The hydrate of CCl 4 and its phase equilibria with O2 and N2

h- o

The hydrate of e c u

and its phase equilibria with O2and N2

*J1 h-^ - rvj

BIBLIOTHEEK T U Delft P 1121 5111

Een groot aantal mensen heeft tot het hier voor u liggende proefschrift in belangrijke mate bijgedragen. Het is mij een oprecht genoegen een aantal van hen hiervoor met name te bedanken, y

Ben Sonneviile bedank ik voor de geduldige wijze waarop hij de langdu-rige experimenten heeft verricht.

Ik dank Cor Peters voor het schrijven van de computerprograirana's, Hans Grondel heeft een deel van de apparatuur ontworpen en de fraaie tekeningen ervan gemaakt, ik dank hem daarvoor; ook dank aan de heren Ruis en Van Willigen die de overige tekeningen hebben verzorgd. Mevrouw Janke Esselink-Postma dank ik voor de verzorging van het type-werk.

Aanmijnouders

VoorMarja,

13 14 42 45 90 96 09 eq. eq. eq. eq. e q . ^ ? ^ - n/yi IT T^ i- . . ( O . Q(N,V.T) ( j j ^ y / , 7 ) : (N^(, _ y ) / i 7 ) . ( 8 ) : F and F- a r e per niHJCl) mole,

n(H20)/17RT = n(Il20)RT/17 ( 4 8 ) , ( 4 9 ) : ^ ( n H ^ O ) " = Vi°(17a20) ( 5 6 ) , ( 5 8 ) , ( 5 9 ) : y(H,0,G)° - U°(H,0,G) T T ^ (A-4): / = - ; T T _{0 o} bottom page: v, = v eq. ( C - 9 ) : .049902 - .049902 t 1

CONTENTS

I Introduction 1 1.1 Gas hydrates 2 1.2 The hydrate of CCl, , with and without help gas 6

1.3 Statistical thermodynamic description of gas hydrates 12 1.4 Classical thermodynamic description of gas hydrates 19

1.5 Synopsis 22 II Procedure and apparatus 25

11.1 Instruments and materials 25 11.2 The measurements of the vapor pressure of CCl,, low

pressure measurements of CC1,-H„0 27 11.3 Low pressure measurements at the systems 0„-CCl,-H„0

2 4 2

and N„-CC1,-H„0 29 2 4 2

11.4 Measurements at the systems 0„CCl,H^O and N„CC1 -2 4 -2 -2 4

H„0 with the apparatus of Cailletet 31 11.5 High pressure measurements with the window autoclave 33

11.6 Lowering of the quadruple points HiceL. and HL.L.G of

CC1,-H 0 by addition of ethylene glycol 37

III Results and calculations 41

111.1 CCl, 41 4

111.2 CC1,-H„0 41

4 I

III.2.a HiceG, HLjG and HL„G equilibria 42 III.2.b HSLj, HSL and HLjL equilibria 51 III.2.C The lowering of the quadruple points HiceL„G and

HL.L.G by adding ethylene glycol 111.3 0_-CCl,-H,,0 and N.-CC1,-H^0

2 4 2 2 4 2

III.5 Conclusions 74 IV Calculations with the LJD cell model 77

IV.1 0 and N in the small cavities of CCl, hydrate 77

IV.2 The structure I hydrate of 0 and N 78 IV.3 Calculation of Ay „ for structure II 83

a 3

IV.4 Conclusion 83

Appendices

A Thermodynamic calculation of the vapor pressure

curve and the melting curve of CCl, 89

A. 1 Derivation of the model 89 A. 2 The vapor pressure curve of CCl, 91

A.3 The melting curve of CCl 94 B Calculation of the fugacities of N and 0„, pure and

in their mixtures 99 B.l The fugacity of pure substances 99

B.2 Calculation of the fugacities of N„ and 0„ in their

mixtures using activity coefficients 102 C The activity of water in mixtures of water and

ethylene glycol 108 C.l The activity of water in the presence of ice 108

C.2 The activity of water in mixtures of water and

ethylene glycol 110 D Solubility of 0 and N in CCl and H O 122

D.l Solutions of gases in liquids treated as liquid

mixtures 122 D.2 Henry's constant; heat and entropy of solution 125

D.3 The solubility of 0 and N in CCl, 127 D.4 The solubility of 0 and N in water 129

The hydrate of CCl^

This research is one of a series of investigations on gas hydrates carried out in our laboratory [1,2,3,4,5], more specifically it is a continuation of the work of Van Cleeff on the structure I hydrates of N„ and 0 [4]. After his discovery of these hydrates it was of practi-cal interest to investigate whether they could be used to separate 0„-N„ mixtures (air). In an early stage of this investigation the dif-ference in composition between the gas phase and the hydrate phase appeared to be small. At low temperatures the rate of formation of the hydrate seems to be unpromisingly low moreover, and at room temperature

the pressure of formation for these hydrates is over one thousand atmospheres, so we decided to use another type of hydrates.

The pressure of formation can be lowered appreciably by using structure II hydrate with large molecules in the large cavities. CCl, was chosen to serve this purpose, mainly because of its inertness

towards 0„. The hydrate of CCl, itself was not known by then, although we were convinced and had calculated that it should exist: we observed it for the first time in a measurement of the melting curve of CCl,,

*)

carried out by two third-year students . To investigate the applicabi-lity of CCl,-hydrate at the separation of gas mixtures two types of data are required: data on phase equilibria and on the rate of forma-tion. Our subject concerns the former type, but from the measurements on phase equilibria some information about the rate of formation can be obtained. It appears to be very difficult to obtain data on the hydrate

2

composition from measurements, directly or indirectly, so an alternati-ve method is needed, particularly for the determination of gas-hydrate composition diagrams with gas mixtures: with a suitable model these compositions can be calculated (cf. III.4.a and III.4.b).

Such a model (and a way to calculate the inclusion parameters) has been derived by Van der Waals I 6J for quinol inclusion compounds and extended to gas hydrates by Van der Waals and Platteeuw using statisti-cal thermodynamics (cf. 1.3). Their model is in fact the ideal solution and it can be handled with classical thermodynamics too (cf. 1.4). When this investigation progressed, the perspective of its practical appli-cation became increasingly gloomy (because of the reaction rates), but its theoretical implications remained interesting. Since the work of Clausen [7] and Von Stackelberg and his coworkers [8] to reveal the structure of these hydrates in the early fifties and the development of the model mentioned above, many investigators carried out experiments and calculations on this subject. A great deal of these publications are mentioned by Davidson in his review [9]. Davidson discusses the application of the model to calculate the inclusion parameters: it appears there are still (after fifteen years since the model was published) loose ends, mostly because of lack of experimental data. Aaldijk [10] has shown that assumptions about the Lennard-Jones para-meters of water (cf. IV.2) are incorrect.

In this investigation our first aim is to collect data which may be of practical interest. Secondly we test the ideal solution model and use it to forecast gas-hydrate compositions (cf. III). From a physico-chemical point of view it is worthwhile to evaluate the usefulness of the Lennard-Jones Devonshire potential in the approximation of Van der Waals and Platteeuw in describing the inclusion of molecules by the ice lattice (cf. IV).

I.1 Gas hydrates

not stable in itself, and enclosed molecules of other substances, most-ly apolar. The ice lattice is built so spacious that cavities occur in it, which are large enough to contain molecules of moderate size. Because the "host lattice" encloses the "guest molecules" this type of solids is called inclusion compounds or clathrates. The deviation from the ideal stoechiometry can be larger with these inclusion compounds than with normal compounds, because vacancies -with inclusion compounds empty cavities- have a relatively low energy of formation. Gas hydrates occur at low temperatures or else at high pressures, for example pure CCl, hydrate exists at temperatures below .67 C and with N„ it has a pressure of 322 atm at 27.5°C.

In 1810 Davy [11] was the first to mention the existence of chlori-ne hydrate. Since then it has been shown that many apolar substances can form hydrates. Von Stackelberg formulated the conditions which a hydrate former has to satisfy as follows:

1 the molecular diameter may not be larger than 6.9 A [12] 2 the boiling point of a liquid hydrate former may not be higher

than 60°C [13].

The hydrate of CCl, exists, but CCl, does not satisfy the second condi-tion (b.p. 76.7 C, cf. Appendix A ) . Von Stackelberg is basing this con-dition on a very qualitative derivation, in which the heat of inclusion is taken equal to the geometric mean of the heats of condensation of water and the hydrate former. In the case of CCl, the heat of inclusion is probably much larger than this geometric mean (cf. III.3). Obviously this second condition is not decisive. Gas hydrates of very polar sub-stances are not known. Ethanol hydrate can presumeably be compared to the hydrates of amines [14,15], where the enclosed molecules are part of the "host lattice" themselves, by means of hydrogen bonds.

