Second virial coefficients for seven fluoroethanes and interaction second virialcoefficients for their binary mixtures with helium and argonC. M. Bignell and Peter J. Dunlop Citation: The Journal of Chemical Physics 98, 4889 (1993); doi: 10.1063/1.464943 View online: http://dx.doi.org/10.1063/1.464943 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/98/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in The effect of intermolecular interactions on the electric properties of helium and argon. III. Quantumstatistical calculations of the dielectric second virial coefficients J. Chem. Phys. 117, 2609 (2002); 10.1063/1.1491402 The effect of intermolecular interactions on the electric properties of helium and argon. II. The dielectric,refractivity, Kerr, and hyperpolarizability second virial coefficients J. Chem. Phys. 111, 10108 (1999); 10.1063/1.480362 The temperature and concentration dependencies of diffusion coefficients of seven helium–fluoroethanesystems J. Chem. Phys. 97, 5638 (1992); 10.1063/1.463771 Dielectric second virial coefficient of polar gases and their binary mixtures J. Chem. Phys. 62, 227 (1975); 10.1063/1.430267 Interaction Second Virial Coefficients in Binary Systems J. Chem. Phys. 55, 2071 (1971); 10.1063/1.1676374

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Second virial coefficients for seven fluoroethanes and interaction second vi rial coefficients for their binary mixtures with helium and argon

c. M. Bignell and Peter J. Dunlop Department of Physical and Inorganic Chemistry, University of Adelaide, Adelaide 5000 South Australia

(Received 10 September 1992; accepted 9 November 1992)

Using an accurate method which has been described in detail previously, data are reported for the second virial coefficients of seven fluoroethanes and for interaction second virial coefficients for their binary mixtures with helium and argon. All oLthe fluoroethanes have large dipole moments and, as expected, have virial coefficients which are much smaller than those of ethane and hexafluoroethane.

I. INTRODUCTION

In a recent publication I we described an apparatus and methods I for measuring the three second virial coefficients which characterize the molecular interactions in a binary gas mixture. These methods essentially involve use of a Texas Instruments (TI) quartz spiral gauge to accurately measure pressure changes when gases are mixed or ex­panded at constant temperature in a cell which consists of two identical volumes. It is suggested that this paper be read in conjunction with that work, where details were given which greatly improve the techniques we used on previous occasions.2-4 The purpose of this paper is to re­port second virial coefficients for fluoroethanes with large dipole moments,5-7 and their mixtures with helium and argon.

II. THEORY

A. Pure gases

The virial equation of state may be written as

PV --=I+B'P+C'p2+··· nRT '

(1)

where P is the pressure, V the volume, T the absolute temperature, R the gas constant, n the number of moles of gas, and B' and C' the second and third pressure virial coefficients, respectively. If two gases, one a reference gas and another of interest, are individually expanded from the same initial pressure Pi and volume VI to the same final

TABLE I. Purities of gaseous components, and their dipole moments at 300 K.

Percent

He 99.99 Ar 99.9 C2HSF 99.5 1,I-C2H4F2 99.6 1,1,I-C2H3F3 99.5 1,1,2-C2HJF3 99.4 1,1,1,2·CzH2F4 99.2 1,1,2,2-C2H2F4 99.0 CzHFs 98.0

"Dipole moments in units of debye.

lL (D)a

1.95 2.26 2.34 1.67 2.06 0.96 1.56

volume V2, then the second virial coefficient of interest is related I to the virial coefficients of the reference gas by the relation

B'= [(P-Pr) +B;(PyP-P?r) +C'(PP7-P?,) ]lA, (2)

where

(2a)

and Pr and P are the final pressures of the reference gas and the gas of interest, respectively, and C; for the reference gas, nitrogen, has been taken as zero. Calculations show that the third term containing C' is negligible for pressures lower than 2 atm.

