THERMODYNAMIC ASPECTS OF CHEMICAL REACTIONS, ASAPPLIED TO THE SMELTING AND REFINING OF LEAD

A. B. CHATTERJEA & B. R. NIJHAWAN

National Metallurgical Laboratory, Jamshedpur

Abstract

With a reference to the formulae employed in

chemical thermodynamics , available data on thermo-

dynamics of chemical reactions involved in theextraction and refining of lead are brought together.

Equilibrium constants of the reactions have beencalculated from the standard free energy data toexplain the desideratum of optimum working con-

ditions required during roasting , smelting and

refining of lead . Graphs showing the changes with

temperature of standard free energies of formation

of oxides , sulphides , chlorides , fluorides , sulphates,

carbonates and silicates have been incorporated for

ready reference.

Introduction

A PPLICATION of the laws of thermo-dynamics permits the study of che-mical reactions involved in different

metallurgical processes . Thermodynamicsthus provides a useful method of predeter-mining the possibility of a chemical reactionto occur under given conditions of tempera-

ture , pressure and composition . Review of

thermodynamical factors of chemical reac-tions involved in the smelting and refiningof lead has been dealt with based on theconventional processes in use thereof. Indoing so it has not been possible to includephysico-chemical studies of all aspects of lead

metallurgy.

Free Energy of Reaction

Available portion of the total energy of asystem is known as free energy (G) (F bysome American authors) and is defined bythe relation

G=H-TS......... ( 1)

where H is the heat content and S is the

entropy of the system. All systems tend toreach maximum stability. The free energyof - any system, therefore, tends to attain aminimum value under conditions of constant

pressure and temperature. Hence, the

change in free energy AG is indicative of thedirection and extent to which a chemicalreaction, phase transformation and change of

state can proceed. It is the driving force of

any chemical reaction. The standard freeenergy change of a reaction (A.G°) is related

to standard enthalpy change of a reaction( OH°) and standard entropy change of areaction (AS°) at constant temperature and

pressure by the equation

AGO = AH°-TAS° ...... (2)

Whether a reaction can proceed in the

desired direction or not depends on twofactors, viz. the sign of the free energy changeand the availability of a suitable reaction

path. If the free energy is lowered by the

reaction proceeding in the intended direction

and a path is available, the necessary pre-

requisites exist for the reaction to proceed.

If the free energy change is not favourable,the mere existence of a reaction path is notenough. Similar reasoning applies to the

other case where the free energy change is

favourable, but the reaction path is either not

available or not straightforward or when the

chances of the reactants meeting each other

are small.

Equilibrium Constant and Free Energy

For any chemical reaction at given tem-perature and pressure

bB+cC=dD+eEin which b, c, d and e represent the number

108

CHAtrERJEA & NIJIIAWAN-THERMODYNAMIC ASPECTS OF CHEMICAL. REACTIONS 109

of molecules of the reactants B and C, and

products D and E taking part in the re-

action, the change in free energy at a given

temperature and pressure is given by the

equation

d e

AGT -_ AGO. -}- RTlnab x aE , ... (3)aBxae

where ae = activity of a constituent E;

T = absolute temperature ('K); and R =gas constant (1-987 cal./degree/mole/mole). AG'is conventionally expressed in cal . per gramatom. When the reaction attains a state ofequilibrium, the free energy change AGT is

zero, and , therefore,

d eAG°_-RTinDXaE

aB xaG_ - RT1nK ... (4)

°T ...... (4a)or log K = - 4 -575

where K is the equilibrium constant of thereaction. This equation shows the relationof standard free energy change AG° to theequilibrium constant (K) of a chemicalreaction. K is a ratio which indicates theextent to which a chemical reaction canproceed. The high magnitude of K, there-fore, indicates that the reaction proceedssubstantially to the right-hand side of theequation. The unit in which K is expressedis generally related to the active mass (oractivity). Change of the equilibrium con-stant (K) with temperature is given by the

equation

log "K 1 775 x TG° ..... (5)

If for any chemical reaction at a particular

temperature AG° can be found, K can be de-termined, and vice versa. It is thus possiblefrom equation (4) to calculate equilibriumactivities for a reaction.

From equations (2) and (4) it follows that

as" AH°1nK = - RT ..... (6)

which shows that the equilibrium constantof any temperature T can be calculated from

the known value of heat of reaction AH° andthe value of change in entropy OS°, whenthe substances are in their standard states.

The variation of the equilibrium constantwith temperature is expressed by van't Hoffequation

d1nK _ LH° (7)dT RT2 '""

If AH ° is positive , i.e. endothermic reac-tion, lnK, or - AG° becomes more negativeand the reaction proceeds further with therise of temperature . If AH ° is negative,then - AG°/T becomes more positive withthe increase of temperature . The possibilityof AH ° changing sign with temperatureshould be considered . From equation (6)

log K - 4-575T plus-constant

as the heat of the reaction does not changeappreciably with temperature and pressure.When logarithm of the equilibrium constantis plotted against the reciprocal of absolutetemperature, a straight line is obtained, theslope of which multiplied by 4-575 will givethe heat of reaction in calories.

Thermodynamic data, therefore, providemeans of ascertaining the possibility of anychemical reaction taking place under givenconditions. It must be mentioned that thereaction rate will depend on factors such asthe form of the reactants and is not predict-able from thermodynamic considerations

alone, e.g. the diffusion of the reactants andproducts from the zone of reaction maydetermine the rate of reaction. Metallurgical

reactions usually take place at high tempera-tures at which diffusion rates are high. So,

if the free energy change is favourable, ametallurgical reaction is expected to pro-gress at a reasonable rate in the desired

direction..