Gas hydrates with one type of guest molecule can be divided in two ways. The distinction between gas hydrates and liquid hydrates can be made depending whether the equilibrium between liquid hydrate former, water, hydrate and vapor phase does or does not exist (fig. I-la and

4 p A H 'ice ice L 1-2 \ H M '•2 . " ' /

A-"

H M 2 — - " " ^ ' y _ _ _ H i c e G — - - - ^ 1 _ i c e . q , . ! - - - " — > t

F-ig-. J-7a P-r diagvam for a liquid hydrate

With liquid hydrates the intersection of the line hydrate-hydrate former-gas (HL.G) with the line hydrate-watery phase-gas (HL G ) , the so-called quadruple point HL L.G (K), exists.

p

vt'f'

s^<^

— - S ^ T S s H ice 1-2 • > ^ [ice 1 L

r^

'i ^ ^ ^ ^ , = G / /

/«

^ • v

W~*f,.-"-- ^ t

Fig. I-lb P-T diagram for a gas hydrate

critical point L. E G before the HL.G line is reached.

Another way to classify hydrates is to use their crystal lattice, this classification grossly coincides with the one mentioned above. The two most important structures are cubic and called structure I and structure II. Structure I is built of pentagon dodekahedrons (radius 3.91 A) -the small cavities- and tetrakaidekahedrons (radius 4.33 A) -the large cavities. Per elementary cell of 46 H.O two small and six large cavities occur. N. and 0. form structure I hydrate [16].

Fig. 1-2 Structure II elementary cell with

only the large cavities oooupied

Hydrates with CCl, have the structure II, it has a diamond lattice of hexakaidekahedrons, the space inbetween is occupied by the small pentagondodekahedrons (fig. 1-2). There are eight large cavities per elementary cell of 136 H O , they have four hexagons and twelve penta-gons, and sixteen small cavities. The radius of the cavities is varying slightly with varying size of the included molecules [17]. If the edge of the elementary cell is 17.44 A, the radii of the small and the large

holes is 3.936 and 4.724 S.

6

1.2 The hydrate of CCl,, with and without help gas

However hydrates of CCl, together with other substances (so-called help gases), like H.S, H„Se, CO. and N_ were known [18], the hydrate of pure CCl, had not been found. As mentioned above, we want to use CCl, as a

4 4 means to lower the equilibrium pressure of the hydrates of 0 and N„.

During our experiments the existence of CCl, hydrate has been establis-hed.

That CCl, hydrate must exist without the help of another gas can be concluded from the curve representing the hydrate-CCl,-water-gas

(HL.L.G) equilibrium in the ln(P)-l/T plot, as given by Von Stackelberg [19] (fig. 1-3).

Fig. 1-3 The HL^L^G lines of N^, CO^ and H^S with

CCl as given by Von Stackelberg 119~\. The

dotted lines are suggested by this author

The change in the slope of the curves is caused by the decreasing amount of "help gas" in the hydrate, as its partial pressure diminis-hes .

In the case of the "help gas" H.S Van der Waals and Platteeuw assu-me [20] that the HL.L.G line does not bow, but ends in a quintuple point HiceL L G. This assumption is contradictory to the quintuple point rule. If the line does not bend then the composition of the hydrate does not change, the five phases must lie in a pentagon (fig. 1-4) and no satisfactory sequence of the four-phase lines can be arranged (fig. 1-5). (Note that the gas composition is less than 2/3 H.S, according to fig. 1-6.)

Fig. 1-4 Arrangement of the five phases,

H, L^, L^, ice and G, if the

composition of H does not vary

The sequence HiceL.G, iceL L.G is impossible, as the three-phase equilibrium iceL.G must exist in the sector between the HiceL.G line and the iceL.L„G line and then two incompatable three-phase equilibria,

8

HiceG and L iceG, remain. In addition the HL L.G and HiceL G equilibria have a tetragon arrangement, so the hydrate would not have to disso-ciate at lowering of the pressure, which is contrary to experimental evidence.

Fig. 1-5 This sequence of the

four-phase lines is

contradic-tory to the quintuple

point rule in case of a

pentagon arrangement

So, in the case of H„S too, the composition of the hydrate changes when the pressure is diminishi?d, then the slope of the four-phase line becomes steeper, it is bending downwards and ends in the quadruple point of the binary side CC1,-H„0, as shown in fig. 1-3 and fig. 1-6.

As stated by Van der Waals and Platteeuw [21], the distinction made by Von Stackelberg [22] between "Mischhydrate" and "Doppelhydrate" (the former with changing composition, like N.-CCl, hydrate, the second with constant composition, like H.S-CCl, hydrate, as he presumes) has no

physical significance.

Von Stackelberg observes that the H.S-CCl, hydrate still exists at pressures smaller than three times the vapor pressure of CCl, [23], cf. fig. 1-6. As we know the composition of the hydrate at high pressures is about 2H„S.CC1,.17H.0, if this would not change at lower pressures than three times the vapor pressure of CCl,, the hydrate would become richer of H.S than the gas phase, so the arrangement of the four phases would change from a triangle into a tetragon. As we have said before,

this would imply that all four phases, including the hydrate, would exist both at higher and at lower pressures than the four-phase equili-brium, but we know that the hydrate does not exist at lower pressures.

Fig. 1-6 M. von Stackelberg observes

H^S-CCl. hydrate below three times

the vapor pressure of CCl . The

dotted line is suggested by this

author

10

Von Stackelberg himself explains this phenomenon by assuming that at lower pressures L does not take part in the equilibrium, but this is impossible, as the HL„G equilibrium cannot be monovariant. The only explanation is given by fig. 1-7: the composition of the hydrate moves, as indicated by the arrow, as the gas phase composition proceeds from the left to the right. Then the HL L G curve bends downwards, the pres-sure is dropping still faster, the amount of "help gas" is diminishing quickly and the curve ends in the quadruple point of the binary side, as shown by the dotted line in fig. 1-6.

L2tH20)

(HjSV L,(CCl4)

Fig. 1-7 When the composition of the gas

phase passes 2/3 H„S, the hydrate

composition has to move in order

to maintain the triangular

arran-gement

Von Stackelberg suggests another way of ending [24], as shown in fig. 1-8: in the system CO -CH.C1„-H„0 he lets the extension of the HL L G curve meet the HL G curve of the binary side CH,C1„-H.0 tangentially. In such a point of tangency, however, the amount of L. cannot be chosen freely, as has to be the case in every point of the HL.L.G curve.

Patm log(P)

1 - - 0

% X , O 3 K - ' ^

S 10 ^ oc •

Fig. 1-8 The draun curve represents the HL^L^G curve of the hydrate of CO^ and CHX1„ as measured by Von Stackelberg 1241.

extension according to Von Stackelberg, suggested by this author

In general the HL L G curve can end in two ways, when the tempera-ture is lowered. Either in a quintuple point HiceL L.G, but then the composition of H must lie within the tetragon iceL.L.G and the total pressure may not become lower than three times the vapor pressure of L . Or the total pressure drops below this limit, the HL L.G curve bows downward and ends in the quadruple point of the binary side. Hydrates with CS. and C.Hj.1 belong to the first category, those with

1,2-dichloro-ethane probably too; those with CH.Cl., CHCl. and CCl, belong to the second category.

As Von Stackelberg has found that double hydrates with CCl, have the structure II, it follows from the foregoing that CCl, hydrate also

12

belongs to this type of hydrates.

1.3 Statistical thermodynamic description of gas hydrates

In 1956 Van der Waals gave a statistical thermodynamic description of clathrates [6], together with Platteeuw he applied this theory on gas hydrates [25]. Barrer c.s. used the same method [26].

Statistical description

We will apply this description on the simple case, that one type of holes (the large cavities of structure II) is occupied by one type of molecules (CCl,). We assume the lattice does not change (in reality the lattice is stretched slightly) and the enclosed molecules do not in-fluence each other. In 1 mole H^O 1/17 mole holes occur, they are not all occupied, a fraction y is. A great number of such systems in a heat reservoir is called a canonical ensemble, its results are also valid for the variations of one system in time. The difference in free energy between the partly occupied and the empty lattice is

F - Eg = -kT In Q(N,V,T), (1)

where F = the free energy of the partly occupied lattice, per

mole H.O,

FQ = the free energy of the empty lattice, k = Boltzmann's constant,

T = the temperature in Kelvin,

Q(N,V,T) = the partition function of a canonical ensemble, con-sisting of N molecules CCl. and 1 mole H.O,

N = the number of enclosed CCl molecules, V = the volume of the empty lattice.

