SOME THERMODYNAMIC PROPERTIES
OF THE SYSTEM
BENZENE - 1,2-DICHLOROETHANE
PROEFSCHRIFT
TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAP AAN DE TECH-NISCHE HOGESCHOOL TE DELFT, OP GEZAG VAN DE RECTOR MAGNIFICUS DR. O. BOTTEMA, HOOG-LERAAR IN DE AFDELING DER ALGEMENE WETEN-SCHAPPEN, VOOR EEN COMMISSIE UIT DE SENAAT TE VERDEDIGEN OP WOENSDAG 1 JUNI 1955, DES
NAMIDDAGS TE 2 UUR
DOOR
LUKAS HANS RUITER
scheikundig ingenieur
GEBOREN TE TANDJONG MORAWA
D. B. CENTEN'S UITGEVERSMAATSCHAPPIJ N.V. Amsterdam — 1955
Dit proefschrift is goedgekeurd door de Promotor Mevrouw Prof. Dr. Ir. A. E. Korvezee.
,,ffi.an allen die belang stelden in hei hierin heschreuen onderzoek
r '^.
„Grote dank ben ik verschuldigd aan het Delfts Hogeschool Fonds, dat mij door ruime geldelijke steun in staat stelde dit onderzoek te verrichten."
C O N T E N T S
page
LIST OF SYMBOLS 9 I INTRODUCTION
1 The object of this research 11 2 Short survey of current theories . . . 12
3 The presentation of experimental values of the excess
functions 15 4 The system involved 17
5 Survey of literature concerning the measurements of
AH, ACp and AV oi the system benzene -
1,2-dichloroethane 17 II PURIFICATION OF THE LIQUIDS
1 Benzene 21 2 1,2-dichloroethane 23
III THE HEATS OF MIXING
1 Introduction 24 2 Apparatus 25 3 Experimental procedure 29
4 Calculation 30 5 Preliminary and additional measurements . . . 36
6 Results 37 IV THE EXCESS MOLAR HEAT CAPACITIES
1 Introduction 48 2 Apparatus 48 3 Experimental procedure 49
4 Calculation 50 5 Results 54 6 Comparison with the excess molar heat capacities,
page V THE EXCESS MOLAR VOLUMES
1 Introduction 64 2 Apparatus . . . 64 3 Calculation 67 4 Results 67 VI CONCLUSION 73 SUMMARY 78 SAMENVATTING 79 AUTHOR INDEX 80
LIST OF SYMBOLS
A constant in Newtons' equation of heat exchange. Cp molar heat capacity of a liquid.
ACp excess molar heat capacity of mixing. E electrical potential difference.
AG molar Gibbs' free energy of mixing.
AG'^ ideal molar Gibbs' free energy of mixing. zlG"* = RT {(1—Jc) In (1—x) + x\nx} AG^ excess molar Gibbs' free energy of mixing. G AlW.
AH molar heat of mixing. AvH molar heat of vaporization. i electrical current. M molecular weight. Mbe„.en. = 78.108 •^1.2-dichloroethane= 9 8 . 9 6 6 n TlD 0 P P" dQ, Q R AS AS'" AS^ t T V V AV W X a e
e
6° Q number of moles. refractive index (Nao). surface area.pressure.
equilibrium vapour pressure of pure liquid. heat absorbed by the calorimeter.
electrical resistance. molar entropy of mixing. ideal molar entropy of mixing.
AS'" = —R {(1—x) In (l—x) + xlnx}
excess molar entropy of mixing. time.
absolute temperature. volume.
molar volume.
excess molar volume of mixing. heat capacity.
mole fraction of the second component (1,2-dichloroethane). temperature coefficient of Pt resistance thermometer. dielectric constant.
temperature (seem).
temperature (degrees Celsius).
E R R A T A ,
behorende bij het proefschrift van L. H. Ruiter.
pag. 15: Uit de laatste regel van de tekst verwijderen de woorden: the solute in.
pag. 31: In het onderschrift van fig. 8 lees O i.p.v. />.
pag. 39 en 40: In de onderschriften van de figuren 10 en 11 lees: 41.85 °C i.p.v. 7.60 °C en
7.60 °C i.p.v. 41.85 °C.
pag. 47: In het onderschrift van fig. 13 dienen de regels 4 t/m 6 gelezen te worden:
AHjx(l—x) at 22 °C, calculated from our measurements. AH/x(\—x) versus x curve stated by Sieg, Criitzen and Jost to represent their experimental data at 20 °C.
CHAPTER I I n t r o d u c t i o n I The object of this research
If we want to test certain consequences of the proposed theoretical models for non-electrolyte liquids by the much used procedure of calculating what happens when two such liquids are mixed, accurate and extensive measurements of thermodynamic properties of these mixtures are needed. The differences which occur between the mixtures of liquids, consisting of molecules with similar properties, and the unmixed liquids are often very small. As has been stressed by several authors (e.g. Everett^)) it is of the greatest importance that when values for the excess Gibbs' free energy, the excess entropy, the heat of mixing and other excess functions of such binary mixtures are used to this end, they should be determined with the utmost care in one and the same laboratory with the same materials. Tests of the con-sistency of the measurements can be applied, because these thermody-namic quantities are related to each other.
Since :
AG^= AH—TAS^ (1) {dAG^IdT)p = — AS^ (2)
(Ó ( AG^IT)löT)p = — AHir (3)
(d AHjdT)p = T{d AS^IdT)p (4)
in which AG^ is the excess molar Gibbs' free energy of mixing :
AG^= AG—AG'",
AS^ is the excess molar entropy of mixing :
^ 5 ^ = AS— AS'" and AH is the molar heat of mixing,
isothermic vapour pressure measurements, yielding AG^, can be correlated with direct measurements of the heats of mixing at different temperatures, thus giving a complete thermodynamic picture of a
1) D. H. Everett, Discussions Faraday Soc. 15, 126 (1953).
binary system from well below room temperature up to the normal boiling points of the components.
As
{öAHlöTjp^ ACp (5)
a control on the directly measured heats of mixing at different tempe-ratures is provided by measurements of the excess molar heat capacities of the binary mixture concerned.
It has been the object of this research to make a contribution to the thermodynamically consistent data of binary solutions for which the deviations from ideality are small. The results of the measurements of the heats of mixing, the excess molar heat capacities and the excess molar volumes, described in this thesis, form part of a research program, which includes in addition isothermic vapour pressure measurements on the same binary system.
Baud^) has published in 1915 the first systematic and extensive
study concerning the heats of mixing of non-electrolyte liquids at room temperature. Ever since many investigators have determined the heats of mixing in varying systems, but unfortunately only a few of them (including are Boissonnaf en Cruchaud^)) have been aware of the temperature dependency of this quantity.
Scatchard*) was the first to study the relation between the excess
molar volume and other excess quantities of mixtures of non-electro-lytes. Since then much attention has been paid to this quantity. More recently, qualitative agreement has been obtained between a better founded theory and experiments concerning mixtures of simple non-polar compounds^). It is evident that, apart from questions of packing, the energy of mixing will contribute to the excess molar volume. Systematic measurements oi AV may therefore clarify some problems concerning the intermolecular forces on mixing.
2 Short survey of current theories
Several theories, which try to account for the changes in the ther-modynamic functions of two non-electrolyte liquids on mixing, have been developed. The most succesful ones are those which are based
2) E. Baud, Bull. soc. chim. France 17, 329 (1915).
3) C, G. Boissonnas and M. Cruchaud, Helv. Chim. Acta 27, 994 (1944). «) G. Scatchard, Trans. Faraday Soc. 33, 160 (1937).
on the assumption that one may consider the pure liquid as a quasi-crystalline state in which each molecule occupies a lattice site and is surrounded by a well defined number of nearest neighbours. In a mix-ture the molecules of the second component are then supposed to occupy each one or more of these lattice sites, according to size.
The first rigorous treatment on this basis has been initiated by Guggenheim^). He developed the theory of the „strictly regular" solution, using the „quasi-chemical" approximation. By considering the inter-change energy w, defined as half the energy required in forming two pairs of AB molecules by breaking one AA pair and one BB pair, to be temperature dependent, Guggenheim could account approximately for the excess thermodynamic functions on mixing of simple non-polar liquids with almost equal molar volumes^). In his theory Guggenheim evaluates only the configurational partition function, assuming the internal partition function and the acoustic factor in the translational partition function to be equal in the pure liquid and in the solution. These assumptions greatly reduce the applicability of this theory to real solutions.
