NOTES
3006
suggested that the effect is associated with differences in the size of the nickel crystallites on the different supports. It is emphasized that such an explanation would require an influence of crystallite size over and above an effect on the extent of metal surface area, since the effect of the latter is accounted for in the determination of specific catalytic activity. Such an effect of crystallite size on specific activity may well exist and may account, in part, for the observed effect of the support. According to this line of reasoning, the higher catalytic activity and greater dispersion of nickel on silica or alumina as compared to silica-alumina indicate that the intrinsic catalytic activity is greater for the smaller crystallites. However, the catalytic data on the effect of nickel concentration indicate just the opposite, since increasing the nickel concentration increases crystallite size and activity correspondingly. Thus, one does not obtain a completely consistent explanation on the basis of crystallite size effects alone. The possibility of an optimum crystallite size for catalytic activity has been considered, but it would be difficult to establish such an effect from the available data. The results of the present study indicate that the influence of the support on the catalytic properties of nickel is a more complex effect than one of gross differences in the reducibility of the metal or of crystallite size. The true nature of the effect remains to be seen. It is to be noted that the effect is particularly important at low metal concentrations.
van der Waals Volumes and Radii of Metals in Covalent Compounds
by A. Bondi Shell Deselopment Company, Emerycille, California (Receiaed April 19, 1966)
In an earlier paper,' an attempt was made to estimate van der Waals radii of metallic atoms. Additional consistent data could not be obtained from X-ray diffraction patterns of organometallic compounds. Yet, the increasing interest in organometallic compounds makes it desirable to correlate their properties within an existing body of property correlations. Hence, those van der Waals volumes of several compounds have been calculated which yield the correct number of external degrees of freedom (3c) per molecule when The Journal of Physical Chemistry
linked with the known density and heat of vaporization data. With most metal alkyl compounds, such as dimethyl cadmium, free rotation of the alkyl group around the metal-carbon bond can be assumed, so that, for example, for Cdhlez 3c = 7 , etc. The van der Waals volume increments and radii of various metallic elements that are compatible with that requirement are listed in Table I. It is noteworthy that these V , increments are of the same order as the electronic polarizability [ R ] ,(and as the atomic volume of the element in its metallic state), a well-known result of classical physics for the case of conducting spheres. Table I : van der Weals Volumes and Radii of Several Metals Derived from Metal Alkyl Data" BL,
Compd
kcal/ mole
OK
3c
X
VW(X). cma/ mole
ZnMen ZnEtz CdMez HgMez PbMec
7.78 10.10 9.57 8.91 9.79
378 445 443 420 482
6.2 6.9 6.5 6.4 6.1
Zn Zn Cd Hg Pb
8.93 8.93 12.46 13.30 17.8
EO,
[Rim,
rw(X), A
cma/ mole
1.39
8.9
1.62 1.70
12.7 13.8 17.9
a Eo is the energy of vaporization a t that t.emperature a t which the ratio of molal volume to van der Waals volume (V/V,) = 1.70. 01,is the characterist'ic temperature of liquid = Eo/5cR, determined experimentally as 1.535 X (temperature (OK) a t which V / V , = 1.80). rw is the van der Waals radius. V , is the van der Waals volume. [ R ] m is the molar refractivity. References to the definitions and physical meaning of the first four items are given in ref 1.
The proximity of the V , incyements to [ R ] ,is somewhat fortuitous because the increments were calculated for connection with carbon and would have been somewhat (but not very) different had they been calculated for combinations with other elements. The primary result of this investigation is the suggestion that the readily available Lorentz-Lorenz refractivity [R], of metals2 can be used as a starting point for the estimation of V , and of T, of metals in metal organic compounds. Should the indicated relation be valid for metal atoms generally, it would mean that the electron density of metal atoms decreases far more steeply with distance outward from the point of maximum electron density3 than is the case with the atoms of (1) A. Bondi, J . Phys. Chem., 68, 441 (1964). (2) S. S. Batsanov, "Refractometry and Crystal Structure," Consultants Bureau, New York, N. y., 1961. (3) J. C. Slater, "Quantum Theory of LMoleculesand Solids," Vol. 11, McGraw-Hill Book Co., Inc., New York, N. Y., 1965,p 106 ff.