The partition function Q(N,V,T) is the number of combinations of N.y/17 molecules (N. is the Avogadro number) in N./17 holes, multiplied by the number of possibilities q for each molecule:

N /17: N y/17

Q(N,V,T) = q "" , (2)

N^y/17: N^(l - y)/17:

where q = the molecular partition function of one enclosed molecule. It follows from (1) and (2) (N k = R ) :

(F - F.)/RT = (l/17)(y In y -^ (1 - y) ln(l - y) - y In q) . (3)

If the hydrate is considered as a mixture of the molecular species H.O and CCl,, then the free energy obeys

dF = y(CCl H) dn(CCl^) + y(H 0,H) dn(H20) - PdV - SdT, (4)

where y(CCl,,H) = the thermodynamic potential of the hydrated CCl, y(H„0,H) = the thermodynamic potential of H.O in the lattice n(CCl,) = the number of moles CCl,

n(H„0) = the number of moles H.O P = the pressure

S = the entropy of the hydrate.

We take n(H 0) equal to 1 mole, then n(CCl,) = y/17 mole. It follows from (4)

y(CCl^,H) = OF/3n(CCl^))^^^^^(jj^Q) (5)

and from (3) and (5)

y(CCl ,H) = RT In y/(q(l - y)). (6)

\

Because of the choice made above of the molecular species constituting the mixture, it is not ideal; the heat of mixing is the inclusion en-thalpy and the volume of mixing is the volume of the CCl.. This is ana-logous to adsorption. In 1.4 we will choose other molecular species to obtain an ideal solution.

14

dF = y(CCl^,H)(n(H20)/17) dy + (y(CCl^,H)y/17 + y(H20,H))dn(H20)

-- PdV -- SdT. (7)

For n(H.O) mole, equation (3) becomes

F - F. = (n(H20)/17RT)(y In y -H (1 - y) ln(l - y) - y In q) . (8)

Furthermore

y(H20,H) = OF/dniR^O))^ ^ ^ - y(CCl^,H)y/l7. (9)

It follows from the combination of (7), (8) and (9) that

y(H20,H) - Ug = (RT/17) ln(l - y ) , (!0)

y. = the thermodynamic potential of pure "empty lattice".

It shows from (10) that the solution of the species "empty lattice" is ideal indeed, adding some of it to the mixture does not cause any heat effect or excess volume.

In the case of gaseous CCl,

y(CCl^,G) = -kT In Q(N,V,T) + PV, • (11)

a term PV has to be added to the free energy. If the gas behaves ideal-ly, the partition function is

Q(N,V,T) = <i>^/N:, (12)

0, the partition function of one gas molecule, can be written as

$ = V $(T)/A^, (13)

2 1

3

molecule, $(T)/A only depends on T and the chosen gas. We find with (11), (12), (13) and the ideal gas law that

y(CCl^,G) = - RT In kT $(T)/(PA^). (14)

When there is equilibrium, the thermodynamic potentials of the gas and the hydrate have to be equal, so, with (6) and (14),

y/(P(l - y)) = A\/(kT <t>(T)) (15)

= K. ' (15a)

K is the equilibrium constant for the reaction

CC1,(G) -H 17H 0 ("empty lattice") J CCl .17H 0 ("completely occu-pied lattice"); (15)

K is also the quotient of the partition functions of the enclosed mole-cule and the gas molemole-cule in the volume of one molemole-cule at 1 atm.

LJD cell theory

In a first approximation the partition function of a molecule in a cavity can be considered equal to that of an ideal gas molecule in a volume v:

q = V $(T)/A^, (13)

furthermore ,

q = exp(-F/RT), (17)

so, if the potential energy of the molecule is raised with an amount (j) , it will show in q as a Boltzmann factor:

16

q = (v (I>(T)/A^)exp(-<l)^/kT). (18)

This <^ is the potential energy in the center of the cavity. V^Jhen the molecule is moving through the cavity its potential energy will vary,

caused by the attraction and repulsion by the wall. The probability to find the molecule in a certain volume is again proportional to a Boltzmann factor exp(-((l)(r) - <}) )/kT):

v = / 4iTr^exp(-((})(r) - (> )/kT) dr (19) hole

and

q = (<J'(T)/A-^)exp(-(})^/kT) .' 47ir^exp(-((|)(r) - ct)^)/kT) dr. (20) hole

If rotation and vibration are not hindered in the cavity, the internal partition function $(T) will be the same as in the gas. In the case of CCl. this is not probable, because it just fits in the cavity. When we neglect the difference, we find with (15) and (19)

K = (1/kT) / 4TTr^exp(-(|)(r)/kT) dr. (21) hole

When (}'(r) is known, K can be calculated. Van der Waals uses the 12-5 potential of Lennard-Jones and Devonshire [27]. They assume that the potential energy of two identical molecules

u(R) = 4e((a/R)'^ - (a/R)^), (22)

where R = the distance between the centers of the molecules, and e and a are the LJD parameters. We assume that the cavity is spheric and that the Z water molecules in the wall are spread evenly thick all over it. Because the molecules are not identical we take the geometric and

arithmetic mean values for c and a. Now the potential energy of the en-closed molecule at a distance r from the center of the cavity (fig. 1-9) becomes

)(r) = (Z/2) / u(R) sin a da. o

(23)

Fig. 1-9 The molecule M is at a distance r from the center C, it is at a distance R from the region P of the wall

When a is the radius of the cavity, (i>(r) becomes

)(r) = 4Ze((a/a)'^(l + 12r^/a^ + 25.2r'^/a^ -H 12r^/a^

-i-^ 8, 8.,, 2, 2,-10 , , .5,, 2, 2,-4, -H r /a )(1 - r /a ) - (o/a) (I - r /a ) ). (24) With 2, 2 X = r /a , Kx) = (1 -H 12x + 25.2x^ + 12x-^ -i- x^)(l - x) '° - 1,

18

m(x) = (1 -H x)(l - x) ^ - 1

and

A = / x^ exp((-4Ze/kT)((a/a)'^£(x) - (a/a)^m(x))) dx,

where s is not equal to unity for economical reasons (after s = 5 the integrand is approximately zero), K becomes

K = (2TTa^A/kT) exp((-4Ze/kT)((a/a)'^) - (a/a)^)). (25)

For the reaction of (16) is

-Ay° = RT In K, (25)

Ah° = R T ^ O l n K/3T) , P

= -RT -H 4N,Ze((a/a)'^(I -H A„/X) - (a/a^(l + A / A ) , (27)

A x , m

(where

s

Aj^ = / X'H(K) exp((-4Ze/kT)((a/a)'^£(x) - (a/a)^m(x))) dx (28) o and A = / x^m(x) exp((-4Ze/kT)((a/a)'^)?.(x) - (a/a)^m(x))) dx) (29) m o and

As° = (Ah° - Ay°)/T, (30)

where Ay = the free enthalpy of inclusion, the difference between the free enthalpies of 1 mole CC1,.17H.0 (y = 1) and 1 mole CCl , vapor next to 17 moles of empty lattice,

Ah = the enthalpy of inclusion and As = the entropy of inclusion.

1.4 Classical thermodynamic description of gas hydrates

Gas hydrates can be described as ideal solid mixtures of occupied and empty lattice. As we have seen in the preceding paragraph, CCl, hydrate is not an ideal mixture of CCl and H.O. To achieve ideality it is necessary to choose the right molecular species or "compounds".

With one hydrate former in structure II we can distinguish eight of such "compounds" (table I-l), of which are only interesting the species "all holes empty", "all small holes empty and the large ones occupied", "all small holes occupied and the large ones empty" and "all holes occupied". The mole fractions of these compounds can be expressed in yj and y , the degrees of occupation of the large and the small cavities. The species "all small holes empty and the large ones occupied"

(M.17H.0) generally has not the mole fraction y., the hydrate former may also occupy the small holes. The probability that both small

cavi-2 ties next to one large hole in particular are empty is (1 - y_) , if there is no preference for the occupation of small holes next to an occupied large one over small holes next to an empty large one. The

2

mole fraction of M.17H_0 therefore is y|(l - y^) (table I-l).