B. Gas mixtures

As explained in detail in several previous publica­tions,l-4 it is possible to measure the excess virial coeffi­cients W for binary gas mixtures in the present apparatus,

(3)

where B 12, which characterizes the unlike interactions, can be obtained from the relation8,9

TABLE II. Second virial coefficients for pure gases (cm3 mol-I). The data in parentheses have been taken from some of the literature values reported in Ref. 12.

290 K 300 K 310 K

He (11.7) (11.6) (11.6) Ar ( -18.0) (-15.6) ( -14.0) C2H6 a -195.7 -182.6 -168.9

( -196.Q) ( -182.0) (-170.0) CzHsF -401.2 -370.7 -340.8 1,I-CzH4F2 -543.4 -492.6 -450.8 1,1,I-C2H3F3 -437.7 -400.8 -367.7 1,1,2-C2H3F3 -664.0b -599.9 -537.7 1,1,1,2-C2H2F4 -536.7 -485.3 -443.0 1,1,2,2-C2H2F 4 -511.2 -468.5 -427.9 C2HFs -395.1 -363.2 -335.5 C2F6

a -276.6 -255.3 _ -237.2

aThe data for C2H6 and C2F6 were reported in Ref. 1. bBecause of the low vapor pressure of 1,1,2-C2H3F3 at 290 K, it was necessary to estimate this value by extrapolation,

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4890 C. M. Bignell and P. Dunlop: Virial coefficients for fluoroethanes

TABLE III. Excess second virial coefficients if and corresponding in­teraction coefficients B12 for 18 binary systems of helium and argon with ethane and fiuoroethanes."

He Ar

T (K) if BIZ if B12

CZH 6 b

290 123.4 31.5 51.7 -55.1 300 117.5 32.0 48.8 -50.3 310 116.6 32.9 46.7 -44.8

CzHsF

290 238.8 44.1 149.3 -60.4 300 221.5 42.0 139.4 -53.8 310 203.8 39.2 123.5 -53.9

1,I-CzH4Fz

290 311.5 45.6 218.1 -62.6 300 286.5 46.0 199.9 -57.2 310 264.6 45.0 179.7 -52.7

1, 1, l-CzH]F]

290 249.5 36.5 161.7 -66.1 300 235.4 40.8 149.6 -58.6 310 220.9 43.1 139.2 -51.4

1,1,2-~H]F]

290 373.1 47.0 273.3 -67.7 300 344.9 50.8 250.1 -57.6 310 312.0 49.0 224.8 -51.0

1, 1, 1,2-CzH 2F4

290 302.2 39.8 203.7 -73.6 300 281.0 44.1 188.8 -61.6 310 254.9 39.2 173.6 -54.9

1, 1,2,2-C2HzF 4

290 293.7 43.9 196.4 -68.2 300 274.4 46.0 182.2 -59.9 310 253.4 45.3 162.0 -59.0

~HFs

290 232.7 41.0 135.8 -70.8 300 219.1 43.4 127.5 -61.9 310 202.8 41.0 119.3 -55.3

CZF6b

290 174.5 41.1 84.4 -63.8 300 167.5 43.9 81.9 -53.5 310 157.1 44.3 73.9 -51.7

aUnits of if and BIZ: cm] mol-I. ~he data for CZH 6 and CZF6 were reported in Ref. 1.

'if? = (2RTAP/P;) [1+ (BII +B22 )P/RT] - [Pi(BII

-B22)2/2RT] [1+2(BlI +B22 )P/RT], (4)

where AP is the pressure change on mixing two gases at identical initial pressures, Pi> and volumes, Vi' and BII and B22 are volume second virial coefficients (units: cm3 mol-I) for the heavy and light components, respec­tively. If third virial coefficients are available for the pure

TABLE IV. Excess enthalpies of mixing, HE, at 300 K and 1 atm pressure for fiuoroethanes with helium and argon.

