aaa
R. Mills
3. 1.27 X lo5 cal mol-l is the dissociation energy of C02. Values of ( Wv,j)/(W,) at different pressures and different ( W ) have been collected in Table 11. One appreciates that, a t 40 Torr, a fraction of about 60% of the energy pumped into the vibrational system of C02 is utilized for the process of dissociation. This fraction decreases with decreasing pressure and power density ( W ) , The observation that in discharges operated at moderate pressures the average electron energy is too low for a mechanism of dissociation by direct electron impact to be important, and that the gas temperature is also too low for a mechanism of thermal dissociation, led to the suggestion,lv5 confirmed by spectroscopic m e a ~ u r e m e n t sthat , ~ the vibrorotational temperature T, should be sufficiently high to warrant the contribution of a mechanism of dissociation involving vibrationally excited molecules. An approximate rate expression has been derived in ref 1and 5 for this type of process, which can be written, for COz dissociation, as
where B is a constant accounting for the dependence of the crude collisional preexponential factor, ko, on the vibrational quantum number. The observed dependence of the experimental results on pressure and power density can be accounted for, at least qualitatively, on the basis of eq 12. Spectroscopic measurements of Ti are actually in progress. A very similar mechanism of molecular dissociation involving vibrationally excited states has been recently suggested in ref 19 to account for the observed rates of N2 dis-
sociation in glow discharges in the pressure range 2-10 Torr.
Acknowledgment. The technical assistance of Mr. V. Colaprico and Mr. G. Latrofa is gratefully acknowledged. References and Notes
(15) (16) (17) (18) (19)
P. Capezzuto, F. Cramarossa, R. d'Agostino. and E. Molinari, J. Phys. Chem., 79, 1487 (1975). A. T. Bell, lnd. f n g . Chem., Fundam., 11, 209 (1972). L. S.Polak, Pure Appl. Chem., 39, 307 (1974). F. Cramarossa and G. Ferraro, J. Quant. Spectrosc. Radiat. Transfer, 14, 159 (1974); F. Cramarossa, G. Ferraro, and E. Molinari, ibid., 14, 419 (1974). P. Capezzuto, F. Cramarossa, G. Ferraro, P. Maione, and E. Molinari, Gazz. Chim. /tal., 103, 1153 (1973); P. Capezzuto, F. Cramarossa. R. d'Agostino, and E. Moiinari, ibid., 103, 1169 (1973); P. Capezzuto, F. Cramarossa, P. Maione, and E. Molinari, ibid., 103, 891 (1973): 104, 1109 (1974) (all in english). For a review see E. Moiinari, Pure Appl. Chem., 39, 343 (1974). N. L. Nigham, Phys. Rev. A, 2, 1989 (1970); Proc. lnt. Conf. loniz. Phenom. Gases, Ilth, 1973, 267 (1974). J. J. Lowke, A. V. Phelps, and 8. W. Irvin, J. Appl. Phys., 44, 4664 (1973). M. J. W. Boness and G. J. Schultz, Phys. Rev. A, 9, 1969 (1974). M. 2 . Novgorodov and N. N. Sobolev, Proc. lnt. Conf. loniz. Phenom. Gases, Ilth, 1973, 215 (1974). L. C. Brown and A. T. Bell, lnd. Eng. Chem., Fundam., 13, 203, 210 (1974). S.M. Smith, "Chemical Engineering Kinetics", McGraw-Hill, New York, N.Y., 1970. 0. A. Hougen and K. M. Watson, "Chemical Process Principles", Wiley, New York, N.Y., 1949. R. D.Hake and A. V. Phelps, Phys. Rev., 158, 70 (1967). W. J. Wiegand, M. C. Fowler, and J. A. Benda, Appl. Phys. Lett., 16, 237 (1970). K. Kutsegi Corvin and S. J. B. Corrigan, J. Chem. Phys., 50, 2570 (1969). M. J. Barton and A. Von Engel, Phys. Lett. A, 32, 173 (1970). S.Rockwood, J. Appl. Phys., 45, 5229 (1974). D. L. Flamm, E. R. Gilliland. and R. F. Baddour, lnd. Eng. Chem., Fundam., 12, 276 (1973). L. S.Polak, P. A. Sergeev, D. J. Slovetsky, and R. D. Todesaite, Proc. lnt. Conf. loniz. Phenom. Gases, 12fh, I ZA, 65 (1975).