The thermodynamic potential of M.17H.0 (all large holes occupied)

y(M. I7H2O) = y°(M. UH^O) -I- RT In y j d - y ^ ) ^ , . (31)

for empty lattice (17H.0) is

y(17H20) = y°(17H20) -H RT In (1 - y ^) ( 1 - y2) ^ (32)

20

Table I-l Schematic representation, formula and mole fraction (expres-sed in y^ and y„) of "compounds" in structure II hydrate with one hydrate former

mole fraction (1 - y , ) ( i - 7 3 ) ^ y , ( i - y / ( . - y , ) y ^ 2 y , y 2 (1 - y , ) ( i - y 2 ) y 2 (1 - y , ) ( i - y 2 ) y 2 y , (1 - ^2^^! y j d - y2)y2 y(M) = y ° ( M , f = l ) + RT I n f. (33)

For the dissociation of the "compound" M.17H.0 in gaseous M and empty schematic representation

a

(3

a

(3

a

Q

(3.

(3

formula I7H2O M.17H-,0 2M.I7H2O 3M.I7H2O M. 17H2O M.I7H2O 2M.I7H2O 2M.17H 0

lattice we may write

M.17H 0 ^ n + 17H 0 (34)

and therefore

RT In y,/(f(l - y,)) = y(M,f=l) + y°(17H20) - y°(M.17H2O) (36)

= -Ay°,

Ay is called the free enthalpy of inclusion for M in the large holes, The equilibrium constant of (35), K , is

K, = y,/(f(i - y,)), (37)

this is the same constant as in equation (15), only P is replaced by f here, because the gases are not necessarily ideal and the fugacity

satisfies by definition. Because of the shape of (37) Van der Waals calls K the Langmuir adsorption constant.

For the small holes can be derived similarly

RT In y2/(f(l - y2)) = M(M,f=l) + iy°(17H20) - iy°(2M.17H2O) (38)

= -Ay°

and

K2 = y2/(f(l - y2))- (39)

The two degrees of occupation are not independent, M has but one fuga-city, so

y,/((i - y,)K,) = y2/((i - y2)K2), (40)

y, = K,y2/((1 - y2)K2 + K|y2). (41)

In the quasi ternary diagram of fig. I-IO this relation is represented by the curve £.

22

M. 17 H2O all large holes occupied 3M.17H20

I7H2O 2 M. 17 H2O

Fig. I-IO t represents the

rela-tion between y^ and

z/„

If more hydrate formers are present at the same time, for every 'guest" i is

K,,=y,,/(f,(l - ^ y , i ) ) ,

^2i = y 2 i / ( ^ : ( ' - ^ y 2 i » '

1

or, analogous to Langmuir adsorption,

(42) (43) y,. =K,.f./(l - S K , . f . ) , y2. =K2.f./(l -2K2.f.). 1 (44) (45) 1.5 Synopsis

The main purpose of this investigation is the measurement and the description of the equilibrium pressures of hydrates of CCl, with 0. and N., because of the possibility to use these hydrates in gas separa-tions. Some remarks are made in III.5 about this possibility: we doubt very much the applicability of CCl, hydrate at gas separations for kinetic reasons, but it is likely that other large molecules form

hydrates with 0. and N reasonably fast, which dissociate at low pres-sures. The calculations described in III.3 and III.4, which have proven to be applicable in this research, will then limit the number of requi-red measurements appreciably. The data on the hydrate of CCl, are not indispensable for the purpose mentioned above, but useful to check the ideal solution model and, as this hydrate was not known before, it was challenging to acquire them.

The measured phase equilibria in this investigation were

CCl, hydrate, ice and gaseous phase (HiceG), CCl, hydrate, liquid CCl, and gas (HL G ) , CCl, hydrate, liquid H O and gas (HL G ) ,

CCl, hydrate, liquid CCl, and liquid H O (HL L ) , CCl, hydrate, solid CCl and liquid CCl, (HSLj), CCl, hydrate, solid CCl, and liquid H O (HSL.),

CCl, hydrate, ice, liquid mixture of H.O and ethylene glycol and gas (HiceL2G),

CCl, hydrate, liquid CCl,, liquid mixture of H O and ethylene glycol and gas (HL.L.G),

hydrate of N. and CCl , liquid CCl,, liquid H O and gas (HL L G ) , and hydrate of 0 and CCl liquid CCl,, liquid H2O and gas (HL L G ) .

In chapter II a description is given of the apparatus with which the measurements were performed and in chapter III the results are given and used for the calculation of thermodynamic properties which are characteristic for these hydrates. In chapter IV the calculated LJD parameters are compared to values from other authors.

24

References

1 F.E.C. Scheffer & G. Meijer, Versl. Akad. Wet. 1]_ (1919) 1104-1112. 2 E.M.J. Mulders, Thesis, Delft 1936.

3 G.A.M. Diepen & F.E.C. Scheffer, Reo. Trav. Chim. Pays Bas 69_

(1950) 593.

4 A. van Cleeff, Thesis, Delft 1962. 5 L. Aaldijk, Thesis, Delft 1971.

6 J.H. van der Waals, Trans. Farad. Soc. 52 (1956) 184. 7 W.F. Claussen, J. Chem. Phys. J_9 (1951) 259-60, 1425-26.

8 M. von Stackelberg, a.o., Zeitsahr. f. Elektroah. 58_ (1954) 25-109, 162-154, 62^ (1958) 130-131.

9 D.W. Davidson in: "Water a Comprehensive Treatise", ed. F. Franks, Vol. 2, New York 1973, p. 115-234.

10 L. Aaldijk, I.e. , p. 95.

11 W. Schroeder, Die Geschichte dey Gashydrate (1926) p. 87. 12 M. von Stackelberg, a.o.. I.e., p. 35.

13 Ibid., p. 106.

14 D.W. Davidson, I.e., p. 135.

15 G.A. Jeffrey & R.K. McMullan, Progr. Inorg. Chem. 8_ (1967) 43-108. 15 D.W. Davidson, I.e., p. 123.

17 M. von Stackelberg, a.o.. I.e., p. 153. 18 Ibid., p. 41.

19 Ibid., p. 41, 101.

20 J.H. van der Waals & J.C. Platteeuw, Adv. Chem. Phys., Vol. 2 (1959) 51.

21 Ibid., p. 52.

22 M. von Stackelberg, a.o.. I.e., p. 100. 23 Ibid., p. 101.

24 Ibid., p. 41.

25 J.C. Platteeuw & J.H. van der Waals, Mol. Phys. J_ (1958) 91-96. 26 R.M. Barrer & W.I. Stuart, Proc. Roy. Soc. A243 (1957) 172. 27 J.E. Lennard-Jones & A.F. Devonshire, Proc. Roy. Soc. A163 (1937)

II PROCEDURE AND APPARATUS

II.1 Instruments and materials

The temperature measurements were made with two types of accurate thermometers: a quartz thermometer (Dymec) with digital readout and a platinum resistance thermometer with resistance bridge (Bleeker). It was aimed at during this research to reach an accuracy in temperature measuring better than .02 C. The pressure measurements were done with the aid of mercury manometers (up to 5 atm), Bourdon gauges (DRD-"Fein-messungmanometer") and deadweight gauges (Barnet and 't Hart). In the low pressure range the mercury manometers were read with a cathetometer (Bleeker). The inaccuracy in the pressure readings was at pressures up to 15 cm Hg ca. .2 mm Hg; in the range from .2 up to 5 atm about .005 atm; from 5 up to 30 atm ca. .1 atm and from 30 up to 1000 atm about .5 atm.

With the experiments described in II.6 burettes were used. The inaccuracy of their calibration was about .1%, the inaccuracy of the reading of the 50 ml burettes was .02 ml, of the 10 ml burette .004 ml.

The materials were all very pure. The water was demineralized and distilled, CCl was of analytical grade (UCB and Merck's UVASOL), ethylene glycol was of analytical grade (Merck) and 0. and N. were 100% or 99.99% pure (Philips and Baker).