Activity

By activity is meant the effective concen-tration of a constituent, which may notalways be equal to its concentration. Activ-

LH°

11o SYMPOSIUM ON NON -FERROUS METAL INDUSTRY IN INDIA

ity is always referred to a standard state.It represents the effective concentration inany desired state when compared to theeffective concentration in the state chosen asthe standard or reference state. In a largenumber of instances, the pure substance istaken to be the standard state. In suchcases, if the solution obeys Raoult's law, theactivity is equal to the mole or atom fraction.When considering dilute solutions, it is some-times inconvenient to refer to the pure sub-stance as the standard state. Hence, we havethe infinitely dilute solution standard, andthe 1 per cent solution (vide Chipman )standard. In dilute solutions, the activityis proportional to the considerations till thelatter become excessive. This is expressedby Henry's law. Activity of a pure solid orliquid is conventionally considered as unity,and that of a gas as equal to its partialpressure.

The ratio of activity (az) to its concentra-tion is called the activity coefficient (Y1)where the concentration is defined by themole fraction (N; ).

Yi - a. ........... (8)Ni

These remarks can be generally applied toheterogeneous systems.

In equation (3), when the reactants andproducts are not in their standard states and,therefore, the activities are not unity, theCree energy change of the reaction AG canbe obtained by adding an activity correction

to AG°. It follows from equation (3) thatAGr AGT + RT1nJa, where Ja is theactivity function at temperature T. An

activity correction chart has been shownwith a AG°/T diagram for chlorides (Fig. 4 ).The correction has to be multiplied by thenumber of molecules. This is to be added

for products of reaction and subtracted forreactants. If a is less than unity, reciprocalof a to be added to AG- for reactants andsubtracted for products.

The change in free energy with temperatureat constant pressure can be expressed as

AG° = IT + AH° - AaT1nT -

AbT2 AcT3 (9)2 6 ...

where I and H° are integration constants.The value of the other three constants a, band c can be calculated from specific heatdata of the constituents while H° and I canbe evaluated from one value of heat effect onthe reaction and a known value of G° at aspecified temperature respectively. It is thuspossible to calculate the standard free energychange of a chemical reaction at a given tem-perature, but the equation is cumbersome.

Graphical Representation of StandardFree Energy Changes with Temperature

Standard free energies of formation ofvarious compounds at different temperatureshave been expressed in the form of equation(9) by Kelly".

Ellingham2 plotted the standard free energychanges with temperature in a graphical form.From such a chart, one can directly see theconditions for a chemical reaction to occur.As 11° and S° change only slightly with tem-perature, such a plot will result approximate-ly in straight lines having a slope of S°,because of the relation

dAG° _ - A$°dT

If AG° is plotted downwards, as is commonpractice, the slope will be - bS°. With the

abrupt change of entropy at transition,fusion, vaporization and sublimation tern-peratures, the slope is usually changed.

The standard free energy for chemical reac-

tion is related to standard electrode potential

( or decomposition voltage) of an electrolyticcell in which the reaction is carried out by

the following equation:

AG° _ -jnE°F . .. . . . (10)

where E° = standard electrode potential involts; F = faraday constant, 96,500 coulombsper mole; n = number of faradays per moleof reaction; and j = conversion factor fromJoules to calories (= 0-239).

CI-IATTP-RJEA & NIJHAWANT--`I1TIERMODiINAIIIC ASPECTS of CHEMICAL REACTIONS Ili

-20

-40

-60

-80

0

oil -18

-20

-2z

24

2b

-28

-3000 Zoo 400 600 $00

A85oL U rI ZERO TEMPERATURE

TEMPERATURE °C.X00 1200 100 (6oo 1800 2,000 2200 2400

m

Yr 4

PZ Z 02 ^ZGflZ, 0

^

a be¢^ ^.,rOZ ^2^4

"-C XZ Z q ^ ^^ r 2

Ara M

M Fe d

O S ,.^ ^3 M1® Irj^'

rk1 {/.^

C

0x x^

A2p3 ^ q̂p i

^3I A

M r

8 ^acp,^2

}M Go,A Prob able accurncy of dol-a

A ± I KilocalorieM ± 3 Kilocalories

c±t0 ., ..

Chun esa slate Flemerit OxideMelting po'ihr m l]Boiling poirF'5ublimation,f

aS

FB7

Tronslhon

00

i'0

-40

-60

-80

l00

120

140

160

180

-zoo

-720

-240

-280

-300

FIG. I - STANDARD FREE ENERGIES OF FORMATION AS A FUNCTION OF TEMPERATURE OF OXIDES INVOLVING

ONE GRAM-MOLE OXYGEN ( RICHARDSON AND JEFFES4

III SYMPOSIUM ON NON- `ERROUS M1TAL INDUSTRY tN INDIA

It is, therefore, clear that the ordinate ofthe iXG°/T chart can represent LG° and E°,if n is constant for all the reactions given in a

chart. In practice, due to internal resis-tance, over-voltage and polarization, voltageshigher than the requisite decompositionvoltage are necessary for electrolysis.

