific for a system.

The equations used to calculate lnγ1 and lnγ2are:

  lnγ1=x22[A12+2(A 21A 12)x1]lnγ2=x12[A21+2(A 12A 21)x2]   ...... (4)

(d)

Expert Solution
Check Mark

Answer to Problem 13.32P

The parameter values for the Margules equation which provide the best fit of Px1data using Barker’s method data are:

  A12=0.758A21=0.435

The plot residuals δP and δy1 versus x1on same graph is:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  32

Explanation of Solution

Given information:

The set of VLE data for the binary system containing methanol(1)/water(2) at 333.15 Kis:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  33

Barker’s Method is the method of determining the parameters by non-linear least squares.

Guess an initial value of A12 and A21 as 0.5 and 1.0respectively, then use it to determine the value of γ1 and γ2using equation (4) for each value of x1 .

Now, calculate the value of (P)calc.for each value of x1using equation (1) and γ1 and γ2 .

Then find the sum of the squared errors (SSE) using the below mentioned formula and minimize this value to get the value of the parameters A12 and A21as:

  SSE=i=1n( Pi ( P i ) calc.)2(Here, n is the number of entries)A12=0.758A21=0.435

Using the equation set (4) and the parameter values, deduce the relation for γ1 and γ2 as:

  ln(γ1)calc.=x22[0.758+2(0.4350.758)x1](γ1)calc.=exp(x22[0.7580.646x1])ln(γ2)calc.=x12[0.435+2(0.7580.453)x2](γ2)calc.=exp(x12[0.435+0.646x2])

Now, using the above relations, calculate the values of γ1 and γ2for each value of x1 and x2and tabulate the data in the excel spreadsheet as:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  34

Again, use the Modified Raoult’s law equation (1) to calculate the pressure at each value of x1 and x2using the calculated values of γ1 and γ2as:

  (P)calc.=x1(γ1)calc.P1sat+x2(γ2)calc.P2sat

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  35

Now, use the below mentioned formula to calculate the value of y1for each of the calculated value of Pas:

  (y1)calc.=x1( γ 1)calc.P1sat(P)calc.

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  36

Using the tools of the excel, plot the graph of (Px)calc.(Py)calc., Px, and Pyand mark labels as shown below:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  37

Calculate the deviation the calculated value of pressure by determining the root mean square (RMS) as shown below:

  RMS= i=1n ( P i ( Pi ) calc. )2nHere, n is number of entries.RMS=0.1667

Since, the RMS value is very small, the experimental and calculated value of pressure do not deviate much from each other.

Now, calculate the residuals δP and δy1as shown. Also, calculate δy1×100as δy1is very small and is difficult to plot on same graph as δP .

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  38

Plot these residuals against x1on same graph as:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  39

(e)

Interpretation Introduction

Interpretation:

The parameter values for the van Laar equation which provide the best fit of Px1data using Barker’s method data are to be determined. Also, a diagram is to be prepared to show the residuals δP and δy1which are plotted versus x1 .

Concept Introduction:

Equation 13.19 to be used for Modified Raoult’s law is:

  yiP=xiγiPisat   ...... (1)

Van Laar equation for excess Gibbs energy in terms of the composition of the binary system in VLE is:

  GERT=x1x2A12A21(A12x1+A21x2)   ...... (6)

Here, A12 and A21are the temperature dependent parameters, specific for a system.

The equations used to calculate lnγ1 and lnγ2from van Laar equation are:

  lnγ1=A12(1+ A12 x1 A21 x2 )2lnγ2=A21(1+ A21 x2 A12 x1 )2   ...... (7)

(e)

Expert Solution
Check Mark

Answer to Problem 13.32P

The parameter values for the van Laar equation which provide the best fit of Px1data using Barker’s method data are:

  A12=0.830A21=0.468

The plot residuals δP and δy1versus x1on same graph is:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  40

Explanation of Solution

Given information:

The set of VLE data for the binary system containing methanol(1)/water(2) at 333.15 Kis:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  41

Barker’s Method is the method of determining the parameters by non-linear least squares.

Guess an initial value of A12 and A21 as 0.5 and 1.0respectively, then use it to determine the value of γ1 and γ2using equation (7) for each value of x1 .

Now, calculate the value of (P)calc.for each value of x1using equation (1) and γ1 and γ2 .