/

\

K5

II.2 The measurements of the vapor pressure of CCl,, low pressure measurements of CCl,-H.O

4 2

The vapor pressures of CCl, and mixtures of CCl, and water were measured from -30 up to -H30 C with tensimeters (fig. II-l). These are glass instruments consisting of a vessel and a mercury manometer. The filling of the tensimeters is carried out as follows. The glass vessel is filled with a few milliliters of the substance to be investigated, the mercury reservoir with ca. 30 ml mercury. Then the concerning orifices are closed by melting the glass and the tensimeter is evacua-ted. During evacuation the vessel is cooled with liquid nitrogen. After some time the valve to the vacuum pump is closed, the cooling of the vessel is removed and the contents are brought at room temperature to let solved or included gases escape. This procedure is repeated several times. After that the mercury is degassed by heating it until boiling. Finally the manometer is filled with mercury and the connection to the vacuum pump melted off. During the experiments the tensimeters are kept at a constant temperature in a thermostat. The temperature fluctuations are smaller than .05 C. Four tensimeters can be in the thermostat at the same time, so multiple measurements can be done. The criterium of equilibrium is an equal reading of at least two tensimeters, the esta-blishing of it may take several weeks. To further the estaesta-blishing of equilibrium mixtures containing a solid phase were stirred. To this purpose the vessels contained magnetic stirrers (r) which could be moved by magnets (m). These magnets were operated by an electric motor and a set of gears. As the absence of liquid is inhibiting the esta-blishment of equilibrium, ethylene glycol is added to the HiceG equi-librium. Part of the ice solves in the glycol phase, but this does not influence the equilibrium condition (III.2.c). Also the pressure is not altered measurably. As shown in fig. II-l the manometers are outside the thermostat. The fluctuations of room temperature are that small they do not add to the inaccuracy of the pressure measuring. In this figure, as an example, tensimeter A is filled with CCl,, water and ethylene glycol; in it exist the phases hydrate, ice, a mixture of

10 11

N3 00

ethylene glycol and water, and the vapor phase. The pressure read cor-responds to the equilibrium pressure of the HiceG equilibrium. Tensi-meter B contains CCl, and water. Now a three-phase equilibrium is mono-variant, the phases hydrate, liquid CCl, and vapor. The hydrate phase can be distinguished from ice by its greater specific mass, this is inbetween those of water and CCl,. Otherwise than in the figure the

4

hydrate floats on CCl., it is a flocculent substance, the crystals growing from the liquid are small and clot. The HL G equilibrium (L is the watery solution) is examined with a filling containing relatively much water. By undercooling a metastable part can be measured too. While the measurements at CCl,-water mixtures are fairly reproduceable, it appears to be unexpectedly difficult to determine the vapor pressure of pure CCl,. To remove traces of water the CCl, is distilled over a molecular sieve and treated with sodium; still readings differing some mm Hg may occur. Two causes of this phenomenon may be the irreproduce-able wetting of glass by mercury and the corrosion of the mercury meniscus by CCl,. The results of the measurements on CCl, are given in appendix A, of those on CCl,-H.O in III.2.a.

II.3 Low pressure measurements at the system 0 -CCl.-H.O and N2-CC1^-H20

The dissociation pressures of the double-hydrates of CCl, with 0. or N. are measured from the quadruple point at 4 cm Hg and .67°C up to 900 atm at 40 C. The low pressure part (up to 5 atm) is measured with a counterpressure tensimeter (fig. II-2). The manometer (M) of this tensimeter indicates the pressure difference between the reaction ves-sel (R) and an open mercury manometer (0). The open mercury manometer can be pressurized with nitrogen supplied from a cylinder, the reaction vessel can be filled with pure 0. or N.. The reaction vessel can be kept at the desired temperature by a thermostat. The temperature of this bath is controlled by pumping into it a small quantity of a liquid that is somewhat colder from a reservoir communicating with the bath,

Q

if the temperature raises above the set value. The temperature fluctua-tions of the bath are smaller than .02 C. The results are given in III.3.

II.4 Measurements at the systems 0„-CCl,-H„0 and N.-CCl,-H.O with the ^ 2 4 2 2 4 2

apparatus of Cailletet

In these measurements the apparatus of Cailletet has been used from 1 atm up to 250 atm. The Cailletet tube (fig. II-3) is a thick-walled glass capillary protruding for the greater part from a steel cylinder. The system and a glass-covered soft iron kernel are in the upper part of the tube, floating on a mercury column. The glass tube has an ori-fice at the bottom, under the meniscus of the mercury with which the cylinder is filled. In this set up a transparent oil-mercury separator has been included to be able to correct for the different positions of

the mercury level in the capillary. These changes are caused by the compression of the system by supplying oil from the spindle or by ex-pansion as a result of the dissociation of the hydrate. The Cailletet tube is kept at the desired temperature by a circulating thermostat (Haake), the liquid runs through a glass jacket with vacuum isolation. The temperature is read with the quartz thermometer 0, the pressure with the gauge M . Before installation the tube is filled with water and CCl, by means of a syringe with a very long needle. The gas is supplied after evacuation at a special gas rack [l]. After the instal-lation of the tube and the jacket the pressure is set at a value higher than the expected equilibrium pressure until a large quantity of hy-drate has been formed. If then the pressure is lowered beneath the equilibrium pressure, it raises slowly again until equilibrium has been reached. To diminish the influence of leakage valve 3 is closed, the rest of the apparatus is surrounded by a thermostat box to avoid volume changes by temperature fluctuations. The results are given in III.3.

32

o

s

'ai

II.5 High pressure measurements with the window autoclave

This window autoclave has been described in several publications [2,3, 4]. The main difference with the Cailletet apparatus is, that the pres-sure resistant glass part has been reduced to two plane securit glass windows in a steel cylinder (fig. II-4). These windows allow much higher pressures than glass capillaries. The glass vessel that sur-rounds the system is completely immersed in the autoclave and therefore may be thin and contain a much greater volume than these capillaries. The system is inbetween the two windows in a glass vessel, which has an orifice at the bottom under the mercury surface. The system and a glass covered soft iron kernel are floating on the mercury. The magnets (m) moving the kernel are inside the cylinder, they in turn are moved by an outside electromagnet (E). The autoclave is in a thermostat, except the part which is surrounded by the electromagnet, the plug (P).

The temperature measuring is done with a platinum resistance ther-mometer, which, covered by a steel jacket, reaches into the cylinder, near the system. The liquid surrounding the glass vessel (at low tempe-ratures a mixture of alcohol, water and ethylene glycol in the propor-tions 1 : 1 : 1) is stirred by the same mechanism which moves the mag-nets. In this way the difference between the real temperature and the measured one is kept as small as possible. The triple point of CCl, found by extrapolation of the melting curve (appendix A) is -22.61°C, while the value determined in the apparatus described in II.6 is

-22.69 C. At higher temperatures the deviation will be smaller, because the temperature difference between the autoclave and the environment is smaller.

The pressure is measured with the Bourdon gauge M., or with the dead gauge D. Pressure changes can be obtained by turning the spindle S or valve 2.

The dissociation pressure of the hydrate is determined in the same way as in the Cailletet apparatus; in allowing a great amount of hy-drate to dissociate the pressure raises until equilibrium is reached (during this procedure valves 1 and 5 are shut). After the

establish-N, 6ato

CM

ez5

fr^-O—VI

UII3

O P I H O H j W _-_ _—_ 1 f^ ^

-i

j~ ~—~ ~_~ 9 r N.

V

ment of equilibrium the reading of the Bourdon gauge is compared with the deadweight gauge.

The filling procedure of the glass vessel is comparable to that of the Cailletet tube. To obtain a satisfactory amount of hydrate a greater quantity gas is needed than could be contained in the normal vessels. Therefore a new type has been designed in which gas can be compressed up to 5 atm (fig. II-5). The procedure is as follows. Water and CCl, are injected into the top of the vessel with a syringe and frozen with liquid nitrogen. After that the vessel is mounted vertical-ly, upright, the cooling jacket is placed on top of it and the plug (p) is hung on the glass supports, so the orifice is still free. A nut is attached to the plug to keep it from being removed prematurely. Now the vessel is connected to the filling apparatus, evacuated and supplied with the proper gas. Afterwards so much mercury is forced into the ves-sel the plug is afloat and can be lifted from the supports and turned slightly by tapping the vessel gently. If the mercury is drained from the vessel the plug goes down into the orifice and closes the vessel. Before the vessel is to be placed in the autoclave the nut of the plug has to be removed, otherwise the plug might be drawn into the orifice again and shut it, in case of a sudden pressure drop in the autoclave. Such an event would result in a great overpressure in the glass vessel, which would make it explode. With the nut removed the plug will float in the entering mercury and take an askew position, so that it cannot reenter the orifice nor contaminate the system. To prevent the solid CCl, from melting before the mercury would have shut off the top of the vessel (liquids enclosed between mercury and glass cannot move), all fillings with CCl are pressurized quickly by supply-ing nitrogen from a cylinder through valve 3. Then water (or the anti-freeze mixture) is forced into the autoclave with the handpump, the nitrogen is removed by opening valve 4. An objection to this method is the solving of some nitrogen in the liquid inside the autoclave which can cloud the view at lower pressures.