Barker has developed in a series of papers')^)^") a theory in which he took account of orientation effects of polar groups in solutions in which association occurs. His approach is along the same line as in the theory of the „strictly regular" solution. Assuming the neighbouring molecules to have different contact points with specific, temperature dependent, interaction energies, he obtained a set of undetermined parameters, that could be adjusted at a certain concentration (x = 0.5) to the experimental values of AG^, AH and TAS^. In this way he obtained in mixtures in which hydrogen bonding occurs reasonable agreement between experimental and theoretical curves for AG^. The agreement between the interchange energies itself is, however, some-times not satisfactory.
A major improvement in the treatment of the lattice model of liquids involving spherical molecules with isotropic force fields, has been obtained by Prigogine etal.^^) by supposing the molecules to move in cells. On assuming the potential energies between two molecules to obey a 6—12 potential energy function and approximating the mean
«) E. A. Guggenheim, Proc. Roy. Soc. A 148, 304 (1935). ') £ . A. Guggenheim, Mixtures, Oxford (1952).
«) ƒ. A. Barker, J. Chem. Phys. 20, 1526 (1952).
°) ƒ. A. Barker, I. Brown, and F. Smith, Discussions Faraday Soc. 15, 142 (1953).
>») / . A. Barker and F. Smith, J. Chem. Phys. 22, 375 (1954).
^'•) I. Prigogine and A. Bellemans, Discussions Faraday Soc. 15, 80 (1953).
In this paper a more general treatment is given than in their preceding papers. 13
field by a smoothed potential model, they arrive at expressions for the excess thermodynamic functions. A comparison of the experimental values of these functions with those calculated from this theory gave a very reasonable agreement between AG^ and AH calculated and observed. The calculated values for TAS^ and for ^ V are systematically smaller than the experimental ones. It must be kept in mind, however, that no constants have been adjusted to the values of the mixtures at any concentration.
Recently Pople^^) has developed a theory in which he accounts for directional interactions between polar molecules. He separates the inter-molecular force fields into a central-force part and one concerned with the directional forces. Using again a lattice model he evaluates the partition functions for axially symmetric molecules in pure liquids as well as in mixtures. The theory succeeds in accounting for a loss of entropy due to hindrance of free rotation of the molecules by directional forces.
Of the recent theories only the theory of „conformal" solutions, put forward by Longuet-Higgins^^), does not imply a lattice model. His treatment involves the use of the law of corresponding states. To this end he generalizes to multicomponent mixtures an equation of Pitzer^*) which gives the mutual potential energies of the molecules in certain pure liquids. Considering only spherical molecules, not necessarily of equal size, or non-spherical molecules of the same shape and size
Longuet-Higgins arrives at expressions for the excess Gibbs' free energy,
the excess entropy and the heat of mixing, similar to those obtained in the theory of the „strictly regular" solution. As a consequence of the use of an equation of state this theory also accounts for the excess volumes of mixing. As all the excess functions depend on one interaction parameter only, one can calculate these quantities when one of them is measured. As one might expect, good agreement is obtained between theory and experiment for simple, non-polar mole-cules. According to Scott^^) it will probably be useless to extend this theory to approximations of higher order than the first, because most liquids obey only roughly the law of corresponding states.
To make the mathematical treatment more tractable, it is assumed in all these theories that the internal energies of the molecules are not affected by their environment. Consequently the internal partition functions are left out of consideration. This assumption might more *") ƒ. A. Pople, Discussions Faraday Soc. 15, 35 (1935).
") H. C. Longuet-Higgins, Proc. Roy. Soc. A 205, 247 (1951). ") K. S. Pitzer, J. Chem. Phys. 7, 583 (1939).
or less be justified when mixtures of non-polar molecules are considered. It will not be justified when the molecules considered have permanent dipole moments. This will be discussed in chapter VI.
3 The presentation of experimental values of the excess functions
The plotting of measured excess thermodynamic functions of binary mixtures against molar concentration can be done in more than one way. The question as to the most efficient manner merits discussion.
First of all we can plot the results of the measurements in a straight-forward manner, that is the excess thermodynamic function (denoted by AY^) against the mole fraction (fig. la). From such curves, however, we cannot conclude much more than that the thermodynamic function is symmetric or not with respect to the mole fraction. These curves do not bring out other special features or small systematic discrepancies and it is generally not easy to express the results in exact language.
Scatchard}^) has suggested the plotting of the excess functions divided
by x(l—x) against the mole fraction, and subsequently the evaluation of the analytical expression of this curve in terms of a potential series in {2x—1) (fig. 16). This seems a more effective manner, and I have used it throughout this work. It turns out that even in accurate measure-ments we usually do not need terms higher than (2x—1)^ as long as we are concerned with slight deviations from ideality. Systematic discrepancies in the results of the measurements are likely to be detected more easily in this way as is shown in fig. 13 and as has been discussed in a previous paper^').
A disadvantage of this method is that the experimental errors at extreme concentrations are exaggerated relatively to those of the mea-surements at 0.15<x<0.85. Consequently we cannot decide in this way if perhaps anomalous phenomena might set in at very low concen-trations of either of the components. It seems not very likely, however, that on mixing two non-electrolyte liquids such deviations will occur, although Kohier and Rott^^) have suggested otherwise. More certainty on this point may be obtained from measurements which deal with the properties of dilute solutions. Thus from the measurements of the freezing point depression of a system we obtain the partial Gibbs' free energy of tha solute an the solvent'^), which can be correlated with the ") G. Scatchard, Chem. Revs. 44, 7 (1949).
") A. E. Korvezee, L. H. Ruiter and A. L. Stuyts, Rec. trav. chim. 72, 462 (1953). ") F. Kohier and E. Rott, Monatsh. 85, 703 (1954).
") A. E. Korvezee, P. M. Heertjes, W. J. Hessels and K. M. Knip, Chem. Week-blad 42, 363 (1946).
same quantity resulting from the vapour-liquid equilibrium measure-ments at higher temperatures, provided the heats of mixing of the system from the freezing point up to the temperature at which the
0.2 0J5
Fig. 1. Plotting of the experimental values of the excess functions against molar concentration.
vapour-liquid equilibria are measured, be known. The data should be consistent when no anomalies occur in the dilute solution.
Recently Adcock and McGlashan^°) have advanced another method for plotting the experimental results, viz. the excess thermodynamic quantity against x(l—x). This is shown in fig. Ic, in which the filled circles refer to fictitious measurements at x<0.5 and the open circles to those at x>0.5. This method seems only reasonable when we suppose the system to obey the requirements of the „strictly regular" solution. In that case the experimental points must lie on a straight line, the slope of which determines the constant in AY^ = ax(l—x). However, in plotting A Y^/x( 1—x) against the mole fraction (Scatchard's method) we ought to obtain in these cases a straight horizontal line, which provi-des an easy check of the experimental points. The disadvantage is, that small deviations of the „strictly regular" behaviour are easily over-looked (as is shown somewhat exaggerated in fig. Ic), and there is no question of graphically evaluating the constants in the case of a more complicated behaviour.
4 The system involved
We have chosen the system benzene - 1,2-dichloroethane as the first object of investigation. Because of the complex phenomena which occur when the two liquids are mixed, this system is not adequate for testing the current theories dealing with binary liquid mixtures. On the other hand, this in itself makes the system interesting.
Our interest was raised too because this system has often been quoted as an ideal one^^), whereas already in 1915 Baud^) had shown that there is a measurable heat of mixing. In 1937 GZossïone^^) has suggested that the apparent ideality might be due to the cancelling of opposing deviations (Cf. chapter VI). Although many investigators have reported thermodynamic properties of this system, a complete description is lacking; it could not be deduced with sufficient accuracy from the data available.
The appreciable difference between the refractive indices of the pure compounds enables an accurate determination of the molar composition of the liquid mixtures by single refractometer reading, which is an important point in the vapour-liquid equilibrium measure-ments.
5 Survey of literature concerning the measurements of AH,
ACp and AV of the system benzene - 1,2-dichloroethane
The heats of mixing of the system benzene - 1,2-dichloroethane have been measured by several research workers. They are represented in fig. 13, together with our curves. Baud^) states the heat of mixing at one concentration {x = 0.74) to be 17.5 cal/mole (73.2 J/mole). The temperature indication is vague (15—20 °C).