Standard Free Energy/TemperatureDiagrams

Figs. 1-9 show the dependence of standardfree energies of formation of oxides3, sul-phides, chlorides5, fluoridess, sulphates7,carbonates7 and silicates8 on temperature.The application of these charts has beenadmirably described , by Ellingham2 andothers3,5-7,s. In each' case, free energychange of the reaction in which 1 gram-mole

of the gas 02, S2, Cl:,, F2, N2, SO3 and CO2 orthe compound 5102 reacts with requisitequantity of the metal or oxide has beenrepresented, as it shows directly the relativestability of the compound or affinity for thegas. The further down a compound occursin the chart, the more stable it is. Whentwo reactions are compared, the vertical dis-tance at a particular temperature separatingthe two characteristic lines represents the free

energy change and, therefore, indicates thetendency of the element represented in thelower line to decompose the compound re-presented by the upper line. For example,if at a particular temperature T, the curve foroxidation of any element X is below that forelement M, then the oxide of the element Xis more stable than that of M and the reaction

M0+X=XO+ M.....(11)

will take place when the constituents are intheir standard states. If, however, X forms

an oxide of lower valency, the reverse reac-tion may be possible.

Thermodynamic data can be added orsubtracted algebraically. The possibility of

oxidation of a sulphide, or of the chlorinationof an oxide or a sulphide at any temperatureT is shown by the free energy of formation ofthe oxide at T minus that of the sulphide at T,or the free energy of formation of the chlorideat T minus the free energy of formation ofthe oxide or sulphide at T. In other words,feasibility of reactions like

MS -}- 3/202 = MO + SO2 ...... (12)MS +2MO = 3M--{-S02 ...... (13)

MS ± C12 = MC12 + 1 /2S2 .... (14)MO ± C12 = MC12 + 1 /202.... (15)MO -{- 2HCl = MCl2 + H2O ..... (16)

can be predetermined by the use of the oxide,sulphide and chloride charts.

Applications to Metallurgy of Lead

The basic concepts of thermodynamics asapplied to equilibrium in chemical reactionswill now be applied to review the importantchemical reactions in the roasting, smeltingand purification of lead.

It can be seen from the L G°/T diagramfor oxides that the free energy of formation ofCO becomes more negative with the rise intemperature and consequently it becomestheoretically possible to reduce all metallicoxides with carbon at very high temperatures.Due to the lower free energies of formation of

sulphides like CS, CS2 and H2S compared tothe oxides CO, CO2 and H2O, the reduction ofmetallic sulphides by carbon and hydrogenis, however, not possible. Sulphides of lowstability can be reduced to metal either bythe application of heat when at moderatetemperature the free energy of formation

becomes zero (e.g. of mercury sulphide) orby oxygen, which is adopted in the roastreaction method of obtaining lead to be de-scribed later. In such cases no reducing agentis required. The smelting of galena, likemost of the sulphide ores of other metals,

FIG. 2 - STANDARD FREE ENERGY OF FORMATION AS A FUNCTION OF TEMPERATURR OF SULPHIDES FOR

REACTIONS INVOLVING ONE GRAM-MOLE OF S2 GAS ( RICHARDSON AND JEFFES4)

CHATT'ERJEA & 1tiIJL AWAN-THERMODYNAMIC A E CTS 01' CHtMICA1. 12EACTIONS 1 3

H2Sf HZ RATIO

20

0

1 PbFt

f7-80

a -I0oJ4

0-120J

X 440

..I -16Of..

t02Q t0'S 1010 108 106 103 i0s

10

"Ir r 1Yr53 ® Q`Lr7

t +CS2 S^ r^y!P '-

G z =5o' _1< 4 ,,.^,- o

,a Ag+59=Zpgz 9 Q

t b^=o_►wo5

s_5►53 Sa Gee,

FaS ^

J c V

R, M

yM

S•Ls}7,

QQ

Y

y Q

1

5®

1

ey/y

g5

M

U

tsa ti,r yGo.

`0a ^Z. ^-

SUcIGE5TED ACCUR AC

rJ1 M G6" ; IKg.C01.^^ .

O .3K .C0%.O1.5 i

9C^ 1' oI3> IO .g

^

" CI1ANG .5 OF EL .^- SUL-

f STATE . MENT. PNIgE

C^ MELTJNO PT M I

BO,UN6 PT S5t]BLtiMATlON 5

1 TlIANS,TIOMPT. T

ps2 a atwm

`yf IO^•

10

yo

1d4a

310

101

Ia'

1O

-10

ID

101

110 ^IO

10^

II '010

8`

Io

li

t'10

Zoo 400 600 BOO 1000 1200 1400 1600 WQQ ?Ay TE PEF1A'i'LIRE °C .

!O o v c P c S (/10 1hb2 t/1o^p rh0% j "1C 1JIG 1h10 1/t0

HzSJ HZ RAT10

Id 1O 42 -34 -30 2$t0 10 Id 1010 3$1p!$O ;p14° 10 lbs0 10 0

iI

ABSOLUTE

--psz atm .

1 ^240

1

I^ 20

FIG. 2

114 87VNMPOSI171i ON NON-FERROUS METAL INDUSTRY IN INDIA

commonly involves roasting of the ore as thefirst stage.

General Aspects of Roasting

Some general aspects of roasting of sulphide

concentrates have been described recently byDjingheuzian10. In oxidizing roasting, theore concentrate is heated below its fusionpoint, to convert the sulphide into the oxide.The reaction may be expressed as

MS + 1O2 = MO + SO2 ..... (17)

For the reaction to proceed substantiallyto the right, the free energy of the formationof the oxide MO should be higher than thatof the sulphide MS, and the concentration ofSO2 in the roaster gases should be low toprevent the reverse reaction. Perettill hasmentioned that at temperatures commonlyemployed for roasting of sulphides of metalslike copper, zinc and lead, the reactionMS + 9 02 = MO + SO2 and the oxidationof sulphur to sulphur dioxide involve suchlarge free energy changes that the S02/02equilibrium ratios need not be considered.This will be later considered in relation toroasting of galena. Though the oxidation ofthe sulphide is the main chemical reactionaimed at, other side reactions usually takeplace and some of these reactions affect theproduction of a desirable calcine. In thepresence of catalysts, SO2 is converted intoSO3

SO2 + 1/202 + catalyst = SO3 .... (18)

SO3 then reacts with the oxide MO to formsulphate

MO + SO3 = MSO4 ..... (19)which is undesirable.

