Thermodynamic Processes 2 E-Book

Salah Belaadi

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 271

Veröffentlichungsjahr: 2020

Beschreibung

Thermodynamic Processes 2 is devoted to the study of equilibrium between phases in the case of the four changes of physical state: fusion, boiling or vaporization, sublimation and allotropy or transition. It also includes a section that addresses energy s relationship to the zero sum aspect of exergy and thermal cycles. This second volume presents scientific and technical examples both theoretical and industrial which are the result of a careful selection, accrued over more than three decades of teaching thermodynamics and in collaboration with the industry sector. The didactic exercises and the practical problems are entirely dedicated to the understanding of this science, and the potential applications for the industrial world. This book is a tool for work and reflection essential for the student in training, as well as the engineer or experienced researcher.

Leseprobe

Table of Contents

Cover

Foreword 1

Foreword 2

Preface

1 Equilibria of Liquid/Vapor Phases

1.1. Exercises

1.2. Problems

1.3. Tests

1.4. Detailed corrections

2 Allotropic Solid/Solid Equilibria

2.1. Exercises

2.2. Problems

2.3. Tests

2.4. Detailed corrections

3 Solid/Vapor Sublimation Equilibria

3.1. Exercises

3.2. Problems

3.3. Tests

3.4. Detailed corrections

4 Process Energetics

4.1. Exercises

4.2. Problems

4.3. Tests

4.4. Detailed corrections

Appendix

Nomenclature

References

Index

End User License Agreement

List of Tables

Chapter 1

Table 1.1. Liquid/liquid solubility limits

Table 1.2. Composition of liquid and vapor phases at equilibrium at 1.009 atm

Table 1.3. Properties of pure bodies (1) and (2)

List of Illustrations

Chapter 1

Figure 1.1. Liquid/vapor equilibrium curve of benzene

Figure 1.2. Curves of g

m

as a function of the MEK titer

Figure 1.3. Curve for

Figure 1.4. Schematic showing the deposition curve as a function of titer

Figure 1.5. Curve for y

1

= f(x

1

) and bubble curve

Figure 1.6. Curves for h

ex

, s

ex

and g

ex

as a function of x

1

Figure 1.7. Curve for h

m

= f(x

1

)

Figure 1.8. Curve for

Figure 1.9. Curves for T = f(x

1

) and T = f(y

1

)

Figure 1.10. Curve for α

12

= f(x

1

)

Figure 1.11. T = f (x,y) diagram

Figure 1.12. Cyclic transformation at the equilibrium state

Figure 1.13. N

2

“pure body” diagram

Chapter 2

Figure 2.1. Iron/carbon equilibrium diagram

Figure 2.2. Phase diagram of the iron/tin binary

Figure 2.3. Phase diagram of the binary Cu(1)/Pb(2)

Figure 2.4. Isobaric l/s equilibrium diagram of Li(1)/Na(2)

Figure 2.5. Equilibrium curve of H

2

O(1)/H

2

O

2

(2) mixture

Figure 2.6. Diagram of cadmium/lead

Figure 2.7. Diagram of a solubility curve of a component

Figure 2.8. Different phases of the iron/tin diagram

Figure 2.9. Deposition curve T=f(x

1

)

Figure 2.10. Indium/tin phase diagram

Figure 2.11. Diagram (T, x

2

) at constant P of Li(1)/Na(2)

Figure 2.12. Thermal analysis curve (T,t) at constant P

Figure 2.13. Phase diagram of water/hydrogen peroxide

Figure 2.14. Thermal analysis curve T = f(t)

Figure 2.15. Crystallization diagram of the binary HNO

3

/H

2

O

Figure 2.16. Thermal analysis curve of the binary HNO

3

/H

2

O

Figure 2.17. Solid/liquid and liquid/vapor diagrams of the binary

Figure 2.18. Thermal analysis curve of the binary H

2

O/C

2

H

5

OH

Figure 2.19. s/l and l/v equilibrium diagrams of the binary H

2

O/C

2

H

6

O

2

Figure 2.20. Thermal analysis curve of the 10% glycol mixture

Chapter 3

Figure 3.1. Curve Cp = f(T)