Kremann^^) calculated the heat of mixing at x = 0.5 from a qualitative
experiment by Young^) at an unspecified temperature. He arrives at
AH = 10.6 cal/mole (44.4 J/mole).
The Chemical Abstracts^) report measurements of Kireev, Bykov and Chodortschenko^^). The only statement given relating to our system, is that there is a positive heat of mixing.
") J. von Zawidzki, Z. physik. Chem. 35, 128 (1900). A, Schulze and H. Hock, Z. physik. Chem. 86, 445 (1914). O. Faust, Z. physik. Chem. 113, 482 (1924).
E. A. Guggenheim, Trans. Faraday Soc. 33, 155 (1937). ") 5. Glasstone, Trans. Faraday Soc. 33, 158 (1937).
*^) R. Kremann, Eigenschaften binarer Fliissigkeitsgemische, Stuttgart (1916). ") S. Young, Fractional distillation, London (1903).
») Chem. Abstr. 32, 7808» (1938).
2») V. A. Kireev, V. T. Bykov and V. V. Chodortschenko, J. Phys. Chem. (U.S.S.R.) 10, 807 (1937).
More recently the heats of mixing have been determined by
Tschamler^^), Sieg, Criitzen and Jost^^) and by Cheesman and Whitaker^^). Tschamler has mixed the liquids at 21—23 °C: he did not expect his
results to be better than to 17 J/mole (68—170 J/mole for AH/x (1—x)). The agreement between his work and our calculated values for 22 °C is clearly much better than that.
Sieg, Criitzen and Jost represent a series of measurements at 20 °C
by the equation:
AHIx (l—x) = 79.0 -f 46.7 (2x—1) + 19.2 (2x—1)^ cal/mole
( = 331 + 195 (2x—1) -f 80 (2x—1)^ J/mole).
The corresponding curve in fig. 13 brings out that the fit might be improved. Besides their AH values turn out to be higher than ours throughout the concentration range. That their results are perhaps not very reliable is obvious from their CP data.
Finally the heats of mixing of this system have been measured by
Cheesman and Whitaker at 24.7 °C. In a previous paper^') we have
already mentioned that their results are in perfect agreement with ours at the same temperature up to x = 0.6. In view of the whole evidence concerning the AHjx (1—x) versus x curves'as stated in fig. 13, it is obvious that their AH values at 1,2-dichloroethane concentrations higher than x = 0.6 exhibit a systematic error, increasing with the mole fraction of this component.
The heat capacities of mixtures of benzene and 1,2-dichloroethane have been the object of a research by Schulze and Hock^''), Tschamler^''),
Sieg, Criitzen and Jost^) and Staveley, Hart and Tupman^^)*). Their
results are represented in fig. 18.
Schulze and Hock have measured this quantity at 20 °C, 35 °C
and 50 °C. Only at 20 °C have they observed in the solutions rich in 1,2-dichloroethane a small negative deviation from linearity.
Tschamler has published measurements at 21—23 °C. It appears
that his results are in qualitative agreement with those described in this work, his values being higher than mine.
The measurements of Sieg, Crützen and Jost were carried out at *) M y thanks are d u e to Dr. Staveley, w h o has been so kind t o send m e t h e detailed results of his measurements before their pubUcation.
" ) H. Tschamler, Sitz.het. Akad. Wiss. Wien A b t . l i b , 157^ 499 (1948). " ) L . Sieg, J. L. Criitzen a n d W. Jost, Z . physik. C h e m . 198, 263 (1951). »») G . H. Cheesman a n d A . M. B. Whitaker, Proc. R o y . S o c . A 212, 406 (1952). 3») A . Schulze a n d H. Hock, Z. physik. C h e m . 86, 445 (1914).
20 °C. They found no significant excess molar heat capacity, the maximum value of ACPIX (1—x) being —0.5 J/moledeg.
Staveley, Hart and Tupman have determined the molar heat capacity of benzene, 1,2-dichloroethane and three of their mixtures in the range from 15—70 °C. The values of ACp, calculated from their measure-ments, show a peculiar behaviour. They do not vary sensibly with temperature. At x = 0.2433, ACpjx (1—x) is of the order of + 4.8 J/moledeg, while at x = 0.7334 this quantity amounts to —6.6 J/moledeg. The mixture with the mole fraction 0.4617 shows no excess molar heat capacity. The value of ZICP/X (1—x) at x = 0.7334 is in agreement with the results described in this work at 20 °C. The dis-crepancy of the results of Staveley c.s. at lower 1,2-dichloroethane concentrations might possibly be due to a slight error in the deter-mination of the mole fraction of the mixtures.
The densities of benzene-1,2-dichloroethane mixtures have been determined by a few authors with reasonable accuracy. Among these are Brown^^) and Linebarger^^), cited by the International Critical Tables^*)*) and Coulson, Hales and Herington^^). The results of their measurements are plotted in fig. 22. They have all carried out their measurements at 20 °C. The excess molar volumes, calculated from the data given, show that the measurements of Brown and Linebarger art in approximate agreement with our results for this temperature. Those calculated from the measurements of Coulson c.s. show a small but distinct deviation from ours. This might be due to the difference in the density of benzene found by Coulson c.s. (0.87904 g/ml) and by us (0.87891 g/ml).
The densities of this system have also been measured by Bragg and Richards^^). The excess molar volumes calculated therefrom show a wide scatter and besides a significant discrepancy from ours at low 1,2-dichloroethane concentrations. They report the density of ben-*) The data of Brown and of Linebarger are represented there in one table, without any distinction between them. The I.C.T. report also measurements of Biron (J. Russ. Phys. Chem. Soc. 41, 469 (1909)). The concentrations are stated to be in weight % . The AV values calculated therefrom are negative. If, however, the values of the concentrations are supposed to be expressed in mole "ó, the agreement is fair.
32) Brown, J. Chem. Soc. 39, 202 (1881). 3^) Linebarger, Am. J. Sci. 2, 226 (1896). 3*) International Critical Tables III, 155 (1928).
3*) E. A. Coulson, J. L. Hales and E. F. G. Herington, Trans. Faraday Soc. 44, 636 (1948).
^•) L. B. Bragg and A. R. Richards, Ind. Eng. Chem. 34, 1088 (1942).
zene to be 0.8775 g/ml, which is much too low. If we calculate from their data the excess molar volumes using for the density of benzene 0.8790 g/ml instead of 0.8775 g/ml, the agreement between their results and ours is much better.
Tschamler^'') has measured the excess molar volumes at 20 °C,
35 °C and 50 °C. Though his measurements are not stated to be very accurate, his temperature variation of zlK is in agreement with ours.
CHAPTER II
P u r i f i c a t i o n o f t h e l i q u i d s 1 Benzene
The purification involves the removal of thiophen, toluene and other possible homologues, and water. To remove the thiophen com-mercially available benzene was shaken three times with concentrated sulphuric acid and washed with water. Tests with isatin proved the absence of thiophen. In order to get rid of toluene and the homologues the benzene was then frozen out as many times as to reach constant freezing point to within 0.05 °C. Next the benzene was stored over CaCla.O aq., and then dried over Na.
The subsequent fractionation was carried out in two steps. First the benzene was distilled in column I (2 m long, vacuum jacket, packed with Berl saddles). The middle fractions, with constant boiling points, were collected. The second distillation was carried out in colunm II (1 m long, silvered vacuum jacket, packed with V4A steel helices : 2 x 2 mm, special construction to prevent wet air entering the column). The distillate was collected in a calibrated vessel, as shown in fig. 1, provided with a jacket that could be kept at any desired temperature. The outlet of the vessel could be connected with any apparatus to be filled with the pure liquid. Only the middle fractions of which no change in boiling point could be detected, were used for the measure-ments. They had the following physical constants :
freezing point: 5.50 ± 0.05 °C boiling point: 80.10 ± 0.03 °C
Q (20.00 °C) : 0.87891 g/ml no (25.0 °C) : 1.49795
Timmermans^) mentions in his compilation the following data:
freezing point: 5.496 — 5.533 °C boiling point: 80.07 — 80.105 °C
Q (20.00 °C) : 0.87888 — 0.87909 g/ml no (25.0 °C) : 1.49790 — 1.49807
^) / . Timmermans, Physico-chemical constants of pure organic compounds, Amsterdam, (1950).
woo
drying lowers
i30
^WO
L 0
Fig. 2. Purification column.
