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1960

A thermodynamic study of the system PbO-PbS A thermodynamic study of the system PbO-PbS

John P. Hager

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A THERMODYNAMIC STUDY OF THE sYSTEM PbO-PbS

BY

JOHN Po HAGER

A

THESIS

submitted to the faeu:tty of the

SCHOOL OF MINES AND METALLURGY OF THE UN·IVERSITY OF MISSOURI

in partial fuI:rillment of the work required for the

Degree of

MASTER OF SCIENCE. IN METALLURGICAL ENGINEERING

Rolla, Missouri

1960

Approved by

ABSTRACT

An experimental investigation t~as conducted 1n· ord·er

to determine the thermodynamic and kinetic behavior of the

system PbO-PbSo

The thermodynamic· behavior of the system PbO-PbS was studied by measuring the P802 in argon-so2 mixtures equili- .

brat_ed with various PbO-PbS mixtures in a recirculating­

type _equilibrium apparatus, and analyzing the condensed

phases by means of X-ray diffractiono

The effect of temperature and PbO/PbS ratio on the

rate of S02 evolution was investigated in order to determine

the reaction mechanisms involved in tpe approach· to equili­

briumo

A sodium hydroxide, hydrogen peroxide titration

technique was employed in the analysis of so2 in the gas

mixtureso

A detailed description of the apparatus and

experimental procedure is given for both the equilibrium

and kinetic s·tudieso

At constant temperature the variation of r802 with

composition was found to consist of several horizontal

lines connected by diagonal 11neso Below 733°C the

is9therms consisted of ttio horizontals connected by one

ii

diagonal line~ Above 733oc the isotherms .consisted of

three, horizontals connected by two diagonal .lines~ . i --ray I •

ana~ysis of the condensed phases showed.that the.horizontals

_represe:p.ted areas· of three~phase stability and the diagonal

lines areas of two-phas.e .sta.bilityo

A phase diagram was constructed for th.e system

PbO-PbSo The equi;:tibrium results indicated the pres.ence

of iiquid solubility in lead and solid-solubility in the

,basic sulfates; however, the exact composition of the

liquid lead and the basic sulfates· was not_ determined. The

Pb-S-0 diagram, proposed. by Kellogg and Basu, has been

corrected to ~oincide with the PbO-PbS diagr~ ~rom this

investigationo

A ·11n~ar free. energy equation was der"ived for the

~For of Pbso4~4Pb0.in the temperature range 7000-760°Co·

Additional calculations trere made r.or the~H0 r :·and '6.S0 r

of PbS04··4PbOo The calculations from the experimental

results agreed very well i-,i th the calculations made from

the ·a.ata of previous investigatorso

The· kinetic· studies indicated that the reaction

mechanism in the system PbO-PbS is '(l) conversion of all .

of the PbO or PbS (~hichever is the minor co~stituent)

to either PbS04°4PbO or PbS04.o2PbO, and (2) reaction

b~t~een _the basic sulfate· ·and either Pb or PbS to produce

111

From the results of this investigatio~ it was

established that the equilibrium 2Pb0 + PbS._-·-;-3Pb + S02,

which was thought to be the basis of ore-hearth smelting,

is unstable e.t all PbO/PbS ratios in the temperature range

7oo0 -760°c.

ACKNOWLEDGEMENTS

The author wispes to express h~s appreciation and

gratitude to Dro Ao Wo Schlechten, C~irinan of the Depart­

ment .of Metallurgical Engineering and Dro A.H.· Larson,

Assistant Professor of Metallurgy for their co-µnsel and

assistance throughout the course of this investigationo

$pecial thanks is also express.ed to Dro WC> J .• · Kroll,

Cons~lting Metallurgist, Corvallis, Oregon for making funds

·available for c:onstruction of the experiµlental apparatus.

The author is also indebted to various members of

the Metallurgical Engineering, Ceramic, and Chemistry

Departments for advice and consultat~on; and, ·to Dro To

Ejima, f~rmer graduate student, for the constru~tion of

the glass portion of the experimental apparatuso

TABLE OF CONTENTS

CHAPTER PAGE

1

;I.

1

1

3

9

!. INTRODUCTION. • • • • • • . •. • • • • • • • •

II.

III.

IV.

v. VI.

VII.

Statement of the_problem. • • • • • • • • •

Organization of the problem • • • • • • • • Importance of the study. • • • • • • • • • •

REVIEW OF THE LITERATURE. • • • • • . . . •· . PREPARATION. OF PbO-PbS MIXTURES • • • • • • •

THE APPAP.ATUS AND E..XPERIMENTAL PROCEDURE • • •

The Apparatus • • • • • • • • • • • • • • • •

The gas purification system

The equilibrium apparatus .••

• •

• •

_Experimental Procedures

EXPERJMENTAL RESULTS • • •

THERMODYNAMIC CALCULATIONS

• • • • •

• • • • •

• • • • •

• • • • •

. .. . . . • • • • •

• • • • •

• • • • •

Calculations from experimental results. . -. Calculations from results of previous

12

12

12

19

27

33

47

47

investigations. • • • • • • • • • • • • • 54

Graphical representation of the thermodynamic

calculations. • • • • • • • • • . . ·• • •

KINETIC STUDIES • • • • • • • • • • • • • • •

59

67

Review of th~ literature. • • • • • • • • • 67

The apparatus and experimental procedure. • 69

Experimental results. • • • • • • • • • • • 76

vi

CHAPTER PAGE

Discussion and conclusions • • • 0 • • • • • 81

VIII. SlllVIM.ARY AND CONCLUSIONS • • • 0 • 0 0 • • 0 88

BIBLIOGRAPHY 0 0 • • 0 • • • .. • • 0 • 0 • • • 98

APPENDICES • • • • • • • C) • • • 0 • • • • • 100

VITA • • • • 0 • • • • • 0 • • • • .. 126

LIST OF FIGURES

FIGURE

l. Composit~on Diagram, after Kellogg and Basu,

. for the Pb-S-0 System_ Between 6160 - 733~C 0 0

2o Composition Diagram, · after Kellcg g and Ba.~u,

for the Pb-S-0 System Above 733°C, but -Below

the Liquidu$ • 0 • • e O O . • . 0 0 • • • 0 . . . .

PAGE

5

6

3. .The Apparatus • o • • • .• • • • • • • • • • • • 13

4 • . Schematic Diagram of Gas ~i~ica~i~n System. o 14

5.

l?.

Gas Purification System 0 . 0 • • 0 0 0 0 o e O •

Schematic Diagram o;f Equilibrium Apparatus. 0 • . .

15

20

7. Eq'q.ilibrium Apparatus o • • • • • • • o •• ·• • • 21

B. Reac_tion ~be and Furnace Assembly for

Equilibrium Apparatus O O O O e • o e • • • •

9 .• Furnace Electrical Power Control. • 0 • • • • •

10.- Gas .Analysis Apparatus. 0 • • • o O O • 0 • . 0 •

23

25

'30

llo Equilibrium Pso2 Values r~r _the Sys~em PbO-PbS

Between 700~ 76o0 c o •••••• o o • ~ • • 38

120 . Proposed Phase Diagram fo~ · the ~y~tem PbO~PbS

Between 7oo0 - .76o0 c •••• 0 0 . • 0 0 44

13. Phase Diagram, after Kellcg g and Basu, for the

System PbO-PbS Between 7oo0 - 760°C .. 0 0 0 0 46

14~ . Temperature Depen~ence . of .6._ F~r of Pb~04°4Pb0

Between .. 7co0 - 76o 0 c 0 • 0 0 0 0 0 0 0 0 ·o 0 0 63

FIGURE

l5o Schematic Diagram or Kinetic Apparatus 0 0 0 0 0

16. Reaction Tube .and Furnace Assembly !'or Kineti·c

viii

.PAGE

70

Apparatus • • • • • • . o • • • o • • • • • o • o 71

17. Effect of Flow Rate on Reaction Velocity. • • • 78

18. Temperature Dependence of the Reaction Velocity. 79

19. Dependence of Reaction Velocity on PbQ/PbS

Ratio O O O O O O O O O O O O O O O O O • 0 0 80

20. Moles of Pbso4.4Pb0 and P~S _per Mole o~ Pb at

Various PbO/PbS Ratios. o • o • ~ • 0 • 0 0 0 85

21. Corrected Composition Diagr~ f"or the Pb-S-0

System Above 733°C o •••• o • o o o. • • • 95

LIST OF TABLES

TABLE PAGE

I. Equilibrium P802 Values for t~e System

FbO-PbS Between 700° - 76o0

c Together -with

the Phases Identiried in the Reacted Charges 34

II. The 2G Values Used in Interpreting the X-ray

Diffraction Data . . . . . . . . . . 39

III. -~quilibria µivestigated Together with the

Equilibr:iu11 Values of' Pso~. . • . • • • . . 49 ~

IV. Equations for the Free Energy of Formation of

PbO, PbS, so2 es a Function of Temperature. 51

V. Ce..lculs. ted Val uas of' .6.. F 0 f of _PbS04. 4Pb0 ·and

_Pbso4 .2Pb0 from the Experimental Data .. . • • . 55

VI. Equilibria Studied by Kellogg and Basu Together

with ~F0 Equations. • • • • • • • • • • • • 56

VII. Calc~atcd Values of ,6.F0r of PbS04·4PbO and_

Pbso4 .2Pb0 ~rom the De.ta or Kellogg and

Basu ••• e O e • e O • • • • • • • • • • •

VIII. S-ummary of Thermo.dynamic Calculations. • • • •

IX. AveragE: Deviation or .6.F0 :r of' PbS04 .. 4PbO .Values

from this Investigation and those rrom

60

61

KBllogg and Basu. • • • • • • • • • • • • • 65

Xo X-ray Identificetion.or Phases in Partially

Reacted PbO-PbS Mixtures • • • • • • • • • • 82

x

TABLE PAGE

XI. Linear·Free Energy Equations for .6.F0 f: of

PbSo4.4PbO o o •••••••• o • o o • • • 91

CHAPTER I

INTRODUCTION

Statement of the problemo The purpose of this

experimental investigation was (1) to determine some of the

thermodynamic properties of the system PbO-PbS,.(2) to

determine the equilibrium phases and their range of

stability in the system PbO-PbS, (3) to determine the

mechanism(s) of the reactions in the system PbO-PbSo

Organization of the problemo The problem consisted

of two types of experim~ntal measurements: (l) equilibrium

measurements, (2) kinetic measurementso The -results have

been presented in separate chapterso

The kinetic study was conducted to supplement the

equilibrium study, in order to determine the possible

reaction mechanism(s) involved in the approach to ~quili­

brium. The kinetic study is discussed separately in

Chapter VIIo

Importance of the study. The process whereby

metallic lead is produced by the reaction 2Pb0 t PbS ~

3Pb+ so2 , is very important in the metallurgy of lead,

because it makes possible the direct smelting of lead . . .

sulfide by controlled ·oxidationo

Consequently, any knowledge of the thermodynamic

or kinetic behavior of the system PbO-PbS would be of

2

prime importance t.o the understanding· and possible i.11prove­

ment of lead smelting :rr ocesses involvfug PbO and PbS.

The terminology "system PbO-PbS" is used in accord­

ance with the thermodynamic definition of syst~,i •. e., the

isolated portion of the universe which is chosen far thermo­

dynamic considerationo This terminology is not to.be

construed as referring to a binary system, whereas the

system PbO-PbS is the vertical section PbO-PbS in the

Fb-S-0 system.

CHAPTER II

REVIEW OF THE LITERATURE

The earliest reported work on ·the thermodynamic

properties of the system Pb-S-0 is that of Schenck and

Rassbach1 (1908). Additional investigations by ~einders2

(1915) and by Schenck and coworkers; Schenck and Albers3 . . . .

(1918)," Schenck and Borkenstein4 (1925), have beenr~portedo

The results·or these investigators have been revie~­

ed by Kellogg and_Basu5 who have recently (1959) reinvesti­

gated the thermodynamic -properties of the system Pb-S-Oo

The results of their investigation have shown that

the early data lack precision and agreement; values of

Pso2 given by Schenck and coworkers are badly scattered

and are 10-20~ higher than those reported by Kellogg 8:D,d

Basuo The data of Reinders likewise give values of Pso2 which are l-5fo highero

The lack of precision of the earlier work is evident

in the report of Schenck and coworkers that PbS0403PbO

rather than PbS04o4PbO is stable at high te~peratureso

The work of Lander6 on the system PbS04°PbO, and the .

results of Kellogg and Basu have substantiated that

Pbso4°4Pb0 r ·ather than Pbso4°3Pb0 is the stable basic

sulfateo

Kellogg and Basu have stated that they believe the

values of Pso2 found by earlier investigato~s are high

because of incomplete removal of moisture and adsorbed

gases from the sample and refractories; a precaution which

was ta.ken in their work. ·

4

The experimental work of Kellogg and Bas~ consisted

of measuring the equilibrium value of _Pso2 for the following

equilibria in the temperature range 800-ll00°K.:

1. PbS + 7PbS04 ~4(PbS04 •PbO) + 4802

2. PbS + lO(PbS04·PbO) ,, 7(PbS04•2PbO) + 4S02

3. PbS + 8(PbS04 •2PbO) ____. 5(PbS04•4PbO) + 4802

4. Pb+ PbS04•4PbO ~6Pb0 + 502

5. 2PbS + PbS04.2PbO ~5Pb + 3S02

From the results of the above equilibria, together

with thermodynamic calculations for three additional

equilibria, they have constructed a consistent thermodyna­

mic phase diagram, and composition diagrams for the system

Pb-s-o. The composition diagram for temperatures below

733oc is illustrated in Figure 1, and for temperatures

above 733°C in Figure 2~

The heat and free energy of .formation of . the _

compounds PbS04.PbO, PbS04•2PbO, and PbS04.4PbO at 298°K

were also determined from the data.

According to the composition diagrams in Figures

5

Pb MOLE •1. 0 ,. PbO

FIG.- I

. so / 3

COMPOSITION DIAGRAM AFTER KELLOGG AND

· BASU, FOR THE Pb - S - 0 SYSTEM BETWEEN

616°-733°C

5

0

s

/

~PbS04

PbSOt • PbCt' , Pb50+· ZPbO ,

• Pb50+·4Pb0 '

Po MOLE •1. 0 _ _....,_

FIG.-2

COMPOSITION DIAGRAM, AFTER KELLOGG AND

. BASU . FOR THE . Pb- s.;.;.o SYSTEM ABOVE . ) .

733°C, BUT BELOW THE LIQUIDUS.

6

.Q

1 and 2, the equilibrium 2Pb0-+ lPbS~::.:~ 3Pb + so2 is

metastable* at all temperatures. Below 733°C the reaction

sequence £or stable equilibrium or a 2Pb0/1PbS mixture is

PbS + 8Pb0--> PbS04•4PbO -t 4Pb

PbS04•4PbO + 3PbS~.=.::.:;8Pb + 4802,

and above 733°C the rea.ction sequence is

PbS -t 6Pb0 -· -~> PbSO 4 • 2Pb0 + 4Pb

PbS04 • 2Fb0 + 2PbS ~-=:;SPb + 3S02•

Since Kellogg and Basu have not measured the Pso2

above PbO-PbS mixtures, the question a.rises as to whether

the reactions between PbO and PbS are metastable or stable

equilibria.