Figure 3.2. Curve lnP = f(1/T)

Figure 3.3. Amount of H

2

produced as a function of moles of Fe

Figure 3.4. Equilibrium diagram of a pure body

Figure 3.5. Breakdown of sublimation process

Figure 3.6. Interpolation curve T = f(P)

Figure 3.7. Sublimation and evaporation curves of H

2

O

Chapter 4

Figure 4.1. Nozzle 1

Figure 4.2. Nozzle 2

Figure 4.3. System overview (σ)

Figure 4.4. The Lenoir cycle

Figure 4.5. Joule cycle

Figure 4.6. Dual cycle

Figure 4.7. Otto cycle

Figure 4.8. Diesel cycle

Figure 4.9. Diagram of a heat transformer

Figure 4.10. Diagram of dry ice production

Figure 4.11. Diagram of a jet

Figure 4.12a. Diagrams of the Carnot cycle in different coordinate systems

Figure 4.12b. Diagrams of the Carnot cycle in different coordinate systems

Figure 4.13. Diagram of the engine

Figure 4.14. Cycle of gas in the turbine

Figure 4.15. Diagram of a combined system

Figure 4.16. Synoptic diagram of the setup

Figure 4.17. Thermodynamic cycle of air

Figure 4.18. Curve P = f(V)

Figure 4.19. Representation of the cycle in coordinates (T,S)

Figure 4.20. Diagram of two different heating modes: (a) cooling using water at ...

Figure 4.21. Diagram of the production area

Figure 4.22. Synoptic diagram of the production area

Figure 4.23. Diagram (P, )

Figure 4.24. Thermal diagram of the skating rink

Figure 4.25. Joule cycle

Figure 4.26. Pulsejet engine cycle

Guide

Cover

Table of Contents

Begin Reading

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In memory of my parents

Series Editor

Jean-Claude Charpentier

Thermodynamic Processes 2

State and Energy Change Systems

Salah Belaadi

First published 2020 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

ISTE Ltd27-37 St George’s RoadLondon SW19 4EUUK

www.iste.co.uk

John Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USA

www.wiley.com

© ISTE Ltd 2020

The rights of Salah Belaadi to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Control Number: 2019953627

British Library Cataloguing-in-Publication DataA CIP record for this book is available from the British LibraryISBN 978-1-78630-514-5

Foreword 1Circular Economy and Engineering

Circular economy and engineering: process thermodynamics as an essential chemical engineering tool for the design and control of the processes encountered in the factory of the future within the framework of Industry 4.0

Process engineering involves the sciences and technologies that optimally transform matter and energies into products required by a consumer and into nonpolluting wastes. Today, it takes part in the framework of circular economy and engineering (monitoring of products and processes from cradle to grave), and the optimal transformations of matter and energies must be carried out to design the factory of the future, taking into account the emergence of Industry 4.0 and the voluminous amount of data (Big Data movement).

Modern (green) process engineering is deliberately oriented toward process intensification (i.e., producing much more and better, with use of much less resources). This involves a physical-chemistry multidisciplinary and multiscale approach to modelling and computer simulation, in terms of time and space, from the atomic and molecular scales. This involves the equipment and the reactor scales, up to the scales of the overall factory (i.e., the design of a refinery, a chemical, a textile or a cement complex plant from Schrödinger equations).

To meet this multidisciplinary and multiscale approach, the preponderant and irreplaceable concept and background of chemical thermodynamics appears in all its splendour, and more generally, this concerns the thermodynamics of processes for the multiscale control of these processes.

