The molar entropy of a racemic mixture of q optical isomers contains a mixing entropy of R In q, which should be subtracted before structural correlations are made. T o analyze molar entropy in terms of structure, allowance should therefore be made for these effects by writing:
+
So R I n u - R In q
=
(group and structural contributions)
However, the effects of the symmetry number for internal rotations may conveniently be absorbed into the group contributions, so that u in this expression may be taken as the symmetry number for external rotations only. The following illustration shows that good structural correlations are obtainable when the equation just given is used. The two heptanes 3-methylhexane and 3-ethylpentane each contain three CHI groups, three CHZ groups, and one CH group; these are convenient structural units for analysis, but if such an analysis is to be useful, the entropies of these isomers, corrected or uncorrected, must be close together. u
Compound (external)
MeEtPrCH
EtgCH
1
3
2
1
7
S" Sa
1298.16" K.
+ R In u - R In 71
S" So
+ R In u - R In 7
1OOO" K.
101.37
98.30 cal./mole deg.
100.00
100.48 cal./mole deg.
180.4
176.5 cal./mole deg.
179.0
178.7 cal./mole deg.
Entropies from Rossini et al. (1953).
The difference between isomers is reduced by the correction from 3.07 to 0.48 cal./mole deg. at 298.16OK. and from 3.9 to 0.3 at 1000° K. It is easy to see that, since the correction propcsed by Rihani and Doraiswamy is opposite in sign to that used here, it would have increased rather than reduced these differences. Despite the above, Rihani and Doraiswamy obtain reasonable agreement between calculated and reported values of entropy in their Table X. Their method may be less satisfactory in other hands, however, as they do not detail the way in which they obtain values of u and q ; and it is not obvious how the values u = 2 for CzHa (page 376) and u = 6, q = 2 for 2-methylhexane (Table I X ) are arrived at. The usual methods of determining these would give u = 18 for CzHc and u = 27, q = 1 for 2-methylhexane (total symmetry numbers). literature Cited
Mayer, J. E., Brunauer, S., hlayer, M. G., J. Am. Chem. SOC. 66, 37-53 (1933).
Rossini, F. D., Pitzer, K. S., Arnett, R. L., Brown, R. AI., Pimentel, G. C., "Selected Values of Physical and Thermodvnamic ProDerties of Hvdrocarbons and Related Compbunds," Cariegie Press, Pgtsburgh, 1953. P. A . Sinall
Imperial Chemical Industries Ltd. Plastics Division Welwyn Garden City Herts., England
ESTIMATION OF IDEAL GAS ENTROPY OF ORGANIC COMPOUNDS SIR:Small has raised a few points in connection with our paper. The first, and perhaps the most important, concerns the dimensional consistency of the equation used. The inclusion of the temperature term in the equation for entropy obviously leads to units of energy and not of entropy. However, the inclusion, though dimensionally inconsistent, represents the data with remarkable accuracy, and has the advantage of similarity with the free energy equation. The concept of structural contributions does not have a very strong theoretical basis. The objective of the present work being the development of a procedure for estimating the entropy of formation from structural contributions, the correction terms can also be regarded as empirical terms which satisfy the data. The illustrative example given b y Small is not very clear to us. The sign of the term for optical isomerism is opposite to that for symmetry corrections, because it increases the number of possible orientations, whereas symmetry decreases
this number. illlowance for this has been made in the derivation of our structural contributions. Our paper stated that the symmetry number used is the number of identical spatial orientations that the molecule may assume by rigid rotation about any axis or by rotation within the molecule. When this definition is employed, the symmetry numbers given by us are correct. I n the case of complicated molecules it is necessary to use three-dimensional models. The symmetry number given in Table IX is incorrect, in that the compound to be used is 3-methylhexane and not 2-methylhexane. Notwithstanding the dimensional inconsistency of the correction term, the proposed method predicts the entropies of formation with remarkable accuracy, the average error being about 1.2%. This should justify use of the method. L. K . Doraiswamy National Chemical Laboratory Poona 8, India
GASEOUS DIFFUSION AND FLOW IN COMMERCIAL CATALYSTS AT PRESSURE LEVELS ABOVE ATMOSPHERIC SIR: I n recent correspondence, Hwang and Kammermeyer (1968) defended their conclusion concerning surface diffusion of helium in porous Vycor. They said that some questions about the validity of their data (Satterfield and Cadle, 1968) were without basis. We believe i t is possible to accept the 600
l&EC
FUNDAMENTALS
data of Hwang and Kammermeyer and still question the presence of helium surface diffusion in their porous Vycor. The currently popular expression for Knudsen flow, as derived by Smoluchowski (Kennard, 1938), predicts a direct dependence of the flux upon the square root of the absolute