Schenck and Borkenstein :found · that the Pso2

above

a mixture of PbO and PbS was .216 atm. at 1100°K. From

the data of Kellogg and Basu, the calculated value of

P802 at 1100°K for the metastable equilibrium 2Pb0 + PbS.

7

~-~3Pb + so2 is .333 atm., and ror the stable equilibrium

PbS04 • 2Pb0 + PbS ~~ 5Pb + 3802 the Pso2 is .1 71 a tm. at

ll00°K.

*Metastable equilibrium is a peculiar state of pseudo-equilibrium in which the system has acquired energy beyond that ror its most stable state, but because or the long period or time required for transition to a state or lower energy it remains in a state 0£ higher energy.

8

The results o:r Schenck and Borkenstein obviously do ·

not indicate which equilibrium, stable or metastable,

represents the thermodynamic behavior· of' the system PbO-PbS.

On the basis of the above information, it was con­

cluded that the thermodynamic behavior of the system PbO-PbS

could be determined by (1) measuring the equilibrium P502

values above various PbO-PbS mixtures at severa1 tempera­

tures, ·and (2) analyzing the reacted mixtures by means of

X-ray diffraction.

CHAPTER III

PREPARATION OF PbO-PbS MIXTURES

In order to measure the equilibrium values of P802 for the system PbO-PbS, it was necessary to prepare PbO-PbS

mixtures with varying ratios of PbO to PbS. These mixtures

were prepared in the 1aboratory by mixing purified PbO and

purified PbS in various mole ratios of PbO to PbS.

To obtain puri:ried PbS, massive crystals or natural

galena were crushed and sized until several po1.lllds of -200,

+325 mesh particles were obtained. The natural galena

crystals were then purified by a dense medium separation

to eliminate the gangue material •. and then an ammonium

acetate leach to remove the lead oxides.

The procedure for the dense medium separation of the

galena. crystals .follows. A few grams or galena crystals

were placed in a. 1000 c. c. beaker containing a derise

medium with a specific gravity of 2.95. Eastman Kodak

tetrabromoethane was used as the dense medium. The crystals

were slowly agitated while the impurities such as silica

and calcite rose to the surface of the liquid and were

removed. The crystals remaining in the bottom or the

beaker were then removed and washed several times with

carbon tetrachloride • .

10

The procedure for the ammonium acetate leaching

follows. The galena crystals frcm the dense medium separa­

tion were placed in ·a boiling solution of concentrated

ammonium acetate, and allowed to boil for a period of 30

minutes. After this time the crystals were removed from

the leach solution and washed several times with boiling

water. The crystals were then washed with. acetone and dried

at 100°c for a period of one hour.

Examination of the dried crystals with a binocular

microscope showed that the galena crys·tals were virtually

free of any gangue materials or surface oxidation.

The purified FbO wa.s Fisher's National Fine-Grade

Pbo. A screen analysis showed that .the average particle

size was -200, +325 mesh. The PbO was dried overnight at

100°c.

The purified PbO and PbS were used to prepare PbO-PbS

mixtures in the following PbO/FbS mole ratios: 20:1, 13:1,

10:1, 9:1, 8:1, 7:1, 6:1, 5.3:1, 4:1, 2:1, 1:1, 1:2, 1:4,

1:6, 1:8, 1:10, and 1:20.

The mixtures were prepared in 30 gram lots, and were

thoroughly mixed to obtain a homogeneous mixture. The PbO

and PbS were weighed on an analytical balance to the near­

est tenth of a milligram.

Each mixture was placed in a. separate bottle with an

air tight lid to prevent adsorption of' moisture. The

reaction boats were filled from the mixtures contained in

these bottles.

11

CHAPTER IV

THE APPABATJJS AND EXPERIMENTAL PROCEDURE

The experimental technique of the equilibrium studies

consisted of (1) measur:ing the P802 in an argon-so2 mixture

which was equilibrated with a PbO-PbS mixture .in a recircu­

lating type equilibrium apparatus, and (2) analyzing ·the

condensed phases by X-ray diffractiono

Io THE APPARATUS

The apparatus used in this investigation can be

divided into two major ·portions: the gas purification

system and the equilibrium apparatus·o The entire ~pparatus

is depicted photographically in Figure 3o

The gas purification systemo The gas purification

system is illustrated schematically in Figure 4, ~d

photographically in Figure 5o The system was composed

entirely of 9 mmo .Pyrex glass tubing with the exception

or the high ·pressure ru~ber tubing between the argon tank

and the pancake regulator, and the tygon tubing_ connecting

the purification furnace to the pressure relief bubbler

and the pancake regulator<>

The gas purification system consisted of two separ­

ate gas train9 which were connected by a three-way stop-

I l

I i . I I

13

FIG.-3

THE APPARATUS

i ..,._ _____________________ . __ .J

• \:RGON F~OM TANI<

PURIFICATION FURNACE

BUBBLER

ATMOSPHERE

~ r i

VACUUM

i....__ ____ _

RESERVOIR BOTTLE

FIG-4

------- ·- -----·----~

MANOMETER

AUXILIARY SYSTEM

NEEDLE VALVE

FLOW METER

SCHEMATIC DIAGRAM OF GAS PURIFICATION SYSTEM

): .GAS , FLOW

BUBBLER

··-··---------·---------------'------------------------~

14

15 .

FIG.- 5

· GAS PURIFICATION SYSTEM

16

cock. One of the gas trains was not used in this investi-·

gation, and in Figure 4 has been labeled auxiliary gas

system. The auxiliary gas system was isolated from the

remainder of the system by a 2-way s·topcock.

Linde, standard-grade argon was used. The gas was ·

supplied in tank form at 2000 psi. - gage. The tank -pressure

was reduced to 10 psi. gage by a single-stage tank regulator

valve. · The tank regulator was connected to a Matheson,

pancake-type regulator which reduced the pressure to 2 psi.

gage.

Af'ter leaving the pancake regulator, the argon

passed through a gas purification .furnace. The gas purifi­

cation furnace consisted of a tube furnace containing a

reaction tube and boats of titanium powder. The titanium

powder was heated to 5oo0 c to remove any traces 0£ oxygen

in the argon. The temperature of the purification furnace

was controlled by adjusting the power input to the.furnace.

A variable resistor was placed in series with the 110 volt

A. c. power supply to allow adjustment or the power input

to the furnace. A chromel-a1umel thermocouple was placed

next to the furnace windings to give instantaneous tempera­

ture reading on a direct reading pyrometer.

From the purirication· furnace the deoxidized argon

entered a 20 1iter,pyrex glass bottle which served as a

reservoir. A rubber stopper was used to make connection

between the bottle and the glass tubing. The rubber

stopper was sealed to' the bottle by High-Pyseal sealing

wax. A mercury manometer was connected to the bottle to

measure the pressure. The large capacity of' the bottle

served to provide a constant gas flow through the flow

meter.

17

A mercury bubbler was placed in the gas line between

the purification furnace and the reservoir bottle. The

mercury bubbler was constructed in such a manner that the

mercury level could be adjusted by lowering or raising a

level bottle outside the bubbler. The purpose of the

mercury bubbler was to act as a safety valve in the event

of the possible failure of the pancake regulator. The

mercury level was adjusted to correspond to a gas pressure

slight1y greater than 2 psi. gage.

From the reservoir bottle the argon gas passed into

a drying chamber containing boats of P205. The boats of

P205 were ch~ged several times during the course of the

investigation, indicating that the argon did contain a

small a.mount of water vapor.

Two valves were placed in the gas line to isolate

the purification furnace and the reservoir bottle fran the

remainder of the system. By closing these two valves the

18

argon tank or the boats of P2o5 could be changed without

the necessity of releasing the pressure from the furnace

and the reservoir .bottle. These two valves were placed

9!ter the pancake regulator and be:fore the drying chamber

respectively. The system was found to be pressure tight ·

as there was no reduction in pressure after the.furnace and

reservoir bottle had been isolated for several days.

'The flow rate of argon was controlled by a Manostat,

teflon needle valve with a special glass to valve ass.embly.

The valve was designed for control of liquid flow, but was

found to give excellent control of gas flow. The needle

valve gave accurate adjustment of the flow rate between

5 and 320 c. c./minute.

The flow rate was measured by a carefully calibrated

manometer-type flow meter. Dibutyl phthalate was used a.s

the manometer fluid because of its low vapor pressure at

room temperature.

Two 3-way stopcocks were placed in the gas line

between the flow meter and the equilibrium apparatus: the

first stopcock connected the dibutyl phthalate bubbler to

the gas line, and the second connected the argon gas.system

and the auxiliary gas system to the equilibrium apparatus.

The gas flow could be·diverted from the equilibrium

apparatus to the bubbler; providing a means or starting

19

the gas flow prior to use in the equilibrium apparatus~

This was particularly useful when the equilibrium apparatus

had been evacuated. a.rid was being filled with the purified

argon: the rate of bubbling ~as a measure or the pressure

in the gas line when argon was being admitted to the

evacuated equilibrium apparatus by .opening the ~econd 3-way

stopcock. The second 3-way stopcock was never opened.far

enough 'to stop the bubbling and allow the dibutyl phthalate

to be drawn into the gas line.

A vacuum line was attached to the gas line between

the second 3-way stopcock and the ball joint, . which connect­

ed the equilibrium apparatus to the gas purification system.

The vacuum line was opened and closed to the gas line by

means of · a 2-way stopcock which was placed in the vacuum

line a few inches from where it entered the gas line •.

Vacuum was provided by a National Research Corpora­

tion, rotary gas ballast pump; a vacuum of 1 m. m. ~of Hg

could be attained after a 5 minute pumping period. The

pressure . in the vacuum line was measured by a mercury

manometer which was placed in the vacuum 1ine. A 3-way

stopcock was placed in the vacuum 1ine to connect th~

vacuum line to the vacuum pump or atmosphere.

The equilibrium apparatus. The equilibrium appara­

tus is depict~d schematically in Figure 6 and photographi-

BUBBLER

PURIFIED • ARGON

FIG.~ 6

l \GAS

\ FLOW

TO GAS ANALYSIS

I i i

SCHEMATIC DIAGRIAM OF EQUILIBRIUM APPARATUS

I ' ---·-··- ·-··---·--------- - ··- -- ------ ·---·- ·-··-------- ··----·-··- - ·· - - ···- --- .•.. . ... . -···· ·-···· - - ....... . . ··- - ···---- - ---····· --·. __ ____ .)

20

FIG.-7

EQUILIBRIUM AP~RATUS

,, --·- ----~-21

~-------------------- ·-----····-- ····· ... . ..... ·-

22

cally in Figure 7.

The equilibrium apparatus was a recirculating-type

apparatus in which. the gas mixture was recirculated over

t~e charge of PbO and FbS. The circulation path consisted

. of the f'urnace, circulating pump, and sample bottle.

The reaction tube and sample bottle were.constructed

of' vycor and pyrex glass. The remainder of the system was

composed of' tygon tubing.

The reaction tube and furnace assembly are illustrat­

ed schematically _in Figure e. The reaction tube was con­

structed from 19 mm. vycor glass tubing, and connections

were made on both ends of the furnace by means of a series

of ground glass joints: both spherical and conical Joints

being used. The vycor gless thermocouple protection tube

was sealed to the reaction tube with High-Pyseal sealing

wax. A spacer, constructed from vycor tubing, was pJa.ced

between.the boat and the end of the reaction tube to

decrease the possibility of thermal segregation of the gases

in the reaction zone.

The furnace was a hinged-type tube furnace, contain­

ing two separate heating coi1s. Being hinged, the fwnace

could be opened to permit rapid cooling of the tube and

sample. Asbestos paper gaskets, constructed .from l}"

e.·sbestos paper tape, were placed around the reaction tube

23

THERMOCOUPLE

ARGON+ S02

-1 ~ 1 FURNACE POWER

FIG~ 8

REACTION TUBE 8 FURNACE ASSEMBLY FOR

EQUILIBRIUM APPARATUS

1------,----------------------- ·-- ----------------·-·------·----'---'

24

on each end of the furnace to minimize convection currents

ap.d increase thermal stability between the furnace and tube.

The regu1ation'of the power supply to the furnace

h~ating elements is illustrated schematically in Figure 9.

Power to the furnace was controlled by means ot a Powerstat,

71 ampere, variable transformer. The transformer was

connected in series with a Wheelco, Model 402-8296, t1me­

proport.ioning controller. The controller was actuated by

a chromel-alumel thermocouple which extended into the

reaction tube to the end of the boat.

A Leeds and Northrup precision potentiometer, Model

No. 8662, was connected.in parallel with the therm.ocouple­

controller circuit to measure the temperature variance of

the furnace. Temperature control was found to ·be within

A Sigma.motor pump was used to circulate the gas

mixture.through the apparatus. Both rubber and tygon tub­

ing were used in the pump; tygon tubing was found to be

far superior. to rubber tubing, and was used in the ma.jori ty

or the runs. The tygon·tubing was replaced after approxi­

mately 100 hours ot use. The circµlation rate could_be

adjusted by changing the speed of the torque converter

between the driving motor and the pump. Darken and Gurry7

found that a linear velocity greater than .6 cm./ sec. was

IIOV AC

IIOV AC

r1L . WHEELCO

CONTROLLER

POTENTIOMETER

CHROMEL-ALUMEL .__----~----------- THERMOCOU~ .

v

--------t A ...____... __ -,--___ _

FURNACE HEATING

ELEMENTS

POWERS TAT

FIG- 9.

FURNACE ELECTRICAL. POWER CONTROL

L ____ ·--------:----------,-------'

.25

26

sufficient to prevent thermal segregation in CO, co2 mixtures.. Since A and S02 have approximately the same

ratio of' molecular weights as CO and co2 , a circulation

velocity greater than •. 6 cm./ sec. should prevent thermal

segregation in the reaction zone. The circulation velocity

used in this investigation was 1.15 cm./ sec •• A circula­

tion velocity greater then this was avoided because of the

appreciable transport of' PbS, as PbS vapor, f'rom the

charge.

A 274.5 c. c., pyrex sample bottle was used to obtain

a gas sample of' known volume, temperature, and pressure.

The bottle was fitted with 3-way stopcocks on both ends.

The temperature of' the gas was measured by a thermometer,

which was placed next to the bottle. The pressure in the

bottle was adjusted to barometric pressure, ±2 or 3 cm of

dibutyl phthalate, by means of a bubbler which was placed

in the line between the furnace and the pump.

The equilibrium apparatus was isolated from the gas

purification system by a pinch clamp, which is represented

as a 2-way stopcock in Figure 6, end by the 3-way stopcock

on the left side of the sample bottle. or these two valves,

the .former was used to admit purified argon to the system

at the beginning o.f a run, the latter to flush the gas

sample into the analysis apparatus at the end of the run.

27

II. EXPERIMENTAL PROCEDURES

A description of the experimental procedure follows.

An ·appropriate PbO-PbS mixture was placed in a 10 mm. x

60 mm. Coors porcelain combustion boat, and the boat placed

in the reaction tube. The si:;ecer was inserted and the cap

replaced on the end of the reaction tube. The valve, a

·pinch ~lamp, to the bubbler was closed, the valves on both

ends of the sample bottle were opened to the circulation

path, and then the valve to the gas purification system

opened. The valve between the furnace and the sample

bottle was onl.y closed.during cooling of the furnace.

