sulphur vapours

7/26/2019 Sulphur Vapours

1/12

J. Chem . Thermodynamics1973, 5, 833-844

h e r m o d y n a m i c s o f su lp h u r v a p o u r

H A N S R A U , T . R . N . K U T T Y , a a n d

J . R . F. G U E D E S D E C A R V A L H O b

Philips Forschungslaboratorium Aachen GmbH, Aachen, Germany

Receive d 1 Janua ry 1973; in revised for m 26 February 1973)

Density measurements of sulphur vapour up to saturat ion in the temperature range

between 823 and 1273 K were performed. F ro m the results, together with literature data ,

a set o f equations was derived wh ich allows the partial pressures o f the different molecular

species to be calculated as a function o f tota l pressure and tem perature. R eal gas corrections

are included, so that these equations can b e used u p to 1273 K and the saturat ion pressure

of 144 arm. A FO RT RA N p rogram for ca lculat ion of the vapou r density and the par t ia l

pressures of 2, S~ . . . , Se from the total pressure and the temperature is avai lable from

the first author.

The standard enthalpy of form ation of S2(g) was found to be

AH (S2, g, 298.15 K ) = (31200 4- 50) calth mo 1-1.

1 Introduction

S u l p h u r v a p o u r s a r e v er y c o m p l e x in c o m p o s i t io n ; m o l ec u le s f r o m 1 to S s a re k n o w n

t o e x i st i n e q u i l i b r i u m . S i n c e t h e s t a b il i t y o f 2 i s h i g h , I m o l e c u l e s b e c o m e i m p o r t a n t

o n l y a t v e r y h ig h t e m p e r a t u r e s a n d l o w p r e s s u r e s. T h e r e f o r e , e i th e r t h e e q u i l i b r iu m

b e t w e e n I a n d 2 o r t h a t b e t w e e n 2 a n d a ll t h e o t h e r s p e c ie s f r o m S s t o 8 i s

d o m i n a n t . T h e f i r s t o f t h e s e e q u i l i b r i a i s w e l l k n o w n c~) a n d w i ll n o t b e d e a l t w i t h i n

t h i s s t u d y .

F o r e v a l u a t i o n o f t h e c o m p l e x e q u i l ib r i a b e tw e e n 2 a n d S s t o 8 t w o d i f fe r e n t

e x p e r i m e n t a l m e t h o d s w e r e u s e d : ( i) d e t e r m i n a t i o n s o f th e m e a n m o l a r m a s s a s a

f u n c t i o n o f t o t a l p r e s s u r e a n d t e m p e r a t u r e a n d ( ii) m a s s s p e c t r o m e t r y . T h e f ir s t t y p e

o f e x p e r i m e n t w a s p e r f o r m e d r e c e n t ly b y B r a u n e , P e t e r , a n d N e v e l i n g , ~2) w h o

m e a s u r e d v a p o u r d e n s it ie s u p t o 1 2 73 K a n d a b o u t 1 a t m . ~ M a s s s p e c t r o m e t r y w a s

d o n e b y B e r k o w i t z et aL 4-6~ a n d , w i t h a s p e c i al t e c h n i q u e , t h e e l e c t r o c h e m i c a l

K n u d s e n c e l l , b y D e t r y

e t aL c7~

T h e s t u d y o f B e rk o w i t z

e t a L

i s m o r e q u a l i t a t i v e i n

c h a r a c t e r , b e c a u s e d i st in g u i s h in g b e t w e e n p a r e n t i o n s a n d i o n s g e n e r a t e d b y f r a g m e n t -

a t i o n i n t h e m a s s s p e c t r o m e t e r w a s d i f f ic u lt , a n d a l s o b e c a u s e t h e s e n s i t iv i t y o f t h e

m a s s s p e c t r o m e t e r f o r t h e d i f fe r e n t s p ec ie s c o u l d o n l y b e e s t im a t e d .

T h e e l e ct r o c h e m i c al K n u d s e n c el l o f D e t r y et al. 7~ a l lo w s p a r e n t i o n s a n d f r a g m e n t s

t o b e m o r e o r l e s s d i s t i n g u i s h e d i n t h e s p e c t r o m e t e r . H e r e a n e l e c t r o c h e m i c a l c e l l

a Present address: In dia n Institute o f Science, Bangalore, Ind ia.

Present address: U niversi ty o f Porto, Facu lty of Engineering, Porto, P ortugal.

t Throughou t this pape r arm = 101.325 kP a; cal th = 4.184 J.


2/12

834 H. RAU, T. R. N. KUTTY, AND J. R. F. GUEDES DE CARVALHO

(Ag[AgIIAg2SIPt) is mounted in a Knudsen cell. With the help of the potential

applied to the cell the chemical potential of the sulphur in the Knudsen cell can be

changed within wide limits up to saturation. On the other hand, the current flowing

through the cell is a direct measure of the amount of sulphur penetrating through the

hole of the Knudsen

c e l l .

When the logarithm of the ion intensity in the mass spectrometer is plotted against

the potential, the different species should have different slopes. When the slope

observed for a certain species is in agreement with its theoretical value, this is thought

to be the parent ion intensity, because fragment ions should show more or less the

slope of the ions from which they were generated.

The current through the cell allows the mass spectrometer sensitivity to be calibrated,

because the total current must be the sum of the currents due to the different ions,

parent and fragmentary. Some difficulties arise for the big molecules. Here the slope

of the curve of the logarithm o f the ion intensity against potential will always show the

theoretical value, because the intensity of these ions cannot be increased by frag-

mentary ions (fragmentary ions will always be smaller). On the other hand, part of

these big molecules will become broken up by the electron beam in the mass spectro-

meter, and determinat ion of this part is not easy.