The roaster gas consists of a mixture of 02,

N21 SO2 and SO3. In a mixture of gases, the

partial pressure of each is, of course, propor-

tional to its volume. The formation of MS04

will depend on the partial pressure of SO3i

temperature and on the characteristics of the

oxide MO. If the partial pressure of SO3 at

the selected temperature is less than its

equilibrium value, then MSO4 will decompose

into MO + SO3 and more of the oxide will.

form. Conversely when the partial pressure

of SO3 is higher than the dissociation pressure

of sulphate, SO3 will combine with the oxide

to form more sulphate till the partial pressure

of SO3 is reduced to equilibrium value. Thus

the roasting reactions can be controlled by

controlling the temperature and the composi-

tion of the gas in the roaster.

Roasting of Galena

The thermodynamical aspects of roasting of

galena have been described by Wenner12.

But whereas he calculated the free energy

data from equations, use has been made of

appropriate OG°/T charts in this review.

In roasting, the following reactions are likely

to take place:

(a) PbS + 3/202 - PbO + SO2 .... (20)

The equilibrium constant of the reaction is

aPbo.pS02

K 20 - aPbs.p01-5

Assuming that the activities of PbO andPbS are unity, the equilibrium constantbecomes

K20 = pros

2

The change in free energy of reaction (20)

can be found from the known values of

standard free energies of formation of PbS,

PhO and SO2 and from the expression

OG20 = -RT1nK20, K20 can be calculated.

Other reactions are

(b) PbS 1- 202 = PbSO4 . . . . . . . (22)

d

FIG. 3 - STANDARD FREE ENERGIES OF FORMATIONJTEMPE RATURE OF CHLORIDES INVOLVING ONE GRAM-

MOLE OF CHLORINE GAS BETWEEN 0 AND -90 K. CAL. (KELLOG5

0-

0.2-

0.4-

0.6

O.8

1.0-

1.2 -

1.4 -

1.6 -I

SnCIY+Ct2= Snc t

149, Cit e IASC%2.=+C12=2HC1^H

'`}3^y AS+Clts 3AsC12Hg-I-clj- H91C1z

2/3gi, C12=21ab;Oft Sb +CI1=213SbCI

ZAg+C12= 2AgcI2CrGI2+C122 2Crcl

2Cu+C1t=Cu1CIZ

2135+CI2=2f3 BCI

NI+Ct2 t NiCI2 =--r

Co- C12 CoCli1!2Si+Clt=ij2SiCl4-,

Fe+Ct2= FeCIxSn}Cti:SnCI1

Pb+C12=PbC12

Cd+ C12: CdC l2

1-8 - Ij2Ti +CI2. 'jZTiC14

Cr+CI1= CrC12

Zn+ CI2. =ZnC%

CHANGES OFSTATE. ELEMENT CHLORIDE.

MELTING POINT. M ElBOILING POINT. B.SUBLIMATION PT. S mTRANSITION PT. T 0

FXG, 3

116 SYMPOSIUM ON NON-FERROUS METAL INDUSTRY IN INDIA

For the reasons mentioned above

K22 = 02 . (23)P 2

(c) 2PbS±71f202 =PbSO4PbO±SO2 ... (24)

K24 - PS02 . . . . . . . , . . (25)or

(d) PbS ± 02 - Pb + SO2 . . . . . . (26)

Kos = PS©2/PO2 .. . . . . (27)

(e) S02± 1 /202= SO3 . . . . . . . . . (28)

pSO3K28 = PS02 x p00 5 . : . (29)

(f) PbO -}- SO3=PbSO4 . . . . . . . (30)

K3oI

(31)pS03 . . . . . . . .

The approximate AG values, as obtainedfrom the appropriate AG°/T diagram, andthe calculated values of the equilibriumconstants of these reactions at 600°, 700° and800°C. are given in Table 1.

TABLE 1-FREE ENERGY OF FORMATION

OF COMPOUNDS AND EQUILIBRIUMCONSTANTS OF REACTIONS (a) TO (d)

DURING ROASTING OF GALENA

TEMPERATURE, C.

600 700 800

AGO PbS cal. -21500 -19500 -17500AGO PbO -32000 -29300 -27000AG- PbSO4 „ - 144280 - 135700 - 127130AG- PbSO4 „ - 180900 -169000 -158300

Pb0*AG° SO2 : - 72000 -70000 -68000(a) K2O 4 . 57x1020 . 8.51x1(117 6.31x10115(b) KS2 5.9 x 100 1 - 3 x 1026 2.14 x 1022( c) K24 2.5 x 1052 8.51 x 1044 9 .55 x 1028(d) Kee 4.4 x 1012 2.2 x1011 2-0 x 1010

*Calculated.