Then find the sum of the squared errors (SSE) using the below mentioned formula and minimize this value to get the value of the parameters A12 and A21as:

  SSE=i=1n( Pi ( P i ) calc.)2(Here, n is the number of entries)A12=0.830A21=0.468

Using the equation set (7) and the parameter values, deduce the relation for γ1 and γ2 as:

  ln(γ1)calc.=A12(1+ A12 x1 A21 x2 )2(γ1)calc.=exp[0.830( 1+0.830 x 10.468 x 2 )2](γ1)calc.=exp[0.705( 1+1.7735 x 1 x 2 )2]ln(γ2)calc.=A21(1+ A21 x2 A12 x1 )2(γ2)calc.=exp[0.468( 1+0.468 x 20.830 x 1 )2](γ2)calc.=exp[0.485( 1+0.5639 x 2 x 1 )2]

Now, using the above relations, calculate the values of γ1 and γ2for each value of x1 and x2and tabulate the data in the excel spreadsheet as:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  42

Again, use the Modified Raoult’s law equation (1) to calculate the pressure at each value of x1 and x2using the calculated values of γ1 and γ2as:

  (P)calc.=x1(γ1)calc.P1sat+x2(γ2)calc.P2sat

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  43

Now, use the below mentioned formula to calculate the value of y1for each of the calculated value of Pas:

  (y1)calc.=x1( γ 1)calc.P1sat(P)calc.

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  44

Using the tools of the excel, plot the graph of (Px)calc.(Py)calc., Px, and Pyand mark labels as shown below:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  45

Calculate the deviation the calculated value of pressure by determining the root mean square (RMS) as shown below:

  RMS= i=1n ( P i ( Pi ) calc. )2nHere, n is number of entries.RMS=0.286

Since, the RMS value is very small, the experimental and calculated value of pressure do not deviate much from each other.

Now, calculate the residuals δP and δy1as shown. Also, calculate δy1×100as δy1is very small and is difficult to plot on same graph as δP .

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  46

Plot these residuals against x1on same graph as:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  47

(f)

Interpretation Introduction

Interpretation:

The parameter values for the Wilson equation which provide the best fit of Px1data using Barker’s method data are to be determined. Also, a diagram is to be prepared to show the residuals δP and δy1which are plotted versus x1 .

Concept Introduction:

Equation 13.19 to be used for Modified Raoult’s law is:

  yiP=xiγiPisat   ...... (1)

Wilson equation for excess Gibbs energy in terms of the composition of the binary system in VLE is:

  GERT=x1ln(x1+x2Λ12)x2ln(x2x1Λ21)   ...... (9)

Here, Λ12 and Λ21are the temperature dependent parameters, specific for a system.

The equations used to calculate lnγ1 and lnγ2from Wilson equation are:

  lnγ1=ln(x1+x2Λ12)+x2( Λ 12 x 1+ x 2 Λ 12 Λ 21 x 2+ x 1 Λ 21)lnγ2=ln(x2+x1Λ21)+x1( Λ 12 x 1+ x 2 Λ 12 Λ 21 x 2+ x 1 Λ 21)   ...... (10)

(f)

Expert Solution
Check Mark

Answer to Problem 13.32P

The parameter values for the Wilson equation which provide the best fit of Px1data using Barker’s method data are:

  Λ12=0.348Λ21=1.198

The plot residuals δP and δy1versus x1on same graph is:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  48

Explanation of Solution

Given information:

The set of VLE data for the binary system containing methanol(1)/water(2) at 333.15 Kis:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  49

Barker’s Method is the method of determining the parameters by non-linear least squares.

Guess an initial value of A12 and A21 as 0.5 and 1.0respectively, then use it to determine the value of γ1 and γ2using equation (10) for each value of x1 .

Now, calculate the value of (P)calc.for each value of x1using equation (1) and γ1 and γ2 .

Then find the sum of the squared errors (SSE) using the below mentioned formula and minimize this value to get the value of the parameters Λ12 and Λ21as:

  SSE=i=1n( Pi ( P i ) calc.)2(Here, n is the number of entries)Λ12=0.348Λ21=1.198

Using the equation set (10) and the parameter values, deduce the relation for γ1 and γ2 as:

Now, using the above relations, calculate the values of γ1 and γ2for each value of x1 and x2and tabulate the data in the excel spreadsheet as:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  50

Again, use the Modified Raoult’s law equation (1) to calculate the pressure at each value of x1 and x2using the calculated values of γ1 and γ2as:

  (P)calc.=x1(γ1)calc.P1sat+x2(γ2)calc.P2sat

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  51

Now, use the below mentioned formula to calculate the value of y1for each of the calculated value of Pas:

  (y1)calc.=x1( γ 1)calc.P1sat(P)calc.

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  52

Using the tools of the excel, plot the graph of (Px)calc.(Py)calc., Px, and Pyand mark labels as shown below:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  53

Calculate the deviation the calculated value of pressure by determining the root mean square (RMS) as shown below:

  RMS= i=1n ( P i ( Pi ) calc. )2nHere, n is number of entries.RMS=4.314

Since, the RMS value is considerable, the experimental and calculated value of pressure deviate from each other by a considerable measure.

Now, calculate the residuals δP and δy1as shown. Also, calculate δy1×100as δy1is very small and is difficult to plot on same graph as δP .