Mass spectrometric studies connected with a Knudsen cell are restricted to pressures

below about 10- 3 atm. This type of experiment was therefore done at low temperatures

only (for vapour not far from saturation) or on diluted vapours

e . g .

vapours above

CdS and ZnS), where only Sa and some $4, besides $2 as the main constituent, are

present.

Nothing is known of dense vapours not far from saturation at high temperatures,

where pressures become high. Mass spectrometric studies are excluded here and it is

only from p, V, T measurements that the equilibria in the vapour phase be derived.

One of us (H. R.)recently designed an all-silica Bourdon gauge(s) which allows

such density measurements to be made with the necessary accuracy. Such measure-

ments, up to 1273 K for diluted and dense vapours (up to their saturation point), are

presented in this paper. From the results and some data from the literature a set of

equations has been derived which allows the partial pressures of all the species from

S2 to $8 to be calculated from the total pressure and the temperature. Real gas

corrections are included in these equations, which can therefore be used between

473 and 1273 K and up to the respective saturation pressures.

2 Experimental

MATERIALS

The sulphur used was high purity sulphur from Johnson, Mat they and Co., London

and sulphur pur iss (i> 99.999 mass per cent) from Fluka AG, Switzerland. The first

sample was used either as delivered or after it had been twice distilled in vacuum to

remove some volatile impurities present (mainly H2S). No significant differences

between the results obtained with the different samples could be detected.


3/12

THERMODYNAMICS OF SULPHUR VAPOUR 835

APPARATUS AND MEASUREMENTS

The apparatus consisted of an all-silica Bourdon gauge of known internal volume,

which was mounted inside a furnace in an autoclave. The pointer o f the gauge extended

from the furnace and could be observed visually through optical windows in the

autoclave. The gauge was used as a null instrument: the internal pressure (sulphur

vapour) which forces the pointer out of the null position is exactly compensated by

external argon pressure. This argon pressure, maintained in the autoclave, is then

measured with a precise gauge (__+0.1 per cent) connected to the pressure line. Details

of the apparatus and its working principle are given elsewhere, t3, s) where the sensi-

tivity, accuracy, and thermal aspects are also discussed.

For a typical experiment a known quantity of sulphur was poured into the silica

Bourdon gauge, the volume of which was exactly known. After evacuation the gauge

was sealed off and mounted in the autoclave. The pressure exerted by the vapour

was measured for a number of temperatures. When the pressure was less than the

saturation pressure at that temperature, t3) the density of the vapour could be easily

calculated from the mass of the sulphur taken and the volume of the gauge.

3 Pr e v ious wor k

In the vapour there exists a complicated equilibrium between the different molecular

species from 2 to S8. A set of equilibrium constants is necessary in order to describe

this equilibrium state. Some thermodynamic values were already known and were

used for the calculations described below.

HEAT CAPACITIES

Values of Cp are known for 2, ~9) 6, ~1) and Sa, cx~) from spectroscopic studies. For

the other species the values of Cp had to be estimated. For that purpose the vibrational

heat capacity per degree of freedom of 2, 6, and Sa was drawn as a function of the

number of atoms in the molecule with the temperature as a parameter (figure 1). It

was assumed that the vibrational heat capacities of all the molecules lie on the same

curves. Thus the heat capacities of 3, 4, 5, and 7 were estimated to be the sum of

the vibrational heat capacities taken f rom figure 1 and the rotational and transitional

increments. The heat capacities used for the calculations are shown in table 1.

ENTROPIES

Entropies for the gaseous molecules are given in the literature for 2, c9) 6, ta~ and

Ss .c11'~2) These quantities are calculated from spectral data. Luft~12) and Guthrie

et aL ~ used different assignments of the known frequencies of 8, resulting in two

widely differing values for its s tandard entropy. Luft's value does not agree with the

equilibrium data of Detry et aL (7) and is expected to be incorrect. We therefore took

the value of Guthrie et aL c11

The entropies of the other molecular species are not known exactly. Values are

given by Detry et aL,(7) calculated from estimated vibrational frequencies. Better

values of these entropies had to be calculated from an adjustment of the equilibrium

constants to the measured vapour densities (see below).


4/12

8 3 6

H. RAU, T . R . N . KUTTY, AND J . R . F . GUEDES DE CARVALHO

[ J |

L- 100 0 K -4

, 2 . 0~ i - - .xx ~ ' ~ K7 0 0 K 1

~ 1.5

0.5 r 1 I I [

2 3 4 5 6 7 8

i

FIG U RE 1. Vibrational heat capacities C~(vib.) per degree of freedom o f gaseous sulphur mo le-

cules S~. Expe rimental points are from spectroscopic investigation. 9-11)

TAB LE 1. He at capacities Cp of gaseous sulphur m olecules. C~ is given by

Cdcalth K -1 m o1-1 = A + I O - a B T / K ) + 1 0 5 C T / K ) 2

(calth = 4.184 J)

A B C

$2 8.54 0.28 -- 0.79

$3 12.854 1.04 -- 1.554

$4 19.092 0.783 -- 2.820

$5 25.558 0.253 -- 3.771

$6 31.580 0.120 -- 4.400

$7 37.038 0.613 -- 4.723

Sa 42.670 0.860 -- 5.110

E N T H A L P IE S O F F O R M A T I O N

E n t h a l p i e s o f f o r m a t i o n c a n b e f o u n d i n t h e l i t e r a t u re f o r $ 2, ) a n d S s. (1 1) T h e v a l u e

f o r $ 2 g i v e n b y K u b a s c h e w s k i e t a l . , 9) ( 3 1 . 0 + 1 . 0 ) k c a lt h m o 1 - 1 , h a s f a r t o o w i d e

l im i t s o f e r r o r t o b e u s e d i n t h i s s tu d y . F r o m t h e p a r t i a l p r e s s u r e s o f S 2 i n t h e s a t u r a t e d

v a p o u r g i ve n b y D e t r y

e t a l . 7 )

a v a l u e o f 3 0 .8 3 k c a lt h m o 1 - 1 c a n b e c a l c u l a t e d .