A glass tube, packed with V4A steel helices; B vacuum jacket; C mercury filled glass tube; D mercury; E "Akulon" plug, which can be adjusted by the
2 1,2-dichloroethane
Since in the presence of moisture 1,2-dichloroethane may decompose
into 2-chloroethanol and hydrogen chloride, the procedure of Barton^)
has been adopted to purify commercially available 1,2-dichloroethane*). The raw material was shaken three times with a 4 N NaOH solu-tion, washed as many times with distilled water and dried over CaCl2. Oaq. Next it was fractionated in column I. T h e middle fractions (boiling range less than 0.10 °C) were stored over CaCl-^.Oaq. Before use this material was fractionated a second time in column I I I (of similar design to column II). The middle fractions, used for the measurements, had now a boiling range of less than 0.03 °C. T h e following physical constants were determined :
boiling p o i n t : 83.50 ± 0.05 °C p (20.00 °C) : 1.25294 g/ml no (25.0 °C) : 1.44220
Unfortunately there are but few reliable data concerning 1,2-dichloro-ethane. Timmermans^) quotes the following :
boiling point : 83.45 — 83.6 °C
Q (20.00 °C) : 1.25278 g/ml (interpolated from data at 15.00 and 30.00 °C)
no (25.0 °C) : 1.4423 (extrapolated from data at 15.0 and 20.0 °C)
Coulson, Hales and Herington^) have reported : o (20.00 °C) : 1.25297 g/ml
Refractive indices have been measured also by Zawidzki*) at 25.2 °C and b y Schwers^) at 25.4 °C. Using dnjdd" = 0.00053 deg-^ their values at 25.0 °C are respectively :
no (25.0 °C) : 1.44236 and 1.4420
*) Barton has elaborated his method in the belief that 1,2-dichloroethane forms an azeotrope with 2-chloroethanol (D. H. R. Barton, J. Chem. Soc. 1949,
148; Nature, 157, 626, (1946)), for which he refers to the investigations of
Kaplan, Grishin and Skvortsova (J. Gen. Chem. (U.S.S.R.), 7, 538 (1937)).
In the original paper of Kaplan c.s., however, no evidence of an azeotrope can be found. This is in perfect agreement with the measurements of Lecat (Bull. classe sciences, Acad. Royale Belg. 5e série, 39, 273 (1943)). The supposition of Barton may be due to a faulty abstract of the paper ot Kaplan c.s. in Chemical Abstracts (31, 4554 (1937)), stating that the system 1,2dichloroethane -2-chloroethanol yields an azeotropic mixture. The abstracts in Chemisches Zentralblatt (108% 2332 (1937)) and British Chemical Abstracts (A 1937 I, 296) are correct.
2) D. H. R. Barton, J. Chem. Soc. 1949, 148.
^) E. A. Coulson, J. L. Hales and E. F. G. Herington, Trans. Faraday Soc. 44, 636 (1948).
*) / . von Zawidzki, Z. physik. Chem. 35, 140 (1900).
*) F. Schwers, Bull, classe sciences Acad. Royale Belg. 623 (1912).
CHAPTER III.
I T h e h e a t s o f m i x i n g
1 Introduction
The molar heat of mixing AH of two liquids is defined by the amoimt of heat absorbed by one mole of the solution formed. To determine this heat effect it is essential to measure the resulting temperature change AmO and the heat capacity W of the system involved :
AH = — Amd.Wjn (6)
where n is the number of moles of the solution in the calorimeter. The observed temperature difference A„6 measured in a mixing experiment equals the „true" temperature change Amd from equation (6) only when the calorimeter is perfectly adiabatic. In all other cases we have to allow for the heat exchange with the surroundings during the measurement.
In our experiments we have used an isothermally jacketed calori-meter. Coops et al.^) have given an account of the line along which the calculation of the amount dQa of heat transferred may proceed in such calorimetric systems. This calculation is based on Newton's law of heat exchange :
dQu = A(9j - d„)dt (7)
where 6j and d„ are the temperatures of the jacket and the calorimeter wall respectively.*)
The application of this theory to our experiments will be given in section 4, where we shall follow the calculation on the basis of a representative heat of mixing experiment.
*) In fact dQa is proportional to the surface involved in the heat exchange. Assuming this surface to be constant it is included in the coefficient A.
') / . Coops, K. van Nes, A. Kentie and / . W. Dienske, Rec. trav. chim. 66, 113 (1947).
J. Coops and K. van Nes, Rec. trav. chim. 66, 131 (1947).
The heat capacity W of the system is determined in each heat of mixing experiment by the introduction of a known quantity of electrical energy after the mixing period is finished. This is called the calibration of the calorimeter.
2 Apparatus
During the past decades different types of calorimeters have been used for determining the heats of mixing of two liquids^). As the pre-hminary experiments were started in 1946 the post-war shortage of material left little choice for the construction. We were forced to construct the simplest type of calorimeter, viz. a Dewar-flask, provided with a stirrer, a thermometer, a device for mixing the liquids and a heating coil for calibration purposes; the whole was immersed in a constant temperature bath. Several investigators^'*) had already reported accurate results with this type. A minor disadvantage is discussed in chapter IV, 5.
The final form of our calorimeter is shown in fig. 3a. It consists of an evacuated, silvered Pyrex flask A with a similar ground stopper B. The stopper is provided with a hollow glass stirrer C, a resistance thermometer E and a NiCr heating coil D . The ground joints F fix the positions of D and E. The calorimeter is made gastight with a mercury seal G of sufficient length to meet the highest pressure changes possible. A glass bulb L contains one of the components. Its stem is enclosed in the copper spiral K to keep it in place during stirring.
The hollow stirrer shaft (internal diameter 1 mm) serves as a supply pipe for the second component. The stirrer is provided with a sharp needle O of stainless steel. A special arrangement makes it possible to move the stirrer 30 or 50 mm down to destroy the bulb whilst the stirring continues. The stirrer, driven by a rotary current electromotor, rotates with a constant speed of 530 revolutions per minute.
Two types of platinum resistance thermometers have been used. T y p e I*) is shown in fig. 36. The Pt wire (length 1000 mm, diameter
^) / . M. Sturtevant, Technique of organic chemistry (editor: A. Weissberger), Vol. I, part 1, 731, New York (1949).
') T. F. Young and O. G. Vogel, J. Am. Chem. Soc. 54, 3030 (1932). *) W. Hieber and A. Woerner, Z. Elektrochem. 40, 256 (1934). ') R. D. Void, J. Am. Chem. Soc. 59, 1515 (1937).
•) K. S. Pitzer, J. Am. Chem. Soc. 59, 2365 (1937). ') / . C. Southard, Ind. Eng. Chem. 32, 442 (1940). «) R. B. Williams, J. Am. Chem. Soc. 64, 1395 (1942).
*) Constructed by Ir. B. Jansen.
,— 20cm
Fig. 3a. Calorimeter. N cork, made gas-tight with "Velpon", P paraffin sealing; U opening of the hollow stirrer; H "Akulon" bearings.
Fig. 36. Pt resistance thermometer. Type I.
T thin glass tubings; W cotton-wool. C Pt wire, wound on a mica cross; D ebonite tubing, filled with sealing wax; E flexible copper wires; F ground joint; G soldered junctions; L copper wires, 0: 0.6 mm; S sealing wax; T thin glass tubings; W cotton-wool.
0.035 mm, resistance about 100 ohm) is wound bifilarly on a mica cross C. The whole is enclosed in a thin copper cylinder A, which is welded to a glass tube B. A small knot of cotton-wool W prevents convection of the dry air inside the lower part of the tube. Type II has been made of a similar, commercially available platinum resistance thermometer („Degussa", Hanau, Germany). Its Pt coil is fused into the surface of a small glass rod (length 30 mm, diameter 5 mm). It has been luted to a glass tube enclosing similar leads as in Type I.
The resistance thermometer R, (fig. 4) is connected to a Wheatstone-bridge arrangement consisting of two resistances of 100 ohm (Rj and Rj) and a variable resistance R3 with decades from 0.1 ohm to 10000 ohm. The resistance of the leads to the resistance thermometer is balanced by an equal resistance Re in the leads to R3. The other leads are all of the same diameter and have equal lengths. The deflection of the reflecting galvanometer G (type Moll A 1, „Kipp", Delft) is read on a glass scale from a distance of 2 m with an accuracy of 0.01 cm. The sensitivity can be adjusted by the resistance R5. At maximal sensitivity (R5 = 0), 0.01 cm of the glass scale equals 0.00014 °C.
i V woo n
Fig. 4. Wheatstone-bridge arrangement.