It is clear that studies that discuss thermodynamics of processes must cover chemical thermodynamics (open or closed systems with or without chemical reaction, phase equilibrium) and the energetics of processes (thermal cycles, heat pump, degraded energy, exergy). However, these studies must also be illustrated with examples of real multiscale physicochemical applications. This will prepare or help or contribute to the design, the development and the control of the processes that will be encountered in the factory of the future, by means of methodologies and techniques to obtain reliable thermodynamic data that will contribute to the abundance of data (Big Data/Industry 4.0).

A big thank you to Professor Salah Belaadi, leading expert in education and research in the field of thermodynamics of processes, for offering such an instructional and didactic book, whose chapters mainly present exercises oriented towards industrial applications.

This book on thermodynamics and energetics of processes is a guide (a vademecum), which I am personally convinced will be of great benefit to a large number of university teachers and researchers, and engineers and technicians active in today’s economy sector, as well in the very near future.

Jean-Claude CHARPENTIER

Former director of ENSIC Nancy and ESCPE Lyon, France

Former president of the European Federation of Chemical Engineering

Laboratoire Réactions et Génie des Procédés

CNRS/ENSIC/University of Lorraine

Foreword 2

Thermodynamics is a universal science that is of great interest in all its applications. The premises of thermodynamics are not always easy to understand, in the eyes of students nor in those of seasoned researchers, nor are the numerous developments that result from it.

Nature is complex and the scientist must be humble with regard to what he/she sees. He/she must scrupulously observe, carefully reflect, attempt to interpret and undertake modeling, a theory which will be deemed valid only until a new observation, or a new experiment comes to question them. From this perspective, it is necessary for the educator to show conviction, insight and passion in order to best convey the thirst for effort and for accomplishing work, to promote vocations and to discover talents.

Professor Salah Belaadi has spent many years teaching thermodynamics. He has enriched his courses with many exercises entirely dedicated to understanding this science and potential applications for the industrial world. Over the years, he has been able to select the most interesting and relevant exercises. The collection he proposes today is therefore an assortment of carefully selected topics for thermodynamic reflection and culture.

I wish him the success he deserves and I hope that a very large number of readers will enjoy this content.

Dominique RICHON

Emeritus Professor at Mines ParisTech

Former director of Thermodynamics and Phases Equilibrium Laboratory

Preface

The aim of this book is to reduce apprehension toward thermodynamics and to make it more familiar to those who have to use it, both on completion of apprenticeships, training and retraining, as well as to those conducting research and reflection on the evolution of processes at the time of transformation of matter and/or energy.

The need to write this book was apparent to me, after so many years of teaching at various university levels, after the unequivocal statement: the difficulty encountered by students – or engineers working in companies or research groups – to solve concrete problems in thermodynamics comes from the fact that the manuals, which cover applications of the concepts of this discipline, are too didactic.

Hence why I propose an original approach for this book - to use thermodynamics as a resolution tool – indispensable for mastering a process of energy transformation and/or matter using one or more thermodynamic concepts. Thus, this book is not structured according to the progression of the teaching of the concepts of thermodynamics, but rather according to the evolution of the scientific difficulty compared to the state of the thermodynamic system studied from closed systems to energy processes. Thermodynamics is above all “the science of the evolution of the states of a system, whatever it is”.

The book derives its interest from the very definition of this science, accepted by the scientific community for a long time as the “mother of sciences”. Indeed, everyone agrees: “If thermodynamics does not solve everything, without it, we will not solve anything.” This is all the more true for the physicochemical processes of matter and energy transformation.

Salah BELAADI

January 2020

1Equilibria of Liquid/Vapor Phases

1.1. Exercises

EXERCISE 1.1.– Vapor tensions of carbon sulfide

Carbon sulfide boils at 46 °C at atmospheric pressure; its vapor is considered an ideal gas; its enthalpy of vaporization under these conditions is 85 cal/g and remains constant between −73 °C and 46 °C.

1) a) Calculate the vapor tensions of the sulfide at temperatures: −73 °C, −45 °C, −23 °C, −5 °C and 28 °C.

b) Compare these results with these below, obtained experimentally, by calculating the relative error for each temperature.