Diffusion Relationships in the Binary System Benzene-Perdeuteriobenzene at 25 OC R. Mills Diffusion Research Unit, Research School of Physical Sciences, Australian National University, Canberra, A.C. T. 2600, Australh (Received December 3, 1975)
Measurements are reported a t 25 "C of the self-diffusion coefficient of perdeuteriobenzene and the tracerdiffusion coefficients of both the components of benzene-perdeuteriobenzene mixtures. It is shown that the ratio of self-diffusion coefficients of benzene and perdeuteriobenzene is approximately equal to the inverse square root of their respective masses and the small deviation that remains can be explained in terms of the intermolecular forces involved. For tracer diffusion a volume effect is found, which is in accordance with theoretical equations formulated by Bearman for this case.
The system benzene-perdeuteriobenzene is a very interesting one in which to study interrelationships among the various diffusion coefficients. The main interest stems from the fact that since the two components differ only in isotopic composition, the system can be regarded as a "regular" one in which the molecules have similar size, shape, and interaction potentials. For such systems Bearmanl has The Journal of Physical Chemistry, Vol. 80, No. 8, 1976
derived equations which relate the mutual diffusion coefficient with the two tracer- (or intra-) diffusion coefficients and also the latter coefficients with the molecular volumes. Another point of interest is that the self-diffusion coefficients for pure normal benzene and for pure perdeuteriobenzene can be compared. For two such closely similar liquids the inverse square root mass dependence which is
Diffusion Relationships in Benzene-Perdeuteriobenzene
predicted by several theories should apply. There are virtually no precise data of this type available with the exception of the analogous coefficients reported by Mills2 for H2O and DzO. Some NMR self-diffusion measurements in pure isotopically related liquids have been made but, with errors ranging from 2 to 5%, data of this type are of little use for testing the theoretical mass dependence. It should be noted that in this paper we restrict the use of the term self-diffusion to that measured in a pure onecomponent liquid. In a binary system of two bulk components there are two diffusion coefficients (which can be defined in terms of the velocity autocorrelation function for each component) as well as the mutual diffusion coefficient. The former coefficients can be termed intradiffusion coefficients as defined by Albright and Mills3 but here are approximated by the respective tracer-diffusion coefficients. Some workers use the term “self-diffusion” to describe these coefficients.
889
TABLE I: Tracer Diffusion in C G H ~ - C ~Mixtures D~
109~~,
X
C6D6 0
25 50
100
Tracer
m2 s-l
C6H5T CsbT C6H5T C6H5T CsD5T C6D5T
2.203 f 0.004 2.207 =t 0.007 2.172 2.142 & 0.005 2.153 =t 0.005 2.090 & 0.001
TABLE 11: Self-Diffusion ia Benzene and Water
5 25 45
1.054 1.054 1.054
1.29 1.23 1.20
1.31 1.23 1.20
Experimental Section Perdeuteriobenzene (99.5% D) was obtained from Merck Sharpe and Dohme, Canada and from CEA, France (99.8% D). Tracers used were C6H5T and C & , T (D = deuterium, T = tritium); their preparation has been outlined in a previous paper.4 The diffusion method was the magnetically stirred diaphragm cell as described by Mills and W o ~ l f . ~ Results a n d Discussion The self- and tracer-diffusion results obtained in this study are given in Table I. As indicated in the introductory paragraphs self-diffusion in the pure liquids and tracer diffusion in the mixtures fall into separate categories. We shall treat the self-diffusion case first. Self-Diffusion For self-diffusion in one-component liquids there have been several formulations which incorporate the effect of mass explicitly among which are derivations by LonguetHiggins and Pople,6 Rowlinson? Brown and March: and Friedman.g In these approaches a simplified picture is assumed; either that the molecules are hard spheres or that molecular interactions between species differing