T h e e n t h a l p y o f f o r m a t i o n o f $ 8 w a s c a l c u la t e d b y G u t h r i e e t a l . H ) t o b e 2 5 . 2 3

k ca lt h m o l - 1 , u s i n g t h e i r o w n e n t r o p y v a l u e a n d v a p o u r p r e s s u r e s o f r h o m b i c s u l p h u r

n e a r r o o m t e m p e r a t u r e t a k e n f r o m t h e l i t e ra t u r e. H e r e S s is t h e o n l y s p ec ie s i n t h e

v a p o u r p h a se . U n f o r t u n a t e ly , G u t h d e e t a L a p p a r e n t l y m a d e a m i s t a k e i n t h e i r

c a l c u l a t io n s . T a k i n g t h e p r e s s u r e s c i t e d b y t h e m a n d t h e h e a t c a p a c i t ie s o f $2 a n d

r h o m b i c s u l p h u r , t h e c o r r e c t v a l u e o f t h e e n t h a l p y o f f o r m a t i o n o f $8 is f o u n d t o b e

2 4 . 3 2 k ca l t h m o l - 2 .

A p p r o x i m a t e v a l u e s f o r t h e e n t h a lp i e s o f f o r m a t i o n c a n b e d e r i v e d f r o m t h e

c o m p o s i t i o n o f t h e s a t u r a t e d v a p o u r s b e t w e e n 4 7 3 a n d 6 7 3 K g i v e n b y D e t r y e t a L 7 )


5/12

THERMODYN AMICS OF SULPHUR VAPOUR 837

4 Calcu lat ions

R E A L G A S C O R R E C T I O N S

F r o m t h e p r e c e d i n g s e c t io n i t f o l l o w s t h a t t h e t h e r m o d y n a m i c p r o p e r t i e s o f S 3 , S , , S s ,

$ 6, a n d $ 7 a r e o n l y a p p r o x i m a t e l y k n o w n a n d t h a t th e s e q u a n t i fi e s h a v e t o b e f i tt e d

t o t h e d e n s i ti es m e a s u r e d h e r e . F u g a c i t y c o e ff ic i en t s h a v e t o b e i n c l u d e d t o c o r r e c t t h e

e q u i l i b r i u m c o n s t a n t s , w h i c h d e s c r i b e t h e e q u i l i b r i a b e t w e e n $ 2 a n d a l l t h e o t h e r

s p e ci es f o r r e a l g a s b e h a v i o u r w h e n p r e s s u r e s a r e h i g h .

T h e c r it ic a l p ro p e r t ie s o f s u l p h u r w e r e r e c e n t ly d e t e r m i n e d b y t h e a u t h o r s . O ) T h e r e

i t w a s a l s o m e n t i o n e d t h a t s u l p h u r v a p o u r s c a n b e a s s u m e d t o b e h a v e l i k e i d e a l

m i x t u r e s o f t h e d i f f e r e n t m o l e c u l a r s pe c ie s . I n o t h e r w o r d s , t h e p a r t i a l m o l a r v o l u m e s

o f t h e s p e ci es a r e e q u a l t o t h e v o l u m e s t h e p u r e s p ec ie s w o u l d h a v e u n d e r t h e p r e s s u r e

o f t he m i x t u re . H e nce t he f uga c i t y coe f fi c ien t s S s a r e equa l fo r a l l t he d i f f e r en t spec ie s

a n d d e p e n d o n o n l y t h e t o t a l p r e s s u r e a n d t h e t e m p e r a t u r e : (13)

( S2 ) --- qS(S3) . . . . . q~(Ss) = qS(Ptota,). (1)

A s i m i la r e q u a t i o n h o l d s f o r t h e p a r t i a l m o l a r c o m p r e s s i o n f a c t o r s Z s , w h e r e

p V = Z R T ,

(2)

w h i ch a r e equa l fo r a l l t he spec i e s t oo :

Z S 2 ) ---~ Z S 3 ) . . . . . Z S s ) = Z P t o ta l ). 3 )

V a l u es o f ~b a n d Z w e r e t a k e n f r o m t h e t a b l e s o f t h e g e n e r a l iz e d p r o p e r t i e s o f

pu r e ga se s an d l i qu i d s , (14) u s i ng a s pa r am e t e r s t he c r i ti c a l p rope r t i e s o f su l phu r . O )

T he t o t a l p r e s su re p i s a su m o f t he pa r t i a l p r e s su re s o f t he spec i e s :

8

p = E p S , ) . 4 )

S = 2

T h e e q u i l ib r i a :

s

= i S 2 , 5 )

a r e g i v e n b y t h e e q u i l ib r i u m c o n s t a n t s

Ks:

K f = p(S2)~/2qbf/2/p(S~)c~,

(6)

F r o m e q u a t i o n ( 6) :

p(S~) = p ( 2 )~ / 2 ~ ( ' / 2 - a ) /K s , (7)

h e n c e

8 )

p = F . p S 2 ) f / 2 4 ~ f / 2 - 1 ) / K ~ ,

f =

wh ere K 2 = 1 .