The high values of the equilibrium con-stants K2Q., K22, K24 and K26 show that thereactions (20), (22), (24) and (26) are thermo-dynamically feasible in the temperaturerange of 600°-500°C., and the reactions willproceed substantially to the right of theequation. The reaction 11252 -t- 02 = SO2has an equilibrium constant of 1.12 x 101$at 825°C. PbO and SO2 will, therefore, bestable phases where there is a minute partialpressure of oxygen. On the other hand, itcan be shown from the free energy data thatthe basic lead sulphate formed in equation(24) should react with SO2 and oxygen toform PbSO4 thus :

PbSO4PbO+S02+11202 = 2PbSO4 .. (32)

which has an equilibrium constant of5.01 X 10 5 at 800°C. It means that

PSO2 X Pa(-5 = 1 (33)5.01x105'''

The partial pressure of oxygen is 0-21 atm.Substituting value of partial pressure ofoxygen in the above equation, it can be seenthat the partial pressure of SO2 for the con-version of basic lead sulphate to lead sulphateis extremely low, which means that very lowconcentrations of SO2 in the roaster gases inpresence of oxygen can react with basic leadsulphate to form lead sulphate. Converselyhigh SO2 concentrations in the presence oftraces of oxygen will convert basic leadsulphate to lead sulphate. The roasted pro-duct will, therefore, consist of little unreact-ed lead sulphide and mainly of lead oxideand lead sulphate.

Smelting of Lead

The smelting of lead follows three methods,viz. (i) the reduction of lead oxide by carbonand carbon monoxide; (ii) reaction between

FIG. 4 - STANDARD FREE ENERGIES OF FORMATION/TEMPERATURE OF CHLORIDES INVOLVING ONE GRAM-MOLE OF CHLORINE GAS BETWEEN - 90 AND -150 K. CAL. (KELLOG5 )

lop

®= A1CI^^)

F

If

I

/I

/Acl=4CcG1

2P ,C12 = 2NOGI.

ACTIVITY CORRECTION CHART

ol I 1-1VALUES OF RT InO► . ^

kip

as {oa=^

0 Soo 1000

TEMPERATURE ,'C.

Fir.. 4

90

100

110

120

130 D

C

150

30

20

10

02000

0In

2r022zfn

118

0.6

0.8 ^

1.0

1.2 -

1.4 -

1.6

1-8 -

SYMPOSIUM ON NON-FERROUS METAL INDUSTRY IN INDIA

CIZ+ FZ = 2CIF

!r35e+F2_ p SeF63

^3S + Z- p-F,.

2.0 -

2.2 -

2.4 ^

3.0-

3.2-

2Ag+F2= 2A9F,

I/37e+Fz=133

TeFs

H2+Fz= 2HF--*

3As+p2. 3AsF3-.,

Pb+F2 - PbF2Cd4

CHANGES OFT

ELEMENT FLUORIDE.F 6F ^° 'ATE.S ajE+ ^ aj

YMELTING POINT M. ^ ;Fti I

BOILING POINT B Al !^. tbSUBLIMATION PT. S L ,.'TRANSITION PT T Q.

iM S

P9M tit ® ^aF

Mrr

Mj^

t,r

AsF3a f

500 1000

TEMPERATURE, C

1500

30

so

60

70

80

90

100

110

120

130

140

ISO

FIG. 5 - STANDARD FREE ENERGY OF FORMATION OF FLUORIDES AS A FUNCTION OF TEMPERATURE INVOLVING

ONE GRAM-MOLE OF FLUORINE GAS BETWEEN -20 AND -150 K. CAL. (KELLOGG

the sulphide and the oxide ; and (iii ) displace-ment of Pb from PbS by other metals. Forthe precipitation method, any metal whoseposition in the sulphide diagram is lower thanPbS will be able to combine with sulphur,displacing lead from its sulphide . Iron is thechief element used for displacement. As the

reaction is reversible, complete decompositionis not possible. As regards the other twoprocesses, argentiferous ores are treated inthe blast furnace and high-grade non-argenti-

ferous ores in reverberatory furnaces. Inthe AG°fT diagram for the oxide, the 2C+02

=2CO curve cuts that for 2Pb+O,=2PbO

mrC0

z1"

CHATTERJEA & NIJHAWAN- THERMOD 'YNAMIC ASPECTS OF CHEMICAL REACTIONS 119

341

3.6

3.8

W 4.0

4.2

4.4

4.6 ^

4.8

5.0

3.6 -

58-

6-0-

Cd+ FZ = CdF2

^U + Fa x ,.3U%

2♦36 -F2 < BF3-Mn+F2 = nF2-%2Si +F2, i SiF4

%AI + F2 = / AIF3

M9- FZ - MgF22K+ F2 = 2KF -2No+F2 = 2.NOF,

Ba+ F2 = Ba FxCo- F2 = Cafe2Li+F2 = '2 Lit;

'^^^r•4^

'^ }AIF,

s

y f-r J ^^^ r ® ' ,^^'L

170

r J ♦

^- •'F 180

190

20C

210^. i CoR=

.+r Bs1 141

^♦22C

23(

MHz 2-41

1f AM250

CHANGES OF ELEMENT FLUOI UDE.i STATE, 260

MELTING POINT. M

BOILING POINT. B 161SUBLIMATION PT. S Q

270

TRANSITON POINT. T T^28C

500 1000

TEMPERATURE °C:.