The vacuum pump was started and the equilibrium

apparatus was evacuated. Arter five minutes,' the pumping

was discontinued and the equilibrium apparatus was filled

with purified argon. As soon as the pressure of argon

in the apparatus reached barometric pressure, the valve

to the bubbler was opened and the argon was allowed to

pass through the sample bottle, over the charge, and out

through the'bubbler. The controller and :furnace power

were turned on and the temperature allowed to reach 300°C.

The system was then flushed for 10 minutes at 300°c·1n

order to remove any moisture and adsorbed oxygen.

After flushing wa~ .complete, the gas flow was dis­

eontinued. the valve connecting the equilibrium apparatus

28

and the gas purification system was closed, and the desired

operating temperature reset on the controller.

After the .furnace had reached the desired tempera­

ture, the circulation pump was turned on and allowed to

circulate. After one hour of circulation, the valve to th€

bubbler was closed and pumping continued for another 12 to

24 hours • .An equilibration period of 24 hours was allowed

at 7oo0 c, and a period of 12 hours at temperatures ·above

7oo 0 c. At the end of the equilibration period, the pump was

stopped and the system opened to the bubbler • . The 3-way

valve on the left side of the sample bottle was first

turned to a neutral position, the other 3-way valve on the

right side to the sample bottle was turned to connect the

sample bottle to the gas analysis apparatus, and finally

the 3-way valve on the lert side of the sample bottle was

turned to connect the argon line to the sample bottle. The

purified argon gas flushed the argon-so2 mixture out of the

sample bottle into the gas analysis apparatus.

As soon as rlushing had commenced, the valve to the

bubbler was closed, the valve between the furnace an~ gas

sample bottle was closed, the controller and furnace power

were turned orr, the furnace-opened, and the charge quickly

cooled.

29

Analysis of the exit gas consisted o:f passing the

argon, S02 mixture through a glass frit which was immersed

in an aqueous solution of H2o2 and NaOH. The so2

was con­

sumed according to the following reactions.

S02 -+ H2o2 ~H2so4

H2so4 + 2NaOH ~2H2o + Na2so4 The solution was stirred with a magnetic stirrer to provide

good contact of the gas bubbles with the solution. The gas

.analysis apparatus is illustrated photographically in

Figure 10.

A given quantity of standardized NaOH was added

prior to the flushing operation, and after 40 minutes o:f

flushing the excess was back-titrated with H2so4 •

The end point when the solution changed from basic

to acid was detected by use of a modified methyl-red indi­

cator*. The color change at the end point was green in

alkaline to violet-red in acid. The str.ength of the NaOH

and H2so4 solutions ~as adjusted to give the largest

possible value for the net c. c. of NaOH used in the

titration, and at the same time a sharp color change at the

end point.

*For instructions ~or preparation of mod~ied methyl­r~d· indicator see Appendix I.

30 I

FIG. -10

GAS ANALYSIS APPARATUS

31

The NaOH solutions were standardized no earlier than·

24 hours after preparation, and were kept in a dark enclo­

sure. The NaOH solutions were standardized with Fisher's

reagent-grade potassium hydrogen phthalate. Blank samples

o:f NaOH were titrated with H2so4 in order to determine the ·

NaOH equivalence or the H2so4 •

During the course or the investigation, 1 t was :found

that a rather appreciable amount of" so2 was collected inside

o:f the glass frit,·giving correspondingly low results f'or

Ps02• This problem was eliminated by flushing the inside

of the :frit with. the basic solution prior to the titration

with H2so4•

The P802 was calculated by knowing (1) the total

moles of gas mixture in the sample bottle, (2) the moles of'

so2 from the titration, and (3) the total pressure of the

system.

The P802 was measured for various PbO-PbS mixtures,

ranging from 20Pb0/1PbS to 1Pb0/20PbS, at 7oo0 c, 720°c,

74o 0 c and 76o0 c. The reacted mater1als were ground to -200 mesh, and

then analyzed by X-ray diffraction using a Norelco, ~-ray

dirfraction unit with goniometer and strip-chart recorder

attachment. The peak counting rate was 80 counts/second,

and the time constant was 4 seconds. The phases were

32

identified using the A. s. T. M. card file index.

CHAPTER V

EXPERIMENTAL RESULTS

The experimental results of this investigation con­

sist of the measured equilibrium values of P802 above

PbO-PbS mixtures at several tempera-tures, and id~ntification

o_t the phases in the reacted materials by interpretation o:f

the X-ray di.ffra.ction data.

The mea.sured. values of -log P~oe obtained for the ..... iC

system PbO-PbS between 7oo0 c and 76o0 c are listed in

tabular form in Table I and are .presented graphically in

Figure 11. A sample caiculation of -log P802 fran experi­

mental data is included in Appendix II.

The results of identification of the phases in the

reacted materials are also included in tabular form in

Table I. The X-ray diffraction data that were used to

identify the various phases are not included in thi~s thesis,

but rather a tabulation of the 29 engles used in interpret­

ing the data is included in Table II.

Identification of the phases in the PbO-PbS system

from the X-ray dirfraction data was complicated.by tbe fact

that an observed 28 value could often be assigned to two

dirferent phases. Lead oxide and the basic lead sulfates

had several sets of 2Q values that were so close together

Rtm #

1

TABLE I

EQUILIBRIUM Pso2 VALUES FOR THE SYSTElv! Pl:?0-PbS

BETWEEN 7000-760°c TOGETHER WITH THE P~SES IDENTIFIED IN. THE REACTED CHARGES

Temp. oc Atomic foS -Log Pso2 Phases

700° 3.58 3.008 Pb, PbS04·4PbO,

4.54 3.041 Pb, PbS04.4PbO,

s.oo 2.933 Pb, PbS04.4PbO

5.56 2.594 Pb, PbSQ4.4PbO

6.25 2.235 Pb, PbS04.4PbO

8.33 2.047 Pb, PbSQ4.4PbO,

10.00 2.070 Pb, PbS04•4PbO,

16.67 2.063 Pb, PbS04•4PbO,

25.00 . 2.078 Pb, PbS04•4PbO,

42.86 2.oe1 Pb, PbS04•4PbO,

34

PbO

PbO

PbS

PbS

PbS

PbS

PbS

35

TABLE I (continued)

Run# Temp. 0 c Atomic foS -Log Pso2 Phases

2 .720° 2.38 2.953 Pb, PbS04•4FbO, PbO

4.54 2.906 Pb, PbS04.4PbO, PbO

5.oo 2.924 Pb; PbS04.4PbO, PbO

5.56 2.565 Pb, : PbS04. 4Pb0

7.14 · 1.910 Pb, PbS04.4PbO

10.00 1.809 Pb, Pb SO 4 • 4Pb0, PbS

16.67 1.819 Pb, PbS04·4PbO, PbS

25.00 1,819 Pb, PbS04•4PbO, PbS

33.33 1.827 Pb, PbS04•4PbO, PbS

· 40.00 1.826 Pb, PbS0404PbO, PbS

44.44 ·1.845 Pb, PbS04·4PbO, PbS

3 740° 2.38 2.780 Pb, PbS04·4PbO, PbO

4.5·4 2.604 Pb, PbS04·4PbO

5~00 2.334 Pb, : PbS04. 4Pb0

36

TABLE . I (continued)

Run# Temp. Oc Atomic foS -Log Pso2 · ·Phases

5.56 2.009 Pb, PbS04.4PbO

6.25 1.777 Pb, PbS04·4PbO

7.14 1.689 Pb~ PbSQ4.4PbO, PbS04.2PbO

8.33 1.€43 ·pb, PbS, Pl;>S04·2Pb0

10.00 1.646 Pb, PbS, PbS04·2PbO

16.67 1.636. Pb, PbS, FbS04.2PbO

25.00 1.642' Pb, PbS, PbS04.2PbO

42.86 1.656 Pb, PbS, PbSQ4.2PbO

4 7600 3.58 2.409 . Pb, PbS04•4PbO, PbO

4.54 2.414 Pb, PWQ4.4Pb0, PbO

5.00 .2.426 Pb, PbS04• 4_Pb0

5.56 2.099 Pb, PbS04.4~bO

6.25 1.787 Pb, PbSQ4.4PbO

7.14 1.592 Pb, PbSQ4.4PbO, PbS04.2PbO

37 TABLE I (continued)

'Run# Temp. oc . Atomic foS -Log Pso2 Phases

7.94 1.593 Pb, PbS04•4PbO, PbS04.2PbO

8,33 1.542 Pb, PbS04•2PbO

10.00 1.416 Pb; PbS04.2PbO

16.67 1.379 Pb, PbS, PbS04•2PbO

25.00 1.379 Pb, PbS, PbS04•2PbO

j

1.4 f . . I. 6

N 0 fl)

a.

(!) '

0 _J

I

1.8

2.0

2.2

2.4

2.s ·

2.8

3.0

3.2

PbO 2

EQUILIBRIUM

v- 760! c El- 740• c A- 120• c 0- 100• c

4 6 8 IO 12 14 16 18 20 22 24 26

MOLE % S . • .

FIG.- II

Pso2 VALUES FOR THE SYSTEM PbO- PbS

100·- 1so•c

42 44 46 48 PbS

BETWEEN

L.~-~~~~~~~~~~~~~~~~~~~~~--~~~~.~~~~---~a--___.

38

2Q Angle

10.8

11.2

15.0

19.9

21.45

23.4

26.0

27.4 -

28.6 -

29.l -

29.8

30.1

TABLE II

THE 2Q VALUES USED IN INTERPRETING THE X-RAY DIFFRACTION DATA

Phases

PbS04 • 4Pb0 ·

PbS04·2PbO

PbO, PbS04.2PbO

PbS04. 2Pb0

PbS04.2PbO

PbSQ4.2PbO

PbS

27.6 PbSQ4.2PbO, PbSQ4.4PbO

213. 7 PbS04.2PbO, PbS04•4PbO

29.2 PbO, FbS04·4PbO

PbS04·2PbO

PbS

30.2 - 30.3 PbS04·2PbO, PbO

30.85 PbS04•2PbO

31.0 PbS04.4PbO

31.3 Pb

33.6 PbS04 .4PbO

35.8 PbO

36.3 Pb

39

2Q Angle

37.75

43.1

46.65

53.l

T.ABLE II (continued)

PbS04.2PbO

PbS

PbS04·4PbO

PbO, Pbso4.4Pb0

40

Phases

41

that a set of 2Q values appeared as a single dllfraction

peak rather than two adjacent peaks. Identification of PbO

was particularly di.fficult as there were only two .major

peaks, and the 2Q value f'or 100%' peak intensity coincided

with one of the major peaks of Pbso4.4Pb0, which was found ·

to occur with PbO. Fortunately, the only inter.f~rence with

the second major peak o.f PbO was Pbso4 .2PbO, which was never

found to exist in equilibrium with PbO. The values · of dhkl

for the phases Pb, PbS, PbO, PbS04.2PbO, PbS04.4PbO agreed

very well with the values published in the A. s. T. M. card

file index.

The isotherms dep1cted in Figure 11 represent the

variation in equilibrium Pso2 :for the· system FbO-Pbs.

Temperatures less than 7oo0 c were not attempted because the

small va.lues of' P802 were beyond the range of the method of

gas analysis used in this investigation. Several experi­

ments were conducted at 78o 0 c, but the entire charge was

molten at this temperature and reaction between the charge

and the porcelain boat was observed. Because of contamina­

tion of the reacting materials, measu.rements above 76o 0 c

were discontinued.

Figure 11 shows that the isotherms at 7oo0 c and 720°c have the same general shape • . Both contain horizontals in

the same composition ranges and a diagonal line connecting

42

the two horizontals. The isotherms at 74ooc and 76QOc

have the same general shape, but differ from the isotherms

at 7oooc· and 72ooc _in'that the former have three horizon­

tals and two diagonal lines.

The X-ray diffraction results (see Table I) indicate

that for the 7oo0 c and 720°c isotherms the horizpntal. at

the PbO end of the diagram represents the three-phase.

regi·on Pb, PbO, Pbso4.4Pb0, and that the horizontal' at the

PbS end of the diagram represents the three-phase region

Pb, PbS, Pbso4.4Pb0. The X-ray results likewise indicate

that the diagonal line connecting two horizontals of the

same isotherm represents the two-phase region Pb, PbS04.4PbO.

The isotherms at 740°C and 760°C show that there are

three, three-phase regions, and two, two-phase regions.

The X-ray results reveal that the horizontal on the Pb_O

side of the diagram represents the three-phase region Pb,

PbO, PbSo4.4PbO, and that the horizontal on the PbS-side o~

the diagram represents the three-phase region Pb, PbS,

PbS04.2PbO. The horizontal between the above mentioned

horizontals represents the three-phase region Pb, PbS04•4PbO

Pbso4.2Pb0. Two diagonal lines connect the three ho~izon­

tals at each isotherm. The diagonal between the three­

phase regions Pb, PbO, PbS04•-4PbO, and Pb, PbS04·4PbO,

PbS04.2PbO represents the two-phase region Pb, PbS04·4PbO.

43

The diagonal between the three-phase regions Pb, PbS04 ·4PbO,

PbS04·2PbO and Pb, PbS, PbS04·2PbO represents the two-phase

region Pb, PbS04 ·2PbO~

On the basis of the ob-served variations in condensed

phases with temperature and composition, a phase diagram

:for the system PbO-PbS has been proposed and is illustrated

in Figure 12.

The composition values f'or the boundary lines were

obtained by using the intersection of the extrapolated

horizontal and diagonal lines.

A diagonal line between two horizontals on the same

isotherm indicates solubility of sul.fur and oxygen in

liquid lead, and solid solubility of ·sulfur, lead and

oxygen in basic lead sulrate. Since the solubility curve

of oxygen and sulfur in liquid lead, and the solubility

curves of oxygen, sulfur, and lead in basic sulfates are

not known, it is impossible to indicate the composition

of the liquid or the basic sulfates. In addition to the

solubility curves, tie lines between the solubility curves

would have to be determined experimentally in order to

show the composition or the liquid lead and solid baste

sulrates phases for any point in these two-phase regions.

Because both the liquid lead and basic sulfates are

of undetermined composttion, the words liquid lead have

44

LIQUID

760 LIQUID LEAD LIQUID LEAD

PbS04 4Pb0 Pb 804 • 2Pb0 Q O PbS

PbO ~f 740 .J •

0 . 0 - g otct 1aa•c u 5 !8

:; A. • LIQUID 1.~AD - 720 0

PbS04 · 4Pb0

a.: PbS

~ w 700 I-

1 PbO 2 4 6 8 10 12 14 46 48 PbS

MOLE % s ....

Fl G. - 12

PROPOSED . PHASE DIAGRAM FOR THE SYSTEM PbO- PbS BETWEEN

700° - 760°C - ·····-------·- -- ---

been substituted for the symbol Pb, and the formulas

PbS04·2PbO and PbS04 •4PbO are used to convey the fact

that one of the condensed phases has a: particular basic

sulfate crystal structure where the composition is not

necessarily that indicated by the stoichiometric formula

of the basic sul:fate.