T h e con t r i bu t i on P s o f t he i - t h spec ie s t o t he dens i t y i s

Ps = P ( S 3 M d Z R T , ( 9)

w h e r e t h e m o l a r m a s s M s is g i v e n b y

Ms = 32 .064i g m o l - 1 . (10)

T h e d e n s i t y p o f th e v a p o u r i s th e r e f o r e g i v e n b y t h e s u m o f t h e c o n t r i b u t i o n s P s:

8

p = Z p s .

f = 2


6/12

838 H. RAU, T. R. N. KUTTY, AND J. R. F. GUEDES DE CARVALHO

A computer program was written which (1) interpolates the fugacity and the

compression factors from the tables of the generalized properties of pure gases and

liquids '(14) by parabolic functions, (2) calculates the equilibrium constants K~ from

a given set of enthalpies of formation, standard entropies, and heat capacities of all

the species, (3) calculates the partial pressures

p S i )

in such a way that the sum of

these is equal to the measured total pressure p according to equations (7) and (8), and

(4) computes the density p from these partial pressures according to equation (I 1).

As already mentioned, exact thermodynamic properties were not known for $3, $4,

$5, $6, and S7. We therefore started with the approximate values derived from the

work of Detry

e t

aL(7) The final set of thermodynamic properties should fulfil the

following conditions: in the temperature range of the investigations of Detry

e t

a/.(7)

the measured partial pressures of the different species should be represented by the

calculated pressures within the limits of error; and the calculated densities of the

vapours should be in agreement with the experiments over the whole range of tempera-

ture and pressure.

Detry

e t

aL(v) accurately measured the equilibria o f Ss with S 7 and of $8 with $6,

respectively. Error limits were small in these cases. Since the thermodynamic properties

of $8 are exactly known, the results of Detry

e t a l .

allow the thermodynamic properties

of $6 (enthalpy of formation) and o f $7 (enthalpy of formation and standard entropy)

to be calculated. At not too high temperatures $6, $7, and $8 are the main constituents

in the vapour phase when the total pressure approaches the saturation point. There-

fore, even if the partial pressures of $2 to S5 were known only approximately from

the data o f Detry

e t a L ,

the densities calculated on the basis o f their data should be in

reasonable agreement with the experiments. A first check in tha t direct ion showed

this not to be the case. Even variations of the equilibrium constants for the formation

of Sa, $4, and $5 f~m S2 could not bring experimental and calculated values into

agreement.

Two possible reasons for this behaviour were considered: either tautomers of the

bigger molecules are present at higher temperatures, or the enthalpy of formation of

$2 derived from the data of Detry

e t

al. (7) is not completely correct.

The possible presence of tautomers of $8 in high temperature vapours was discussed

by Guthrie

e t a l . a a)

on the basis of machined models of the $8 molecule. They found

that besides the normal molecule of D d symmetry ( crown modification) two other

molecules o f D2a and of Ca symmetry should be taken into account. Estimates of the

difference in internal energy of these molecules compared with the crown modification

were made by Guthrie

e t a L a l )

from the energy of bond rotations of molecules like

S2C12, and by Pauling(aS) from the difference in the enthalpies of formation of $6

and Ss, with quite different results. These lie in the range between 4.9 kcalth tool -a

(Pauling) and 9 to 15 kcalta tool -a (Guthrie

e t a L ) .

The symmetry numbers o f the tautomeric molecules are 2 (D2a) and 8 (C0 , (ta)

where the second number must be doubled because of d- and 1-isomers. For the

simplest case, where only the symmetry number of the molecules contributes to the

entropy, one has for Ks, the equilibrium constant of the reaction:

S8 -- 4S2, 1 2 )


7/12

THERMODYNAMICS OF SULPHUR VAPOUR 839

the expression:

K~ = Ks/{1 + 18 e x p - E / k T ) } , (13)

where/(8 is the constant of reaction (12) formulated for the crown modification only

and E is the difference in internal energy between the crown form and the 18 tauto-

meric molecules. Differences in moments of inertia and vibrational frequencies from

those of the crown modification will alter the entropy contribution somewhat from

Rln 18.

Similar tautomeric molecules could be thought of for the other molecules, and a

set of equations similar to equations (13) can be expected in this case. When the energy

differences lie below about 8 kcalth mo1-1, as estimated by Pauling,(15) these tauto-

meric molecules will contribute appreciably to the vapour composition.

We have attempted to fit the experimental results to equilibrium constants based on

the thermodynamic properties given by Detry

et

aL, (7) especially the enthalpy of

formation of 2 derived from their results, taking into account the possible presence

of tautomeric molecules in the way discussed here. The result was negative: (i) syste-

matic deviations of the calculated densities from the measured ones at medium

temperatures were found, and (ii) the partial pressures of 6, S7, and S s showed, at

lower temperatures, a completely different variation with temperature to that found

experimentally by Detry et al. 7) Consequently, the presence of significant amounts of

tantomeric molecules even at the highest temperatures under consideration was ruled

out. This means that the energy difference between the tautomeric and the normal

molecules is higher than about 10 kcalth tool-1.

The second possibility, tha t the enthalpy of formation of Sz(g) is incorrect, implies

that the partial pressures of Sz in the saturated vapours given by Detry

et aL 7)

are

not correct. This is not easy to understand from the type o f measurements (electro-

chemical Knudsen cell) performed. The calibration of the Knudsen cell is then easy,

because 2 is the main or even only constituent in diluted vapours, and the extra-

polation to the saturation point was done with the theoretical slope of the curve:

logarithm of the current connected with the Sz molecule against the potential of the

cell. This seems to be a sound procedure. On the other hand, it will now be shown that

the enthalpy of formation of 2 is higher by some 100 calth mo1-1 than that derived

from the data of Detry

et

a/. (7) Perhaps there was an overpotential or an electrical

leakage in the cell used by these authors.