1500

FIG, 6 - STANDARD FREE ENERGY OF FORMATION OF FLUORIDES AS A FUNCTION OF TEMPERATURE INVOLVING

ONE GRAM-MOLE OF FLUORINE GAS BETWEEN -150 AND -280 K. CAL. ( KELLOG6)

at about 200°C., which means that thereducing effect of CO theoretically commencesat that temperature. The reducing action

of C commences at 400°C. and the rateof reduction is comparatively slow. Themain reactions of the lead blast furnace andtheir equilibrium constants are as follows:

(a) PbO - CO = Pb + CO2 . . . . .. (34)

1.C34 - pCO2pC0 . . . ..... (35)

(h) PbO+C^Pb+-CO . . .... (36)

K36 = pCO . . .... .. (37)

(c) CO2 + C = 2CO .. . . ... .. (38)

La

zat

0DJIL

to

to0

200

Lij 30

40

50

w 600

70

80

90

120

130

10

01

o,

.b^Oa

M D!o-

001, 10I.-e

20

.100

CH! AtJ ES OF ELEMEN SULPHATE. STATE

MELTINGr POINT MH

O0B

0,0

BOILING ^•

SUBLIMATION - S

tI,

S^00, TRANSIT I Ot%I n T I t I

200 400 600 800 . 1000 Izoo 1400 1600

TEMPERATURE 0C.FIG. 7

CHATTERJEA & NIJHAWAN-THER&10DYNAMIC ASPECTS OF CHEMICAL REACTIONS 121

K3a = pCO2 (39)PC02

(d) PbSO4 + 4CO = PbS -}- 4002 . (40)

pCO2K4Q =

PC04. . (41 )

(e} PbS ± 2PbO = 3Pb ± S02 . . (42)

K42 = PS -02 - • - (43)

(f) PbS + PbSO4 2Pb 4- 2SO2. . (44)

K41 = pSO2 . . . . . (45)

(g) PbS + Fe = FeS ± Pb . . . . . (46)

K46 _ aFeS . . . . . .wpbs

(47)

All these reactions occur around 900°C.

Reaction (36) is really a combination of thereactions represented by equation (34) andthe producer gas reaction (38). The approxi-mate values of free energies of formation ofvarious compounds at 900°C. taken from theappropriate AG' /T diagrams and the equili-brium constants of these reactions are givenin Table 2.

Roast Reaction Process

TABLE 2-FREE ENERGY OF FORMATIONOF COMPOUNDS, EQUILIBRIUM

CONSTANTS AT 900°, 1000° AND 1100°C.OF REACTIONS IN LEAD BLAST FURNACE

TEMPERATURE,

900 1000

AGO PbS cal. -15200 -13000

LG° CO -51500 -53000AGO CO2 -94000 -94000

AGO PbSO4'1 -118600 -110000AGO PbO -24000 -22000

AGO FeS -21500 -20000

AGO SO2 -66000 -64500(a) Ksa 3.2 x 103 2-2 X103

(b) K36 1.05 x 1015 2.14 x 1012

(C) K,a 2.0 X 1013 3-1 x 1011

(d) Kd2 0- 71 1.30

{e) K44 4-5 x 10-1 1.03

{f) K42 1-17 1-26

°C.

1100

-11500

-55500-94000

-101000-19800-18600

-630001.1 X1036-3 x 10'1

2.0 x 101°

1-91

2-31

1-13

*Pb(5)+S(s)+202(g)= PbSO4 (S) AGT =

-219000+85.6 T. cal.

TABLE 3-EQUILIBRIUM CONSTANTS OFTHE CHEMICAL REACTIONS OF ROAST

REACTION METHOD

E" QL'ILIBRI UM TEMPERATURE, °C.

CONSTANTS OF r---•------'^^-- ^!

CHEMICAL REACTIONS 800 900

The desirable reactions in the process aregiven in equations (42) and (44), but in thepresence of excess of PbS or PbO than isrequired by equations (42) and (44), theexcess remains unaltered , while with excessof PbSO4 either a mixture of Pb and PbO, orPbO alone, results as shown in equations

(48) to (51).

PbS+3PbO = 3Pb+PbO ±SO2 . (48)

2PbS ± 2PbO = 3 Pb ± PbS -}- S02 . . (49)

PbS±2PbSO4 = Pb-4-PbO± 3SO2 . (50)

PbS±3PbSO4 = 4PbO± 4SO2 . . . . (51)

K44

K 44

Kso

K51

0-21 0-71

2.0x10-2 4.5 x10-32.14x10-6

2-0 x 10-11

The equilibrium constants of the reactions

(42), (44), (50) and (51) at 800° and 900°C.are given in Table 3.

K42 has values of 0-71 at 900°C., 1.3 at1000°C. and 1-91 at 1100°C. and the corres-

ponding values of K44 are 4-5 x 10-1, 1-03 and2-31 respectively. These indicate that if the

partial pressure of SO2 attains these values,

FIG. 7 - TEMPERATURE DEPENDENCE OF STANDARD FREE ENERGIES OF FORMATION OF SULPHATES FROM

THE OXIDE AND SO3 GAS INVOLVING ONE GRAM-MOLE OF SO3 GAS (OSBORN7 )

122

t7el

SYMPOSIUM ON NON-FERROUS METAL INDUSTRY IN INDIA

5

25

30

35

40

45

50

55

60

6 65

70

omv/

i

JJ

/ i

100 200 300 400 500 600 700

TEMPERATURE

800 900

FIG. S - TEMPERATURE DEPENDENCE OF STANDARD FREE ENERGIES OF FORMATION OF CARBONATES FROM

THE OXIDE AND CO2 INVOLVING ONE GRAM-MOLE OF CO2 GAS (OSBORN'

CHATTERJEA & NIJHAWAN_THERMODYNAMIC ASPECTS OF CHEMICAL REACTIONS 123

the production of lead will stop. But as SO2is allowed to escape from the furnace, thepartial pressure of SO2 cannot attain any

value excepting 4.5 x 10-1 so that the desiredreactions will go to completion. For the

same reason, reactions (50) and (51) will notproceed substantially to the right of the

equations.

