Thermodynamics of liquid (hydrogen chloride + dinitrogen oxide)

M-1679 J. Chem. Thermodynamics 19&1, 16, 653-659

Thermodynamics of liquid (hydrogen chloride + dinitrogen oxide) LkLIO Q. LOBO” and LIONEL A. K. STAVELEY Inorganic Chemistry Laboratory, Oxford OXI 3QR, U.K.

Oxford University,

(Received 16 January 1984) The vapour pressuresand densities of {xHCl+(l -x)N,O}(l) have been measured at 182.32K (the triple-point temperature of dinitrogen oxide). The excess molar enthalpy Hfi, has been determined calorimetrically at a slightly higher temperature (184.03 K). This system was chosen as a model for a binary liquid mixture in which the molecules of one component have a dipole moment, while those of the other component have no dipole moment but have a quadrupole moment. The excessmolar Gibbs energy GE has been calculated from the vapour pressures.GE, the excessmolar volume V,E,and H,f,are all positive over the whole composition range, the values for GE and V,” for x = 0.5 at 182.32K being 146.9J’mol-’ and 0.146 cm3.mol-’ respectively, while Hi for x = 0.5 at 184.03K is 105.4J’mol-‘. SE, the excessmolar entropy, is therefore the only primary excess function which is negative at these temperatures.

1. Introduction The experimental work carried out in this laboratory on the thermodynamic properties of binary liquid mixtures of molecularly simple substances has in the last few years been particularly concerned with a systematic examination of the influence on those properties of polarity in the molecules of one or both components of the mixture. The properties of the mixture which are determined are the excessmolar functions Gk, Hz,, and Vz (and hence SL). Recent papers have dealt with mixtures of the type (non-polar + dipolar),“**) (non-polar + quadrupolar),‘3) (non-polar + octopolar),‘4’ (dipolar + dipolar),“’ and (quadrupolar + quadrupolar).@’ This paper is concerned with a mixture of (dipolar + quadrupolar) molecules. While it is highly desirable that, in a mixture chosen as a model, the molecules involved should be as simple as possible, the choice of the actual components must of course be determined to some extent by their physical properties, notably the range of temperature over which they exist as liquids, since the mixture should be studied over the whole range of composition at total vapour pressureswhich are not too high. If these pressures are too large, apart from purely technical difficulties which can arise, the correction for the non-ideality of the vapour phase, which particularly affects the determination of Gi and Hz, can become considerable, and ’ Permanent address: Chemical Engineering Department, University of Coimbra, 3000 Coimbra. Portugal. OO21-9614/84/160653+07 %02.00/O

0 1984 Academic Press Inc. (London) Limited

654

L. Q. LOB0

AND L. A. K. STAVELEY

its estimation with sufficient accuracy can present problems. For practical reasons of this kind, carbon dioxide, with its relatively high triple-point temperature and pressure, is not a very convenient representative of substances with quadrupolar molecules, although the molecule is acceptable in having no dipole moment and a relatively large quadrupole moment. We have therefore preferred to use dinitrogen oxide, N,O, which has a lower triple-point temperature and pressure than carbon dioxide, while its molecule is isoelectronic with, and structurally similar to, that of carbon dioxide. For a model mixture of (dipolar + quadrupolar) molecules we have chosen (hydrogen chloride + dinitrogen oxide). The total vapour pressure as a function of composition, from which the excessmolar Gibbs energy GE is derived, was measured at 182.32 K, the triple-point of N,O. V,” was measured at the same temperature, but the excess molar enthalpy Hz, for reasons of experimental convenience, at a slightly higher temperature (184.03 K). The dipole moment of HCl is’@ p = 3.57 x 10e3’ C. m and the quadrupole moment of N,O is 0 = - 10.0x 10m40C.m2. It is of course unavoidable that a dipolar molecule like HCl also has a quadrupole (the moment of which has been estimated’@ as (0 = + 12.7x 10m4’ C. m’). Also, the molecule of N,O has a dipole, but the value of this is so small@)(p = 0.55 x lo- 3o C. m) that its effect on the excessthermodynamic functions can be only a very minor one. Our recent papers have contained the experimental results for particular mixtures, and also the values of the excess functions calculated using the perturbation treatment developed by Gubbins and his collaborators. For reasons briefly explained later, this paper, however, is essentially limited to the presentation of the experimental results for GE, Hk, and V,“.