When the enthalpy of formation of S2 is varied, then, the bigger the molecules

involved, the greater is the variation of the equilibrium constants of the reactions

S ~ = i S 2 . 5 )

Thus, with a value of

AH~(S2, g, 298.15 K) = 31.20 kcalth mol- ~,

the measured densities at all temperatures and the partial pressures of S 6 to S a found

by Detry

et al. 7)

at temperatures between 473 and 673 K are represented well by the

values calculated from the equilibrium constants (see equations (4) to (11)). Some

smaller corrections of the thermodynamic properties of Sa, 4, and Ss were necessary

in order to bring the values calculated as near as possible to those measured. These


8/12

84 H . R A U , T . R . N . K U T T Y , A N D J . R . F . G U E D E S D E C A R V A L H O

c o r r e c t io n s a r e w i t h i n t h e e r r o r l i m i t s g i v e n b y D e t r y et a f o r t h e i r r e s u l t s . T h e

t h e r m o d y n a m i c p r o p e r t i e s o f th e d i ff e re n t m o l e c u l a r s p e c i es f i t t ed t o t h e e x p e r im e n t a l

r e s u l t s a re g i v e n i n t a b l e 2 . T a b l e 3 c o m p a r e s t h e m e a s u r e d v a p o u r d e n s i t i es (p r e s e n t

v a l u e s ) w i t h t h e d e n s i t i e s c a l c u l a t e d f r o m t h e e q u a t i o n s f o r t h e e q u i l i b r i u m c o n s t a n t s

u s i n g t h e d a t a i n t a b l e s 1 a n d 2 . T a b l e 4 c o m p a r e s t h e p a r t i a l p r e s s u r e s d e r i v e d f r o m

t h e s e e q u a t io n s w i t h t h o s e f o u n d e x p e r i m e n t a l l y b y D e t r y

et

a l . (7 ) A s c a n b e s e e n ,

t h e d e n s i t ie s a g r e e m o s t l y w i t h i n _+ 4 p e r c e n t w i t h t h o s e c a l c u l a t e d ; a n d t h e p a r t i a l

p r e s s u r e s , e x c e p t t h o s e o f S 2 w h i c h a r e d e a r l y s m a l l e r , a r e i n a c c e p t a b l e a g r e e m e n t

w i t h t h e e x p e r i m e n t a l v a l u e s .

T h e d e n s i t i e s m e a s u r e d b y B r a u n e , P e t e r , a n d N e v e l i n g (2) a r e a l s o i n c l o s e a g r e e m e n t

w i t h t h o s e c a l c u l a t e d f r o m t h e d a t a g i v e n i n t a b l e s 1 a n d 2 .

F i g u r e 2 i s a s u r v e y o f t h e m o l e f r a c t i o n s o f t h e d i f f e r e n t s p ec i e s i n t h e s a t u r a t e d

v a p o u r s b e t w e e n 7 7 3 a n d 1 27 3 K . A t l o w t e m p e r a t u r e s t h e b i g m o l e c u l e s , S 6 t o S s ,

p r e d o m i n a t e , b u t t h e i r a m o u n t s d e c r e as e w i th t e m p e r a t u r e , a n d s o o n 2 a n d S a

p r e d o m i n a t e .

TA B LE 2 . The r m od yna m ic da t a o f t he ga se ous su lphur m o le c u le s S~ ( i = 2 t o 8 ). The s t a nda r d s t a t e

is the idea l gas a t 1 a tm p ressure and 298.15 K

(caltn = 4.184 J)

i AHt /kca lt~ to ol - 1 S /ca l~hK - x m o l - 1

2 31.20 54.40 ()

3 33.81 64.39

4 34.84 74.22

5 26.14 73.74

6 24.36 84.60 el)

7 27.17 97.41

8 24.32 102 .76 (11)

TA B LE 3 . C om p a r i son o f c a l cu l a t e d a nd m e a su r e d va p our de ns i t i e s p a s a f unc t ion o f p r e s su re p .

The c a l c u l a t i ons a r e pe r f o r m e d wi th t he t he r m odyna m ic da t a i n t a b l e s 1 a nd 2 a c c o r d ing to

equa t ions (8) and (11) . Exp er imen ta l resul ts f rom th is wo rk only .

(a tm - - 101.325 kPa)

p(expt) p(ca lc ) p(expt) p(ca lc )

p / a t m p / a t m

m g c m - a m g c m - a m g c m - 8 m g e m - a

T = 823 K

0.689 1.721 1.755 1.864 5.409 5.454

0.762 1.852 1.974 2.295 7.005 6.863

1.157 3.059 3.191 3.150 9.695 9.723

1.757 5.076 5.104 3.559 11.28 11.18

T - - 873 K

0.905 1.721 1.797 2.783 7.005 7.043

0.966 1.852 1.952 3.695 9.695 9.786

1.442 3.059 3.215 4.164 11.28 11.23

2.109 5.076 5.084 4.008 10.64 10.75

2.218 5.409 5.397 4.722 13.09 12.98


9/12

p / a t m

T H E R M O D Y N A M I C S O F S U L P H U R V A P O U R

T A B L E 3 continued

p exp t ) p c a lc ) p exp t )

p / a t m

m g c m 3 m g c m - z n ag c m - 3

841

p cale)