45

The phase diagram for the system PbO-PbS was also

constructed :from the Pb-0-S composition diagrams presented

by Kellogg and Basu, and is illustrated in Figure 13.

Comparing the two phase diagrams shows that the

boundary lines in Figure 13 become areas, where either or

both of the phases have ·a variable composition, 1n Figure

· 12.

Thermodynamic calculations based on the experimental

data will be presented in the next chapter.

I .

! I i I I I

:! I

-<..) 0 -a.. ~

,------- ·---r---1 •b I .. j

PoO 760 i..... l•

0 0 I PbS04 • 4Pb0

f i i.

I N •

. 740 r I o-. j co f lf f I

!

! !

720

Pb

Pb

PbS04 • 2P~O

PbS

PbS04 · 4Pb0

PbS

46

w 700 .r t- I . I

i l ____ L ___ J _ __ J __ ~~L ~-- -· '~-'--L-~~~~~~~~~~~~~~~

PbO 2 4 6 8 10 12 14 . 46 .48 .. PbS MOLE . 4Y• S

. .,..,.

FIG.~ 13

PHASE DIAGRAM, AFTER KELLOGG 8 BASU, FOR THE

PbO- P'oS BETWEEN •100·-1so·c SYSTEM

i ... ... _ . . ... . ......... - ...... --·-··-------------~----------------------~-.J

CHAPTER VI

THERMODYNAMIC CALCULATIONS

The thermodynamic calculations· have been divided in

three parts. The first part is concerned with the the.rmo- ·

dynamic calculations based on the experimental r~sults.

The second part is concerned with the same type of calcu­

lations~ but based upon the experimental results of . previous

~nves·t1gators. The third part is concerned with the

graphical representation of the thermodynamic calcu1ations.

Calculations from. Experimental Results. The

equilibrium values of P802 and the re.sults or .the corres­

ponding X-ray analysis of the condensed phases, which have

been tabulated in the previous chapter,can be arranged in

a more convenient form ror purposes of calculation. Table

III lists the equilibrium values of -log Pso2 and t~e

equilibria, based upon the results of the X-ray analysis

of the condensed phases, representing these data.

If the· assumption. can be made that the activity of

each condensed phase was unity, then the standard free

energy change (.6.F0 ), hereafter referred to as the free

energy change, of each reaction can be expressed as

fo;t.lows:

.(6-1) Pb+ PbS04 •4Pb0~6PbO + 802

~F0 = -4.576Tlog P802

( 6-2) 3PbS- +. PbSO 4 • 4Pb0 ~ 8Pb ·+ . 4S02

'6.F0 = -4.576(4)Tlog Pso2 (6-3) Pb+ 3(PbS04•2PbO) ,. 2(PbS04•4PbO) + S02

.6.F0 : -4.576Tlog P802

(6-4) 2PbS+ . PbS04 .2PbO 4 • 5Pb + 3S_Q2

~Fo = -4.576T(3)log P_~o2

48

Since the P802

is a direct measure of the free energy

change of' each rea_ction, the free energy · change of reactions

(6-1) through (6-4) can be calculated .from the · experimental

values o:r P802•

The assumption that the activity of each condensed

phase was·unity· was assumed to be valid .for the following

reasons:

l. According to Hansen9 the solubility of su1fur ·

in liquid lead is 3.5 atomic foS at 75o0 c, and the solubil­

ity of oxygen in liquid lead is .10 atomic ~oat 75o0 c. This indicates that at 750°C: the activity of Pb is approxi-

mately .96.

2. Lead oxide and lead sulfide have no reported

s:, lid-solubility.

3. The solid-solubility of Pb, O, and.sin the basic

· suirates was rather limited as.: indicated by the fact that

Reaction

6-1

6w2

6-3

6-4

TABLE III

EQUILIBRIA INVESTIGATED TOGETHER WITH THE EQUILIBRIUM VALUES OF Pso2

Equilibrium

Pb+ PbSO 4 • 4Pb0 ~ 6Pb0 + S02.

3PbS + PbSO 4 • 4Pb0 ~ 8Pb -t 4S02

Pb+ 3(PbS04 ·2PbO) ~ 2(PbS04•4PbO)+ S02

2PbS + PbS04•2PbO ~ 5Pb + 3802

_49

Temp 0c -Log Pso2

100° 3.025

720° 2.950

740° 2.779

760°. 2.410

700° ·2.070

720° 1.826

740° · 1.690

7500 1.592

740° .t.640

760° 1.379

the dhk1 values ~or the basic sulfates remained constant

within the error of experimental measurement.

The AF0 r of PbS04.4PbO and PbrS04.2PbO can be

calculated by combining the 6F0 r date for PbO, PbS 1 and

50

_so2 , which is available in the literature, with calculated·

values or l).F0 :f'or the reactions (6-1) through (6-4)-. The

~F0 r equations for PbO, PbS, and so2 are tabulated in

Table :rv. Two values o:f .6F0r of Pbso4 .4Pb0 can be calculated

at each experimental temperature. Us1ng reaction (6-1)

.6F0 f o:f Pbso4.4Pb0 can be calculated at 7oooc, 720°c,

740°c and 760°c. The .6F0 :r of Pbso4 .4PbO at 7oo0 c and 720°c

can be calculated from reaction (6-2)~ and the ~F0 :r of

Pbso4.4Pb0 at 74o0 c and 76o 0 c :Crom the combination of

reactions (6-3) and (6-4).

Th9 .6 F0 f of PbSO 4• 2Pb0 can be calculated at 7 40 °c

and 760°c from reaction (6-4).

The calculations of .6F0 f of PbS04.4PbO and

FbS04•2PbO fol1ow.

A. t::.F0 r of Pbso4.4PbO at 7oo 0 c, 720°c, 74o0 c,

and 76ooc from reaction (6-1).

Pb + PbS04 • 4Pb0 "4 ,. 6Pb0 + S02

4.576T(-Log Pso2> : [6(.6F0 :r PbO)-t- (.6.F0 r S02)J

- [(.6F0 ;r PbS04•4PbO)]

TABLE IV

EQUATIONS FOR THE FREE ENERGY OF FORMATION

OF Pbo(lO), PbS(ll), and S02(lO) AS

A FUNCTION OF TEMPERATURE

~Fof PbO ~ -54,950 - 8.05TlogT+ 50.lT (6000-1150°K)

~For PbS: -38,640+ 20.65T (8580-1200°K)

~F0 r so2 : -86,620 + 17.31T (298°~2000°K)

51

52

· 4.576T(-Log Pso2) "= [6(-54,950-8.05Tlog'Pt- 50.lT) ·

+ (-86, 62.0 + l 7.31T)]

- [AF0 r PbS04·4PbO]

~Fof PbS04 .4PbO - -4.576T(-log Pso2 ) -416,320

-48. 30TlogT + 317. 91T

T : 973°K, -Log Pso2 ~ 3.025, AF0 r PbS04·.4Pb0 :

-260,890 cal.

T : 993°K, -Log Pso2 = 2.950, AF0r PbS04·4PbO -

-257,779 cal.

T 0

-Log Pso2 2.779, • 1013 K, = -254,217 cal..

T : 1033°K, -Log Pso2 - 2.410, --249,696

B. · L:::..F0 r of PbS04•4PbO at 7oo 0 c and 720°c fran

reaction (6-2)

3PbS + PbSO 4 • 4Pb0 ~ 8Pb + 4802

4.576T(4)(-Log P802 ) : [4(.6.F0r so2)] - ·

[3(AF0r PbS)

+(AFof Pbso4 .4Pb0)]

4.576(4)T(-L6g Pso2) = [4(-86, 620 + 17.31T)]

{:_3(-38, 640 + ff).$5T) +

AF0 r PbS04·4PbO]

·~For PbS04·4PbO ~ -4(4.576)T(-Log Pso2) -

230, 560 + 7.29T

T ~ 973°K, -Log Pso = 2.070, .6F0~ PbS04·4PbO: . 2 .l.

-260 ,333 cal.

0 , 0 T - 993 K~ ~Log Pso2 = 1.826, b.F .f PbS04·4PbO:

-256,510 cal.

c. .6F0r of Pbso4.2Pbo at 74o0 c and 7so0 c .from

reaction (6-4)

2PbS + . PbSO 4 • 2Pb0 ~ 5 Pb + 3S02

4.576(3)T(-Log Pso2) = [3(.L\F0r S02)J - ·

[2(.L\F0 .r PbS) +

(~For PbS04·2PbO)]

4.576T{3)(~Log Pso2l : [3(-86, 620 + l 7.31T)]

53

· - [2(-38, 640 + 20.65T)

+· A F 0r PbS04·2~0]

b.F0 f PbS04 .2PbO • -3(4.576)T(-Log Pso2 )

182, 580 + 10.63T

T : 1013°K, - LogPso2 - 1. 640, 6F0 Pbso4.2Pb0:

-194,618 cal.

T - 1033°K, - Log Pso2 = 1.379, .6F0

PbS04·2PbO -- 1_91, 155 cal.

D. ~For of PbS04~4PbO at 740°C and 760°C from

reaction (6-3) and calculations in Part .. _ C

Pb + 3(PbS04·2Fb0) +----;' 2(PbS04•4PbO) + S02

4.576T(-Log Pso2) · : [2(.6F0:r PbS04·4PbO) +

AF0r S02J -[3(;6.F0 .r PbS04.2PbO)]

--

4.576T(-Log Pso2' - [(-86, 620 + 17.31T)+

2AF0r PbS04_•4PbO] 0 . .

-- [3(.AF_f PbS04•2PbO)]

2AF0 PbS04.4PbO • 4.576T(-Log Pso2>+ 86,620

-l7.31T+ 3AF0 r PbS04·2PbO

T = 1013°K; AF0 :r PbS04 •2PbO ·:: -19.4, 618. cal.;·

-Log P~o2 ~ 1.690

.AF0r Pbso4 .4Pb0: -253,468 cal.

T : l033°K; -~F0 r PbS04.2PbO ~ -191,155 cal.;

-Log ~so2 : 1.592

AF0:r PbS04 .~PbO = -248,600 cal.

54

The results of the above calculations are summarized

·1n Table v.

Calculations from Results o.f Previous Investigations.

Since the experimental data of Reinders, and Schenck and co­

workers have been shown to be in error, the thermod~namic

calculations will be limited to the experimental results

of Kellogg and Basu.

Table VI lists th~ equilibria studied by Kellogg

and Basu, and the corresponding AF0 equations f~r these

equilibria. These .AF0 equations were derived from the

experimental va1ues o.f Pso2 with the assumption that the

. ac.tivity of ea.ch condensed phase was unity. Two o.f these ' .

eq~ilibria, .rea~tions (6-1 and (6-4),are the same as those

TABLE V

CALCULATED VALUES OF AF0 f OF Pbso4.4Pb0

AND PbS04·2PbO FROM TEE EXPERIMENTAL DATA

Reaction

(6'.""'l) (6-2)

(6-1) (6-2)

(6-1) (6-4), (6-3)

(6-1) ( 6-4) ,' . ( 6-3) .

Reaction

(6-4) (6-4)

0 Temp- C

70.0° 100°

720° 720°

740° 740°

760° 760°

Temp-°C

-AFor PbS04·4PbO

260,890 cal~ 260,333 cal.

257;779 cal. 256,510 cal.

254;217 cal. 253,468 cal.

249,697 cal~ 248,600 cal •.

194;618 cal~ 191,155 cal.

55

TABLE VI

EQUILIBRIA STUDIED BY KELLOGG AND BASU TOGETHER WI TH 6, F 0 EQUATIONS

(6-.1) Pb+ PbS04 .4Pb0____.6PbO + S02

~ FO = 24. 99T + 7.46 x 10-3T2 + 2.81 x 105T-l

-22.496TLogT + 46,340

. (6-4) 2PbS + PbS04 .2PbO~ 5Pb + 3802

. ~ Fo : -20.13T + 23.86 x 10-~T2 + 4.2·3 x l05T-1

-44.924TLogT + 154, 780

(6-5) PbS + 8(PbS04.2PbO) >5(PbS04•4PbO) + 4S02

6.Fo : 83.32T + 30.58 x 10-3T2 + 9.14 x 105T-l

-78.703TLogT +153,250

56

studied in this investigation. The other equilibrium, ·

r_eaction (6-5), was not studied in this inve~tigation.

57

Two values of ~For of Pbso4 .4Pb0 can be calculated

at each experimental temperature. The ~F0 r of Pbso4 .4Pb0

at 7o'o0 c, 72ooc, 74o0 c and 76o0 c can be calcula.ted :from . ·

reaction (6-1), and also from the c-ombination of. reactions

(6-4) and (6-5).

The ~For or Pbso4 .2PbO can be calculated at 740°c

and 760°C from reaction (6-4).

The ~For ~qua.tions :for PbO, Pbs,· and S02 were taken

from Table IV.

The calculations ·or~ F 0r of PbS04.4PbO and

·PbS04 .2PbO follow.

A.· b.F0 r of Pbso4.4PbO at 7oo0 c, 720°c~ 740°c,

and 76o 0 c from reaction (6-1)

Pb+ PbS04·4PbO > 6Pb0 + S02

24. 99T + 7. 46 x 10-3T2 + 2.81 x 105T-l -

-22.496TlogT + 46,340 : [(-86,620 +17.31T)

6(-54,950 - 8.05TlogT

+ 50.1T)]

_ -[ ~F0 r PbSQ4 .. 4PbO]

b.Fof Pbso4 .4Pb0 ~ -462,660 + 292.92T -

7.46 x 10-3T2 - 2.81 x 105

T-l - 25.80 TlogT

. T: 973°K t::,.F0 f PbS04.4PbO = -260,012 cal.

T ~ 993°K ~F0r PbS04·4PbO :: -£56,209 cal.

T ':1013°K .6.F0r PbS04 .4PbO :-25'2,417 cal.

T :1033°K .6.F0r PbS04·4PbO =-£.47,636 cal.

B. .6.F0 r or Pbso4.4PbO at 7oo0 c, 720°c·, 74o 0 c,

and 76o 0 c using Reactions ( 6-4) ·and ( 6-5)

(6-2); . 3 PbS + PbS04•4PbO , (?Pb + 4802 . ·

where C:6-2) : 1/5 [ 8(6-4) - (~-5)] .

. 58

.6 Fo : 1/5( 8 [ -20.13T + 23.86 x 10-3T2 +

4.23 x 105T-l - 44.924TlogT + 154,780]

- [83.32T + ·30.58 x l0-3T~ + 9.14 . .

x 105·T-l - 78.703TlogT + 153~250])

.6F0 : . -48.87T + 32.06 x 10-3T2 + ·4.94 x; l05T-l

-56.138TlogT + 216,998 : [4(-86,620 +

17.31T)] .- [ 3(-38,640 + 20.65T) + .

.6. Fo f PbSO 4 • 4Pb0]

.6F0r PbS04·4PbO: - 447,558 - ·32.06 x 10-3T2

-4.94 x l05T-l + 56.16T +

56 •. l38TlogT

T = 973°K .6,F0 PbS04e4PbO : -260,557 cal.

T = 993°K .6.F0 PbS04 .4PbO a ~256,836 cal.

T :1013°K t::,.FO PbS04.4PbO ~ -253,132 cal.