only in mass are the same. In all the derivations D sis found to be proportional to rnd1l2. Friedmang made a more detailed study of the effect of isotopic substitution distinguishing between fully and partially substituted molecules. He suggested that in the latter case moments of inertia are changed and therefore rotational motions might be affected which in turn could cause deviations from the simple proportionality. Results for self-diffusion in C6H6 and in C6D6 are shown in Table I1 together with our previous results2 for H2O and D20 and some relevant viscosity data.1° I t will be seen that the viscosity and self-diffusion ratios are practically identical both for the water and benzene isotopic pairs. However, the transport ratios are in both cases higher than the respective mass ratios and in the water case the difference is quite large. In view of the assumptions made in the theoretical approaches the simple mass law can only be expected to apply to monatomic liquids. Deviations from it as shown by more complex liquids must be attributed to such factors as correlated motions, coupling between rotational and translational motions, and differences in intermolecular potentials. For the water case, McLaugh-
linll has attributed the high viscosity ratio to the moment of inertia difference between H20 and D20. These moment ratios vary from 1.3 to 1.4 and might be expected to affect the viscosity through rotational-translational coupling. From the equality of the transport ratios in Table I1 it would appear that in water the diffusion process is similarly affected which leads to the corollary that rotationaltranslational coupling is similar for both transport processes. I t is noteworthy that the viscosity ratio for the pair H21sO/H2160 at 25 OC as measured by Kudish, Wolf, and Steckel12 is 1.054 in exact agreement with the square-root mass law. Since the center of mass of the water molecule is only slightly displaced from the oxygen atom, the moments of inertia for this pair will change very little upon isotopic substitution. For the benzene case it will be seen from Table I1 that both transport ratios are -2% higher than the mass ratio. The square root of the moment of inertia ratio ( I D / I H ) ~between /~ C6H6 and C& can be calculated to be 1.024 for all three axes. (This assumes the center of molecule to carbon distance to be 1.30 A and both the C-H and C-D distances to be 1.08 A.) I t would seem unlikely therefore that rotational effects are causing the higher transport ratios in this case. An alternative explanation of the higher ratio for C6H6/ C6D6 is available which does not involve moment of inertia changes. Steele12 in a study of isotopically substituted classical fluids has given expressions for the differences in their transport properties in terms of a corresponding states treatment. These equations incorporate the changes in the potential parameters t and u and so reflect the difference in intermolecular potentials (which are assumed to be conformal) between normal and deuterated molecules. It may be noted also that these expressions contain the inverse square root mass relation so that one can test directly the difference between the ratios in Table 11. Values of 6t and 6u for the benzene case have been given by Steele and values of (a In D / ~ P ) Tand (a In D / a T ) p were calculated from the data of McCool, Collings, and Woolf,14 and Collc ~ D ~ from ings and Mills.15 The value for D c ~ H ~ / D calculated The Journal of Physical Chemistry, Vol. 80, No. 8, 1976
890
R. Mills
2.20
:2.1 5 0
r
2.10
0
I
I
I
I
0.25
0.50
0.75
1
x
tC,D,)
Flgure 1. Diffusion coefficients for the C&-C&
system at various tracercompositions: (e)tracer-diffusion coefficient for CeD5T; (0) diffusion coefficient for CeH5T; (+) mutual diffusion data of Shankland and Dunlop.16
TABLE 111: Comparison of Tracer-Diffusion Data with Eq 1
1.002 1.003 1.005 1.003 1.004 1.003 C6H12 a Molar volume data from Dixon and Schie~s1er.l~ C6H6
50% C6H6-C&
Steele’s equations is 1.057 in excellent agreement with the experimental ratio. The correlation is not successful for water.