P

(mmHg)

1

10

40

100

400

T

(°C)

−73

−45

−23

−5

28

2) Explain the difference between the measured and calculated values, and justify the direction of variation of the error.

Answers: (1) (a) ; (b) and (2) see corrections.

EXERCISE 1.2.– Vaporization of benzene

The vapor pressure curve of benzene is given experimentally by values in the following table:

T

(K)

262

285

299

301

340

350

360

P

(mmHg)

10

50

100

250

500

700

1,000

We aim to determine the entropy and enthalpy of vaporization of benzene at its boiling point, assuming that benzene vapor is an ideal gas.

1) Plot the curve

P

= f(

T

) using the scale (1 cm ↔ 40 mmHg and 1 cm ↔ 5 K).

2) Deduce the boiling point.

3) Calculate the entropy of vaporization at this temperature; is this result consistent with that predicted by Trouton’s rule?

4) Calculate the enthalpy of vaporization at this boiling point.

Answers: (1) See corrections; (2) Tb.= 79.35 °C; (3) ΔS = 20.51 u.e; yes; (4) ΔH = 7,229.63 cal/mol.

EXERCISE 1.3.– Distillation of the benzene/toluene mixture

Liquid benzene(1)/toluene(2) mixtures form, at atmospheric pressure, an ideal solution in all proportions.

Draw a diagram of the liquid/vapor equilibrium, by calculating the titers of the vapor and liquid at the following temperatures: 83.1 °C, 86.1 °C, 89.1 °C, 92.1 °C, 95.1 °C, 98.1 °C, 101.1 °C, 104.1 °C and 107.1 °C.

Data:

Benzene

Toluene

T

b

(°C)

80.10

110.60

Δ

H

f

(cal/mol)

7,353

8,000

Answer: See corrections.

EXERCISE 1.4.– Activities of binary liquid mixtures

At 400 K, two liquid bodies (1) and (2) have the respective vapor pressures and ; at this temperature, their mixture is azeotropic with a vapor pressure of 900 torr and the composition of body (1) in the liquid phase is 0.2 at equilibrium.

1) Calculate the values of the partial pressures of this solution at

T

= 400 K.

2) Calculate the activity coefficients and activities of the solution at

T

= 400 K.

Answers: (1) P1 = 180 torr and P2 = 720 torr; (2) γ1 = 0.90 and γ2 = 0.50; a1 = 0.18 and a2 = 0.40.

EXERCISE 1.5.– Activities of the bromine/carbon tetrachloride mixture

The diagram for the vapor tension of the Br(1)/CCl4(2) mixture was proposed by Barthel at 0 °C; an azeotrope was found with the molar titer of bromine of x1 = 0.857 and vapor tension P = 71.2 mmHg.

1) Choose an appropriate development with two parameters A and B.

2) Calculate A and B, and write the relations giving the activity coefficients of each constituent in the solution.

3) Calculate these coefficients for a mixture with a molar titer of Bromine equal to 0.7 and deduce the composition of the vapor phase.

Data: At 0 °C, the vapor tensions of the pure bodies are and .

Answers: (1) See corrections; (2) A = 0.076; B = 1.308; and ; (3) γ1 =1.525; γ2 = 0.961 and y1 = 0.58.

EXERCISE 1.6.– Binary mixtures MEK/water with azeotrope

The methyl ethyl ketone(1)/water(2) system is characterized by an azeotrope whose temperature, pressure and composition were measured. The results are given in the following table:

T

(K)

489.2

453.8

412.1

385.3

346.4

P

(atm)

34.02

17.01

6.804

3.402

1.000

x

MEK

0.410

0.456

0.508

0.572

0.655

The saturation pressure of each component is given by the relation whose coefficients are given in the following table:

Tc

(K)

Pc

(atm)

A

B

C

MEK (1)

535.6

41.0

9.9653

3,150.42

36.65

H

2

O (2)

647.3

217.6

11.6703

3,816.44

46.13

1) Using the Van Laar and Redlich–Kwong equations, estimate the free energy of the mixture at different titers for the five proposed temperatures in the first table.