T .l033°K .6.F0· PbS04 .4PbO • -249,444 cal.

c. .6.F0 r of Fbso4.2PbO at 74o0 c and 7So0 c from

reaction (6-4)

2PbS + .PbS04 ·2PbO-. 5Pb+ 3802

59

-20.13T+ 23.86 x 10-3T2 +· 4.23 x 105T-l+ 154,780

T --T :

-44.924TLogT :[3(-36,620 + 17.31T)]

-{€(-38, 640 + 20. 65T) +

.6_~·0 :f PbS04• 2Pb0]

6F0r FbS04 .2PbO : -337,360 + 30.76T - 23.86

x 10-3T2 - 4.23 x 105T-l

+ 44. 924TlogT

1013°K .6.F0r ~bS04 .2PbO : -194,323 cal.

1033°K .6.F0r PbSO 4 • 2Pb0 · :-191,581 cal.

The results of the above calculations are summarized

in Table VII.

For purposes of comparison, the thermodynamic calcu­

lations from the experimental data of both this investiga­

tion and .the work of Kellogg and Basu are presented 1n

Table VIII.

Graphical Representation of the Thermodynamic

Celculations. The temperature dependence of .6.F~ is given

by the Gibbs-Helmholtz equation .6.Fo ~o - T AS0 • If

.6.Ho is independent of T, and _ .6. CP equal . to zero, a plot

· _ of .AF0 versus T should yield a straight line where

TABLE VII

CALCULATED VALUES OF b.F0 f OF PbS04•4PbO AND

PbS04•2PbO FROM THE! DATA OF

Reaction

(q-1) .. (6-4), (6-5)

(6.:.1, · (-6-4), (6-5)

(6-1) · (6-4), (6-5)

(6-1) · (6-4), (6-5)

Reaction

(6-4) (6-4) .

KELLOGG AND BASU·

Temp-°C

7000 700°

7200 720°

"7400 740°

7600 760°

Temp-0 c

740° 760°

0 . - .6:F f PbSO 4 • 4Pb0

260;012 cal. 260,557 cal.

256,209 ca1. 256,836 cal.

252;417 cal. 253,132 cal.

247,636 cal~ 249,444 cal. _.

- ~F0r PbS04·2PbO

194,323. cal~ 191,581 cal.

60

61 TABLE ·VIII

SUMMARY OF THERMODYNAMIC CALCULATIONS

COMPARIIDN OF THERMODYNAMIC PROPERTIES

THIS INVESTIGATION KELLOGG AND BASU

Reaction Temp-0c - ~For Reaction Temp-0c - i::).F f

PbS04· .. 4PbO PbS04.4PbO

(6-1) 700° 260,890 caJ.. (6-1) 700° 260,012 cal~ (6-2) 700° 260,333 cal. (6-4),(6-5) 700° 260,557 cal.

(6-1) 720° 257,779 cal. (6-4) 720° 256;209 cal. (6-2) 720° 256,510 cal. ( 6-4), ( 6-5) 720° 256,836 cal.

(6-1) · 74:00 254,217 cal. (6-1) 740° 252, 417 ce.1. (6-3),(6-4) 740° 253,468 cal. (6-4),(6-5) 740° 253,132 eal. ·

(6-1) 760° 249,697 cal. (6-1) 760° 247;636 cal. ( 6-3) , ( 6-4) 760° 248,600 cal. (6-4),(6-5) 760° 249,444 cal •.

Temp-0 c -flFo f

Temp-°C - -!:).For

Reaction PbS04e2PbO Reaction PbS04.2PbO

(6-4) 740° 194,618 cal. (6-4) 740°·., 194,323 cal. (6-4) 760° 191,155 cal. (6-4) 7600 191,581 cal.

slope : - A s0

Intercept = ~Ho

. 62

A plot of AF0 i of PbS04·4PbO versus T is illustrated

in_Figure 14. As indicated in the leg~nd, the values o:f 0 . . .

. AF r o:f P.bso4 .4Pb0 calcul·ated :from the results c:£ this

investigation and also those calculated from · the .work c:£

Kellogg and Basu have been included. ' .

Using the "method of least-squ~res", a- straight 1ine

was drawn through the points representing the data of this

investigation, an~ another straight line . through the points

representing the data of· Kellogg· and Basu.

The equation of the line representing the result s of

·this investigation is as follows·.: ' 0 + AF~ PbS04•4PbO = -444,207 + l88.45T; cal,-.65 Kcal

(7oo 0 -76o0 c), where t..65 Kcal represents an error

limit of one standard deviation (la-). In accordance

1d. th the Gibbs-Helmholtz equation,

~Hof Pbso4.4Pb0 : -444,207 cal,, (7oo 0 -76o0 c)

AS0 f ~bS04 •4PbO = -188 .. 45 e.u.., (7oo0 -76o0c).

The equation of the line through the points of

Kellogg and Basu is

AFof' PbS04 .4P°?O: -450,022 + 194.91T;cal, ±.58Kce.1

(7oo0 -76o0 c); where ~Hof' PbS04·4PbO: -450,022 cal, 0 .

(7oo0-760°c) AS f PbS04·4PbO ~ -194.91 e.u., ·(70o0 .:...·76QOC)

r -- -- -------=~- ----·· ····· ______________________________ &_,·3 I .

248 _

i . I 249::....

I r . : 1 250 L.· : ........ . : ,J l ~ 251 _ !~ · !

~ - 252 i--

i ' . I

. 0253 ;·

..0 ' a.. I . v·254 t-• "i ~2551

0.. 2,6 t-o'+- I l.L.257 t-

. <l . . I 2se t--

259

260

261

[.\ - - - -

/ /

"/ /

/

980

/ /

/

990

KELLOGG a BASU

THIS INVES TIGA110N

/ /

/ /

/ . /

N /

/

0

/ /

/ /

1000 IOIO 1020

Ti K

FIG.-14·-

A I' p/1

1030

I . TEMPERATURE DEPENDENCE OF ~ Ff OF PbS04-

. 4Pb0 BETWEEN I I

f

I 700•-:-7so·c

The calculations of' the two free en~rgy equations,

and the standard deviation error limits are included 1n

Appendix III and IV, respectively.

64

The average deviation of AF0 r' of PbSo4 .4PbO· values

calculated from both free·energy equations is ±.71 Kcal 1n·

the. temperature range 7oo0 c to 76o0 c. The ca.lculation of

the average deviation is included in Table.IX.

Because onl.y two values of .6.F0 r of PbS04 ·2PbO were

calculated from the results of this investigation, no

attempt was made to derive a linear free· energy equation 0 .

for ,6.F f o.f Pbso4.2Pb0 or compare it with a l·inear free

energy equation derived from the data of Kellogg and Basu.

TABLE IX

AVERAGE DEVL~TION OF ~For OF PbS04 .~PbO

VALUES FROM THIS INVESTIGATION AND THOSE FROM KELLOGG AND BASU

A. This Investigation

~F0r PbS04·4PbO = ;..444,207 + l88.45T

T-°C

700° 720°

0 7400 760

B. Kellogg and Basu

260,840 cal. 257,171 cal. 253,302 cal. 249,633 cal.

~F0 f PbS04·4PbO: -450,022+ 194.91T

T-°C

260;377 cal. 256,478 cal. 252; 580 cal. 248,682 cal.

65

TABLE IX (continued)

O' -~Ff PbS04 .4PbO (cai.)

T-<;>C A B d

700° 260, 84.Q 260;377 463 720° 257;171 256;478 693 740° 722 253.,302 252,580 . 760°. 249,633 248, 682 951·

2d = 2829

Average deviation_ - t 2 d. - t 2829 : ± • 71 Kcal - ~- -4-

66

CF..APTER VI I

IQ:NETIC STUDIES

A series of e xper1ments were conducted to determine

qualitatively the effect of (l) temperature, and (2)

PbO/PbS ratio on the rate of so2 evolution, with .the purpose

of gaining an insight into the reaction mechanism(s) in­

volved in the approach to equilibrium..

Review of the literature. The kinetic behavior of

the system PbO-PbS has been studied by several investigators,

but with varying results. ·

Kohlmeyer and Monzer12 have stated that the reaction

mechanism consists of (1) formation of "basic sulfates",

and (2) reaction between the "basic sulfates" and PbS to

yield Pb and so2• The exact composition of the "basic

sulfates" was not established. . 13

Merrick has also investigated the kinetics of the

reactions between PbO and PbS, and has proposed the follow­

ing mechanism:

l. PbS(solid)~ PbS(vapor)

2. PbS(vapor) transported to PbO solid surface

3. PbS(vapor) + Pb - O(_site)~ Pb - o ••• PbS

(equilibrium chemisorption)

68

4. Pb - o ••• PbS : (xPbO-Pbsif' activated complex~ ·

(x + l)Pb + SOX (adsorbed)

5 • sox (adsorbed)~S03 (gas)·

or

so . x (adsorbed)~ so2 (gas) + !02 (gas)

6 • S03 (gas)~ S02 (gas) + }02 (gas)

7. Transport of so3 , so2 , and o2 gases from solid

surface.

The mechanism proposed by Merrick presents one basic

objection. Since kinetics is tbe rate of approach to

equilibrium, any proposed reaction mechanism must include

a step involving the formation of the equilibrium, reactants.

The results of' the equilibrium studies show tt.at either

PbS04.2PbO or Pbso4.4Pb0 is an equilibrium reactant in the

system PbO-PbS. Consequently, any proposed reaction

mechanism must include a step involving the :formation c£ a

basic sulfate phase.

A more realistic mechanism has been proposed by

Kellogg and Basu. They have proposed the f'ollowing mechan­

ism for a mixture of 2Pb0/1PbS at 1100°K:

PbS + 6Pb0~ PbS04·2PbO + 4Pb(liquid)

PbS04 .2PbO + 2PbS >5Pb(liquid) +'3802

(rapid)

(slow)

However, their proposed mechanism was not substantiat­

ed by experimental kinetic measurements.

69

On the basis of the above information, a kinetic

study was initiated to determine the reaction mechanism(s)

in the system PbO-PbS~

The apparatus and experimental procedure. The

kinetic measurements consisted of passing argon gas at a

constant flow rate over a charge of PbO and PbS, and measur­

ing the .so2 in the ·exit gas as a function or time.

The kinetic apparatus is schematically illustrated

in Figure 15. The argon gas was purified in the srune system

described in the equilibrium studies (see Figures 4 and 5).

The reaction tube and furnace assembly are illustrat­

ed in Figure 16. The reaction tube was constructed from

19 mm. vycor glass tubing, and connections were made on both

ends of the tube by means of a series of ground glass joints;

both spherical and conical joints being used. The exit tube

was connected to the gas analysis apparatus by a shar t piece

of rubber tubing. The vycor glass thermocouple protection

tube was sealed to the reaction tube with High-Pyseal seal­

ing wax. The ·remaining ~ystem was composed entirely of

pyrex and vycor glass.

A spacer, constructed from vycor tubing, was placed

between the boat and the end of' the reaction tube to pro­

vide preheating of the inlet_ gas, and to decrease the

possibility of ~hermal segregation of the gases in the

/ PURIFIED ARSON

~, -··---F-U_R_N-AG_E ____ _

Fl G.-- 15

\ \

\ ~

ARGON+ :S02

\ TO GAS ANALYSIS

SCHEMATIC DIAGRAM ·oF KINETIC APPARATUS

70

----,,,,--.

PURIFIED ARGON

_/

REACTION

FURNACE POWER

FIG.-16

TU6E AND FURNACE ASSEMBLY FOR

KINETIC APPARATUS

THERMOCOUPLE

ARGON + so2

~

--, I

I

TO GAS

ANALYSIS

I I I I I

-·· .... ·-· ·--· . ·-··- . - .. -.. - .. - · .. •»•··---·---· .. . ···-·-· ·-· -·-···-·· - ···-···--···· .. ---.. -·-· · ··-·· ·"-····· .... ... ···-···" ________ ... .---J:

72

reaction zone.

The furnace was a hinged-type tube furnace, contain­

ing 'two separate heating coils. Being hinged, the furnace

could be opened to permit rapid cooling of the tube and

sampl'e. Asbestos paper gaskets, constructed f'rom 1}11

asbestos paper tape, were placed around the reac:tion tube

on each end of the furnace to minimize convection currents

and increase thermal sta,bi1ity between the .furnace and tube.

The regulation of the power supply to the furnace

heating elements is schematically illustrated in Figure 9.

Power to the furnace was controlled by means of a Powerstat,

7-i ampere, variable transform.er. The transformer was.

-connected in series with a wneelco, Model 402-8296, _time­

proportioning controller. The controller was actuated by a

chromel-alumel thermocouple which extended into the reaction

tube to the end of the boat.

A,Leeds and Northrup precision potentiometer; Model

No. 8662, was connected in parallel with the thermocouple­

controller circuit to measure the temperature variance of

the furnace. Temperature control was found to be within

+ ,...oc - G •

The procedure used in making the kinetic measurements

follows. The appropriate PbO-PbS mixture was placed in a

· tai'ed, 10 mm. x 60 mm., Coors porcelain combustion boat and

73

weighed; the difference in weights being the weight of' the ..

mixture. Charge weights were usually 3-4 grams. Af'ter the

boat had been prepared, the reaction tube was evacuated and

filled with puri.fied argon. The furnEce was turned on and

allowed to reach the desired temperature. After the con­

troller had maintained the desired .temperature f'or at least

5 minutes, the conical ground joint cap was removed from

the end of the reaction tube, the boat inserted in the fur­

nace,. and the cap replaced. During the period that the cap

was·removed, argon gas was directed from the inside of the

tube th.rough the open end of the reaction tube, thus

preventing air from entering the reaction tube. After the

boat was in position and the cap replaced, 2 minutes were

allowed .for the boat to reach thermal equilibrium with the

furnace, then the flow of argon gas was started.

Analysis of the exit gas consisted of passing the

argon, so2 mixture through a glass fri t which was immersed

in an aqueous solution of H2o2 and NaOH. The S02 was con­

sumed according to the rollowing reactions:

H2so4 + 2NaOH ~2H2o + Na2po4

The solution was stirred with a magnetic stirrer to provide

good contact of' the gas bubbles with the solution. The gas:

analysis apparatus is illustrated photographically in

74

Figure 10.

The rate of so2 evolution was measured by recording

the.time necessary ror a given quantity of standardized NaOH

to neutralize. The size of: tha NaOH ·additions was adjusted

to give a time period of 1-2 minutes between successive

NaOH additions. Time t.o was determined by star.ting the

stop watch when .05 c.c. excess of NaOH was neutralized.

The time was recorded on a precision, 7 jewel movem.ent,

stop ·watch, graduated in seconds.

The end point when the solution changed from basic

to acid was detected by use of a modif:ied methyl-red

indicator*. The color change at the end point was green

-in alkaline to violet-red in acid. The estimated a~curacy

of detecting the end point was± 3 seconds.

The accuracy of adding NaOH was estimated to be

± .05 c.c., which is~ .lfo cf the reaction completed for a

sample wnere 50 c.c. of NaOH represents 100~ reaction com­

pleted. The concentrations o~ the NaOH solutions were such

tha. t lOOfo completeness of the reaction required between

35-70 c.c. of NaOH.

The NaOH solutions were standardized no earlier than

24 hours after preparation, and were kept in a dark enclosure.