The resistance thermometer in fig. II-4 is a four-threaded type. The terminals I are connected to a source with internal resistance 2 x

36

lOkfi. The terminals P give the potential difference between the ends of the platinum resistance. This potential difference is compared to the potential drop over the resistance bank, which is connected to the same source, also in series with 2 x 10kf2. The reading of the resistance bank would now indicate the resistance of the platinum probe if the connecting wires would have no resistance, this deviation is taken into account in the calibration. A change of or a difference between the resistance of the two wires of .1 corresponds to a deviation in the temperature reading of .004 C, but the total resistance of the wires is only a few ohms, so fluctuation of room temperature will not play an important roll.

The deadweight gauge of fig. II-4 is from 't Hart. It has one pis-ton with two ranges. If valve 7 is open and 8 closed, the oil exerts pressure on the whole surface, if 7 is closed and 8 open one-fifth of the surface is being used and pressures five times higher are required to lift the same weight. The Barnet gauge has two separate weighing pistons.

The following equilibria were investigated with the window auto-clave. With the melting curve of CCl, (appendix A) and the HSL equili-brium (hydrate, solid and liquid CCl,, III.2.b) the pressure was kept constant and the temperature varied. CCl, crystallized in large cubes, as criterion for equilibrium the sharpening or rounding off of the edges could be taken. With the HL L. equilibrium (hydrate, water and CCl,, III.2.b) the temperature was varied too. Here the criterion is the dissociation or growing of the hydrate. The same procedure was applied to the HSL equilibrium (hydrate, solid CCl, and water, III.2.b). Some measurements were done at the HLG equilibria of the systems 0_-H 0 and N.-H.O. Here the growing or melting of one little crystal was observed. If enough gas is produced the dissociation of the hydrate can result in such a change of volume that the pressure inside

the autoclave is increased considerably and so equilibrium can be at-tained. This method was applied to the HL L.G equilibria (hydrate, CCl , water and gas. III.3) of the systems O.-CCl -H 0 and N -CCl - H O .

II.6 Lowering of the quadruple points HiceL G and HL L G of CC1,-H_0 by addition of ethylene glycol

Fig. II-6 represents the apparatus that has been used. A reaction vessel (R) is in a double-walled glass thermostat bath. The thermostat liquid is supplied from a Lauda "Ultrakryostat". The reaction vessel is pres-sed against an o-ring in the stainless steel mounting with a split, externally threaded nut. In this steel mounting also the thermometer

(th) is screwed and three valves (A) are fitted. With these valves the dosing of water, CCl, and ethylene glycol can be regulated. In R is a "teflon" clad magnetic stirrer (r) which can be rotated by a magnet (m). The vessel K contains mercury, which serves to force the three liquids into R.

The procedure is as follows. After the bath and R are removed the burettes are filled. I'Jhen K is connected to the vacuum pump and one of

the capillary drains is immersed in the right liquid the corresponding valve is opened and the liquid sucked into the burette. This is

repea-ted for the two other liquids. Then the reactor is mounrepea-ted and evacua-ted to remove the remainder of the different liquids in the dead volume of the valves. After the reactor has been cleaned again it is filled with 50 ml very pure water and mounted for the second time. Now the

thermometer is calibrated at the triple point of water (-t-.Ol C) . After the dosing of CCl. and extra water the reactor is cooled deeply to obtain nuclei of the hydrate. Between 0 and .6 C the hydrate is allowed to grow until all CCl, has been used. Then the reactor is cooled until ice appears, ethylene glycol is added under further cooling until the desired temperature is attained. Now the temperature is raised slowly until the ice melts completely: that is the criterion for a HiceL.G point. If the temperature is increased further the hydrate will start to dissociate. The very start of it is a HL L G point (where CCl, first appears). The temperature at which the last hydrate crystal disappears can be used also (III.2.c).

The freezing point lowering of water by adding ethylene glycol, mentioned in appendix C, can be measured in the same way.

U ) CO

Fig. II-6 Apparatus for the lowering of the quadruple points

HiceL G and HL^L^G in the system CCl^-H^O

The glass vessel V serves to measure the gas volume of the appara-tus (273 ml). By filling V with a known amount of gas and allowing this to expand into the apparatus the gas volume can be calculated from the pressure drop.

The manometer is only used to check possible leakages in the appa-ratus, the pressures can be compared roughly with those of the tensi-meters .

The quartz thermometer can be read in .0001 C. This was used in calibration to check the constancy of the temperature and the stability of the apparatus. Both were very good, so readings in .001 C were meaningful.

40

References ^

1 L. Aaldijk,

Thesis,

Delft 1971, p. 38.

2 G.S.A. van Welie & G.A.M. Diepen,

Rec. Trav. Chim.

80 (1961) 566.

3 J.A.M. van Hest,

Thesis,

Delft 1962.

III RESULTS AND CALCULATIONS

III.l CCl, 4

We have measured the vapor pressure of CCl, because it is required in the calculation of the HL G equilibrium and insufficient data are given in the literature, in the range we need (-20 up to 0 C ) . The calcula-tions and the measurements of the vapor pressure curve and the melting curve are given in appendix A, the procedure in II.2. The triple point of CCl, has been located in the apparatus of II.6 at -22.69 C. By extrapolation of the calculations of A.2 its pressure is found to be

.85 cm Hg*-*.

III.2 CCl,-H.O 4 2

The measurements at the hydrate of CCl, are discussed in three

sections: ' a) measurements of HiceG, HL G and HL.G equilibria,

b) those of HSL., HSL. and HL L equilibria, of which no calculations are carried out, and

c) the lowering of the quadruple points HiceL.G and HL.L G by adding ethylene glycol.

*)

' Throughout this work is 1 cm Hg = 1333.22 Pa; 1 atm = 101325 Pa;

- 3 3

42

*)

III. 2.a HiceG, HL.G and HL^G equilibria

CCl, and water form a stable hydrate with a (slightly) variable compo-sition. Therefore the hydrate can have different vapor pressures at one temperature. It can be in equilibrium with ice (up to 0.00 C ) , with liquid CCl, (from -22.69 up to -I-.57 C) and with water (from .00 up to .67 C ) , always accompanied by a gas phase (saturated vapor), if the three dense phases do not occupy available space completely. The pres-sure of the gas phase is low: < 4 cm Hg. Although the different gases are not considered ideal in the next calculations, it is reasonable to assume that the mixture behaves ideally (no heat of mixing and no excess entropy), so

p. = x^ P, (46)

where P is the total pressure, p. the partial pressure and x. the mole fraction of i in the gas phase. Wit>i CCl, f. is calculated from p. with

'^ 4 1 1 (B-5), (B-6), (A-10) and (A-11) (at 0°C and p = 3 cm Hg, p - f = .012

cm Hg).

For the equilibrium between hydrate and ice is, according to 1.4,

y(17H20) = 17y(ice). (47)

Because CCl, does not fit into the small cavities it follows from (32) and (47):

RT ln(l - yj) = 17y(ice) - y(17H20)°. (48)

If we call the empty water lattice the 3-modification and ordinary (hexagonal) ice the a-modification, then

y = y(17H20)°/17 (49)

Fig. III-l The melting curve and vapor pressure curve of CCl according to Appendix A

and, with (36) and (37),

RT ln(l - yj) = 17(y^ - y ^ ) , and

- RT ln(l -H Kjf(CCl^)) = 17(y^ - y^),

(50)

(51)

Equation (51) can be transformed into

f(CCl^) = (exp(Ay^g/RT) - 1)/exp(-Ay°/RT), (52)

sub-44

tracting from the total pressure the vapor pressure of ice, calculated by the method given in appendix A with the data of [1], see table

III-l. However the calculation mentioned in paragraph IV.2 at the HL.G equilibrium data of O.-H.O and N -H.O, where six parameters were sol-ved, did result in physical relevant values, the solution of (52) has not been succesful, not even when this equation was combined with (60) and (52) and the corresponding measurements. The reason is that the exponential term in the numerator of (52) >> 1 (the investigation of this cause was carried through with an analog computer. Ah „, As ,,, Ah and As, were varied and the obtained curve was compared with the measurements).