m g c m - 3

T = 923 K

1.204 1 .721 1 .802 5 .049 11.28 11.39

1.273 .852 1 .941 5 .661 13.09 13.10

1.817 3 .059 3 .12 0 7 .213 7 .46 17.58

2 .651 5 .076 5 .094 7 .445 18 .51 18 .27

2 .770 5 .409 5 .387 8 .316 20 .87 20 .90

3 .414 7 .005 7 .017 8 .486 21 .55 21 .42

4 .471 9 .695 9 .808 9 .030 22 .95 23 .11

4 .845 10 .64 10 .82

T = 973 K

1.551 1 .721 1 .770 6 .893 13.09 12.98

1 .620 1 .852 1 .874 8 .764 17 .46 17 .73

2.313 3 .059 3 .021 8 .982 18.51 18.30

3 .396 5 .076 5 .078 10 .04 20 .87 21 .11

3 .518 5 .409 5 .326 10 .76 22 .95 23 .06

4 .301 7 .005 6 .972 12 .13 27 .31 26 .84

5.531 9 .695 9 .73 2 13.93 31.88 3 .96

6 .022 10 .64 10 .88 15 .45 37 .55 36 .44

6.246 11.28 11.41

T = 1023 K

T = 1173 K

12 .83 10 .64 10 .67 55 .66 79 .82 78 .86

21 .94 20 .87 21 .02 63 .21 100 .0 95 .90

35 .25 40 .08 40 .22 71 .31 121 .2 115 .9

46 .54 59 .45 60 .21

T----- 1273 K

15 .32 10 .64 10 .69 100 .7 120 .4 122 .5

27 .92 20 .87 21 .17 102.3 121 .2 125 .8

46 .82 40 .08 40 .19 109 .4 142 .6 140 .9

62 .88 59 .45 59 .89 120 .4 168.1 168 .9

77 .30 79 .82 80 .79 130 .8 211 .7 202 .1

89 .96 100 .0 102 .1 143 .6 254 .1 259 .7

1.858 1 .721 1 .724 10.74 17.46 17.55

1.980 1 .852 1 .861 11.04 18.51 18.21

2 .886 3 .059 2 .979 12 .32 20 .87 21 .12

4 .293 5 .076 5 .031 13 .12 22 .95 22 .99

4 .430 5 .409 5 .248 14 .72 27 .31 26 .82

5 .417 7 .005 6 .894 16 .92 31 .88 32 .30

6 .893 9 .695 9 .586 18 .54 37 ,55 36 .49

7 .778 11 .28 11 .31 22 .35 47 .52 46 .84

8 .574 13 .09 12 .92 22 .63 47 .67 47 .62

T---- 1073 K

2 .109 1 .721 1 .723 15 .16 20 .87 21 .02

2 .266 1 .852 1 .865 15 .25 20 .87 21 .19

3 .429 3 .059 2 .998 16 .04 22 .95 22 .74

5 .233 5 .076 5 .024 17 .98 27 .31 26 .64

5 .437 5 .409 5 .274 20 .65 31 .88 32 .32

6 .655 7 .005 6 .849 22 .52 37 .55 36 .47

8 .520 9 .695 9 .516 23 .86 39 .13 39 .52

9 .316 10 .64 10 .74 24 .29 40 .08 40 .52

9 .642 11 .28 11 .26 27 .03 47 .52 47 .03

10 .58 13 .09 12 .77 27 .44 47 .67 48 .04

13.20

7 .46 17.35 29.97 55.63 54.35

13 .56 18.51 17 .99


10/12

84

r I . R A U , T . R . N . K U T T Y , A N D J . R . F . G U E D E S D E C A R V A L H O

T A B L E 4 . C o m p a r i s o n o f t h e p a r ti a l p r e s su r e s p , i n s a t u r a te d s u l p h u r v a p o u r s g i v e n b y D e t r y

et al. cv~

f o u n d b y m e a s u r e m e n t s w i t h t h e e l e c t r o c h e m i c a l K n u d s e n c e ll , w i t h t h o s e c a l c u l a te d f r o m

e q u a t i o n s ( 8 ) a n d ( 11 ) u s i n g t h e t h e r m o d y n a m i c d a t a i n t a b le s 1 a n d 2

(a tm = 101.325 kPa )

S p e c ie s p d a t m S p e c ie s p , / a t m

D e t r y

e t a l .

T h i s s t u d y D e t r y

e t a L

T h i s s t u d y

T = 4 7 3 K T = 5 2 3 K

2 1 . 40 x 10 -6 8 .92 10 -7 2 2 .60 X 10 -8 1 .69 10 -5

Sa 1.70 x 10 -7 1.47 x 10 -7 Sa 3.38 10 -6 3.23 10 -6

4 1 .65 x 10 -T 1 .26 X 10 -7 4 3 . 04 X 10 -8 2 .81 10-n

S~ 1 .56 x 10 -5 1 .93 10 -n 5 1 .72 10 -4 1 .63 x 10 -4

Se 5 .50 x 10 -4 5 .63 X 10 -4 6 3 .60 X 10 -a 3 .65 10 -3

ST 3 .28 X 10 -4 3 .30 X 10 -4 ST 2 .63 10 -a 2 . 61 X 10 -3

8 1.89

x 1 0 8 1 . 8 8 1 0 3

8 1 . 02 10 - z 1 .02 x 10 -2

T = 5 7 3 K T = 6 2 3 K

2 2 .68 10 -4 1 .85 x 10 -4 2 1 .90 x 10 -a 1 .34 x 10 -z

Sa 3 .66 x 10 -8 3 .93 X 10 -8 Sa 2 .68 10 -4 3 .08 10 -4

4 3 .25 x 10 -5 3 .42 10 -8 4 2 .15 10 -a 2 .65 x 10 -4

5 9 . 64 1 0 - 4 8 . 8 1 X 1 0 - 4 8 4 . 2 0 1 0 - a 3 .4 3 X 1 0 - 3

5 1 .60 X 10 -2 1 .56 X 10 -2 8 5 .25 10 -z 4 .96 10 -2

ST 1 .27 10 -2 1 .30 X 10 -2 7 4 .55 10 -2 4 .64 10 -2

8 3 .64 10 -2 3 .65 10 -2 5 9 .70 10 -z 9 .87 10 -2

T = 6 7 3 K

Sa 9 .40 x 10 -a 7 .11 10 -a 6 1 .37 x 10 -1 1 .28 x 10 -1

Sa 1.34 x 10 -a 1.73 x 10 -a 7 1.26 x 10 -1 1.31 x 10 -1

4 1.04 10 -a 1.47 x 1 0 a S o 2 . 1 4 x 10 -1 2 .19 x 10 -1

So 1 .43 x 10 -2 1 .05 x 10 -a

T h e a c c u r a c y o f t h e t h e r m o d y n a m i c p r o p e r t i e s i n t a b l e s 1 a n d 2 c a n h a r d l y b e