*For instructions f'or preparation of' modified methyl­red indicator see Appendix I.

75

The NaOH solutions were standardized with Fisher's reagent­

grade potassium hydrogen phthalate.

After the kinetic measurements were completed, the

furnace \vas opened and the charge quicld.y cooled (for runs

at 750°c the boat cooled to 6oo 0 c in 1 minuteJ. ·After the

furnace had cooled to room temperat~re, the boat was. removed

and weighed to determine the weight change o:f the charge.

The efficiency of the gas analysis was checke·d by

calculatins total so2 formation co~responding to weight

change against total so2 formation calculated from the

titration data. The so2 value by weight change was repeat­

edly 4-6~ higher than the so2 value by titration. This was

understandable as the loss o:f weight by volatilization of

PbS would give a larger weight loss than weight loss by

so2 formation alone.

To eliminate the effect of variable particle size,

-200, + 3_25 mesh particles of PbO and PbS were used through­

out the entire series of experiments. The same PbO-PbS

mixtures were used in the kinetic experiments as those in

the equilibrium studies. ·

To determine the minimum flow rate of argon necessary

to make the reaction rate independent of flow rate, the

reaction rate was measured at several flow rates when the

cha:-rge temperature was .803°c· (the highest temperature used

76

in its kinetic measurements).

The temperature dependence of the reaction rate

was'observed by me~sUTing the reaction rate at temperatures

between 704°C and 803°c using a constant PbO/PbS ratio.

The effect of the PbO/PbS ratio on the reaction rat.e

was determined by measuring the re~ction rate ·at copstant

temperatures and various PbO/PbS ratios. In addition to

the -rate measurements, X-ray patterns were obtained from

the reacted materials.

Experimental Results. All of the rate measurements

in this investigation have been expressed as (o(.), percent

of theoretical reaction completed, as a !unct~o~ of time.

This convention was adopted in order to make the reaction

rate· independent of ~harge weight, and to express the

reaction rate of charges not containing the stoichiometric

mixture of 2 moles of PbO to 1 mole of PbS. An attempt

was made to derive an empirical relationship between °'and

time, such that a plot of some flmction of °" versus time

would yield a straight line. However, no rela.tionship

was found that could be used £or any two rate curves which

were taken under different experimental conditions.

The rate curves were first plotted on t x 1 meter,

10 squares to the cm., graph paper in order to detect any

trends or peculiarities that would be unnoticed on conven-

77

tional size graph paper.

The effect or flow rate on the reaction velocity is

illustrated in Figure -17. These data ·are tabulated in

Appendix V. The reaction velocity appeared to increase

with 'increasing flow rate ·until a flow rate of 170 c.c./min.

was reached. Increasing the flow rate beyond 179 c.c./min.

appeared to decrease the reaction rate. The temperature was

constant at 803°C ~nd a charge ratio of 2Pb0/1PbS was used.

The results ·of the temperature dependence of the

reaction rate are tabulated in Appendix VI and illustrated

graphically in Figure 18. The rate was observed to increase

proportionately with increasing temperature, with the excep-o O ·

tion of the increase between the 733 C and 753 C curves. . 0

This rate increase which represents a 20 C increase in

temperature was larger than other increases representing

temperature changes of w 0 c. The flow rate was constant

at 260 c.c./min., and a charge ratio of 2Pb0 to lPbS was

used.

The results of measuring the reaction rate at various

FbO/PbS ratios are tabulated in Appendix VII and illustrated

graphically in Figure 19. The temperature was held constant

at 722°c, and a flow rate o:f 260 c.c./min. was used. No

appreciable reaction occurred .in charges lOPbO/lPbS and

8Pb0/1PbS. The reaction rate was essentially constant over

,, 90

,---i ! i l i I·

~ I

so L . .

I i i O 70 .__ I W I t-, (.)

'1 <( 60 ...__ - ~

' 50 r· ~

' -40 L

~ 30

20

10

10 20

0 - 82 · c.c./MIN. a -· 130 c.c./ MIN. l> - 260 c.c./ -MIN.

a ---- ·-170 c.c.1 M_IN.

30 40

t (MIN)

FIG:- 17

EFFECT OF FLOW RATE . . ON ; 'REACTION VELOCITY

78

I. ' I .

I I

i i

I

I

I

i I

I I !

l I

r----·-- ·-··-------------- . 1 . ~ -- 803° c

100 .. _.

·90~ I .

.. i

SOL ! I

--,-- --- 783° c El ---- 753° c A - 733~C

0 -- 704°C

. - . I . o·. 70·~· ·· w .. . ...... . . · .

~-6oL w . 1-cr . I o· 50l-~ . I

~ 40r 30 r-

1

20

10

10 20 30 40

-t ( MTN )

FIG.- 18

TEMPERATURE DEPENDENCE OF THE

REACTIO.N VELOCITY

I I I I

-I

I ! i

~-;~;~----! IO : I· NO, REACTION I

I 00 r- 8 : 1 NO REACTION l

l

L

eoL I

~ . {

_fa 1·0 · ~ ...... 0 ·~. 6oL ti: ! . '

~ · 50.·~ i i

.. 40 h-~- !

·I 30 L

10

6 : I A

4 .= , - 0

~ : l -- El

I: I. ~ -t

I ~ 2 --.- t->

1 ·:· 4·. -- X·

10 20

t · (MIN)

FIG.- 19

Pb 0/

I~ 6

I: 8

I :'10

30

80

PbS

~

- e (>

I i

L__ ---_J - -- __ J_ ---- -_ _J 40

DEPE-NDENCE OF REACTION VELOCITY ON

Pb O I PbS RATIO

81

the composition range 6Pb0/1PbS to 2Pb0/1PbS, but began

increasing at lPbO/l~bS and continued to do so until the

composition was 1Pb0/8PbS. The. rate a:t iPb0/8PbS. -ana. lPbO/lOPbS was essentially. the same. · The results o:r the

X-ray analysis of the reacted materials are summarized in

Table X • . Tetra-basic lead sul:rate and lee.d were. present

in all or the samples. Lead oxide was pre~ent in charges

containing PbO/PbS ratios greater than 8:1, and lead

sulfide was present in charges containing PbO/PbS ratios

less than 8 :·l. In no event were PbO and· PbS present in the

same sample.

Discu.ssion end conclusions. The results or measuring

the reaction rate a. t various flow rates indicate tha·t a flow

rate of 170 c.c~/min • . was suf'ficient to remove the so2 as

quickly as it was formed, and that rlow retes greater than

260 c.c./min. caused appreciable cooling of the charge and

a subsequent decrease in the reaction rate. Thus, a

maximum flow rate o~ 260 c.c./min. was used jn the remaining

experiments.

The explanation of the large increase in the reaction

rate between 733°c and 753°C appears to lie in the results

obtained from the equilibrium studies. Above 733°C the

equilibrium phases ror a 2P~0/1PbS mixture are Pb, PbS, and

Pb~o4.2PbO, _wh~le be1ow 733°C the equilibrium phases are

TABLE X

X-RAY IDENTIFICATION (F PEA.SES IN PARTIALLY REACTED PbO .. /.PbS MIXTURES

Temp. .... 722°c Flow Rate 260 c. c./min.

PbO/PbS Ratio 1oConversion Phases

10:l o.o Pb, PbS04 .4PbO, PbO

8:1 o •. o Pb, PbS04 .4PbO, PbO

6:·l 20.0 Pb,. PbS04 .4PbO~ PbS

4:1 22.0 Pb, PbS04 .4PbO, PbS

2:1 ·20.0 Pb, PbS04•4PbO, PbS

1::1 32.0 Pb, PbS04·4PbO, PbS

1:2 21.0 Pb, PbS04 .4PbO, PbS

1:4 21.5 Pb, PbS04·4PbO, PbS

1:6 21.5 Pb, PbS04•4PbO, PbS

1:8 9.;3 Pb, PbS04 •4PbO, PbS

1:10 12.0 Pb, PbSO 4 • 4Pb0., PbS

82

Pb, PbS, and Pbsc4.4Pb0. Consequently, th~ reaction

mechanism at temperatures above 733°C might be

6Pb0-+ ::bs--t 'bS04 .2PbO + 4Pb

PbS04 .2PbO + 2PbS-__.,.5Pb + 3$02

and at temperatures lower· than 733°C

8Pb0 + PbS-----+ PbSO 4 • 4Pb0 + · 4Pb

PbS04.4PbO + 3PbS 8Pb + 4S02

83

The ·rac·t that the charge was not in a state of chemica.l

.equilibrium during· the kinetic measurements does not pre­

clude the possibility or having only the equilibrium phases

present. As a matter of' fact, the only phases that were

present in the materials obtained from reacting various

PbO/PbS mixtures, see Table X, were the equilibrium phases.

If the equilibrium phases were present below 733°c, it seems .

logical that the equilibrium phases were present above 733°c.

Thus, it was concluded that the increase in rate between

733°c and 75o 0 c was attributed to the change in the-reaction

mechanism, because the equilibrium phases are different

above 733°c. However, the question arises as to why the

reaction

PbSO 4 • 2Pb0 + 2PbS --> 5Pb + 3802

proceeds at a greater rate than the reaction

PbSo4

.4PbO + 3PbS ----..8Pb + 4802 •

There does not seem to·be an immediate solution from the

84

data that .were obtained in this investigation.

The sudden increase in reaction rate .in going from

8Pb0/1PbS to 6PbO/lPbS results, no doubt, from the change

in the reaction mechanism as indicated by the X-ray analy­

. sis of the reacted materials. In charges containing more

PbO than 6Pb0/lPbS the proposed mechanism is a·s .follows!

8Pb0 + PbS~ PbS04 ·4PbO + 4Pb (fast)

PbS04·4PbO + Pb > 6Pb0 + S02 · (very slow)

and in charges containing more PbS that 8Pb0/1PbS the pro­

posed mechanism is as follows:

8Pb0 + PbS > PbS04•4PbO + 4Pb

PbS04·4PbO + 3PbS > 8Pb + 4S02 •

(fast)

(slow)

Again the question arises as to why the difference in the

relative ·rates of the two mechanisms.

The explanation of the constant rate at ratios

between 6Pb0/1PbS and 2Pb0/1PbS, and the increased rate

at ratio.s between 2Pb0/1PbS and 1Pb0/8PbS may be :round by

calculating the moles of PbS04•4PbO and PbS per mole of Pb

which are present at various PbO/PbS ratios after the PbO

and PbS have reacted to form PbS04·4PbO and Pb. These

calculations are illustrated graphically in Fig\lre 20. At

all PbO/PbS ratios, the number of moles of PbS04.4PbO per

mole o~ Pb is the same. However, the number of mo1es of

PbS per mo1e of Pb increases as the PbO/PbS ratio decreases.

-·- -- ·· -·· ----------·----3 ~----

. a __ _; \r".',:

. 7 .. - .:.,~}

6 . - r~~ ~'+'

5 '. . \

4. ~ 0 - --- MOLES Pb S04

· 4Pb0 I MOLE Pb ,,

MOLES PbS/MOLE Pb

2 ~-I I

I \

? '\ I

I

I I \ (/) I i._ _o ·9~­a.. .a·~ ' .7~ 0 .6 l-~ I

a.. .5 -­I

,4 ~---1 I

.3 ~-I I I

.2L

I

i

} i } .

. !

! . l (:.") L. -~.:L--

0

_ l __ ___ __ l ~ _ _L ___ J_.· __ J __ . _L __ I r 2 . 3 4 s: s 1 8

l 9 10

M9~ES . OF Pb SCk ·· 4Pb0 O.R PbS I MOLE Pb

FIG.-20''

~ i i I I I I

!

~ --------- t. I· I I - .. T-~~

II · 12 13 14 10

MOLES OF PbSO- 4 PbO AND PbS I MOLE OF Pb . AT VARIOUS PbO I PbS RATIOS ~- -·--·· - · --~----· .. 3---------------------------------,-.---------

Between 6Pb0/1PbS and 2Pb0/1PbS the ratio of PbS to

PbS04·4PbO slowly increases. The mean rree _path between . . .

the. PbSo4.4PbO and PbS particles: was decreased, but the

86

rate change was not dete_cted experimentally. However, the

PbS/PbS04 ·4PbO ratio increased almost exponentially at

ratios less than 2Pb0/1PbS, and the rate was noticeably

increased. The same rate at 1Pb0/8PbS and lPbO/lOPbS

indicated that dii'fusion of the Pbso4 .4Pb0 and PbS particles

through the molten Pb was no longer rate controlling, but

rather the chemic_al reaction between PbSo4.4PbO and PbS.

The conclusions as to the kinetic behavior of the

system PbO-PbS can be summarized as follows:

A. At temperatures below 733°C three .possibilities exist.

l. The reaction mechanism for charges containing

PbO/PbS ratios greater than 8:1

8Pb0 + PbS~ PbS04·4PbO + 4Pb

PbSO 4 o 4Pb0 + Pb----> 6Pb0 + 802

(fast)

(very stow)

2. The reaction mechanism for charges containing

PbO/PbS ratios less than 8: but greater than 1:8.

8Pb0 + PbS ~ PbS04 • 4Pb0 + 4Pb (fast)

PbS04•4FbO + 3PbS >8Pb + ,4802 (slow, where

the rate is dependent upon the rate of diffusion of

PbS and PbS04·4PbO in ·the molten Pb.)

3. The reaction· mechanism :for charges containing

87

PbO/PbS ratios less·than 1:8.

8Pb0 + PbS -~) PbSO 4• 4Pb0 + 4Fb (fast)

PbSo4 .4FbO + 3PbS ----,.8Pb + 4S02 (slow, where the

ra.te is dependent upon .the rate of the ·chemical

reaction between Pbso4 .4Pb0 and PbS.)

B. ?it temperatures above. 733°C only one mechanism was

proposed.

The reaction mechanism for 2Pb0/1PbS is as follows:

6Pb0 + PbS ~ PbSO 4 • 2Pb0 + 4Pb

PbS04•2PbO + 2PbS--.+5Pb + 3802

(:rast)

(slow)

The results of this investigation are in ae;reement

with the findings of Kohlmeyer· and Menzer wh~re the "basic

sulfates" formed by PbO and PbS have been more specifically

identified es FbS04.4PbO and Pbso4.2Pb0.

The proposed mechanism of Kellogg has been substan~

tiated, and expanded to include the reactions between

PbS04.4PbO and PbS, and PbS04.4PbO and Pb.

Although the results of this investigation~do not

contradict the proposed mechanism of Merrick, the absence

of .a step involving the formation and subsequent reaction

of basic lead sulfates -detracts from the reality of his

mechanism. Perhaps the equation 2PbS04.xPbO + · (2 + ~)PbS

--. -> (4 + 3x)Pb + (4 + x)so2 should replace his equation

(xPbO-Pbs):f= activated complex • (x+ l)Pb + S02 (adsorbed).

CH.APTER VIII

SUMMARY AND CONCLUSIONS

The thermodynamic behavior of the system PbO-PbS was

studied by measuring the Pso2 in argon-so2 mixtures equi11-

bra.ted with various PbO.-PbS mixtures between 7oo0 -76ooc,·

and analyzing the condensed phases by means ·o~ the X-ray.