Refining of Lead

Besides lead, copper and iron, galena con-tains a large number of other metals like gold,silver, zinc, tin, arsenic, antimony, bismuth,nickel, cobalt, which need removal, with the

sulphur, to obtain pure lead.The elimination of impurities norm illy

takes place in two main ways, volatilizationof easily volatile oxides, like arsenic and anti-mony oxides, and slagging, in which theelements having higher free energy of forma-tion of their oxides than that of lead oxideare readily oxidized and taken up by the slag.It can be seen with the aid of Fig. I thattin, zinc, sulphur, iron, nickel and cobalt areoxidized at a low temperature preferentially

to lead and may thus be slagged off. Coppercan only be partially removed by oxidation.

It, however, forms an alloy of higher meltingpoint than lead and, on slow melting, dross

containing Cu, S, As and Pb separates out.As the free energy of formation of bismuthoxide is lower than that of lead oxide, re-moval of bismuth is not possible by eitheroxidation or vaporization (in a way similar

to its removal from copper matte).

Removal of Bismuth

It is well known that Parkes's processdoes not remove bismuth, but that it can beremoved by Pattinson's process, but atconsiderable cost. Betterton and Lebedeff13

have developed a process in which calcium,magnesium and antimony are used for theremoval of bismuth. The principle is similar

to that of Parkes's process in which partition

of silver between alloys, rich in zinc and lead,

takes place- In this method, bismuth com-

bines with calcium, magnesium and antimonyforming a dross, and leaving lead which con-

tains only 0.005 per cent Bi.

Removal of Zinc from Lead

From Parkes's process, lead contains 0.5-

0.6 per cent zinc. The older practice was topass air through molten lead kept at 1200°-1300°F. to oxidize zinc, because of higherfree energy of formation of ZnO compared tolead oxide. But, in practice, oxidation oflead cannot be altogether prevented and

3-5 per cent lead is lost by oxidation.Bettertoni4 has described a method of puri-fication by chlorine gas. In this process theloss of lead has been practically eliminatedand zinc chloride is recovered as a valuablebyproduct. The reaction is conducted undervacuum at a temperature of 350°-390°C. Thereaction is exothermic, but ZnCla does not

volatilize until a temperature of 730°C. isattained. At the end of the operation, the

lead contains about 0.005 per cent Zn and the` crust ' contains 2.5 per cent lead. Dezinc-ing by chlorine evidently depends on the fact

that the standard free energy curve for ZnCI2is below that of PbCl2. The standard freeenergy of formation of ZriCl2 at 390°C. is-76,640 cal. and that of PbCI is -61,550cal. as shown in Fig. 3. If any PbCl2 is form-ed, it will be decomposed by Zn according to

the equation

Zn + PbCI2== Pb(l) -}- ZnCl2 (52)

in which the standard free energy change is

-15,090 cal. at 390°C. Kellog5 has calculat-ed the residual zinc in lead treated in this way,on the assumption that equilibrium betweenthe metal and chloride phases is attained.

AG° = -15090 = -RTin apb x aznc', . . . (53)azn x apbct,

As the final lead is of over 99.9 per cent

purity, it can be assumed that apt, = 1.The final chloride has a mole fraction of

0-983. On the assumption that the solution

ox.

5

-10

-15

-20

-25

-30

-35

0uOh40

-50

-55

-60

-65

-70

Fe0'XFe+ iO, n Pe5i0a Ail fiofi d) Fe XFe+SiOa= e5i03(Atl Liquid)

„ a 5i

0 + Si

0i' MnS12F

Oa ° NI95iO

Nodal iGe3 toe t 55a

+2ye

1lClineeY15t1

t Fe

tC•}

x +i0} Ea n( Y 1i1C} f

X Q

^

- MLM 1510 9 5i0 ( FOrsterite)

hnt`l+ SiOi( tut 5n511 10>1^L^s)

a i

CaO+ 5iO aslo%(Wollastonite A o

m I^4 13W, : Lit i0S DCli.,O

-2ca0+A1i03,Sioa' C*,AI,Si0,

= ga Si0BQO • SiO t

x3c ao + Siot - Cass i os @

3

2Ca0+ Si Qt = Cn15i04

A1t03Si0 = AI15i0 ,,.(Gyante.)

AI1Oj. SIO1 _ All i03 (AtldaiuSit,.) ®

AIX03 * SiOi a AI=5103 (Simmanite•

0s0 • Siol Noa Si4o SUGGESTED ACCURACY.

® ± I K col .g.0 ± 31cg . 001.© = IoK%.Cai.p ±>to1Sgcal.

K10+SiOz a K,SiO3 O CHANGE OF RSTATE.

EACTANT PRODUCT

MELTING PT.BOILING: PT.

M

SUELIMATIOI 0

JRAr4$tTtCA PT.