e s t i m a t e d . T h e e n t h a l p y o f f o r m a t i o n o f 2 m a y b e q u i te c o rr e c t , p e r h a p s t o w i t h i n

___ 5 0 c a lt a m o l - 1 , b e c a u s e a v a r i a t i o n o f th i s o r d e r o f m a g n i t u d e a l r e a d y r e s u l t s i n a

s y s t e m a t i c d e v i a t i o n o f t h e c a l c u l a t e d f r o m t h e m e a s u r e d d e n s i t ie s . T h e o t h e r v a lu e s

m a y b e s l i g h t l y l es s a c c u r a t e , b e c a u s e s o m e o f t h e m c a n b e v a r i e d a p p r e c i a b l y

( a l t h o u g h n o t i n d e p e n d e n t l y ) w i t h o u t m u c h e f fe c t. T h i s is e s p e c ia l l y t r u e f o r t h e

m i n o r c o n s t i t u e n ts , 4 a n d S s , t h e p r o p e r t i e s o f w h i c h a r e c e r ta i n l y n o t v e r y c l o se l y

d e f in e d . T h e e n t r o p y o f 6 ( l o) i s p e r h a p s n o t c o m p l e t e l y c o r r e c t , a s c a n b e s e e n f r o m

t a b l e 4 . H e r e t h e p a r t i a l p r e s s u r e o f 6 d e v i a t e s i n a s y s t e m a t i c m a n n e r f r o m t h e v a l u e s

d e t e r m i n e d b y D e t r y

e t a l .

O n t h e o t h e r h a n d t h e t h e r m o d y n a m i c p r o p e r t i e s i n t a b l e s 1 a n d 2 r e p r e s e n t a

s y s t e m w h i c h i s o n t h e w h o l e c o n s i s t e n t w i t h t h e e x p e r i m e n t a l r e su l ts . I f m o r e d e t a i le d

i n f o r m a t i o n o n t h e p r o p e r t i e s o f o n e o f t h e c o n s t i t u e n t s b e c o m e s a v a i l a b l e , it w i l l

p e r h a p s b e n e c e s s a r y t o r e - e v a l u a t e t h e o t h e r v a l u e s t o o .

T h e e q u i l i b r i u m c o n s t a n t K 3 f o r t h e r e a c t i o n

3 = g2S2, (14 )

i s i n c l o s e a g r e e m e n t w i t h t h e v a l u e f o u n d b y B e r k o w i t z a n d M a r q u a r d t (4) f r o m m a s s

s p e c t r o m e t r i c w o r k o n v a p o u r s a b o v e C d S a n d Z n S . O n t h e o t h e r h a n d , t h e p ar t i a l

p r e s s u r e s o f 4 a t h i g h t e m p e r a t u r e s a r e fa r le s s t i t a n e x p e c t e d f r o m t h e e x p e r im e n t s


11/12

T H E R M O D Y N A M I C S O F S U L P H U R V A P O U R 8 4

1.0

$2

0.5

0.2 S3

$4

0 . 1 -

0.05

0.02

7 I t

.01 ~ F I

800 900 1000 1100 1200 1300

T / K

FIG UR E 2. M ole fractions x of the different molecular species in saturated sulphur vapours as

calculated from the data in table 1 and 2 according to equation (8).

o f t h e s a m e a u t h o r s . A l l t h e o t h e r c o n s t a n t s d o n o t d i f fe r m u c h f r o m t h o s e e x p e c t e d

f r o m t h e s t u d y o f D e t r y e t a L c7~

T h e c a l c u la t io n s p r e s e n t e d h e r e a r e b a s e d o n t w o a s s u m p t i o n s : ( i) t h e h e a t c a p a c i -

t i e s c a n b e i n t e r p o l a t e d i n t h e w a y d e s c r i b e d a b o v e a n d ( i i ) t h e f u g a c i t y a n d c o m -

p r e s s i o n c o e ff ic i e n ts o f a ll t h e s p e c i es i n t h e g a s p h a s e a r e f u n c t i o n s o f t e m p e r a t u r e a n d

t o t a l p re s s u re o n l y a n d c a n b e t a k e n f r o m t h e t a b l e o f g e n e ra l iz e d p r o p e r t ie s o f p u r e

gases an d l iqu ids . (~4)

T h e i n t e r p o l a t i o n o f t h e h e a t c a p a c it ie s m a y b e d o u b t f u l f o r S 3, S4 , a n d S 5 a n d m a y

i n t r o d u c e s o m e e r r o r i n th e t h e r m o d y n a m i c p r o p e r ti e s d e r i v e d f r o m t h e f it ti n g o f th e

e q u i l i b r i u m c o n s t a n t s s o a s t o r e p r o d u c e t h e m e a s u r e d d e n s i t i e s a s c l o s e a s p o s s i b l e .