Table III-l Data for the calculation of the vapor pressures of ice and

water

C (ice) = -.05725 -i- .033552 T cal mole"' K~' [2]

P O _ft -5

C (water) = 79.50765 - .5643114 T + .00171357 T - 1.72079x10 T cal P -1 -1

mole K [2]

C (G) = 8.122 cal mole"' K"' (from best fit) p _, H(LG, 0°C) = 10764 cal mole (from best fit)

second virial coefficient of water vapor:

B = .4153 - 1.044xlO^/T^ - 1.98725 T exp(2300/T - 11.3) cal atm mole [3]

pressure of the triple point:

p(triple) = .006031 atm (from best fit)

Physically this means, that the transition at 1 atm from the a-modifi-cation to the 3-modifia-modifi-cation is far remote from the region of the measured values (according to the values for Ah „ and As ., mentioned

at the end of III.3, this temperature would be ca. 900 K ) . If the term - 1 in the numerator of (52) is neglected, then

f(CCl ) = exp(A/T + B ) , (53)

where

A = (17Ah + Ah°)/R, and (54)

B = -(17As -I- As°)/R. • (55)

With the HL G equilibrium the fugacity of CCl, can be calculated from the vapor pressure of liquid CCl, (the solubility of water in CCl, can be neglected, x(H 0) = 4.28xl0" at 0°C [4]). Tlie difference

between the total pressure and the vapor pressure of CCl, is p(H.O), in the case of water we neglect the difference between p and f:

y(H20,G) = y(H20,G)° -i- RT In p(H20), and (56)

y(17H20) = 17y(H20,G). (57)

From (32), (36), (37), (56) and (57) follows

RT In p(H20) = Pg " y(H20,G)° - (1/17) RT ln(l + K|f(CCl^)). (58)

For convenience p(H.O) is compared with the vapor pressure of ice, p(ice):

y(ice) = y(H20,G)° + RT In p(ice). (59)

By substitution of (59) in (58)

RT ln(p(H20)/p(ice)) = Ay^^ - (1/17) RT ln(l + Kjf(CCl^)). (60)

By applying the same simplification as in (53) this becomes:

\

46

The L phase of the HL G equilibrium is nearly pure water (x(CCl ) = 9x10 at 25°C [4]), its pressure can be calculated in the same way as with ice (table III-l). If this vapor pressure is subtracted from the total pressure p(CCl,) is obtained. The fugacity is found again (f = p exp(Bp/RT)) by using (A-11), it obeys:

f(CCl^) = ((p(ice)/p(H20)))'^exp(Ay^g/RT) - 1)/exp(-Ay°/RT). (62)

Neglecting - 1 as before

f(CCl^) = ((p(ice)/p(H20)))'^exp(A/T + B ) . (63)

By optimizing simultaneously the data of HiceG with (53), those of HL.G with (61) and the values for HL.G with (63) A and B can be obtai-ned from the greatest possible number of data:

A = -4620 K,

B = 18.05.

If A and B are calculated only using the HiceG data, the linear least squares method can be applied and the standard deviation can be calcu-lated:

A = -4673 + 50 K,

B = 18.25 + .18.

By comparing these results we conclude that the first set (which has been obtained by using three times more data) is correct within 1%. For a comparison between model and data cf. table III-2 and fig. III-2.

The points of intersection of the three lines are the two quadruple points:

p c m H g In p

3.88 3.84 3.80 3.76 3.72 3.68 3.64 0

^ t » C

Fig. III-2 Equilibrium pressures of HL^G {o), HiceG (-H) and HL G (A) in the system CCl -HO

HiceL G, at .16 C and 3.632 cm Hg, and

HLjL2G, at .56 C and 3.952 cm Hg.

These temperatures differ considerably from the most reliable results obtained in this research: .00 and .67 C (III.2.c). These deviations are not caused by the inaccuracy of the temperature measurements in the first place, but by the poor pressure measuring. If this deviation was caused by inadequacy of the model, also because the calculated slope of the HL.G line is steeper than corresponds with the data, the assumption that the CCl, hydrate is an ideal mixture could be taken for unjusti-fied. This opinion is supported by the evidence in the next paragraph

48

Table III-2 HiceG, HL..G and HL^G equilibria

HiceG equilibrium pressures in cm Hg

t/°C

-17.220 -17.202 -14.970 -14.970 -13.740 -13.740 -12.390 -12.390 -10.645 -10.615 -8.510 -8.495 -6.010 -5.982 -4.060 -4.020 -3.540 -3.540 -2.470 -2.470 -1.490 -1 .490 T/K +255.930 +255.948 +258.180 +258.180 +259.410 +259.410 +260.760 +260.760 +262.505 +262.535 +264.640 +264.655 +267.140 +267.168 +259.090 +269.130 +269.610 +259.610 +270.580 +270.580 +271.660 +271.660 P +1.101 +1.071 +1.265 +1.255 +1.395 + 1 .410 +1.564 +1.584 +1.808 +1.778 +2.070 +2.042 +2.466 +2.451 +2.740 +2.765 +2.819 +2.817 +3.022 +3.042 +3.259 +3.253

Pcci,

4 +1.000 + .970 + 1 . 141 +1.141 +1.256 +1.271 + 1 .407 +1.427 +1.524 +1.593 +1.348 +1.319 +2.190 +2.184 +2.414 +2.438 +2.478 +2.476 +2.549 +2.669 +2.854 +2.848 P • _•^ice + .101 + . 101 + .124 + .124 + . 139 + .139 + .157 + .157 + .184 + .185 + .222 + .223 + .276 + .277 + .326 + .327 + .341 + .341 + .373 + .373 + .405 + .405 ^CCl^ + .998 + .968 +1.139 +1.139 + 1 .253 +1.258 +1.404 +1.424 +1.520 +1.590 +1.843 +1.815 +2.183 +2.178 +2.406 +2.430 +2.470 +2.458 +2.640 +2.660 +2.844 +2.838 CCl, 4 + 1 .002 +1.003 + 1 . 172 + 1 .172 + ! .276 +1.276 +1.399 +1.399 +1.574 +1.578 +1.814 +1.816 +2.137 +2.140 +2.422 +2.428 +2.503 +2.503 +2.679 +2.679 +2.849 +2.849 f - -1-+ + + -+ + -+ --f c .003 .035 .034 .034 .023 .008 .004 .024 .046 .012 .028 .002 .047 .037 .016 .002 .033 .035 .039 .019 .005 .01! HL.G equilibrium

t/°c

-17.220 -17.220 -14.980 -14.970 -13.740 -13.740 -12.400 -12.390 -10.615 -10.500 -8.495 -8.480 -5.990 -5.981 -4.030 -4.015 T/K +255.930 +255.930 +258.170 +258.180 +259.410 +259.410 +260.750 +260.750 +252.535 +262.550 +254.555 +264.670 +257.160 +267.169 +269.120 +269.135 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 2 + 2 + 2 +2 +2 + 2 +3 +3 D 335 .365 .559 .519 654 584 843 833 077 .062 326 326 725 715 014 024 pressures ' C C l , +1.240 +1.240 +1.425 +1.425 +1.537 +1.537 +1.665 +1.657 +1.853 +1.854 +2.097 +2.099 +2.421 +2.422 +2.703 +2.705 P • •^ice + .101 + . 101 + .124 + .124 + .139 + .139 + .157 + .157 + .185 + .185 + .223 + .223 + .277 + .277 + .327 + .328 in cm H ^CCl^ +1.238 +1.238 +1.422 +1.423 +1.533 +1.533 +1.662 +1.563 +1.848 +1.849 +2.091 +2.093 +2.413 +2.414 +2.693 +2.696 g

^n.^0

+ .095 + .125 + .134 + .093 + .117 + .147 + .177 + .166 + .223 + .208 + .229 + .227 + .304 + .293 + .311 + .319

\ o

+ .100 + .100 + .123 + .123 + .138 + .138 + .155 + .155 + .183 + .183 + .221 + .221 + .275 + .275 + .325 + .326 P"Pc -.005 + .025 + .01 1 -.030 -.021 + .009 + .021 + .010 + .041 + .025 + .008 + .006 + .029 + .018 -.014 -.007