Within the desired accuracy of 0.1%, the deflection of the galvano-meter used for the majority of the heat of mixing experiments turned out to be proportional to the temperature variation, recorded by the
resistance thermometer. Only in the last few measurements, where another galvanometer of the same type was used, a slight non-linearity could be detected. In these cases a correction was applied. Another correction was the reduction of the tangent to the true deflection. In all our calculations we have used the corrected scale centimeter (seem), viz. one cm on the glass scale, as a unit of temperature.
In order to keep the current through the thermometer low enough to prevent an undesirable production of heat, a resistance of 1000 ohm is connected in series with the 4 V accumulator.
The NiCr heating coil*) is essentially of the same construction as the Pt resistance thermometer of Type I. The NiCr wire (length 800 mm, diameter 0.1 mm) has a resistance of about 100 ohm. Fig. 5 shows the arrangement for measuring the potential drop across the heating coil during the supply of electrical energy to the calorimeter. The potentiometer (type 2165, „Nedoptifa", Zeist) can be read with an
potentio-meter Nedoptifa type 216S
Fig. 5. Diagram of the device for the supply of a measured quantity of electrical energy to the calorimeter.
accuracy of 0.1 mV. The resistance of the NiCr coil is determined in the Wheatstone-bridge arrangement of fig. 4.
Of the thin glass bulbs, containing one of the components, two types have been used (fig. 6). The larger type, used for mole fractions between 0.35 and 0.65, is shown in position in fig. 3a (L). The other type, for smaller concentrations, is held in upside down position by copper clamps as shown in fig. 7.
The calorimeter is placed in a 70 liter water thermostat. Originally the temperature was controlled by a toluene-mercury regulator; the residual temperature fluctuations did not exceed 0.005 °C at 24.67 °C and 0.015 °C at 41.76 °C. Afterwards a specially designed mercury contact thermometer was used; at 7.50 °C the thermostat temperature had fluctuations not greater than 0.010 °C.
The room temperature was kept constant at 27.0 ± 0 . 1 °C.
eo : 15-25 iO-50 marks ^ W -2S 60.75 — 20-iO — - 5 0 . 55 —
Fig. 6. Glass bulbs. Fig. 7. Copper clamp for the small glass bulbs 3 Experimental procedure
To avoid contamination of the liquids with moisture the utmost care must be used in filling the calorimeter. The following procedure has been adopted.
The glass bulb was thoroughly dried by a stream of dry air. After weighing the bulb was filled directly from the distilling column and allowed to reach the temperature of the calorimeter thermostat. Excess 29
liquid above the mark at which the stem is to be fused was then removed by suction. The filled bulb was weighed to determine its volume. Next 3—7 ml more of the liquid were removed by suction and the stem was fused at the mark. The closed bulb and the remainder of the stem were weighed separately before the bulb was stored in the calorimeter thermostat.
To start an experiment the filled glass bulb was taken from the thermostat, cleaned and placed as quickly as possible in the Dewarflask. The calorimeter was then closed using silicone grease when the liquid outside the bulb was to be 1,2-dichloroethane and a mixture of glycerol, dextrin and mannitoP) in the case of benzene. A stream of dry air was then passed through the stirrer. The vessel was filled with the second liquid, also directly from the distilling column, and weighed before and afterwards. To close the seal G (fig. 3a) mercury was introduced to the desired level; the junction between flask and stopper was filled with molten paraffin. After this the calorimeter was fastened in the thermostat and finally the stirrer was connected to the driving shaft and the Pt resistance thermometer as well as the heating coil soldered to their respective devices. The contents of the calorimeter were allowed to reach the convergence temperature (see section 4), which on account of the large quantity of liquids inside the Dewarflask (about 350 ml), took at least one night. This disadvantage, however, is more than balanced by the greater accuracy gained in using these large quantities of liquids.
Before starting an experiment the constancy of the galvanometer reading was controlled during at least 20 minutes. Then the glass bulb was crashed by pushing down the stirrer. This caused a sharp temperature drop. The next three readings were made at 10 second intervals, subsequent readings at 30 second intervals. After the calori-meter temperature had exhibited a regular increase for at least 10 mi-nutes a current was passed through the heating coil till the temperature approached its original value again. During this period simultaneous potentiometer readings were taken. Afterwards galvanometer readings were continued during 15 more minutes. The whole course of a 6—t variation is given in fig. 8.
4 Calculation
In our calorimeter there is, apart from the instantaneous heat of mixing or the heat supply for calibration and besides the heat of radiation and conduction, a constant production of heat by the stirrer and by
9n=59.23 \ e^=59.;5 ©mrsao? 25 .»initial period -30 35 iO main period— iS 50 • Imal period^ 55 . t (min)
the current through the resistance thermometer. As long as these two are the only heat generators in the calorimeter, there will be a heat flow from the calorimeter to the jacket. When the stirrer rotates with constant speed so that a constant amount of heat is produced per second, we may expect that after some time a stationary condition establishes itself in which the heat produced (dQr) equals the amount of heat removed by radiation and conduction :
— dQa = dQr (8) The constant temperature then reached by the calorimeter is called the
convergence temperature 0^.
It is obvious that, when the calorimeter temperature d„ is lower (higher) than 0^, the calorimeter will absorb (give off) heat from (to) the jacket. Taking dQr into account equation (7) may be transformed^) into :
dQ'a = dQa + dQr = A {6k —e„) dt (9)
Consequently the heat exchange with the surroundings in any time-interval («2—f]) is given b y :
t2
Q» = A J id^d„) dt. (10)
t,
The „true" temperature change J mo in a heat of mixing experiment, defined in section 1, can now be written as the difference between the observed temperature change Ao6 and of a correction term Ac6 due to the total heat exchange during the main period (section 3) :
Amd = AoS- A,e (11) AcO follows from :
Acd = Qa'IW = GJidk—e„)dt (12)
ti
where G = A/W (13) From equation (12) it is obvious that a temperature versus time
curve is essential for the determination of the correction term Acd. Fig. 8 shows the curve representing measurement no. 55. As an instance the elaboration of this experiment is given.
According to Coops the convergence temperature can be calculated from the slopes of the (Ö—() curve of the initial (i) and final (ƒ) periods of the calibration :
e,iddidt)i-d,{ddidt)f
* iddidt)i—{ddidt)f ^^'
_ 59.15 (46.74—45.78)/360 — 46.28 (59.07—59.23)/600 _ * "" (46.74—45.78)/360 — (59.07—59.23)/600 ~"
= 57.98 seem. The value of G follows from :
G = {(ddldt)i—{deidt)f)l(d,—d,) (15) (46.74—45.78)/360 — (59.07—59.23)/600
G = ^ ^ 59.15-46.28 = '''''^'' '"'=-'• The observed temperature change on mixing is du—Ob = — 11.52 seem. The correction term zlc^ in the time interval (tb—tu) is given b y :
tu
Acd = GJ(B,i—Q„)dt = G.O,.p
tb
where p is a factor converting the planimetered surface from em* in scem.see.
AcQ =- 228 • 10-« • 89.6 • 60 = 1.23 seem.
Consequently the „true" temperature change on mixing is : J „ e = — 11.52—1.23 = — 12.75 seem. The same procedure has been applied to the cahbration : Observed temperature change : d„—ö„ = 12.49 seem. Correction term : Jcö = G.(Oi—Og) • p
Acd = 228 • 10-^ • 61.8 • 60 == 0.85 seem.
„True" temperature change : A^d = 12.49—0.85 = 11.64 seem. To determine the amount of electrical energy supplied to the calori-meter the potential drop EPQ across the points P and Q (fig. 5), the resistance Ra of the NiCr wire and the resistance R/ of the leads from P and Q to the wire are measured.
The amount of heat supplied is :
Qh= {EpQl(Ra + R')}^^at (16) QH = { 4.0510/(100.313 -f- 0.042) )^ • 100.313 • 780
= 127.50 J
The time t = 780 see is determined with an accurate chronometer. The heat capacity W of the filled calorimeter follows from :
W = QHI And (17)
W = 127.50/11.64 = 10.954 J/sccm.
Finally AH is calculated from equation (6) with n = 4.1268 mole of the mixture :
AH = 12.75 • 10.954/4.1268 = 33.84 J/mole
It must be stressed that the derivation, given above, is based on the assumption that the heat exchange between the contents of the calori-meter and the surroundings takes place only through radiation and conduction, and not through convection. The temperature of the inner wall of the calorimeter is supposed to determine the rate of heat ex-change between the calorimeter and the thermostat.