The reaction mechanism(s) involved in the approach

to equilibrium were studied by determining. the er~ect of

temperature and PbO/PbS ratio on the rate of' so2 evolution.

The PbO-PbS mixtures were prepared in the laboratory

by mixing purified PbS and PbO in various PbO/PbS mo1e ratios

· between 20 :1 and l: 20.

The method of so2 analysis consisted of passing the

argon-so2 mixtures through a glass frit immersed in a water

solution of H2o2 arid NaOH, and measuring the· NaOH co~sumed

by the so2 • The analysis was found to be accurate and

reproducible.

At constant temperature the variation of Pso2 with

composition was found to consist or several horizontal lines

connected by diagonal lines. Below 733°c the isotherms con­

sisted of' two horizontals connected by one diagonal_line.

Above 733°c the isotherms consisted of three hori20nta.ls

connected by two diagonal lines.

89

Isotherms were constructed a.t 7oo0 c, 7?o0 c, 74o0 c and 760~C. The values of P802 were not measured below 7oooc

because the P802 values were too small to ~e accurately

·measured by the ~ethod of gas_ analysis employed in this

investigation. Measurements above ·760°C were avoided

because o:f the observed.contamination of the ·reacting

material by the porcelain boats at the higher ~emperatures.

X-ray analysis of the condensed phases showed that

the horizontals represented areas of three-phase ·stability,

and the diagonal· lines areas of two-phase s 1a bili ty. At

least one of the condensed phases was -a basic sulfate or

lead. Liquid lead also was one of the condensed phases

in each phase region. ·

The diagonal lines indicated· solubility of sulfur

and oxygen in liquid lead, and solid-solubility or sulfur,

oxygen, and.lead in the basic sulfates. Because of the lack

of knowledge of the solubility curves for liquid lead and

basic sulfates of lead, the exact composition of the lead

and basic sul..fates could not be established.

A phase diagram for the system PbO-PbS was proposed.

The proposed diagram was compared to the diagram constructed

from the Pb-0-S composition diagrams of Kellogg and Basu.

A region of two-phase stability is indicated as a line on

the diagram rrom Kellogg and Basu, and as an area on the

90

diagram from this investigation. The composition of the

liquid lead was not indicated, and the symbols Pbso4 .4Pb0

and Pbso4.2PbO were restricted to mean that one of the

condensed phases ha'd a particular basic sulfate structure,

but the composition was not necessarily that indicated by

the stoichiometric formula.

Below 733°C, the phas·e regions in going from PbO to

PbS are (1) PbO, Pb1 , PbS04.4PbO, (2) Pb1 , Pbso4.4Pb0, and

(3) PbS, Pb1 , PbS04·4PbO. Above 733°C, the phase regions

in going from PbO to PbS are (1) PbO, Pb1 , PbS04 .4PbO, (2)

Pb1

, PbS04•4PbO, (3) Pb1 , PbS04•4PbO, PbS04•2PbO, (4) Pb1,

PbS04•2PbO, and (5) PbS, Pb1, PbS04•2PbO.

The thermodynamic calculations of the experimental

data consisted of the derivation of a linear equation for

the ..6.F0 r of · PbS04·4PbO in the temperature range 7oo 0 c -

760°C. The thermodynamic calculations of the experimental

data of Kellcgg and Basu likewise consisted of the deriva­

tion of a linear equation for the .6F0r of PbS04·4PbO in •

the temperature range 7oo0 c - 760°c. The linear free energy

equations and the .6 H0r and ~s0 :r of PbS04 ·4PbO calculated

in accordance with the· Gibbs-Helmholtz equation are summari­

zed in Table XI.

Because of the limited experimental data on the

.6Fof of PbS04.2PbO, only two values were determined

TABLE XI

LINEAR FREE ENERGY EQUATIONS FOR

.6. F 0 f OF PbS04 • 4Pb0

A. This Investigation:.

.6.F0 r PbS04 .4PbO ~ -444,207 + 188.45T; ± .65 Kcal c 7ooo-7.6o?c)

where ~H0 r Pbso4 .4Pb0 = -444,207 cal.

~s0r PbS04·4PbO :! -l88.4f e ... u.

B. Kellogg and Basu:

,6.F0 r PbS04·2PbO ~ -450,022 + l94.91T;± .• 58 Kcal (7uoo-76ooc)

where b.H0r Pbso4 .4Pb0: -450,022 cal.

~ s0 '£ PbS04· 4Pb0 - -194. 91 e. u.

91

92 . 0

experimentally, a free energy equation for f:l.F f of

PhS04-2PbO was not derived.

The small deviation, ±.65 Kcal, of ~he experimental

data from the Cl. F 0 r' of Pbso4 • 4Pb0 values calculated from the

linear free energy equation indicates that the ~H0 r of

Pbso4 .4Pb0 is essentially constant and that ~CP is approx­

imately zero in the temperature range studied.·

The close agreement of ~F0 r of Pbso4 .4Pb0 values

calculated at the same temperature, but from different

reactions, indicates that although the activity of each

condensed phase may not be unity, the activity of each

condensed phase is approximately constant within the range

of experimental detection.

The accuracy and reproducibility of' the experimental

technique can be evaluated as follows. The average devia­

tion of i.71 Kcal between the ~F0 r of PbS04 .4PbO values

calculated from the linear free energy equation derived from

the experimental data and the linear free energy equation

derived from the data of another technique is well within

the accepte~ experimental accuracy oft 1 Kcal for most

free energy data. The excellent reproducibility of the

experimental technique is evidenced by the large number or points that were taken for the 8-48 mole foS horimntal on

the 720oc isotherm, end the . small variance of any point from

93

the horizontal line.

On tha basis of the results obtained in this

investigation, serious objection is raised as to the valid­

ity of the Pb-0-~ composition diagrams · proposed by Kellogg

and Basu. The diagrams as presented, see Figures 1 and 2,

do 'not violate any principles of construction. However,

these diagrams indicate that pure lead is · one .of -the stable

phases, while it is an established fact ·that both sulfur .

and oxygen are soluble in liquid lead. The importance of

this solubility was established by the fact that the two­

phase regions (Pb1 and basic lead sulfate) appeared as

regions of liquid and solid-solubility on the Pso2-compos1-

tion isotherms. Although the degree of solid-solubility in

basic lead sulfate is probably small, the possibi1:-ity of'

solid-solubility or the basic sulfates together with liquid

solubility of lead must be taken into consideration in

construction of the Pb-0-S composition diagrams. In this

respec~, the Pb-0-S composition diagrams are likely to be

more complex th.an those presented by Kel1cg g and Basu.

Since the solubility curves for· liquid lead and condensed

basic sulfates are not · available, the only correction to

the diagrams of Kellogg and Basu is the indication that the

lines representing two-phase regions are in reality areas of

two-phase stability. The corrections ·to the composition

94

diagram Pb-0-S for temperatures above 733°C are illustrat­

ed in Figure 21.

It is recommended that in order to complete the

P0

bO-PbS phase diagram, and possibly· to obtain a better

understanding of the Pb-0-S ternary diagram, ·cooling curves

be obtained for various PbO-PbS mixtures as well as chemical

8!1Etlysis of the liquid lead phase. The degre~ of solid­

solubility in basic lead sulf'ate could possibly be determin­

ed by accurately measuring the lattice parameters of the

basic suli'ate with a more refined X-ray technique, and

correlating the changes in lattice parameters with composi­

tion of the basic lead sulfate phases.

The data of the kinetic measurements could not be

treated in a quantitative manner because of the inapplica­

bility· of classical reaction kinetics to systems involving

solids, liquids, and gases, where the activity of each solid

phase was unity. The results were treated in a qualitative

manner to illustrate the effect of temperature and PbO/PbS ,

ratio on the rate of so2 evolution, for the purpose of

gaining an insight into the reaction mechanisms in the

system PbO-PbS.

The results of the kinetic study indicated ~hat the

reaction mechanism between PbO and PbS is (1) conversion of

all of the PbO or PbS (whichever is the minor constituent)

'l­!

•.;-

.~

> _. ·

PbSO • 4

-/ ,lio: .. . PhO

-~.lG .. ~ 2l ·

CORREOTfD COMPOSITnt· 'DfAGRAM FOR--:~E, .. Pb- s-.o.: SYSTEM .A80VE 733•c.

95

96

to either PbS04 ·4PbO or PbS04·2FbO, and (2) reaction

between the basic sulfate and either Pb or PbS to produce

so2 • In mixtures containing more PbO than 8Pb0/1PbS the

so2 producing reaction is

PbS04 ·4PbO + Pb 6Pb0 + S02 •

In -mixtures containing more PbS than 8Fb0/1PbS the reaction

is

2(PbS04•XPbO) + (2+ x)PbS ~(4+ 3x)Pb + (4+x)S02,

where xis 2 at higher temperatures (greater than 733°C) '

and 4 at lower temperatures (less than 733°C).

Perhaps the conclusion o.f greatest signi.ficance is

that the equilibrium 2Pb0 + PbS~ 3Pb + S02 , which is

thought to be the basis o.f ore-hearth roasting, is unstable

at all PbO/PbS ratios in the temperature range 7oo0c to

760°c. The results of the equilibrium and kinetic measure­

ments show that the reaction sequence for a mixture of 2

moles or PbO and 1 mole of PbS is as follows:

A. Below 733°c

8Pb0 + PbS--+ 4Pb + PbS04·4PbO

PbSO 4 • 4Pb0 + 3~bS =:::::; 8Pb + 4502

B. Above 733°c

6Pb0 + PbS ----+ 4Pb + PbSO 4 • 2Pb0

(Fast, non-equili­brium)

(Slow, stable equilibrium)

(Fast, non-equili­brium)

97

PbSO 4 • 2Pb0 t 2PbS =:::::; 5Pb + 3S02 (Slow, stable equilibrium)

Using the thermodynamic data available in the 11ter-

·ature and the results of this investigation, calculations

of a quantitative nature can be made to determine the effect

·of _temperature, composition, and pressure on .processes .

involving lead oxide and lead sulfide. This, it is hoped,

will lead to eventual improvement of existing processes, or

the possible development of a new process.

In addition, the results of the kinetic measurements

can be used to predict the qualitative effect of temperature

and composition·on the rate of processes involving lead

oxide and lead sulfide.

BIBLIOGRAPHY

1. Schenck, R. end W. Rassback "Uber die chemischen Gleichgewichte bei der Reaktion Zwischen Belisulfid und seinen Oxydationsprod.ukten". (An Account of the Chemical Equilibria in the case of the Reactions between Lead Sulfide and its Oxidation Products.) ~· d. D. Chem. Ges., 41, ·p. ~917, (1908).

2. Reinder~.w. "Physikalisch-Chemische Studien Uber die Rostprozesse". (Physical Chemical Studies Concerning Roasting Processes.) z. anorg. Chem., ~3,.p. 213, (1915). --

· 3. Schenck, R. and A. Albers •Uber die chemischen Gleichgewichte Zwischen Bleisulfid und seinen Rostprodukten 11 • (An account of the Chemical Equilibric between Lead Sulfide and its Roast Products.) z. anorg. Chem., 105, p. 145, (1919).

4. Schenck, R. · and W. Borkenstein •Uber die Chemischen Gleichgewichte Zwischen". (An account of the Chemical Equilibria between Lead Sulfide and its Roast Products.) ~. anorg. Chem.·, 142, p. 143, (1925).

5. Kellogg, H.H. and S.K. Ba.su "Thermodynamic Properties of the System Pb-S-0 to 1100°K." Trans. AlME,' 218, p. 70-81, (1960).

6. Lander, J.J'. "The Basic Sul:f'ates of Lead." Trans. Electro-chem. Soc., 95, p. 174, (1949)

7. Darken, L.S. and R.W~ Gurry · "The System Iron-Oxygen.", . J. Am~ Chem. Soc., 67, p. 1398, (1945) ~

8. Gillham, E.W.F. in Flue Gas. 11

.(1946 ).

"The Determination of Oxides of Sullur J. Soc. Chem. Industry, 65, p. 370,

9. Hansen, M. Constitution of .Binary Alloys. 2nd ed., McGraw-Hill, New York, p. 1065, p. 1100, (1958).

10. Kubaschewski, o. and E. Evans Metallurgical Thermo­chemistry. 3rd ed., Pergamon Press, New York (1958).

11. Stubbles, J.R. and C.E.· Birchenall

99

of the Lead-Lead Sulfide Equilibrium between 585° and 920°c.A Trans. AIME., 215, p. 535-538, (1959).

12. Kohlmeyer, E.J. and W. Monzer "Uber die Reaktionen von Bleisul.fid mit Bleioxyd bzw. Sulfat." (.An Account of the Reactions of Lead Sulfide with · Lea_d Oxide, or Sulfate.) z. anorg. Chern., 252, p. 74-85, (1943).

13. Merrick, s. ttA Kinetic Study of the Roast-Reaction of Lead Sulfide." M •. t. Sc. Thesis, University of British Columbia, p. 65,- (1957).

14. Mellor, J.W. Higher Mathematics. 4th Ed~, Dover Publi­cations, Inc., p. 327, (1955).

APP~1)ICES

APPENDIX I

PREFARATION' OF MODIFIED METHYL-RED INDICATOR

Modified methyl-red indicator was prepared by the

formula given by Gi1lham8• The color was violet-red in

acid solutions, colorless in neutral solutions, and green

in alkaline solutions. Procedure for preparation of

modified methyl-red indicator follows.

1. Dissolve 0.40 grams of methyl-red 1n 15.2 ml. of

1/10 N. Na.OH,

2. dissolve 0.20 grams of methylene blue chloride

1n distilled water, and

3. mix the two solutions and dilute to one liter.

APPENDIX II .

SAMPLE CALCULATIONS OF -LOG Pso2

FROM EXPER!MENTAL DATA :

Run #3 Furnace Temperature_ : 740°c

Sample: 6Pb0/1PbS: 7.14 Mole fo S

Volume of gas bottle - .2745 Liters

Pressure= 745.7/760: .98118 atm.

Gas Temp.: 27. s0 c + 273 = 300. s°K

nT = ~: (.98118)(.2745)/(.08205)(300.5)

n.ir = 1.09237 x 10-2 Moles

c.c. NaOH Added

c.c. c.c. c.c.

- 20.00 Na.OH - 9.30 H2S04 .

c.c. NaOH consumed by so2 10.70

n.502 .... 10.70 x 2.1267 x 10-5 Moles so2·

- 2.27557 x 10-4 Moles

nso2 x PT nT

c.c. NaOH

: (2.27557 x 10-4/1.09237 x 10-2 ) x .98118 -2

: 2.0439 x 10

Log P802 : -2 +_.31046: -1.68954

:. - Log Pso2 = 1.689

APPENDIX III .