2. Experimental The techniques used for measuring Gi and V,” have already been described”**) as has the calorimeter for determining H,.E (‘) Since the literature on the effect of liquid hydrogen chloride on metals is still rather fragmentary, and some of it of long standing, it may be noted that no problems of corrosion were encountered in the experiments with the metal calorimeter. The volumes of the two cavities in the calorimeter were identical with those previously given.t3) The preparation and purification of the sample of hydrogen chloride used should have ensured that it was very dry. (l) Its purity was checked by the constancy during melting of its triple-point pressure, for which an average value of (13.807f0.005) kPa was obtained (compare 13.811kPa, reference 10, where other values are cited). The preparation and characterization of the N,O have already been described.‘3’5’ The vapour pressure of liquid HCl at the N,O triple-point temperature (182.32 K) was found to be 72.134 kPa (compare 72.147 kPa, reference 1l), while the value obtained for the molar volume of liquid HCl at the same temperature was (30.413f 0.005) cm3 *mol- ’ (compare 30.477 cm3 *mol- i, reference 12), the pyknometer having been calibrated at this temperature using a 99.96 moles per cent sample of C2H6 and the results of Haynes and Hiza.‘13)

THERMODYNAMICS

655

OF {xHCI +(I -x)N,O}(l)

The sources of the ancillary data needed in the evaluation of GE, V,“, and Hi from the actual experimental results have already been stated as far as N,O is concerned.(3*‘) For HCl, we used values of the second virial coefficient B determined by Dr U. Leuchs (1979) and kindly communicated to us privately. These gave B = -500 cm3.mol-’ at 182.32 K and -144 cm3*moll’ at 298.15 K. The cross virial coefficient B,, was assumed to be the mean of the coefficients for the two pure components. The thermal expansivity a, of HCl(1) at its saturation vapour pressure was calculated to be 2.1 x 10e3 K-’ from unpublished results of Prichard and Staveley.“‘) The molar enthalpy of vaporization AfH, of HCl at 184.03 K, needed in the determination of Hi, was estimated to be 16270 J. mol- ’ from the value of AfH, at the normal boiling temperature given by Giauque and Wiebeo4) and their heat capacities for the liquid. The isothermal compressibility icr- of HCl(1) at 184.03 K was estimated to be about 0.8 x 10m3MPa-’ from the approximate relation:” 5, xr M aTl/,/(AfH,-RT).

3. Results and discussion The total vapour pressure p for (xHC1 +(l -x)N,O}(l) is given in table 1. The mixture forms a positive azeotrope at x z 0.25, as shown in figure 1. However, GE (as evaluated by Barker’s method,“@ minimizing the pressure residuals 6P = Pcxpt-pcalc.) is an almost symmetrical function of the mole fraction, as is so often the case for binary liquefied gas mixtures. The Gf7,values fit the equation: G2JRT= x(l-x){A+B(2x-1)+C(2x-1)2}, (1) with the values of the parameters A, B, and C and their standard deviations: A = 0.3875, sA = 0.0022; B = -0.0171, sB= 0.0045; C = 0.0209, sc = 0.0108. For x = 0.5 Gi = (146.9kO.8) J.mol-‘. Some early p(x) results for this mixture obtained by Klemenc and Khol at the temperatures 173.15, 178.15, and 183.15 K are quoted in the International Critical . Tables as a “personal communication “(l’) These lead to the values of Gz(x = 0.5): 162 J*mol-’ at 173 K, 148 J*mol-’ at 178 K, and 156 J*mol-’ at 183 K. The trend of these values suggestsa rather large uncertainty, but they are approximately the same as our own value of 146.9 J *mol- I. The molar volumes of mixtures of known composition and the derived values of V,” are recorded in table 2. The values of V,” refer to mixing at the saturation vapour pressure, and fit the equation: V~/(cm3.mol-‘) = x(1 -x){D+E(2x-

l)+F(2x-

l)‘},

(2)

with D = 0.583, E = 0.083, and F = 0.129, the standard deviation being s = kO.007. V,“(x =0.5) = 0.146 cm3.mol-‘. The results for HE are presented in table 3 in the form used in previous papers.(‘* 18) HE m is listed as HE@ m = 0), its value at zero pressure, but in fact for the relatively low vapour pressures involved the difference between Hi at zero pressure and at the saturation vapour pressure is negligible ( < 0.1 J *mol - ‘). The HE values can be represented by the equation: HDRT = x(l-x){G+H(2x-1)+J(2x-1)2}, (3)

656

L. Q. LOB0 AND L. A. K. STAVELEY

TABLE 1. Vapour pressuresand excessmolar Gibbs energies of {xHCl+(l -x)N,O}(l) the mole fraction of HCI in the gaseousphase x