In our calorimeter the heat exchange through convection between the inner and outer wall can be neglected. Thus we may safely assume that the heat exchange is only effected through radiation and conduction.
When the temperature in the calorimeter changes rapidly, as is the case at the moment the two liquids are mixed, the temperature recorded by the resistance thermometer will exceed the actual change in tempera-ture of the inner wall. Consequently our calculation of the correction term in equation (12) cannot be exact.
It turned out, however, that within three minutes after such a sudden temperature change a quasi-stationary condition is reached, in which the variation in dd/dt is only due to the error in the galvano-meter reading. We may assume that the calorigalvano-meter mass, involved in the heating processes, has then reached its momentary equilibrium temperature. In the slowly proceeding mixing experiments and in the calibration, where the temperature changes per unit time are relatively small, no error will be introduced by assuming that the thermometer temperature equals the inner wall temperature. In experiments in which the mixing proceeds quickly, a small error will occur owing to this assumption. Since in these cases the correction term for heat exchange ( Acd) is small as compared with the „true" temperature change (Amd), this error can be neglected. Moreover, there is no alternative in calculating the correction term.
The values obtained for AH must be subjected to another correction. When the two liquids are mixed in the calorimeter some evaporation and condensation will occur. These phenomena will result in a positive or negative heat effect. In order to be able to calculate this effect the following assumptions are made :
a. The mixtures of benzene and 1,2-dichloroethane are ideal. Since the heat effects to be calculated are small we may neglect the small deviations from Raoult's law.
b. The new vapour - liquid equilibrium is established almost instanta-neously after the bulb has been crashed.
c. There will be no significant gas stream along the lower bearings of the stirrer (H, fig. 3a) during the time the experiment proceeds.
Because the stirrer is moved downward to crash the bulb, a relatively high pressure arises in the gas space above the bearings of the stirrer. This pressure can be calculated to be about 1050 mm mercury. The pressure changes below the bearings, due to the mixing of the liquids, will not exceed 20 mm mercury. Consequently no vapour will pass the bearings in the upward direction. The calculation of the heat effect occuring in the calorimeter may then proceed as follows.
bet or a mixing otttr mitring
Fig. 9. Schematic drawing of the situation before and zhev crashing the glass bulb.
Fig. 9 shows schematically the situation inside the calorimeter before and after mixing. We suppose the total volume of the calorimeter below the lower bearings to be v ml. Initially we have v^ ml of compo-nent 1 inside the bulb and v^ ml of compocompo-nent 2 outside the bulb. The volume of the glass of the bulb is Vg ml, its gas space v^ ml and its total outer volume (I'l+1^4+1^5) ml. Consequently the gas space in the calorimeter is f3 = v—V2—(Vi+v^+v^) ml. When the mixing is completed we have Vg ml mixture, equalling (v^+V2+ Av) ml, when zlv represents the expansion of the volume on mixing. The gas space is then v^ — (v—Vg—v^ ml.
There will be an evaporation of component 1. The amount (expressed in moles) is given by the equation :
Ag, = 1.60 • 10-s • (v,p, — v^X)\T (18)
Some of the vapour of component 2 originally present will condensate. This amount (also expressed in moles evaporated) can be calculated with the equation :
Ag2 = 1.60 • 10-5 • (v,p2- V^PX)\T (19)
In these equations
p\ and p° are the equilibrium vapour pressures of the components
1 and 2 at the temperature T,
Pi and P2 are the partial vapour pressures of the components 1 and 2
(at the temperature T) after mixing, calculated with Raoult's law. 35
T h e small temperature change, due to the mixing is neglected. T h e resulting heat effect AHr is given by :
AHr= Ag,A„H,+ Ag^AMz (20)
in which A^H^ and A^H^ are the heats of vaporization of the
com-ponents 1 and 2 at the temperature T. Correcting the measured values for the heats of mixing, AHr should be added (table VI).
5 P r e l i m i n a r y and additional experiments
The heats of mixing have been determined at the three different thermostat temperatures mentioned in section 2. We want to know in each ease the actual mixing temperature 0b (fig. 8), which is recorded by the resistance thermometer at the beginning of an experi-ment. Platinum wire resistance RQ and temperature centigrade 0° are correlated by Callendar's formula :
In addition to R^oo and RQ one more calibration value is wanted for each thermometer in order to determine the constant 6. As our thermometers were not proof against high temperatures, we have used to this end the transition point Na2SO4.10 aq -> Na2SO4.0 aq (32.38 °C). T h e accuracy obtained is limited by the precision of R^, Rg and Rg (fig. 4). This is stated to be 0.01%, consequently the stated temperatures are correct to 0.03 °C.
The constants of our thermometers are listed in table I. For the heat of mixing experiments at 7.60 °C, 25.00 °C and 41.85 °C the thermo-meters I, I I and I I I have been used respectively. Thermometer IV was used for the excess molar heat capacities measurements.
T a b l e 1.
Constants of the resistance thermometers. No. I 11 I I I IV Type I I I I I I Ohm 99.95 90.06 90.79 100.02 Rioo Ohm 138.51 125.19 126.24 138.65 Ras'ss Ohm 112.58 101.50 102.42 112.65 Rioo/Ro 1.386 1.390 1.391 1.386 Ö 1.7 0.9 1.8 1.5 a d e g - ' (0.003911 at 7.7 °C ) 0.003896 at 20.5 °C ) 0.003879 at 35.7 °C (0.003861 at 50.6 °C
The subscripts to R refer to the temperatures at which the resistance of the ther-mometers have been determined.
According to the latest requirements the ratio Rjgo/Ro should be at least 1.3910 for platinum resistance thermometers which are used in absolute temperature measurements. Only thermometer III satisfies this requirement. It must be remarked, however, that in our case constancy of dR/(f0° is the only important requirement, which, as has appeared from our measurements, is satisfied by all our thermometers. To test the method employed, chiefly as to equality of the initial temperatures of the components, we have carried out in each series a number of blank tests, consisting of benzene benzene and water -water mixing experiments. In 5 out of 7 cases a small heat effect was pereeptable (table II). Since the calorimeter contains about 4 moles of liquid in the mixing experiments, the mean effect amounts to —0.08 J/mole, whereas the measured heats of mixing range from 6 to 100 J/mole.
The constancy of A (equation (7)) during a measurement proves the system to obey Newton's law of heat exchange. We have calculated values for A from a measurement in which the readings are extended for more than one hour after the input of electrical energy. By com-bining successive intervals of 360 seconds of the final period with the same interval of the initial period a series of values of 0^ and A is obtained. They are shown in table III. It is obvious that these quantities show no tendency to increase nor to decrease. The values found for A in each series of heat of mixing experiments confirm the conclusion that J4 is a constant in our calorimetric system (table V). A has been calculated by multiplying G by the total heat capacity of the calori-meter, assuming that there is no heat capacity change on mixing
( ACp = 0). This assumption is justified in this case because the
experimental error in the determination of G is relatively large. Another test on the efficiency of the Acd computation is shown in table IV. In experiment no. 5 we have calculated .^„0 starting from different tu values. It appears, that 13 minutes after the bulb has been crashed, the mixing is not yet completed. After 17 minutes a constant value for Amd is obtained, which proves our method of calculating
zlc0 to be correct. 6 Results
The results of the heat of mixing experiments are represented in table V. The measurements at 25.00 °C that have been carried out by Ir. A. L. Stuyts, are included in this table. The values of the mixing temperature 0^ are stated in column 17.
T a b 1 e II. Blank tests. No 15 16 34 35 36 56 57 Contents (inside and outside the bulb) H^O C,He H^O H^O C,He H^O CeHe Total amount of liquid in calori-meter g 349.71 304.89 333.81 329.61 283.40 348.98 292.90 A.l(fi J/sec deg 106 113 126 183 123 134 143 Ahd secm 4.17 8.38 6.64 4.79 8.97 5.43 9.10 Bu-db seem 0.00 0.06 0.25 0.40 0.00 0.02 0.05 Acd sccm 0.00 0.00 —0.26 —0.37 0.00 0.00 —0.01 Amd sccm 0.00 0.06 —0.01 0.03 0.00 0.02 0.04
t
95.42 75.51 155.85 110.71 80.88 139.99 97.49 W J/scem 22.88 9.011 23.47 23.11 9.017 24.81 10.71 Heat effect J 0.00 —0.54 0.23 —0.69 0.00 —0.50 —0.43 Heat effect per mole J/mole —0.14 0.00 —0.11 Tem-perature °C 7.60 7.60 25.00 25.00 25.00 41.85 41.85T a b l e III. Experiment with extended final period.