CALCULATION OF THE LINEAR FREE ENERGY EQUATIONS

USING THE METHOD OF LEAST SQUARES

Method of Least Squares (l4) for y: mx + b

m : ~n~ :l:yx - ~x~y (n) ~x2 - (~x)2

~

b :~r 2:Y -4x ~~ (n) .~x2 - (:l:x)

where y : /;),. F 0 t: PbSO 4 • 4Pb0

x: T° K

A. Data .from this investigation •.

# x x2 y XY

1 973 94.6729.104 -260,890 -253_, 845 , 970

2 973 94.6729.104 -260,333 -253,304,009

3 993 , 4

98. 6049.10· -257,779 -255,974,547

4 993 98. 6049·104 -256,510 -254,714,430

5 1013 102. 6169.104 -254,217 -257,521,821 -

6 1013 102.6169.104 -253,468 -256, 763,084

7 1033 106.7089.104 -249,697 -257,937,001

8 1033 ,106. 7089, 104 -248, 600 -256,803,800

~X:8024.0, :;Ex2 : 805.2072.104 , ~y : -2,041,494 ~xy :

~2,046,864,662

( ~x) 2 = 64.384,576 x 104 ,

:;EX • ~ y : -16, 380, 947, 856.0

B.

II

1

2

3

4

c:: v

APPENDIX. III (continued)_

('")

~X,::, • ~y: -16,438,256,675,568

~x • ~x.y :. -16,424,042,047 ,888

m : (8) [-2,046,864,662] .. G-16,380,947,856] (8) [ 8,052,072] - [6.4,3,'.34,576]

m = (-16,374,917,296) + (16,380,947,856) 64,416,576 - 64,384,576

m = 6,030, 560 .32,000

m = 188.455

b = -16,438,256,675,568 ~ 16,424,042,047,888 (8)(8,052,072) - 64,384,576

b = -14i214,627,680 c = 64,416,576 - 64,384,576

b = -14,214.627,680 32,000

·b :: -444,207

• ~ Fo! Pbso4 .4Pb0 : -444,207 + l88.45T • •

Data from Kellogg and Basu.

x x2 y XY

973 946,729 -260,012 -252,991,676

973 ' 946,729 -260,557 -253,521,961

993 986,049 -256,209 -254,415,537

993 986,049 -256,836 -255,038,148

1013 1,026,169 -252,417 --255,698,421

103

#

6

7

8

~x =

APPENDIX' III (continued)

x x2 y

1013 1,026,169 -25G,I~2

1033 1,067 ,089 -247,636

1033 1,067,089 -249,444

8,024 ~x2 : <3,052,072 ~y : -2,036,243

( ~x)2 : 64,384,576

~ x • ~ y : - 16 , 338 , 813 , 832

~x2 • ~Y = - 16, 395, 975, 245, 496

~ • ~xy ~ - 16,381,574,522,376

104

XY

-256,422,716

-255,807,988

-257,675,652

~xy = -2,041,572,099

m • - -16 338 813 832 64,384,576

m = -16,332,576,792 + 16 1 338 I 813 a 832, 64,416,576 ... 64,384,576

m - 6,237.040 - 32,000

m - 194.908 -b - (-16,395,975,245,496) - (-16,381,574,522,376)

32,000 -

b: -14,400,723.120 32,000

b : ' -450,022

• •• ~ Fo PbS04• 4Pb0 : -450 ,022 + 194, 908T

AP·PENDIX IV

CALCULATION OF ERROR LlMITS · OF THE LINEAR FREE ENERGY EQUATIONS

Error limit equals one . standard deviation (1 a- ) •

The f onnula for calculating tr is as follows:. 2· l

(J : ~ [_ ~ (d) . )2 \.:n-1.

· where d - the deviation of a single measurement

· n = number of samples

A.'. Error Limit for Linear Free Energy F,quation From This

Investigation.

I::,. F0 f PbSO 4 • 4Pb0 (Exp.) _6F0 f PbS04· 4Pb0 d d2

(Equation) ·

. -260 ,"890 -260 ,840 50 2,500 ..

-260,333 -260,840 507 · 257 ,049

-257,779 -257,1'71 608 369,664

-256,510 -257,171 661 436,921

-254,217 -253,302 915 837,225

. -259,468 -253,302 166 27,556

-249,697 -249,633 64 4,096

-248, 600 -249,633 1033 1,067,089

~d2 - 3,002,100 -

106

APPENDIX ·IV (continued)

u: "' ~ 1 00~ 1 100"3':; €e,an.:v! c; : ;: • 655 -Kcal

B. Error Limit for Linear Free Energy Equation .from

· Kellogg and Basu.

!::,. F 0 r PbSO 4 • 4Pb0 (Exp) l:l. Fo f PbS04-4PbO d (Equation)

-260,012 -260,377 365

-260,557 -260,377 180

-256,209 ~256,478 269

-256,836 -256,478 358

-252,417 -252,5'80 163

-252,132 -252,580 ·552

-247, 636 -248,682 1046

-249,444 -248,682 762

~d2 = . u= '+

(j: ;

@.·37~,18!) t = + ~8,883.9t .582 Kcal

d2

133,225

32,400

72,361

128, 164

26,569

304,704

l _,094,116

580,644

2,372,183

Run#

1

APPEI'-J'"DIX V .

KINETIC DATA:. REACTION VELOCITY VERSUS FLOW RATE

Temperature: 803°c

PbO/PbS: 2 :1

Flow Rate -(c. c./min.) Time - (Min)

82 0

1.0.

2.23

3.32

4 •. 45

5.63

6.90

8.25

9.75

11.38

13.08

14.73

16.43

18.20

20.25

21.03

(% Reacted)

0

1.83

7.33

12.82

18.32

23.82

29.31

34.81

40.31

45.80

51.30

56.80

62.29

67.79

73.29

75.12

108

APPENDIX V (continued)

Flow Rate~ Run# ( c. c ./min.) Time - (Min) · (~ Reacted)

l 82 21.88 76.95

22.75 78.78

23.73 80.62

25.00 82;.45

31.65 84.28

34.2S 84.46

36.00 84.65

2 130 1.00 1.49

2.12 5.97

3.05 10.45

4.88 19.41

5.87. 23.89 . ~

6.90 28.37

8.00 32.84

9.22 37.32

10.47 41.80

11.83 46.28

13.30 50.76

14.78 55.24

109

APPENDrx·v (continued)

Flow Re.te -Time· -Run # ( c. c ./min.) (Min) Ci Reacted)

2 130 16.28 59.78

17.80 64.20

19.27 68.68

21.22 74.65

22.33 77.64

23.52 80.62

24,.92 83.61

27.43 86.59

33.50 87.34

170 l.~5 1.67

2.32 6.67

:1.07 11.67 . -

3.87 16.67

4.67 21.67

6.55 26.67

6.47 31.67

7.48 36.68

8.58 41.68

9.77 46.69

110

APPENDIX ·v (continued)

Flow Rate -Run# ( c .• c .• /min.) Time · - (Min) (" Reacted)

3 170 11.03 51.69

12.30 56.69

13.55 61.69

14.80 66.70

16.01 71.70

17.62 76.70

20.30 83.37

4 260 .85 1.52

1.·ao 6~10

2.57 10.68

3.32 15.25

4.10 19.83

4.95 24~41

5.83 28.98

6.77 33.56

7.80 38.13

8.90 . 42. 71

10.07 47.28

11.35 51.86

111

APPENDIX V (continued)

Flow Rate -Run # (c.c~/min.) Time ·- (Min) (fo Reacted)

4 260 12.70 56.44

14.08 61.01

15.47 65.59

16.83 70.16

18.67 76.27

19.18 77.79

19.67 79.32

20.78 82.37

22.48 . 85.42

·24.07 86.'18

27.18 86.64

30.00 86.94

36.00 87.32 .

50.00 87.74

Run#

5

APPENDIX VI

KINETIC DATA:. TEMPERATCRE DEPENDE~CE OF REACTION VELOCITY

Flow Rate : · 260 c. c./min

PbO/PbS: 2:l

Temp.(°C) Time - (Min)

704° 5~38

7.75

10.05

12.2a-

14.38

16.42

18.47

ro.68

22.80

25.02

27 •. 13

29.65

31.97

34.28

36.58

39.00

(~ Reacted)

1.30

2.60

3.91

5.21

6.51

7·.a1

9.11

10.42

11.72

13.02

14.32

15.62

16.93

18.23

19.53

20.83

113

APPENDIX ·vI (continued)

Run# Temp.( 0 q) Time - .(Min') (~Reacted)

5 704° 41~45 22.13

43.93 23.44

46.50 24.74

49.08 26.04

51.65 27.34

54.28 28.64

6 733° 2.07 1.53

3.43 3.06

4.92 4.59

6.53 6~12

8.33 7.65

10.17 9.18

12.13 lQ.71

·14.08 12.24

16.17 13.77

l.8.33 15.30

20.48 16.83

22.63 18.36

24.83 19.89

27.05 21.42

114

APPENDIX VI (continued)

Run# Temp. (OC) Time - (Min) ('% Reacted)

6 733° 29.23 22.95

31.47 24.48

33.73 26-.0l

35.97 27.54

38 •. 23 29.07

40.43 30.60

42.72 32.13

44.97 33.66

47.18 35.19

49~45 36.72

51.70 38.25

53.87 39.78.

7 753° 1.73 1.42 -

3.50 4.26

s.12 7.09

6.58 9.93

8.03 12.76

9.48 15.60

10.93 18.44

12.40 21.27

115

APPENDIX'VI (continued)

Run# Temp (°C) Tim~ - (Min) '" Reacted)

7 753° 13.85 2·4.11

15 •. 33 26.94

1.6.78 29.78

18.33 32.62

19.88 35.46

21..50 38.29

23.12 41.13

24.78 43.97

· 26.52 46.80

28~30 49.64

30.12 52.48

32.02 55.32

33.98 58.15 -

36.07 60.99

38.23 63.83

40.48 66.66

44.07 70.91

46.73 73.75

49.60 76.59

53.00 79.42

116

APPENDIX VI (continued)

·Run# Temp (°C~ Time - (Min) (9' Reacted)

8 783° 1.57 1.34

2.57 4.03

3.40 6.72

4.17 9.41

4.93 12·.07

5.72 14.78

6.50 · 17.47

7.33 20.15

8.13 22.84

9.·00 25.53

9.87 28.21

10.72 30.90

11.63 33.59 ·

12.57 36-". 28

13.52 38.96

14.52 41.65

15.55 44.34

16.62 4_7.02

17.73 49.71

18.87 52.40

117

APPENDIX VI (continued)

Run# Temp (OC) Time - (Min) (~ Reacted)

8 783° 20.:08 55.08

21.33 57.77

22.67 60.4.6

24.12 63.14

26.48 67.18

28.32 69.86

29.25 - 71.21

30.25 72.55

31.23 73.89

32.·23 75.24

33.22 76.58

34.25 77.93_

35.28 79.27 ·

36.32 80~62

37.37 81.96

38.50 83.30

39.97 84.65

41.62 85.~9

803° (See Run #4)

Run#

9·

10

ll

12

APPENDIX VII

KINETIC DATA: DEPE.t.1mENCE OF REACTION · VELOCITY ON PbO/PbS RATIO

· Flow Rate: ·260 c.c./Min

Temperature:: . 722°c

PbO/PbS Ratio Time - (Min) . (9' Reacted)

10:1 (Reaction Velocity = 0)

8:1 4.58 2.00

·4.00

6:1 1.25 .1.42

2.42 2.84

4.62 5.68

7.88 8.52

13.05 11.36

22.25 14.20

28.50 15.62

36.42 17.04

46.17 18.46

4:1 1.83 1·.79

3.62 3.58

5.95 5.36

119

APPENDIX VII (continued)

Run# PbO/PbS Ratio Time - (Min) (~ Reacted)

12 4:1 9.oo 7.15

12.58 8.94

16 •. 67 10..72

21.25 12.51

23.50 13 •. 41

26.05 14.~0

28.62 " 15.19

31.42 16.09

34.02_ 16.98

36.78 17.88

39.67 18.77

42.25 19.66

45.42 20.56

48.35 21-.45

13 2:1 1.60 1.10

:3.40 2.19

5.42 3.28

7.78 4.38

10.12 5.48

12.75 6.57

120

APPENDIX, VII (continued)

Run# PbO/PbS Ratio Time - (Min) (fo Reacted)

13 2:1 15.35 7.67

18.20 8.76

21.03 9.86

24.10 10.95

27.10 12·.05

30.13 13.14

33.13 14.24

36.33 15.33

39.72 16.43

42.93 17.52

46.32 18.62

49.60 19.72

14 1:1 1.43 1.37

2.88 2.75

4.33 4.12

5.78 5.49

7.42 6.8'7

I 8.95 a.24

10.57 9.61

12.17 10.99

121

APPENDIX .VII (continued) .

Run# PbO/FbS Ratio Time - (Min.) (foReacted)

14 1:1 13.88 12.36

15.67 13.73

17.47 15.11

19.33 16.48

2J..28 17.85

23.35 19.23

25.58· 20.60

27.87 21.98

. 30.33 23.35

32·.95 24.72

35.73 .26.10

38.52 27.47

41.52 28.84

45.00 30.22

48.28 31.59

15 1:2 1.33 2.29

2.73 4.57

4.18 6.86

5.63 9.15

7.22 11.43

122

APPENDIX.VII (continued)

Run# PbO/PbS Ratio Time-(Min) (~ Reacted)

15 1:2 8.88 13.72

10.73 16.01

12.62 18.29

14.63 20.5.8

16.65 22.87

19.00 25.15

21.35· 27.44

23.78 29.73

26.45 32.01

29.13 34.30

32.00 36.59

35.00 38.8?

37.97 41.16

41.15 43.45

44.40 45.74

47.83 48.02

51.43 50.31

~5.12 52.59

16 1:4 1.30 3.26

2.58 6.52

123

APPENDIX .VII (continued)

Run# PbO/PbS Ratio Time - (Min) (" R_eacted)

16 1::4 4.05 9.78

5.65 13.03

7.23 1~.29

9.13 19.5~

11.12 22.·a1

13.27 26.07

15.58· 29.32

17.98 32.58

20.58 35.84

23.35 39.10

26.25 42.36

29.45 45.62

32.73 48.88

36.18 52.13

39.97 55.39

43.78 58.65

47.88 61.91

17 1:6 1.45 5.42

2.97 10.85

4.58 16.28

124

APPENDIX .VII (continued)

Run# PbO/PbS Ratio Time - (Min) (~ Reacted)

17 1:6 6..45 21.70

8.52 27.13

10.80 32.56

1.3.42 37.98

16.23 43.41

19.47 48.83

22.98 54.26

26.87 59.68

31.13 65.11

37.40 70.16

18 1:8 1.67 6.79

3.35 13.58

5.27 20.37

7.43 27.16

9.87 33.94

12.75 40.73

15.98 47.52

'19.50 54.-31

23.92 61.10

27.17 64.50

125

APPENDIX. VII ( continued)

Run# PbO/PbS Ratio Time - (Min) (~ Reacted)

18 1:8 34.58 67.89

43.58 69.25

J.9 1:10 1.57 7.85

3.50 15.70

5.77 23.55

8.40 31.40

11.67 39.25

15.27 47.10

19 •. 58 54.94

25.65 62.89

50.75 70.64

VITA

The author was born on October 2,. 1936 in Miles C.ity 1

Montana. He received his primary and secondary education

in Big Timber, Montana. He entered the Montana School of:

Mines, in Butte, Montana in September, 1954, receiving a

Bachelor of Science Degree in Metallurgical Engineering _

in June, 1958 • .

He has been enrolled in the Graduate School of the

University of' Missouri School of Mines and Metallurgy since

September, 1958. He was appointed an Assistant Instructor

in Metallurgical Engineering in September, ·1959.