2) What can be deduced?

3) Represent this energy as a function of the MEK titer.

Answers: (1) ; (2) existence of a solubility deficiency at three lower temperatures; (3) see corrections.

EXERCISE 1.7.– Vapor extraction of quinoline

Quinoline C9H7N is prepared by the extraction of the reactive medium with steam, due to their immiscibility.

1) Calculate the boiling point of

H

2

O

/

C

9

H

7

N

at pressure of 740 torr.

2) Calculate the maximum mass of quinoline extracted by 1 kg of steam at 740 torr.

Data:

T (°C)

98.0

98.5

99.0

99.5

100.0

707.27

720.15

733.24

746.52

760.00

7.62

7.80

7.97

8.15

8.35

Answers: (1) Tb = 98.95 °C; (2) m = 77.52 g.

EXERCISE 1.8.– Sea water equilibria with reference to pure water

The Mediterranean Sea is characterized by a salinity of 35 g/L. We will boil this sea water at the boiling point of pure water at 1 atm.

1) Calculate the vapor pressure

P

at this boiling point.

2) At what pressure will this water be in equilibrium with ice at 0 °C like pure water at 1 atm?

3) Conclusion.

Data: MNa = 23 g/mol; MCl = 35.5 g/mol; ρs = 916.8 g/L; ρl = 1,000 g/L and at Pa = 1 atm = 1.013 bar, we obtain: Tb = 373.15 K and Tf = 273.15 K.

Answers: (1) P = 0.9916 bar; (2) P = −2.97 × 107 Pa; (3) see corrections.

EXERCISE 1.9.– Activity coefficient of a body in ethylbenzene

Here, we study the binary mixture ethylbenzene(1)/C(2), where C is a compound whose melting point is 325 K and standard enthalpy of melting is 15,000 cal/mol.

Measuring the vapor pressure of ethylbenzene over the binary mixtures at 350 K gives the following values:

x

1

0.1

0.3

0.5

0.7

0.9

1.0

P

(torr)

3.35

12.5

29.5

59.2

96.7

111.4

The activity coefficient of ethylbenzene is represented by the expression:

1) Calculate the value of the activity coefficient of liquid compound C when

x

1

=

x

2

, knowing that the initial solidification temperature of the solution defined by

x

1

= x

2

is 315 K.

2) Calculate the value of the activity coefficient of liquid compound C under these conditions.

3) Calculate the partial molar enthalpy of mixing and the partial molar entropy of excess of component C in this equimolar solution.

Answers: (1) γ2 = 0.739; (2) γ2 = 0.957; (3) and .

1.2. Problems

PROBLEM 1.1.– Equilibria with azeotropes

The system 1,4-dioxane(1)/water(2) at 70°C and 390 mmHg gives an azeotrope whose dioxane titer is 0.514, whereas at T = 35 °C and P = 80.8 mmHg, the azeotrope has the titer x1 = 0.599. Assuming the system is ideal and that the vapor obeys the ideal gas law, calculate by means of the Wilson equation:

1) the equilibrium curve at 70 °C;

2) the activity coefficients at infinite dilution;

3) the activity coefficients and the excess Gibbs free energy for different titers;

4) the bubble pressure and vapor composition at equilibrium for a mixture with a water titer of 0.2 at

T

= 70 °C;

5) the equilibrium conditions of the mixture with a water titer of 0.749 at

T

= 50 °C, knowing the experiment gives

P

= 160.8 mmHg and

y

1

= 0.505; estimate the enthalpy and entropy of excess.

Data: vwater = 18.1 cm3/mol; v1−4 D = 85.3 cm3/mol; P of saturation: ; .

Answers: (1) See corrections; (2) and ; (3) see corrections; (4) P = 374.5 mmHg; y1 = 0.443; (5) P = 154.9 mmHg and y1 = 0.4487; and .