No 37 Contents of calori-meter CoHj 0. sccm 47.53 du sccm 47.21 01 sccm 47.37 tv-tu sec 360 0m sccm 58.40 57.97 57.57 57.20 56.85 56.54 56.24 55.96 55.72 55.50 55.28 55.07 dn sccm*) 58.90 58.40 57.97 57.57 57.20 56.85 56.54 56.24 55.96 55.72 55.50 55.28 0. sccm 58.65 58.19 57.77 57.39 57.08 56.70 56.39 56.10 55.84 55.61 55.39 55.17 tm-tn sec 360 360 360 360 360 360 360 360 360 360 360 360 dk sccm 51.77 51.99 51.99 52.03 52.01 52.11 52.03 52.03 52.21 52.25 52.15 52.08 G.106 s e e ' 197 192 192 191 192 188 191 191 184 182 187 189 A.W J/sec deg 121 118 118 118 118 116 118 118 113 112 115 116
T a b l e I V . Calculation of A„d, taking different values of 9u. No. 5 G sec-i 0.000170 P sec/cm 60 0fc sccm 25.33 Time after the bulb has been crashed min. 13 17 21 24 27 30 33 du seem 13.60 13.68 14.07 14.40 14.72 15.02 15.33 du-db sccm —11.73 —11.65 —11.26 —10.93 —10.61 —10.31 —10.00 O3 cm^ 160.4 194.4 227.6 259.6 290.7 320.8 350.5 Zlc0 sccm —1.64 —1.98 —2.32 —2.65 —2.97 —3.27 —3.58 Amd sccm —13.37 —13.63 —13.58 —13.58 —13.58 —13.58 —13.58 CiH^a^
Fig. 10. AH versus x plot. A measurements at 7.60 °C, ''•' •*•' 7
O measurements at 25.00 °C (carried out by Ir. A. L. Stuyts), [3 measurements at 41.85 °C. '^ ' •
Table VI shows the corrections for evaporation and condensation during mixing, to be added to the AH and AHjx(\—x) values of table V. Because of the small vapour pressures at 7.60 °C, the heat effect, due to evaporation and condensation, can be neglected. The heats of vaporization of benzene at 25 °C and 42 °C are taken from the
CiHiClj
Fig. 11. AHIx(i -x) versus x plot. / \ measurements at 7^.60° C, ' /1, r Ï
O measurements at 25.00° C (carried out by Ir. A. L. Stuyts), El measurements at 41.85° C. 1 (• r
compilation of Timmermans^''). Those of 1,2-dichloroethane are calcu-lated from the vapour pressure curve (determined in this laboratory), using Clapeyron's equation. On account of the small corrections in-volved, the application of the latter equation is justified.
Finally a small correction is to be applied to bring the AH and
AHlx(l—x) values in each series to a standard temperature. The
following temperatures have been chosen : series I : 7.60 °C; series II : 25.00 °C; series I I I : 41.85 °C. These corrections, calculated with the numerical values of d AH Id T derived from the three series of mea-surements, are shown in table VI.
The corrected values for AH and AHlx(l—x) are collected in table VI. The AH versus ;c and AHjx(\—x) versus x plots are rendered in fig. 10 and fig. 11.
The following family of curves has been drawn through the observed values :
7.60 °C: AHIx(\—x) = 361 + 200(2x—1) + 105(2x—l)2 J/mole (I) 25.00 °C: AHIx(\—x) = 254 + 208(2x—1) -f 86(2x—l)2 J/mole (II) 41.85 °C: AHIx(l—x) = 178 + 229(2x—1) + 84(2x—l)2 J/mole (III)
Table VI shows the deviation of the observed values from those, calculated from the formulae given above. It is obvious that with all three series (especially those at 7.60 °C and 41.85 °C) the deviations at lower concentrations of 1,2-dichloroethane (x < 0.5) are greater than at higher concentrations. This can be explained by the fact that the rate of mixing at JÏ < 0.5 is relatively slow, because in these cases the hquid with the greatest density is inside the bulb. As the bulbs, used at the measurements at 7.60 °C and 41.85 °C had to be made of rather thick glass in order to be able to resist pressure differences of about 100 mm mercury, they are not completely crashed. Often only the upper part is destroyed, the bottom remaining intact and forming a bowl. In consequence of the slow rate of mixing, the correction term
Acd in equation (11) is comparatively large and the accuracy of the
measurement will depend largely on the precision with which 0^ and G can be determined. This is illustrated in fig. 12, showing heat of mixing experiments at x = 0.3075 (a) and x = 0.9127 (b). Both measurements are of the 41.85 °C series (measurements no. 43 and 55). With the 7.60 °C series the measurements between x = 0.15 and
X = 0.5 show negative deviations from equation (I). This may be caused
by incomplete mixing of the liquids, due to the incomplete crashing of the bulbs and the relatively high viscosities of the liquids at this temperature.
') J. Timmermans, Physico-chemical constants of pure organic compounds, Amsterdam (1950).
1 1 2 3 4 5 6 7 8 9 9a 10 11 12 13 14 21 21a 22 23 24 25 26 27 28 29 30 31 32 33 41 42 43 44 45 45a 46 47 48 49 50 51 52 53 54 55 2 0.0426 0.0867 0.1406 0.1570 0.2926 0.2941 0.4568 0.5826 0.5904 0.5904 0.7280 0.8631 0.9167 0.9301 0.9316 0.0469 0.0469 0.1021 0.1874 0.2728 0.3987 0.3988 0.4456 0.4986 0.5273 0.6493 0.7723 0.8354 0.9176 0.1479 0.1724 0.3075 0.3810 0.3945 0.3945 0.3986 0.4358 0.5691 0.6150 0.6341 0.6883 0.7476 0.7724 0.8704 0.9127 3 27.55 26.20 24.17 31.46 24.92 25.28 26.43 27.31 25.91 26.32 27.72 22.82 28.53 26.16 33.61 55.77 54.95 57.11 57.06 54.81 52.73 62.80 65.77 68.54 65.78 56.72 60.32 57.28 66.42 57.19 55.91 57.04 52.57 56.46 58.12 52.61 52.11 54.06 51.20 54.61 50.56 54.72 53.31 55.66 57.98 4 169 170 174 167 170 181 176 182 178 161 161 274 169 165 145 212 204 218 217 214 201 221 217 203 208 198 198 208 212 207 207 224 204 225 227 202 242 233 317 206 303 159 211 227 228 5 109 110 114 107 110 117 114 120 116 105 108 185 114 113 99 131 126 137 136 136 124 139 137 128 133 124 128 129 133 138 141 152 139 156 157 138 156 155 219 142 210 111 147 161 158 6 6.59 10.21 6.95 14.00 5.32 6.64 7.41 6.01 6.02 7.65 11.38 7.20 12.66 8.42 7.71 5.31 7.83 8.64 8.76 13.89 18.14 16.77 18.82 23.09 23.57 10.47 19.65 11.08 12.95 7.37 8.17 9.23 7.14 8.48 4.09 7.09 4.44 5.92 5.58 5.62 5.10 6.57 9.09 7.95 12.49 7 0.38 0.09 0.00 —0.56 —0.72 —0.86 —1.05 —1.00 —0.87 0.10 —0.66 —1.30 —0.30 —0.29 —0.60 0.30 1.17 —0.39 —0.65 —0.96 —0.96 —1.53 —3.34 —3.07 —3.96 —1.03 —2.61 — 1 . 4 0 —1.22 0.24 0.45 — 0 . 2 4 0.13 —0.39 0.32 —0.20 —0.55 —1.13 —0.97 —1.15 —1.06 —0.88 —1.06 —1.22 —0.85 Tab Results of the he^
8 6.97 10.30 6.95 13.44 4.60 5.78 6.36 5.01 5.15 7.75 10.72 5.90 12.36 8.13 7.11 5.61 9.00 8.25 8.11 12.93 17.18 15.24 15.48 20.02 19.61 9.44 17.04 9.68 11.73 7.61 8.62 8.99 7.27 8.09 4.41 6.89 3.89 4.79 4.61 4.47 4.04 5.69 8.03 6.73 11.64 9 27.60 1 26.03 24.31 31.07 25.33 25.93 26.60 28.28 27.60 — 28.13 27.10 28.48 26.70 34.92 55.15 — 51.34 53.89 51.05 51.37 61.48 61.87 66.40 61.59 57.48 56.41 54.68 62.96 55.82 55.17 55.55 52.22 56.77 — 52.10 51.84 53.99 53.00 53.18 53.15 55.39 53.43 56.07 57.30
Explanation of the column numbers. 1 number of measurement.