T h e s p e c ie s S~ a n d S 4 a r e o f i m p o r t a n c e o n l y a t h i g h t e m p e r a t u r e s ( s e e f i g u r e 2 ) . A t

l o w t e m p e r a t u r e s t h e i r m o l e fr a c t io n s w e r e a s s u m e d t o b e n e a r t h o s e f o u n d b y D e t r y

e t a l . 7 ) T h u s , i f th e h e a t c a p a c i t ie s o f t h e s e s p e c ie s w e r e n o t q u i t e c o r r e c t , t h i s w o u l d

r e s u l t i n a c e r ta i n , b u t s m a l l, i n a c c u r a c y o f t h e i r e n th a l p i e s o f f o r m a t i o n a n d e n t r o p i e s ,

w h i c h w e r e d e r i v e d f r o m t h e e q u i l i b r i u m c o n s t a n t s b y a s e c o n d - l a w t r e a t m e n t . S i m i l a r

a r g u m e n t s h o l d f o r S s t o a h i g h e r d e g r e e , b e c a u s e S 5 i s a l w a y s p r e s e n t a t l o w m o l e

f r a c t io n s o n l y . T h e h e a t c a p a c i t y o f t h e b i g S 7 m o l e c u l e is e x p e c t e d t o f i t w e l l t o t h e

cu r v es o f f i g u r e 1 .

T h e a s s u m p t i o n c o n c e r n i n g t h e f u g a c i t y a n d c o m p r e s s io n c o e f fi ci e nt s h a s b e e n

d i s c u ss e d i n c o n n e x i o n w i t h t h e e s t i m a t i o n o f t h e c r i ti c a l q u a n t i t i e s o f s u l p h u r . (3 ) I f

t hi s a s su m p t i o n w e r e n o t c o m p l e t e l y t r u e , t h is w o u l d h a v e n o g r e a t i n fl u e n c e o n t h e

t h e r m o d y n a m i c d a t a p r e s e n t e d i n t a b l e 2 . T h e s e v a lu e s a r e o n l y p a r t i a ll y b a s e d o n t h e

d e n s i t y m e a s u r e m e n t s a t h i g h p r e ss u r e s . I n m o s t c a se s , w h e n p r e s s u r e s a r e n o t t o o

h i g h , t h e fu g a c i t y a n d c o m p r e s s i o n c o e f f i c ie n t s a r e c l o s e t o u n i t y . O n t h e o t h e r h a n d ,

t h e f a c t t h a t t h e t r e a t m e n t a p p l i e d h e r e d e s c ri b e s th e e x p e r i m e n t a l r e s u l ts b o t h a t

l o w a n d a t h i g h p r e ss u r e s s u p p o r t s s t r o n g l y t h e a s s u m p t i o n s m a d e .


12/12

844 H . R A U , T . R . N . K U T T Y , A N D J . R . F : G U E D E S D E C A R V A L H O

5 Com puter program

A c o m p u t e r p r o g r a m w r i tt e n in F O R T R A N a c c o r d in g t o t h e s p e c if ic a ti o ns o n th e

p rev ious page i s ava i l ab le f rom H. R . The da t a fo r c a l cu l a t i on o f t he fugac it y and

com pres s ion coe f f ic i en t s a r e a l so p rov ided . Th i s p ro g ram a l lows t he p a r t ia l p r e s su re s

o f 2 t o 8 and t he dens i t y o f t he vapo ur t o be ca l cu l a t ed f rom the t o t a l p re s su re and

the t empe ra tu r e .

R E F E R E N C E S

1 . B ud in inka s , P . ; Edw a r ds , R . K . ; W a h lbe c k , P . G . J . Chem. Phys . 1968, 48, 2859.

2 . Braune , H. ; Pe te r , S . ; Neve l ing , V. Z. Naturforsch. 195 , 6a, 32.

3 . R a n , H . ; K u t ty , T . R . N . ; G ue de s de C a r va lho , J . R . F . J . Chem. Thermodynamics 1973, 5, 291.

4 . B e r kow i t z , J . ; M a r qua r d t , J. R . J . Chem. Phys. 1963 , 39, 275.

5 . B e r kow i t z , J . ; C hup ka , W . A . J . Chem. Phys . 1964, 40, 287.

6 . Berkow itz , J . ; L i f sh i tz , C . J . Chem. Phys. 1968 , 48, 4346.

7 . D e t r y , D . ; D r o w a r t , J . ; G o ld f inge r, P . ; K e l l e r , H . ; R ic ke r t , H . Z . Phys . Chem. N .F. 1967, 5 5, 314.

8 . R a n , H . Rev . Sc i . Ins trum. 1972 , 43, 831.

9 . Kubaschewski , O. ; Evans , E . L1. ; Alcock, C . B . Metallurgical Thermochemistry 4th edi t ion ,

P e r ga m o n P r e s s : O xf o r d . 1967.

10 . B e r kow i t z , J . ; C hnpk a , W . A . ; B r om e l s , E . ; B e l f o r d , R . L . J . Chem. Phys. 1967 , 47, 4320.

11. G u th r i e J r . , G . B . ; S c o t t , D . W . ; W a dd ing ton , G . J . Amer. Chem. Soc . 1954 , 76, 1488.

12 . Lu f t , N . W . Monatsh . Chem. 1955, 86, 474.

13. K or t i im , G . Einfiihrung in die Chemisehe Thermodynamik 3r d e d i t i on , V e r l a g V a nde nhoe c k a nd

R u pr e c h t : G 6 t t i nge n . 1963 , p . 202 .

1 4. H o u g a n , O . A . ; W a t s o n , K . M . ; R a g a t z , R . A . ChemicalProcess Principles pa rt I I second edi t ion ,

John W i le y S ons , I nc . : N e w Y o r k , Lon don , S idne y . 1966 .

15 . Paul ing , L . Proc . Nat . Acad. ScL U.S . 1949, 35, 495.

sulphur vapours

Documents