PROBLEM 1.2.– Distillation of acetone/chloroform mixture

If we plot the boiling point diagram of the chloroform(1)/acetone(2) binary from the following experimental data: at T = 35.8 °C, there is an azeotrope with a vapor tension of P = 247.5 torr for a composition x = 0.387; at this T, the vapor tensions of the pure bodies are and ; at atmospheric pressure, the boiling points of the pure bodies are and ; the enthalpy of mixing hm of the equimolar binary at 25 °C is − 145.0±1.0 cal.

1) Establish an approximate relation for the vapor pressure of each pure body as a function of

T

.

2) Assuming that the excess Gibbs free energy obeys the following equation , where A and B are independent of composition; establish an expression for the activity coefficients of each constituent in the solution.

3) Show that you can determine the activity coefficients of both constituents from the azeotrope data at this point and deduce the values of A and B.

4) Can the values of A and B be considered to be independent of

T

? What does this hypothesis assume? Is it compatible with the value of the enthalpy of mixing at 25 °C?

5) Calculate the total pressure and titer of the vapor over the liquid equimolar mixture at 60 °C.

6) Establish the equation for the McCabe–Thiele curve at a total pressure of 1 atm.

Answers: (1) ; ; (2) and ; (3) A = −666.7 cal/mol; B = 1.284 cal/mol; (4) gex = −145 cal; (5) P = 627.2 torr; (6) see corrections.

PROBLEM 1.3.– Isopropanol/dioxane binary

Experimental measurements relative to isopropanol(1) and dioxane(2) solutions confirmed the validity of the Antoine equation , where T is expressed in °C and the saturation vapor pressure of the pure component (i), is expressed in torr. Using these, we can obtain the values of the following parameters at the normal boiling points:

T

b

(°C)

A

i

B

i

C

i

Isopropanol

82.4

8.3113

1,686.8

228.2

Dioxane

101.3

7.2180

1,424.4

227.1

This experimental data obtained at a total P pressure of 1 atm are shown in the table below:

x

1

y

1

T

(°C)

h

m

0.05

0.115

99.2

74

0.10

0.22

96.9

140

0.20

0.385

93.10

248

0.30

0.505

90.15

325

0.40

0.59

87.9

372

0.50

0.663

86.40

395

0.60

0.729

85.25

395

0.70

0.788

84.35

355

0.80

0.849

83.6

300

0.90

0.919

82.95

205

0.95

0.957

82.60

130

These components do in fact behave like ideal gases in the vapor phase.

1) Estimate the standard enthalpy of vaporization of both pure components, specifying any assumptions.

2) Calculate an approximate limit value for the partial molar enthalpy of the dioxane mixture when

x

1

→1.

3) Note that 24 moles of (1) are mixed with 16 moles of (2) at

T

= 85.80 °C; calculate the number of moles of each body, in each phase at equilibrium, under a total pressure of 1 atm.

4)

k

i

and

a

ij

are the equilibrium coefficient of constituent (i) and its relative volatility with respect to constituent (j) defined, respectively, by: and .

a) What is the value of

α

ij

when there is an azeotrope?

b) Establish the relation whereby

α

ij

only depends on

T

and

x

i

.

c) Determine the limit value of

α

12

when

x

1

→1 at

T

= 82.4 °C.

d) Deduce the limit value of

γ

2

when

x

1

→1 at the same temperature.

5) Establish the relation describing the variation in

α

12

as a function of

T

at constant composition in the liquid phase (assuming that

h

ex

and

s

ex

do not vary with

T

).

6) From the previously established results:

a) at what

T

will we obtain an azeotrope for

x

1

= 1?

b) therefore what would be the total pressure?

c) at what

T

would we obtain an azeotrope for

x

1

= 0.55 and what would be the total pressure?

Answers: (1) ; ; (2) ; (3) n1l = 14.67 and n1v = 9.33; n2l = 12 and n2v = 4; (4) (a) αij = 1; (b) see corrections; (c) α12 = 1.08; (d) ; (5) ; (6) (a) T = 351.9 K; (b) P = 503.2 torr; (c) T = 282.75 K; P = 21.4 torr.