Y

0

0

0.11657 0.20700 0.29698 0.40511 0.50823 0.61785 0.72879 0.81522 0.89145 1

0.12751 0.21259 0.28897 0.37614 0.45885 0.54926 0.65140 0.74055 0.83316

@Pa

WPa

87.866 89.789 90.185 90.357 89.657 88.242 86.292 83.364 80.707 77.684 72.134

+20 -132 +79 +85 -41 +23 -105 +35 +41

at 182.32K; y is

Gp(J.mol-‘) 0

65.0 98.5 127.3 144.8 146.6 138.4 113.6 88.2 57.1 0

with G = 0.2757, H = -0.0547, and J = -0.0461, the standard deviation being s = +0.0018. HE(x = 0.5) = 105.4 J.mol-‘. Si as obtained from Gz and Hf, is given by the equation: S3JR = x(1-x){K+L(2x-l)+M(2x-1)2},

(4) with K = -0.1118, L= -0.0376, and M = -0.0670. TSz(x=0.5)= -41.4 J.mol-‘. GE, HE, and TSfi,are plotted against x in figure 2; V,” is plotted in figure 3. V,Eis positive while SE is negative. The V,” and SE curves are both slightly skewed in the same direction, with the maximum and minimum respectively falling at x > 0.5. The quantitative application to a mixture such as this of the perturbation theory developed by Gubbins requires explicit representation of the three intermolecular pair potentials appropriate to the mixture. Experience has already shown that the calculated excessfunctions are sensitive to the precise forms of these potentials, and particularly so when HCl is one of the speciesinvolved. Exploratory calculations by Gubbins and his collaborators have so far given results for (xHC1 +(l -x)N,O} which are not in close agreement with experiment, even though quite sophisticated potentials have been used. Thus, the HCl-HCl potential has involved not only terms

80 -

70 0

I

I 0.2

I

I 0.4

1

I 0.6

I

I 0.8

1

xory FIGURE 1. Vapour pressure of {xHCl+(l and against y at T = 182.32K.

-x)N,O}(l)

= {yHCl +(l - y)N,O}(g) plotted against x

THERMODYNAMICS

OF {xHCl+(l

657

-x)N,O}(l)

TABLE 2. Molar volumes and excess molar volumes of {xHCI +(l -x)N,O}(I) saturation vapour pressure

v,

X

cm3.mol-’

0

0.09936 0.19562 0.30555 0.31585 0.40180 0.41212

35.487 35.044 34.592 34.052 34.002 33.579 33.535

Vi cm3.mol-’ 0 0.061 0.097 0.115 0.118 0.131 0.139

V,E- V,“(eqn2)

cm’.mol-’ + 0.007 +0.006 -0.006 -0.005 -0.007 +o.ooo

X

VI cm3.mol-’

0.52436 0.62469 0.71618 0.79611 0.88900 1

32.982 32.464 31.981 31.562 31.039 30.413

at 182.32K and at the

V,” cm3.mol-’ 0.156 0.147 0.128 0.114 0.063 0

V,E- Vz(eqn 2)

cm3.mol-’ +0.009 +0.004 -0.003 +0.004 - 0.009 -

TABLE 3. Excess molar enthalpy of {xHCI +(l -x)N,O}(l) at (184.03+0.02) K; Q is the energy supplied to the calorimeter to maintain it at the initial temperature n,/mol

