Application of the principle of congruence to ternary alkane mixtures

J. Gem. Thermodynamics 1974,6,1171-1174

Application to ternary

of the principle alkane mixtures

C. K. LOOI, C. J. MAYHEW,

of congruence

and A. G. WILLIAMSON

Department of Chemical Engineering, Christchurch, New Zealand

a

University of Canterbury,

(Received 22 November 1973; in revisedform

26 March

1974)

Excessenthalpies and excessvolumes at 298.15 K and atmospheric pressure have been measured for mixtures of n-hexane + (an equimolar mixture of n-tridecane + n-nonadecane). The agreement of the results with the corresponding results for mixtures of n-hexane+ n-hexadecaneis interpreted as confirmation of the applicability of the principle of congruenceto multicomponent mixtures.

1. Introduction The principle of congruence in its most general form(‘) asserts that the configurational properties of members of a homologous series and of mixtures of members of such series at a given temperature and pressure are a function only of the number average chain length. Thus, for a property X such as the enthalpy or volume, we may write x(T,

P,

x19

x2,

*

-

*3

nl,

n29

*

* -1

=

x(T

P>

Cxini)*

(1)

Various experimental studies have been made of the applicability of this principle to binary systems, particularly for excess enthalpies and volumes. However, apart from an early study by Brnrnsted and Koefoedc2’ on the solubilities of sym-tetraphenylbutane in binary ester mixtures, little attention appears to have been paid to the validity of the principle for multicomponent mixtures. The simplest kinds of multicomponent systems to which one might expect the principle to apply are ternary mixtures of members of a homologous series. For such systems, several possible experimental tests of the principle of congruence suggest themselves, some of which are outlined as follows. (1) Null experiments involving mixing of a binary mixture with its congruent pure homologue. For example, one would expect the excess enthalpy and excess volume of, say, pure n-hexane in any proportion with any mixture of alkanes of chain lengths n1 and n2 and composition such that nlxl + n,(l -x1) = 6, to be zero. (2) Experiments in which a binary pseudo n-alkane of integral average chain length n1 is mixed with a number of other n-alkanes of various chain lengths n2, n3, . . . . The excess functions for such experiments would be expected to be the same as those for binary mixtures of pure component of chain length n, in the same proportions with alkanes of chain length n2, n3, n4, . . . a To whom correspondenceshould be addressed.

1172

C. K.

LOOI,

C. J. MAYHEW,

AND

A.

G. WILLIAMSON

We have chosen, as a preliminary test of the extension of the principle, to carry out experiments which are a sub-set of class 2 above. One of the most thoroughly examined binary n-alkane mixtures is n-hexane +n-hexadecane. We prepared an equimolar mixture of n-tridecane+n-nonadecane; this mixture has a mean chain length of 16 and is henceforth referred to as “pseudo-hexadecane (13-19)“. The excess enthalpies and excess volumes of pseudo-hexadecane (13-19) + n-hexane were measured at 298.15 K. The choice of a pseudo-alkane of fairly large chain length enables us to prepare it from components which themselves differ considerably in chain length and which are still very different from the third component.

2. Experimental Excess enthalpies were measured with the calorimeter described by Beath et aZ.c3) Excess volumes were measured in the apparatus described by Beath et ~1.~~) The compositions in the excess volume measurements were calculated from the volumetric characteristics of the apparatus with the measured value of the density of the tridecane + nonadecane mixture, viz., p(298.15 K) = (0.7695 +0.0003) g cmm3. This value was determined using a standard density bottle method. The excess enthalpies are believed to be accurate to rt3 J mol-’ and the excess volumes to +0.004 cm3 mol-‘.

3. Materials Koch-Light “puriss” grade n-alkanes were used from freshly opened bottles without further purification. The pseudo-n-hexadecane was made by weighing the appropriate amounts of n-tridecane and n-nonadecane into a clean dry container to achieve a mixture of x = 0.5.