PROBLEM 1.4.– Purification of lead

During lead manufacturing operations, bismuth, which makes it brittle, must be removed by the action of magnesium. Lead is thus obtained with traces of this expensive metal, a part of which is recovered by prolonged pumping of steam at 850 K, using a pumping unit which makes it possible to reach and maintain a pressure P of 3 × 10−4 torr. The thermodynamic properties of the Pb(1)/Mg(2) liquid binary mixtures are represented at 833 K by the following expressions:

1) Show that the vapor pressure of liquid

Mg

super cooled at 850 K is 0.59 torr.

2) Calculate the limit value of the activity coefficient of

Mg

in

Pb

at 850 K.

3) Estimate within 1% the titer of

Mg

, which remains in the lead after the prolonged pumping.

Data: At 850 K: and ; standard variables:

T

f

(K)

Pb

600.6

1 140

Mg

923

2 140

Answers: (1) ; (2) ; (3) x2 = 6.45 ×10−4.

PROBLEM 1.5.– Physical equilibrium of mercury

Inhaling Hg vapor can cause a serious condition, known as “hydrargyrism”. International standards are set at 0.1 mg/m3 for the maximum tolerable concentration of Hg vapor in air to man.

We therefore consider the physical equilibrium to be: Hgliq ⇄ Hgvap, whose saturation vapor pressure as a function of T is written as: , where and are variations in enthalpy and entropy of evaporation, respectively.

1) Calculate the approximate temperature of evaporation of

Hg

at a pressure of 1 atm, disregarding any heat capacity effects.

2) a) Give the expressions of and as a function of

T

, taking into account the heat capacities.

b) Deduce the new expression of log .

c) Verify that the boiling point of

Hg

is close to 361 °C under 1 atm.

Mercury vapors, assumed to behave like ideal gases, are regularly distributed into the atmosphere.

3) a) Calculate the saturation vapor pressure of

Hg

at 25 °C.

b) What mass of

Hg

vapor is there per m

3

of air in the presence of liquid Hg at 25 °C?

c) Under these conditions, is it wise to leave uncovered a flask of liquid mercury in a laboratory?

Data:

Standard values

C

p

(cal.mol

-1

.K

-1

)

Hg

liquid

0

18.5

6.66

Hg

vapor

14.54

41.8

4.98

MHg = 200.6 g/mol.

Answers: (1) Tb = 350.88 °C # 351 °C; (2) (a) and ; (b) ; (c) T = 361 °C = 634.15 K; logP = 0.001 # 0, which verifies that Tb ≈ 361 °C; (3) (a) P = 2.25 × 10−3 torr; (b) m = 24 mg/m3; (c) see corrections.

PROBLEM 1.6.– Isobaric diagram of nitrogen/oxygen mixtures

Air is considered as a mixture of N2 and O2, which is separated in numerous industrial applications. We propose to construct the liquid/vapor diagram, at constant atmospheric pressure, of N2(1)/O2(2) mixture whose liquid solutions are assumed to be ideal.

The literature gives, for each pure body, the following expressions, linking saturation vapor pressure (in torr) to temperature (in Kelvin): and .

1) a) Determine for each body the standard temperature of vaporization.

b) Calculate the latent heat of vaporization of

N

2

and

O

2

.

In the isobaric diagram (T, x and y), with abscissa of x1 for the liquid phase and y1 for the vapor phase, we consider that for a determined temperature, the phases (l) and (v) are in equilibrium at a total pressure of 1 atm.

2) a) Express

x

1

and

y

1

as a function of

P

, and .

b) Calculate the

x

1

of points −193 °C and −188 °C on the boiling point curve and

y

1

on the dew point curve.

c) Draw the diagram (scale: 1 cm ↔ 1 °C; 1 cm ↔ 0.05) specifying the significance of the domains separated by the curves.