He Ar

CZH 6 14.9 6.3 C2H5F 37.8 25.3 1,I-CzH4Fz 50.1 37.1 1,1,I-CzH]F] 33.6 24.6 1,1,2-C2H]F] 64.0 49.4 1,1,1,2-CzH zF4 50.1 32.4 1,1,2,2~c;HzF4 44.6 35.4 CzHFs 33.9 19.0

~F6 21.7 12.1

"The results for CZH 6 and CZF6 have been reported previously (see Ref. 1). For equimolar mixtures.

components, a very small correction may be applied to the above expression for 'if? to obtain a slightly better value. The cross term coefficient is obtained from Eq.(3) and the experimental B II and B22 values reported in Table II.

Excess molar enthalpies jjE may also be obtained 10

from values of 'if? and their temperature derivatives at low pressures _

(5)

where XI and X2 are the mole fractions of the two compo­nents.

III. EXPERIMENT

With use of the present apparatus second virial coeffi­cients have been measured for seven fluoroethanes at 290, 300, and 310 K: the purities of the gases given by the manufacturer, and their corresponding dipole moments,5-7 are listed in Table I. The results are listed in Table II. We were unable to find any comparable data in the literature. We estimate the experimental errors in each value to be approximately ±2 cm3 mol-I.

Excess virial coefficients were measured for the same ftuoroethanes in binary systems with helium and argon, and interaction virial coefficients, B l2, calculated using Eq. (2) and the BII and B22 values in Table II; the experimen­tal values of 'if? and Bl2 are listed in Table III. We estimate the errors in the 'if? values to be less than ± 1.0 cm3 mol-I; the errors in the B 12 values are larger because of the errors in BII and B22.

- --Excess molar enthalpies of mixing were calculated us­ing Eq. (5) and the data in Table IV; we estimate the errors in each value of jjE to be approximately 2 J mol-I.

IV. DISCUSSION

Inspection of the data in Table II for the second virial coefficients of the pure components indicates that the val­ues for those molecules with dipole moments (see Table I) are much smaller than the corresponding values for C6H6 and C6F6 which have zero moments; the temperature de­rivatives of the virial coefficients of the seven former mol­ecules are also smaller than the latter two. There is no

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C. M. Bignell and P. Dunlop: Virial coefficients for fluoroethanes 4891

o 0.2 0.4 0.6 0.8

x 1 -

FIG. 1. Graph of excess enthalpies of mixing at 300 K and 1 atm pressure for O. He~H6; /:;. He-C2F6; •• He-(1.1.1-C2H3F3); and .... He­( 1.1.2-C2F3H3)·

simple correlation between the virial coefficients of this series of seven molecules and their dipole moments. but there are significant differences in the virial coefficients of the conformers 1. 1. l-C2H3F3 and 1.1.2-C2H3F3, and 1,1,1,2-C2H2F4 and 1,1,2,2-C2H2F4, due to differences in the dipole moments of each conformer of a given pair.

In Table IV the excess enthalpies of mixing for ethane and fluoroethanes with helium and with argon indicate large variations. For example, at x, =0.5 the value of HE for He-(1,I,2-C2H3F3) is almost twice the corresponding value for He-(1,I,I- C2H3F3), and the same situation ap­plies for the same two conformers with argon; in both cases

the larger value of HE corresponds to the conformer with the lower dipole moment (see Table I). The results for the above two systems containing helium together with He-C2H6 and He-C2F 6 are displayed in Fig. 1.

In a previous publication" we reported a limiting dif­fusion coefficient at 300 K for the system He-(1,1,2-C2H3F3) which was approximately 0.5% lower than the corresponding value for the system He-(1,1,1-C2H3F3). It appears that those results are consistent with the results for HE reported here for the same two systems.

ACKNOWLEDGMENTS

We are grateful to Dr. A. R. H. Goodwin, u.s. Na­tional Institute of Standards and Technology, for sending us some of their dipole moment measurements before pub­lication. This work was supported in part by a grant from the Australian Research Council.

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