Tracer Diffusion Tracer-diffusion data from Table I for tritiated benzene and perdeuteriobenzene in mixtures of the bulk components are shown in Figure 1. Mutual diffusion data for the same system as reported by Shankland and Dunlop16 are shown also. For regular systems of this type, Bearman,l from statistical mechanical considerations, has derived relations between tracer and mutual diffusion coefficients. He has analyzed also the older diffusion equations and shown that with suitable restrictions they give essentially these same results. His equations are
D=D1-
a In a1 a In c1 a In a1
= [DlJZ + D2Jll a
The Journal of Physical Chemistry, Vol. 80,No. 8, 1976
(3)
where D is the mutual diffusion coefficient, and Di, vi, ai, ci, and xi are the tracer (or intradiffusion) coefficient, molecular volume, activity, concentration, and mole fraction of component i, respectively. Unfortunately there are no published data for the thermodynamic activities of the benzene-perdeuteriobenzene system so eq 2 and 3 cannot be tested at this time. However, inspection of Table I and Figure 1 shows that there is a small but apparently real difference in the tracer-diffusion coefficients of the tracer species C&bT and C&T in 50 mol % mixtures. Friedman9 has made a theroetical study of isotopic mass effects in “solute” diffusion of this kind and his equations predict that the inverse square-root mass law ought not to apply. This prediction has in general been borne out by recent experim e n t ~In . ~the present case, the difference between the two tracers is also obviously not a normal mass effect as the heavier tracer diffuses faster than the lighter one. It may be noted that closer examination of our previous results4 for tracer diffusion in pure benzene and pure cyclohexane shows the same small effect. I t is known that the molar volume of deuterated compounds is smaller than their hydrogenated analogues and one might therefore suspect that the difference is due to a volume effect. As indicated above, Bearman has derived eq 1which predicts that tracer-diffusion coefficients in regular mixtures should be inversely proportional to the molecular volumes. In Table 111, we compare eq 1 with our results for the diffusion of the two tracers in 50 mol % C6He-c~D6, pure C6H6, and pure C6H12. The subscripts H and D represent the hydrogenated and deuterated tracer species, respectively. It is evident that there is a correlation between the tracer-diffusion mobilities and molecular volumes of the tracer species. It will be realized that due to the similar volumes of the two isotopically related species the test is not as definitive as, for example, a system such as krypton and argon. Nevertheless the agreement in three different systems is good evidence that eq 1 is valid for this type of diffusion. References a n d Notes (1)R. J. Bearman, J. Phys. Chem., 65, 1961 (1961). (2)R. Mills, J. Phys. Chem., 77, 685 (1973). (3)J. G.Albright and R. Mills, J. Phys. Chem., 69, 120 (1965). (4)R. Mills, J. Phys. Chem., 79, 852 (1975). (5) R. Mills and L. A. Woolf, “The Diaphragm Cell”, ANU Press, Canberra,
1968. (6)H. C. Longuet-Higgins and J. A. Pople, J. Chem. Pbys., 25, 884 (1956). (7)J. S.Rowllnson, Physica, 19, 303 (1953). (8)R. C. Brown and N. M. March, Phys. Chem. Liquids, 1, 141 (1969). (9)H. L. Friedman, “Molecular Motions in Liquids”, J. Lascombe, Ed., D. Reidel, Dordrecht, Holland, 1974,p 87. (IO) J. A. Dixon and R. W. Schiessler, J. Phys. Chem., 58, 430 (1953). (11)E. McLaughlin, Physica, 26, 650 (1960). (12)W. A. Steele, J. Chem. Phys., 33, 1619 (1960). (13)A. J. Kudish. D. Wolf, and F. Steckel, J. Chem. Soc., Faraday Trans. 1, 68, 2041 (1972). (14)M. A. McCool, A. F. Collings. and L. A. Woolf, J. Chem. SOC.,Faraday Trans. 1, 68, 1489 (1972). (15) A. F. Collings and R. Mills, Trans. Faraday SOC.,66, 2761 (1970). (16)I. R. Shankland and P. J. Dunlop, J. Phys. Chem., 79, 1319 (1975). (17)J. A. Dixon and R. W. Schiessler, J. Am. Chem. Soc.,76, 2197 (1954).