Liquid air, composed of 24.3% of oxygen by mass, is heated to its boiling point at 1 atm.

3) a) From the previous diagram, deduce the boiling point and the composition of the vapor at equilibrium with the liquid at this temperature.

b) Explain the principle behind the fractional distillation of air.

Answers: (1) (a) Tv1 = −196.14 °C and Tv2 = −183.13 °C; (b) and ; (2) (a) and ; (b) (x1 = 0.61; y1 = 0.88)−193 and (x1 = 0.23; y1 = 0.56)−188; (c) see corrections; (3) (a) Tb. ≈ −194.5 °C; x2 = 0.22 and x1 = 0.95; (b) see corrections.

PROBLEM 1.7.– Liquid/vapor equilibrium of pure benzene

We know that the vapor tension, or saturation vapor pressure, of a liquid is always a function of temperature. Now we aim to study the liquid/gas equilibrium of benzene, assuming that in the gaseous state, it obeys the ideal gas law and the molar heat capacities at constant pressure remain constant between 80 °C and 25 °C.

1) Calculate the enthalpy of vaporization of benzene at 25 °C, disregarding the molar volume of liquid benzene.

2) In mmHg/K and Pa/K, what is the slope of the liquid/gas equilibrium curve of benzene at its boiling point under a pressure of 1 atm?

3) Calculate in mmHg the vapor tension of benzene at 25 °C, disregarding the variation in enthalpy of vaporization between 80 °C and 20 °C.

4) What are the saturation molar volumes of the vapor at 80 °C and 25 °C?

5) Determine the equation that expresses the saturation molar volume of the vapor as a function of pressure.

6) What is the variation in enthalpy of 1 mole of liquid at equilibrium with the vapor between 80 °C and 25 °C?

Data: Tb = 80 °C; ; Cpl = 33 cal/mol.K and CPv = 20 cal/mol.K.

Answers: (1) ΔHv(25) = 8,056 cal/mol; (2) ; (3) P(25) =117.08 mmHg; (4) v(80) = 28.96 l; v(25) = 158.71 L; (5) ; 6) .

PROBLEM 1.8.– Vaporization of nitrogen

The physical characteristics of a nitrogen molecule are given in the table below, and its vapor pressure is 96.4 mmHg at −200.90 °C and 561.3 mmHg at −198.30 °C.

T

f

(°C)

T

b

(°C)

T

C

(°C)

P

C

(atm)

v

(L)

M

(g)

M

spc

(g.cm

-3

)

−210

−195.85

−147.15

33.5

20

28

0.3110

1) Plot the diagram of the pure body “

N

2

” specifically indicating:

a) all points given in the following table;

A

B

C

D

E

T

(K)

50

5

126

100

130

P

(atm)

1

75

33.5

35

35

b) the state of nitrogen in different domains formed by the equilibrium curves.

2) a) Indicate on the diagram the points A, B, C, D and E:

A

B

C

D

E

T

(K)

50

5

126

100

130

P

(atm)

1

75

33.5

35

35

b) What is the state and variance in the system at these points?

3) Calculate the average variation in enthalpy during the vaporization of one mole of nitrogen:

a) between 63.2 K and 74.8 K;

b) between 74.8 K and

T

b

;

c) explain the difference between both values.

Consider the transformation: N2liq ⇄ N2gas at 77.3 K and under 1 atm, assuming that N2 behaves like an ideal gas and disregarding the volume of the liquid with respect to the gas.

4) What are the variations in free enthalpy and molar entropy?

In reality, nitrogen is not an ideal gas; but its behavior does obey the Van der Waals equation: .

5) a) Give the meaning of the constants a and b, and calculate their values.

b) Deduce the expression of the Van der Waals equation.

6) What is the relative error of

V

and

P

when nitrogen is deemed an ideal gas under standard conditions?

Answers: (1) (a) and (b) See corrections; (2) (a) and (b) see corrections; (3) (a) ΔHv = 1,426.6 cal/mol; (b) ΔHv