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  54

Plot these residuals against x1on same graph as:

Introduction to Chemical Engineering Thermodynamics, Chapter 13, Problem 13.32P , additional homework tip  55

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 13 Solutions

Introduction to Chemical Engineering Thermodynamics

Ch. 13 - A binary mixture of mole fraction z1is flashed to...Ch. 13 - Humidity, relating to the quantity of moisture in...Ch. 13 - A concentrated binary solution containing mostly...Ch. 13 - Air, even more than carbon dioxide, is inexpensive...Ch. 13 - Helium-laced gases are used as breathing media for...Ch. 13 - A binary system of species 1 and 2 consists of...Ch. 13 - For the system ethyl ethanoate(l)/n-heptane(2) at...Ch. 13 - A liquid mixture of cyclohexanone(1)/phenol(2) for...Ch. 13 - A binary system of species 1 and 2 consists of...Ch. 13 - For the acetone(l)/methanol(2) system, a vapor...Ch. 13 - The following is a rule of thumb: For a binary...Ch. 13 - A process stream contains light species 1 and...Ch. 13 - If a system exhibits VLE, at least one of the...Ch. 13 - Flash calculations are simpler for binary systems...Ch. 13 - Prob. 13.25PCh. 13 - (a) A feed containing equimolar amounts of...Ch. 13 - A binary mixture of benzene(1) and toluene(2) is...Ch. 13 - Ten (10) kmolhr-1 of hydrogen sulfide gas is...Ch. 13 - Physiological studies show the neutral comfort...Ch. 13 - Prob. 13.30PCh. 13 - Prob. 13.31PCh. 13 - Prob. 13.32PCh. 13 - If Eq. (13.24) is valid for isothermal VLE in a...Ch. 13 - Prob. 13.34PCh. 13 - The excess Gibbs energy for binary systems...Ch. 13 - For the ethanol(l )/chloroform(2) system at 50°C,...Ch. 13 - VLE data for methyl tert-butyl...Ch. 13 - Prob. 13.38PCh. 13 - Prob. 13.39PCh. 13 - Following are VLE data for the system...Ch. 13 - Prob. 13.41PCh. 13 - Prob. 13.42PCh. 13 - Problems 13.43 through 13.54 require parameter...Ch. 13 - Problems 13.43 through 13.54 require parameter...Ch. 13 - Prob. 13.45PCh. 13 - Problems 13.43 through 13.54 require parameter...Ch. 13 - Prob. 13.47PCh. 13 - Prob. 13.48PCh. 13 - Prob. 13.49PCh. 13 - Prob. 13.50PCh. 13 - Problems 13.43 through 13.54 require parameter...Ch. 13 - Prob. 13.52PCh. 13 - The following expressions have been reported for...Ch. 13 - Possible correlating equations for In 1 in a...Ch. 13 - Prob. 13.57PCh. 13 - Binary VLE data are commonly measured at constant...Ch. 13 - Consider the following model for GE/RT of a binary...Ch. 13 - A breathalyzer measures volume-% ethanol in gases...Ch. 13 - Table 13.10 gives values of parameters for the...Ch. 13 - Prob. 13.62PCh. 13 - A single P-x1- y1data point is available for a...Ch. 13 - A single P- x1, data point is available for a...Ch. 13 - The excess Gibbs energy for the system...Ch. 13 - Prob. 13.66PCh. 13 - A system formed of methane(l) and a light oil(2)...Ch. 13 - Use Eq. (13.13) to reduce one of the following...Ch. 13 - For one of the following substances, determine...Ch. 13 - Departures from Raoult's law are primarily from...Ch. 13 - The relative volatility a12is commonly used in...Ch. 13 - Prob. 13.74PCh. 13 - Prob. 13.75PCh. 13 - Prob. 13.76P
Knowledge Booster
Background pattern image
Chemical Engineering
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemical-engineering and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Text book image
Introduction to Chemical Engineering Thermodynami...
Chemical Engineering
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:McGraw-Hill Education
Text book image
Elementary Principles of Chemical Processes, Bind...
Chemical Engineering
ISBN:9781118431221
Author:Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:WILEY
Text book image
Elements of Chemical Reaction Engineering (5th Ed...
Chemical Engineering
ISBN:9780133887518
Author:H. Scott Fogler
Publisher:Prentice Hall
Text book image
Process Dynamics and Control, 4e
Chemical Engineering
ISBN:9781119285915
Author:Seborg
Publisher:WILEY
Text book image
Industrial Plastics: Theory and Applications
Chemical Engineering
ISBN:9781285061238
Author:Lokensgard, Erik
Publisher:Delmar Cengage Learning
Text book image
Unit Operations of Chemical Engineering
Chemical Engineering
ISBN:9780072848236
Author:Warren McCabe, Julian C. Smith, Peter Harriott
Publisher:McGraw-Hill Companies, The
Homogeneous and Heterogeneous Equilibrium - Chemical Equilibrium - Chemistry Class 11; Author: Ekeeda;https://www.youtube.com/watch?v=8V9ozZSKl9E;License: Standard YouTube License, CC-BY