Table III-2 Continued

L G equilibrium t/°C -1.910 -1.910 -.950 -.950 -.140 -.140 + .040 + .040 + .300 + .300 + .470 + .470 + .550 + .550 T/K +271.240 +271.240 +272.200 +272.200 +273.010 +273.010 +273.190 +273.190 +273.450 +273.450 +273.520 +273.620 +273.700 +273.700 P +3.467 +3.447 +3.651 +3.641 +3.821 +3.816 +3.840 +3.855 +3.915 +3.905 +3.945 +3.955 +3.965 +3.955 pressures Pcci, 4 +3.039 +3.039 +3.202 +3.202 +3.345 +3.345 +3.378 +3.378 +3.425 +3.426 +3.457 +3.457 +3.472 +3.472 P • _ice + .39! + .391 + .423 + .423 + .453 + .453 + .459 + .459 + .469 + .469 + .476 + .476 + .479 + .479 in cm Hg ^CCl, +3.027 +3.027 +3.189 +3.189 +3.332 +3.332 +3.354 +3.364 +3.412 +3.412 +3.443 +3.443 +3.458 +3.458 PH2O + .428 + .408 + .449 + .439 + .475 + .470 + .462 + .477 + .489 + .479 + .488 + .498 + .493 + .493 PH2O + .389 + .389 + .421 + .421 + .45! + .45! + .457 + .457 + .467 + .467 + .474 + .474 + .477 + .477 P-P, + .039 + .019 + .027 + .017 + .025 + .020 + .004 + .019 + .022 + .012 + .014 + .024 + .015 + .016 IL G equ t/°C -1.900 -1.900 -.930 -.930 -.110 -.110 + .050 + .050 + .310 + .310 + .480 + .480 + .570 + .570 ilibrium T/K +271.250 +27!.250 +272.220 +272.220 +273.040 +273.040 +273.200 +273.200 +273.460 +273.460 +273.630 +273.530 +273.720 +273.720 P +2.436 +2.421 +2.939 +2.929 +3.452 +3.437 +3.567 +3.547 +3.756 +3.745 +3.880 +3.880 +3.940 +3.930 pressures Pcci, 4 +2.037 +2.022 +2.510 +2.500 +2.997 +2.982 +3.107 +3.087 +3.287 +3.277 +3.405 +3.405 +3.462 +3.452 PH2O + .399 + .399 + .429 + .429 + .455 + .455 + .450 + .460 + .459 + .469 + .475 + .475 + .478 + .478 in cm P-•^ice + .391 + .391 + .424 + .424 + .454 + .454 + .460 + .460 + .470 + .470 + .475 + .475 + .480 + .480 ^CCl, 4 +2.032 +2.017 +2.503 +2.493 +2.986 +2.97! +3.095 +3.075 +3.274 +3.264 +3.391 +3.391 +3.447 +3.438 CCl, 4 + 1 .978 +1.978 +2.456 +2.466 +2.972 +2.972 +3.081 +3.081 +3.269 +3.269 +3.397 +3.397 +3.467 +3.467 f-f c + .054 + .039 + .036 + .025 + .014 -.000 + .013 -.005 + .005 -.005 -.006 -.006 -.019 -.029

50

p Qtm

600

AOO

> I "C

Fig. III-3 Equilibrium pressures of HSL

(+),

HL L

(o)

and

HSL„

(A).

The drawn line for HSL.. is the melting

curve of CCl according to A. 3

about the volume of the hydrate varying with its composition, the lat-tice is being expanded at increasing occupation. If the volume increa-ses proportional to the degree of occupation, the mixture is ideal, otherwise it is not. Data concerning the volume as a function of the degree of occupation of the cavities are lacking however, so a final judgement about the ideality of this hydrate cannot be given yet on these grounds.

III.2.b HSL^, HSL^ and HL,L^ equilibria

In respect to the HL.L equilibria and those with solid CCl, no compu-tations have been made. In table III-3 and fig. III-3 the data are given, measuring procedure is g.iven in II.5. From the steep slope of the HL.L. curve may be concluded that Av for the reaction

CCl .17H 0 ->- CC1,(L) + 17H„0(L)

at 1 atm is approximately equal to 0 and becomes < 0 at higher pres-sures, the latter would correspond with an expected difference in the compressibility of the two liquids on the one hand and of the solid on the other. From Av = 0 follows for the molar volume of the hydrate:

v(CCl,.17H20) = 17 X 18.015 x .999841 + 153.823 x .61275 =

400.46 ml mole"',

(here the degree of occupation is assumed to be = 1, if the value .9996 is taken, as calculated by Davidson [5], v(CCl .17H 0) becomes 400.39

-! . . 4 2

ml mole ) , this is 23.55 ml per mole H.O. Davidson [6] gives the average value for structure II hydrates 22.97 ml (mole H.O) , Von Stackelberg [7] mentions for 2H.S.CC1, .17H 0 the value 24.15 ml (mole H.O) : as Von Stackelberg suggests, the lattice is probably stret-ched as the degree of occupation of the cavities increases and as the size of the enclosed molecules increases.

52

Table III-3 HSL HSL and HL^L^ equilibria

HSL (the calculated pressures are from the calculated melting curve, accord T/K 273.18 273.17 272.84 272.60 272.36 272.18 270.73 270.71 269.80 269.27 268.76 267.97 267.95 266.33 265.06 263.66 263.59 262.22 260.33 259.66 258.25 257.55 255.59 253.65 HSL 2 T/K 273.2 273.1 272.9 272.6 ing to A.3)

t/°C

0.03 0.02 -0.31 -0.55 -0.79 -0.97 -2.42 -2.44 -3.35 -3.88 -4.39 -5.18 -5.20 -6.82 -8.09 -9.49 -9.56 -10.93 -12.82 -13.49 -14.90 -15.59 -17.55 -19.50 t/°C -0.0 -0.1 -0.3 -0.6 P/atm 594.3 596.2 580.3 571.5 57^.9 568.1 523.6 527.5 501.4 489.8 470.4 454.0 452.5 409.9 376.0 341.7 335.9 302.5 252.2 234.7 199.9 180.1 129.2 79.9 P/atm 688 737 785 881 P /atm c 595.3 595.0 586.0 579.3 572.8 557.8 528.3 527.7 503.1 488.8 475.0 453.8 453.3 410.0 375.3 339.4 337.5 301.5 252.3 234.9 198.4 180.6 129.9 80.3 (P - P )/atm -1.0 1 .2 -5.7 -7.8 1.1 0.3 -4.7 -0.2 -1.7 1 .0 -4.6 0.2 -0.8 -0.1 -0.3 2.3 -1.6 0.9 -0.1 -0.2 1,5 -0.5 -0.7 -0.4

Table III-3 Continued

«^S

T/K

273.80 273.78 273.74 273.58 273.53 273.41 273.30 t/°C 0.65 0.63 0.59 0.53 0.38 0.26 0.15 P/atm 1 .0 1 14.7 223.5 323.8 419.5 497.5 597.7

melting curve of pure CCl,, as :an be expected according to the slight solubility of water in CCl,.

The sign of the slope of the HSL. curve corresponds to the diffe-rence in volume between solid and liquid CCl, (at 0 C and 598 atm v =

-I ^

85.742 - 87.658 = -1.916 ml mole , calculated with the data m A.2) and the slope of the HL L curve.

III.2.C The lowering of the quadruple points HiceL^G and HL.L^G by

adding ethylene glycol

With the apparatus described in II.6 a mixture of water, CCl, and ethylene glycol can be prepared and investigated under its own vapor pressure. In this way it is possible to measure the temperature of the equilibria HiceL.G and HL,L.G at different compositions of L„. These different compositions are obtained by adding ethylene glycol to L.. Ethylene glycol is not appreciably soluable in CCl, (the triple point of CCl, is not noticeably lowered by it), it has a negligeably low vapor pressure (.015 cm Hg at 0 C) and it is not included in the hy-drate (it forms a chemical compound with water, ethylene glycol.H.O [5], which is considered to be prohibitive for the formation of an inclusion-hydrate). In appendix C the temperature dependence of the activity of water next to ice is derived and a model is chosen to approximate the activity of water in mixtures with ethylene glycol in

54

this particular composition range. With (C-10) a (the index 1 is for water) can be calculated if the temperature is known. If follows from

(C-35) with (C-27):

In Y, = (1 - x,)^(T,(G,/(Xj + (1 - Xj)G,))^ + T2G2/(1 " x^ +

+ x,G2)^) (64)

and then x can be solved with x = a./y,. With a so-called ice dis-appearance point, the temperature where the last ice is just melting, the water is distributed over two phases, the hydrate and L (the vaporization of water can be neglected in this respect). Let the total amount of water be A mole, the amount of ethylene glycol B mole and the amount of hydrated CCl, C mole, then

A = 17C/y| + XjB/(l - X|) • (55)

and

y, = 17C/(A + B - B/(l - x^)). (66)

The dosed amount of CCl, is partly in the vapor phase. The total avail-able volume is 273 ml, it is partly occupied by liquid and hydrate (the ice is on the point of disappearing), the hydrate has about the same volume as the liquids from which it is formed (cf. III.2.b), so the amount of CCl, in the vapor phase is about

(273 - 18.02A - 55.64B - 94.26C)p(CCl,)/RT mole.

The fugacity from (53) is taken instead of the pressure, because it concerns a correction only. In table III-4 are given the values for A and B, the corrected values for C and the values for a,, x, and y. for every temperature measured. From the calculated degrees of occupation nothing more can be concluded than that y, is about equal to unity, the