n,/mol

x

Q/J

0.01240 0.02021 0.01922 0.02439 0.03223 0.03419 0.04387 0.05619 0.06163 0.05490

0.04938 0.06975 0.05996 0.05021 0.05740 0.05063 0.04392 0.03483 0.02382 0.01162

0.2007 0.2246 0.2427 0.3270 0.3597 0.4033 0.5000 0.6177 0.7217 0.8259

6.474 8.679 7.831 8.267 10.204 10.247 10.784 9.806 6.888 3.414

G(P = 0) J.mol-’ 78.8 79.3 79.3 90.9 98.1 104.8 109.3 97.6 73.0 46.5

Hk - Hz(eqn 3) J.mol-’ + 7.2 f1.5 -2.7 -6.4 -3.2 fO.0 + 3.9 + 3.6 -1.5 -2.0

for the interactions arising from the presence in the molecules of a dipole and a quadrupole, but also terms allowing for induction effects and for the anisotropy of the overlap and dispersion forces. A priori, it would seem possible that there is hydrogen-bonding between the two components of the mixture. Molecules of hydrogen chloride are capable of hydrogen-bonding with one another (as witness, for example, the structure of the ordered low-temperature form of the solid), while the terminal atoms of the linear molecule of dinitrogen oxide might act as acceptors to the hydrogen atom of a hydrogen chloride molecule. Sufficiently strong hydrogen-bonding between the two components would be expected to lead to negative values of the primary excess functions. (A well-known example of this is provided by (trichloromethane + propanone), though this mixture is not truly analogous to (hydrogen chloride + dinitrogen oxide), since the molecules of trichloromethane do not significantly hydrogen-bond with each other). It is therefore interesting that the calculations so far carried out on (xHC1 +(l -x)N,O} tend to produce negative values of Gfj, HE, and V,” (at least over much of the composition range). If hydrogen-bonding does play an important role in this mixture, then in view of the highly directional nature of this kind of interaction it is possible that, simple

L. Q. LO30

658

AND L. A. K. STAVELEY

FIGURE 2. Excess molar functions Xg for {xHCI +(l -x)N,O}(l) plotted against x; G,!$excessmolar Gibbs energy at 182.32K; Hi, excessmolar enthalpy at 184.03K; TSE = HE-GE.

0

0.2

0.4

0.6

0.8

1

X

FIGURE

3. Excess molar volume Vk for {xHCl +(l -x)N,O}(l)

at 182.32K plotted against x.

though the molecules may appear to be, the successful calculation of the excess functions will require the use of even more sophisticated potentials, which take a more refined view of the electron distribution within the molecules. Be that as it may, the experimental results are presented here since the experimental study is regarded as being complete, while further theoretical work is contemplated. This work was partially supported by NATO Research Grant No. RG 146.81, and by Junta National de Investigacao Cientifica e Tecnolbgica (Portugal) under Research Contract No. 204.80.11. REFERENCES 1. Calado, J. C. G.; Gray, C. G.; Gubbins, K. E.; Palavra, A. M. F.; Soares, V. A. M.; Staveley, L. A. K.; Twu, C. H. J. Chem. Sac. Faraday I1978, 74, 893. 2. Lobo, L. Q.; Staveley, L. A. K.; Clancy, P.; Gubbins, K. E. J. Chem. Sot. Faraday I1980, 76, 174. 3. Machado, J. R. S.; Gubbins, K. E.; Lobo, L. Q.; Staveley, L. A. K. J. Chem. Sot. Faraday I 1980, 76, 2496. 4. Lobo, L. Q.; McClure, D. W.; Staveley, L. A. K.; Gubbins, K. E.; Gray, C. G. J. Chem. Sot. Faraday II 1981, 77,425. 5. Lobo, L. Q.; Staveley, L. A. K.; Clancy, P.; Gubbins, K. E.; Machado, J. R. S J. Chem. Sot. Faraday II 1983, 79, 1399. 6. Stogryn, D. E.; Stogryn, A. P. Mol. Phys. 1966, 11, 371. 7. Davies, R. H.; Duncan, A. G.; Saville, G.; Staveley, L. A. K. Trans. Faraday Sot. 1967, 63, 855. 8. Calado, J. C. G.; Staveley, L. A. K. Trans. Faraday Sot. 1971, 67, 289.

THERMODYNAMICS

OF (xHClc(1 -x)N,O}(J)

659

9. Lewis, K. L.; Staveley, L. A. K. J. Chem. Thermodynamics 1975, 7, 855. IO. Staveley, L. A. K.; Lobo, L. Q.; Calado, J. C. G. Cryogenics 1981, 21, 131. Il. Calado, J. C. G.; Kozdon, A. F.; Morris, P. J.; Nunes da Ponte, M.; Staveley, L. A. K; Woolf. L. A. J. Chem. Sot. Faraday Il975, 71, 1372. 12. Prichard, P. C.; Staveley, L. A. K. unpublished results. 13. Haynes, W. M.; Hiza, M. J. J. Chem. Thermodynamics 1977,9. 179. 14. Giauque, W. F.; Wiebe, R. J. Am. Chem. Sot. 1928, 50, 101. 15. Hildebrand, J. H.; Scott, R. L. The Solubility of Non-Electrolytes, 3rd edn. Reinhold: New York. 1950, p. 424. 16. Barker, J. A. Aust. J. Chem. 1953,6, 207. 17. International Critical Tables [III]. McGraw-Hill: New York. 1928, p. 285. 18. Lobo, L. Q.; Calado, J. C. G.; Staveley, L. A. K. J. Chem. Thermodynamics 1980, 12, 419.