4. Results The excess volumes of n-hexane + pseudo-n-hexadecane (13-19) are shown in table 1 in which the mole fraction x16 is calculated by using the mean molar mass of the pseudo-n-hexadecane and regarding it as a single substance. These results are

TABLE

1. Excess

x

--vE cm3 mole1

0.097 0.175 0.241 0.298 0.346

0.291 0.476 0.544 0.576 0.589

volumes

of VE of (1 -

X

0.388 0.425 0.458 0.487 0.514

-P cm3 mol-l 0.585 0.572 0.558 0.550 0.526

x)CaHls

of x(O.SC~~H~~

x

0.538 0.449 0.487 0.533 0.586

+ 0.%&H,,)

- VE cm3 mol-l 0.511 0.565 0.553 0.519 0.483

at 298.15

x 0.654 0.739 0.848

K

-VE cm3 mol -l 0.421 0.328 0.201

TERNARY

I

I

ALKANE

I

0.2

0

I

MIXTURES

I

0.4

I

0.6

1173

I

I

I

0.8

1

X

--,

FIGURE 1. Excess volumes. 0, (1 - x)CSH14 + x(O.~C~~H~~ + O..5C&H& at 298.15 K; (1 - x)&H,, + xC~H~~: smooth curve through the results of Diaz Pefia and de Soto.@)

TABLE X

0.4472 0.4974 0.5467

2. Excess enthalpies HE of (1 - x)C~H~~ + x(O.~C~~H~~ + 0.5&H& HE/J mol - 1 108 113 113

X

0.6156 0.3154 0.5098

HE/J mol-l 109 85 111

X

0.3794 0.2300 0.7145

HE/J mol - 1 102 72 88

at 298.15 K X

0.2707

HE/J mol - 1 85

FIGURE 2. Excess enthalpies. 0, (1 - x)C,H,, + x(0.5ClsHzs + 0.5&H& at 298.15 K; - - -, (1 - x&H,, + xCleH34: smooth curve through the results of Larkin et al.;@) . . . ., (1 - xGHI, + xCd&: smooth curve through the results of McGlashan and Morcom;(*) -, HE/J mole1 = x(1 - x)(440.6 - 48.2(1 - 2x)).

1174

C. K. LOOI, C. J. MAYHEW,

AND A. G. WILLIAMSON

compared in figure 1 with the published data for the mixing of n-hexane + n-hexadecane. The agreement with the work of Gomez-Ibafiez and Liu@) is similar to that shown and all three sets of measurements are numerically slightly larger than those of Desmyter and van der Waals.(7’ A similar presentation and comparison of the excess enthalpies is shown in table 2 and figure 2 where our results are compared with those interpolated from the work of McGlashan and Morcom(*’ and with the direct measurements of Larkin et ~1.‘~’

5. Discussion The excess enthalpy HE of n-hexane + n-tridecane at 298.15 K (X = 0.5) estimated from the results of Larkin and McGlashan(“’ at 293 K is about 60 J mol-‘. For n-hexane + supercooled n-nonadecane (melting temperature: 305 K) at 298.15 K, we estimate a value of HE(x = 0.5) M 190 J mol-I. In view of these values, we believe that the results shown here indicate that the principle of congruence can be profitably extended to include ternary and higher combinations of homologous series. We propose to continue these studies by carrying out some of the other mixing experiments outlined above and by extending our examination to liquid-vapour equilibria. We thank the New Zealand University this work.

Grants Committee

for financial support for

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Brernsted, J. N.; Koefoed, J. Kgl. Dansk. Videnskab. Selskab Mat.-Fys. Medd. xxii 1946, No. 17,l. Koefoed, J. Disc. Faraday Sot. 1953, 15, 207. Beath, L. A.; Williamson, A. G. J. Chem. Thermodynamics 1969, 1, 51. Beath, L. A.; O’Neill, S. P. ; Williamson, A. G. J. Chem. Thermodynamics 1969, 1, 293. Diaz Pefia, M. ; Benitez de Soto, M. An. Real Sot. Espan”. Fis. Q&m. Ser. B, 1965, 61, 1163. Gomez-Ibafiez, J. D.; Liu, C. J. J. Phys. Chem. 1963,67, 1138. Desmyter, A.; van der Waals, J. H. Rec. Trav. Chim. Pays-Bas 1958, 77, 53. McGlashan, M. L.; Morcom, K. W. Trans. Faraday Sot. 1961, 57, 581. Larkin, J. A.; Fenby, D. V.; Gilman, T. S.; Scott, R. L. J. Phys. Chem. 1966, 70, 1959. McGlashan, M. L. Personal communication.