2 mole fraction of 1,2-dichloroethane in the mixture. 3 convergence temperature 0* (sccm).
4 G.IO» (sec-i). 5 A.lO^ (J/sec deg). 6 Aod (secm). )
e V. )f mixing experiments. 10 — 3.01 — 5.88 — 5.28 —12.50 —10.00 —11.71 —12.42 —12.70 —12.31 — —15.09 —15.25 — 9.85 — 7.36 —13.61 — 2.06 — — 4.08 — 7.74 —11.24 —15.53 —16.84 —21.60 —22.70 —22.86 —11.87 —19.69 —10.69 —12.43 — 1.95 — 2.45 — 6.37 — 4.30 — 8.46 — — 5.32 — 6.55 — 9.86 —10.27 —10.65 —11.68 —10.93 —10.67 —14.68 —11.52 11 —0.71 —1.47 —0.67 —2.58 —3.58 —2.02 —2.32 —0.78 —1.44 — —1.63 —2.69 —0.83 —0.50 —1.28 —0.44 — —1.34 —1.85 —2.98 —5.64 —3.65 —2.70 —1.25 —5.56 —2.68 ^ . 6 0 —2.74 —3.13 —0.46 —0.49 —1.58 —1.52 —2.88 — —1.36 —0.96 —0.86 —1.19 —1.41 —0.40 —1.27 —1.28 —1.44 —1.23 12 — 3.72 — 7.35 — 5.95 —15.08 —13.58 —13.73 —14.74 —13.48 —13.75 — —16.72 —17.94 —10.68 — 7.86 —14.89 — 2.50 — — 5.42 — 9.59 —14.22 —21.17 —20.49 —24.30 —26.95 —28.42 —14.55 —24.29 —13.43 —15.56 - 2 . 4 1 — 2.94 — 7.95 — 5.82 —11.34 — — 6.68 — 7.51 —10.72 —11.46 —12.06 —12.08 —12.20 —11.95 —16.12 —12.75 13 81.71 120.69 154.01 122.20 80.76 101.18 149.94 153.23 151.85 227.84 261.02 93.64 226.70 182.85 81.02 50.51 81.12 74.34 73.39 117.47 154.63 145.24 139.05 181.03 178.35 181.20 192.35 161.00 106.40 82.68 95.60 97.49 139.97 88.49 48.05 133.94 69.75 89.20 89.22 87.73 79.38 113.47 159.40 76.23 127.50 14 11.72 11.72 22.16 9.09^ 17.56 17.51 23.58 30.59 29.49 29.40 24.35 15.87 18.34 22.49 11.40 9.OO4 9.OI3 9.Oil 9.04o 9.O85 9.OO1 9.53„ 8.983 9.04^ 9.095 19.19 11.29 16.63 9.07i 10.87 11.09 10.84 19.25 10.94 10.90 19.44 17.93 18.62 19.35 19.63 19.65 19.94 19.85 11.33 10.95 15 10.89 21.72 32.86 35.21 59.19 60.11 85.27 98.66 98.84 98.54 94.76 66.40 45.55 39.92 38.62 6.14 6.14 13.19 23.54 34.46 51.48 51.51 56.93 63.88 66.56 73.40 69.69 59.38 36.53 7.05 8.49 22.14 28.64 30.91 30.79 32.84 36.62 51.89 54.88 58.54 58.28 58.92 57.94 43.39 33.84 16 267.0 274.3 272.0 266.1 286.0 289.5 343.7 405.7 408.7 407.5 478.5 561.9 596.5 614.1 606.1 137.4 137.4 143.9 154.6 173.7 214.7 214.8 230.4 255.5 267.0 322.3 396.3 431.8 483.1 55.9 59.5 104.0 121.4 129.4 128.9 137.0 148.9 211.6 231.8 252.3 271.7 312.2 329.6 384.7 424.7 17 7.60 7.58 7.55 7.55 7.60 7.60 7.63 7.55 7.68 7.68 7.63 7.58 7.63 7.58 7.58 24.98 24.98 24.93 24.95 24.93 24.93 24.84 24.81 24.90 24.81 25.12 25.01 25.04 25.09 41.85 41.85 41.85 41.85 41.82 41.82 41.85 41.85 41.85 41.85 41.85 41.87 41.87 41.87 41.85 41.87 9 06 (sccm). 10 Aod (sccm). 11 AcB (sccm). I mixing 12 Amd (sccm).
13 the amount of electrical energy supplied Qh (J). 14 the heat capacity of the filled calorimeter W (J/scem). 15 AH (J/mole).
T a b I The corrected values i
No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 21 22 23 24 25 26 27 28 29 30 31 32 33 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 44 X 0.0426 0.0867 0.1406 0.1570 0.2926 0.2941 0.4568 0.5826 0.5904 0.7280 0.8631 0.9167 0.9301 0.9316 0.0469 0.1021 0.1874 0.2728 0.3987 0.3988 0.4456 0.4986 0.5273 0.6493 0.7723 0.8354 0.9176 0.1479 0.1724 0.3075 0.3810 0.3945 0.3986 0.4358 0.5691 0.6150 0.6341 0.6883 0.7476 0.7724 0.8704 0.9127 AHr J/mole _ — — — — — — — — — + 0 . 0 5 + 0 . 0 8 + 0 . 1 0 + 0 . 1 4 + 0 . 7 1 + 0 . 2 1 + 0 . 2 2 + 0 . 2 4 + 0 . 2 4 —0.06 —0.01 —0.01 + 0.01 + 0 . 3 4 + 0 . 3 2 + 0 . 6 1 + 0 . 6 7 + 0 . 6 5 + 0 . 6 6 + 0 . 6 6 + 0 . 2 3 + 0 . 2 3 + 0 . 2 2 + 0 . 1 8 + 0.23 + 0 . 1 5 + 0 . 0 9 + 0 . 0 1 . AHr x ( l - x ) J/mole _ — — + 1.1 + 0 . 9 + 0 . 7 + 0.7 + 3 . 0 + 0 . 9 + 0 . 9 + 1.0 + 1.0 —0.3 —0.1 —0.0 + 0 . 1 + 2 . 7 + 2 . 2 + 2 . 9 + 2 . 8 + 2 . 7 + 2 . 8 + 2 . 7 + 0 . 9 + 1.0 + 0 . 9 + 0 . 9 + 1.2 + 0 . 8 + 0 . 8 + 0 . 1 Temp. corr. J/mole _ —0.02 —0.05 - O . 0 5 + 0 . 0 5 —0.10 + 0 . 1 4 + 0 . 0 4 —0.02 + 0 . 0 2 —0.01 —0.01 —0.00 —0.04 —0.05 —0.08 —0.10 —0.24 —0.27 —0.15 —0.27 + 0.16 + 0.02 + 0 . 0 3 + 0 . 0 4 — — — —0.01 — — — — — + 0 . 0 1 + 0 . 0 1 + 0 . 0 1 — + 0 . 0 0 Temp. corr X ( l — X ) J/mole _ —0.2 —0.4 - 0 . 4 + 0 . 2 —0.4 + 0 . 6 + 0 . 2 —0.2 + 0 . 2 —0.2 —0.2 —0.1 —0.4 — 0 . 3 —0.4 —0.4 —1.0 —1.1 —0.6 —1.1 + 0 . 7 + 0 . 1 + 0 . 2 + 0 . 5 — — — —0.1 — — — — — + 0 . 0 + 0 . 0 + 0 . 0 — + 0 . 0 AH J/mole 10.89 21.70 32.81 35.16 59.19 60.11 85.32 98.56 98.83 94.80 66.38 45.57 39.91 38.61 6.19 13.23 23.59 34.52 52.09 51.48 56.88 63.97 66.53 73.50 69.70 59.40 36.58 7.39 8.81 22.75 29.31 31.49 33.50 37.28 52.12 55.11 58.76 58.47 59.16 58.10 43.48 33.85