NOTES
nonmetallic elements. I n view of the comparatively lower ionization potentials of the metallic elements, this is a rather unexpected result worthy of further investigation.
Studies on Solutions of High Dielectric Constant.
VIII. The Cationic Transport Numbers of Potassium Bromide in N-Methylformamide at Different Temperatures and Concentrations
by Ram Gopal and 0. N. Bhatnaga? Department of Chemistry, Lucknow University, Lucknow, I n d i a (Received February 7, 1066)
I n view of the lack of the transport number data of ions in N-methylformamide, it was considered desirable to extend the previous work3v4 on the determination of the transport numbers to solutions in N-methylformamide (NAIF) in order to evaluate the limiting ionic mobilities from the existing electrolytic conductance data and also throw some light on the ion-solvent interaction in this solvent of very high dielectric constant (e 182.4 at 25").4a With this aim in view, the cationic transport numbers of KBr in NMF, a t different temperatures and concentrations, have been determined and are reported in the present communication.
Experimental Section Potassium bromide was found to be an appropriate electrolyte on account of its appreciable solubility in NAIF so that the transport numbers could be determined at the significantly different concentrations. The A.R. grade KBr was recrystallized from conductivity water, thoroughly dried in an electric oven at 110", and was used for preparing the solutions. The NMF of specific conductance 10-4 mho was dried over freshly ignited quicklime and distilled twice under reduced pressure. The process of drying, distilling, and collecting the middle fraction for redistillation was repeated until the conductance of the sample was reduced to about mho. The sample of NMF thus obtained was kept in an amber bottle and stored in the dry nitrogen box. The sample was used for preparing the solutions soon afterward as the solvent appeared to be slightly more unstable than the other solvents of this family used However, the variation of conductance with time was found to be very little and was not expected to affect the results on
3007
the transport numbers a t ordinary temperatures. All of the solvent transfers were made in the dry nitrogen box. The transport number cell was similar to that used in formamide3 and N-methyla~etarnide~solutions. The cathode of the cell was a silver bromide electrode and was prepared as described el~ewhere.~The anode was a silver wire wound in the form of a spiral of about 4-5-mm diameter and 7-8 cm in length. The solution of any desired concentration was prepared in the manner described earlier and all possible precautions, given in detail in the previous comm~nications,~~4 to keep away the atmospheric moisture while preparing the solutions and during the course of experiments, were taken. The experimental results are summarized in Table I.
Table I : Cationic Transport Numbers of Potassium Bromide in N-Methylformamide Concn, M
15'
0.00 0.05 0.10 0.20 0.25 0.30
0.4945 0.4909 0.4881 0.4804 0.4765 0.4723
a
Transport number, t, 25' 359
0.5080 0.5048 0.5037 0,4980 0.4953 0.4931
0,5210 0.5184 0.5169 0.5119 0.5097 0.5084
450
-.
0.5290" 0.5288 0.5257 0.5210 0.5148 0.5130
From t h e graph by interpolation.
From the transport numbers given in Table I, the limiting transport numbers, t+O, of potassium ion at different temperatures were evaluated by using the Longsworth pro~edure.~The values of the various terms involved in calculating the Longsworth function were as follows. Limiting equivalent conductivities of KBr at 15 and 25" were 36.51 and 43.69, as given by French and Glover,'j while those at 35 and 45" were 53.00 and 60.75 and were determined experimen(1) Work supported by the Council of Scientific and Industrial Research (India). (2) CSIR Junior Research Fellow. (3) R. Gopal and 0. N . Bhatnagar, J. Phys. Chem., 68, 3892 (1964). (4) R. Copal and 0. N . Bhatnngar, ibid., 69, 2382 (1965). (4a) NOTEADDEDIN PROOF.G. P. Johari and P. H. Tewari [ibid., 70, 197 (196S)l have published the cationic transport numbers of KCl in formamide and in NMA without discussing and referring to the data given in ref 3 and 4. It is interesting to note that t h e "ever-vigilant" refereeing staff of the Journal of Physicd Chemistry appears to have failed to draw the authors' attention to the already existing detailed investigations',' of such a recent publication. ( 5 ) L. G. Longsworth, J . Am. Chem. Soc., 54, 2741 (1932). (6) C. M .French and K. H. Glover, Trans. Faraday SOC.,51, 1418 (1955).
Volume 70,Number 9 September 1066