S

T

$^

0 200 400 600 800 1000 1200

TEMPERATURE ,°C1400

1 t6 10 t41012

1010

I600

10

-I

10

-110

-310

10

'107

zO

F I G. 't)

CHATTERJEA & NIJHAWAN-THE RMO DYNAMIC ASPECTS OF CHEMICAL REACTIONS 125

of ZnC12 PbC12 is ideal, the activity of ZnC12

was taken as its mole fraction. Similarly,

the activity of PbCI2 was assumed as its mole

fraction of 0.017 while the azn accepted asthe reported value of 29Nzn. Substitutingthese values in equation (47) Kellog5 foundthat under equilibrium conditions, 0.00066per cent zinc should be present in the lead.In view of the assumptions made, the discre-pancy between the theoretical value and that

obtained in practice is not great.Recently a vacuum distillationi5 process

for separating silver from silver-zinc alloy

obtained from Parkes's process has beendescribed, The principle of separation by

vacuum distillation depends on the differ-ence of vapour pressures of the metals con-

cerned. As the vapour pressures of lead andzinc are much higher than that of silver,distillation under vacuum at 800°C. canseparate lead and zinc from metallic silver.

Vacuum dezincing of desilverized leadbullion has also been developed at the St.Joseph Lead Company and the Broken HillAssociated Smelters ( South Australia). Thisis carried out under a vacuum of 0-01-0.1 mm.mercury, when the zinc atoms from thebullion surface diffuse out to a neighbour-

ing condensing surface. The design of theapparatus ensures that there is no resistanceto the flow of zinc vapour apart from that due

to the residual gas pressure within thevacuum dezincer. Davey"' has discussed the

fundamental aspects of vacuum distillationprocesses with special reference to vacuum

dezincing and has shown that the actualremoval of zinc in practice has reasonablygood agreement with theoretical calculations.

Summary

The application of thermodynamic princi-ples to some of the chemical reactions involv-

ed in the metallurgy of lead has been made to

illustrate the importance of thermodynamicsand free energy data in studying chemical

reactions of value in extraction and refiningof metals. It has been mentioned that

chemical thermodynamics can predict thecourse of chemical reaction and enables to

calculate the value of equilibrium constant.The application to practical problems de-pends on the availability of activity data.In this brief article it has .not been possibleto discuss all applications of physical chem-

istry to the extractive metallurgy of lead.The reproduction of standard free energy

charts of various compounds in this papershould bring together for ready reference use-ful thermodynamic data scattered in the

technical literature, which may be appliedon similar lines to other cases than themetallurgy of lead extraction, provided thesimplifying assumptions made in this treat-

ment are, and remain, valid,

Acknowledgement

The authors wish to record their indebted-ness to those authorities in this field whoseworks have been referred to in the text.They are specially indebted to Richardsonand Jeffes and Kellog and Osborn for theirdiagrams which have been reproduced.

References

1. KELLY. K. K., " Contributions to the Data onTheoretical Metallurgy ", Bull . U.S. BureauMines, 384 (1935 ); 406 (1937); 407

(1937).2. ELLINGHAM , H. J. T., " Reducibility of Oxides

3.

and Sulphides ", J. Sac. Chem. Ind., 63 (1944),125.

RICHARDSON , F. D. & JEFFES, J. H. E., " The

Thermodynamics of Substances of Interest

in Iron and Steel Making from 0°C. to 2400°C.",

J.I.S.I ., 160 (1948 ), 261.

f--

FiG. 9 --- FREE ENERGIES OF FORMATION OF SILICATES AS A FUNCTLON OF TEMPERATURE, INVOLVING ONEGRAM-MOLE OF SiO^ ( RICHARDSON , JEFFES AND WITHERS" )

126

4.

SYMPOSIUM ON NON-FERROUS METAL INDUSTRY IN INDIA

RICHARDSON , F. D. & JEFFES, J. H. E., " The

Thermodynamics of Substances of Interest in

Iron and Steel Making ", J.I.S.I ., 171 ( 1952 ),

165.5. KELLOG, H. H., " Thermodynamic Relationship

in Chlorine Metallurgy Trans. A.I.M.E.,

188 (1950), 862.6. KELLOG, H. H., " Metallurgical Reactions of

Fluorides ", Trans. A,I.M .E., 191 (1951),

137.

7. OSBORN, C . J.. " Graphical Representation of

8.

9.

Metallurgical Equilibria", Trans. A.I.M.E.,188 (1950), 600.

RICHARDSON , F. D., JEFFEs, J. I-f. E. &

WITHERS, G., " The Thermodynamics of

Substances of Interest in Iron and Steel

Making ". J.I.S.I., 166 (1950), 213.DANNATT , C. W. & ELLINGHAM , H. J. T.,

" Roasting and Reduction Processes, AGeneral Survey ", Discussion Faraday Soc., 4

(1948 ), 126.

10. DJINGHEUZIAN, L. E., " Theory and Practice of

Roasting Sulphide Concentrates ", Canadian

lliss.:llet. Bulletin, 45(482) ( 1952), 352.

11. PERETTI, E. A., „ A New Method for Studying

the Mechanism of Roasting Reactions ",

Trans. Faraday Soc., 4 ( 1948 ), 174.

12. WENNER, it. R., Thermochemical Calculations

13.

14.

15.

(McGraw-Hill, New York ), (1941), 298.BETTERTON, J. O. & LEBEDEFF, Y. E., " Di-

bismuthizing Lead with Alkaline Earth

Metals Including Magnesium, and with Anti-

mony ", Traits. .4.7.1I. E., 121 (1936), 205.BETTERTON, J. 0., " Chlorine Dezincing in Lead

Refining ", Trans. A.I.M.E., 121 ( 1936 ), 264.SCHLECHTEN, A. W. & SHIN, C. H., " Vacuum

Furnace Separation of Silver from Zinc-

Silver ", Engineering & Min. Journal, 150(12)(1949 ), 80.

16. DAVEY , T. R. A., " Vacuum Dezincing ofDesilverized Lead Bullion ", Trans. A.I.M.E.,

197(1953),991.