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a careful analysis of the contributions to the volume of activation is necessary. The present results emphasize the conclusion drawn some years ago in connection with mechanisms of acid cetalysisl2 that a relatively simple discussion was possible only if the catalyzing proton was transferred from an acid to a molecule containing the same proton-accepting atom as the acid. Other subtle points in the determination of mechanism in acid catalysis from volumes of activation have been discussed recently. ~
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(14) B. T. Baliga and E. Whalley, Can. J. Chem., 42, 1835 (1984).
Electrical Conductance and Density of
Alkali Metal Nitrate Melts by M. A. Bredig ChemMtry D i v k b n , Oak Ridge NataOnal Laboratory,* Oak Ridge, Tennessee (Received October 8, 1964)
Measurements of conductivity and density of nitrate melts, recently reported by Papaioannou and Harrington,‘ are of more than usual interest; the effects of very small additions of halides were so large that, if real, they would seem to require major revisions in our thinking about molten salts, if not liquids in general. Absence of numerical values for partial molar volumes and large errors in calculation that appear to have occurred in Table XIV of ref. 1 summarizing conductivity results may have obscured the disturbingly vast magnitude of the effects. The following is a brief discussion, which does not claim to be comprehensive, of outstanding examples from this publication. (1) An addition of 10 X lo-* mole % of K F or NaF to a eutectic melt of (Li,K)NOa, that is, of 1 molecule of fluoride to 10,OOO molecules of nitrate (Figure 3, ref. l), produced a decrease of as much as 5% in density corresponding to the enormous partial molar volume of approximately 23,000 cm.a for KF, more than 500 times the expected value. The conductivity increased 15%, corresponding to a partial equivalent conductance, dm = 6A/6nm, of approximately 20,000 mhos cm.2, i e . , perhaps lo00 times the expected value. The writer was unable to discover how the much more modest number, 1280 mhos cm.-l, in Table XIV of ref. 1 was obtained from the experimental data.2 The equation used, A, = (6&,/6X,),,,,, is incorrect and should have read d, = d&,/dX, dr, as dX, = d(l - X,) = -dX, # 0. Also, the
+
correct dimensional unit is mho cme2rather than mho cm. -I. mole % of CoFz or (2) The addition of 6 X of 1 molecule CoF2 to 16,000 nitrate molecules (Figure 4, ref. 1) caused an increase in conductivity of 14%, corresponding to A I / ~ c ~=F ~14,000 mhos cme2. Table XIV of ref. 1 states 1770 mhos crn.-I. The density dropped again sharply by 5%, giving the abnormally large partial molar volume of 37,000 cm.a for CoF2. Such vast density changes are characteristic of phase transitions which, however, even in solids, are rarely, if ever, produced by impurities in these minute concentrations. mole % of KBr or NaBr (3) Addition of 36 X or of 1 bromide molecule to 2800 nitrate molecules caused a decrease in electrical conductivity of 40% (Figure 2, ref. 1) corresponding to a (negative) partial equivalent conductance of KBr of approximately -14,000 mhos cm.2. The paper states: -815 mhos cm.-I. Addition of 0.027 mole % of another bromide, CoBrz, to KNOa (no LiNOa!) produced no significant effect upon either specific conductivity or density (ref. 1, Table VIII, columns 1-5). Therefore, the large drop of 23% in the equivalent conductance of the solution (ref. 1, Table VIII, columns 6 and 7) and the large negative value of A c ~ B ~in, Table XIV of ref. 1 (-2210 mhos cm.-l) must represent arithmetical errors. (4) The effect of KC1 and NaCl on the (Na,K)NOa melt, quite reasonably, was found to be negligible in ref. 1 on p. 2431, left column, and 0 in Table XIV. However, and this is one of the most startling features of the report, this negligible effect is just the one chosen in the last section of the first paper for the illustration of an explanatory hypothesis. According to this hypothesis, the “tighter grip of the ionic atmosphere on the central metal ion” that is said to result when a chloride ion (1 C1- in 1000 Not-, Table 11, ref. 1) occupies an anionic hole, produced-according to the text of this section--“a linear decrease” in conductance, Le., an effect which on p. 2431 or Table XIV of ref. 1 was reported to be negligible, or zero. As this illustration, in the interest of brevity, was the only one considered, one presumes that it was meant to stand in for some of the other findings and that the decrease in conductivity of 40%, produced by 1 molecule of
* Operated by Union Carbide Corp. for the U. 9. Atomic Energy Commission. (1) P. C. Papaioannou and G. W. Harrington, J . Phye. Chem., 68, 2424,2433(1964). (2) Communication between the authors and the writer has revealed the source of the discrepancy in a calculating error. All numbers in Table XIV of ref. 1 need to be multiplied by factors of 8 to 20 in order to reflect the actual magnitude of the observed effects. Volume 69, Number 6 May 1966
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1754
KBr in 2800 nitrate molecules (paragraph 3, above), was also covered by the hypothesis and by the model of Figure 5, ref. 1. It is not clear why the bromide case was not used for illustration instead of the chloride system. Could it be that the authors themselves did not quite understand how a single Br- ion would immobilize at least as many as 40% or slow down all of the 2800 Li+ and K+ ions? The model, obviously, is not able or meant to explain the enormous alleged mobility of the fluoride ion (paragraphs11 and 2, above). ( 5 ) Very large conductance changes were also described in the second paper which is said to support the existence of transition metal halide complexes, partly of extreme stability (e.g., ref. 1, Figure 6, cobalt fluoride), in astoundingly dilute solution and in absence of halide ion excess. In summary, instead of accepting what would indeed be an unexpected development in the field of fused salt chemistry, it seems preferable to assume that these effects are not real but are artifacts. Some may have been produced by gas bubbles from catalytic decomposition of nitrate, especially LiN03. Others, such as the large increases in conductivity, all of which occurred in melts containing LiN03, probably had their origin in partial short-circuiting through the wall of the capillary cell (glass? quartz?) as a result of penetration by the decomposition product, lithium oxide, with its highly mobile Lif ions.
An Examination of the Johnston-Ogston Equation and the Moving Boundary Equation
by L. W. Nichol and A. G. Ogston Department of Physical Biochemistry, John Curtin School of Medical Research, Australian National University, Canberra, A.C.T., Australia (Received October 23,1964)
When a mixture of two components is subjected to mass transport, the resulting experimental pattern is markedly dependent on the operation of either chemical or physical interactions or both.'-* With interactions of either kind, it is advantageous to consider the constituent concentrations and v e l o c i t i e ~ ,as ~ ~ this ~ results in the same fundamental relation expressing conservation of matter. 3v6 The constituent concentration of a component at any point in the cell is merely the total concentration of that component regardless of the form in which it exists. In a rapidly reacting The Journal of Physical Chemistry
+
system, A €3 e C, there are two Gibbs components and their constituent concentrations in the undisturbed equilibrium mixture (termed the a-phase) may be chosen as EA" and EBa; in the transport of two components which interact only physically, the same terminology may be employed to define their concentrations in the mixture (a-phase). The corresponding constituent velocities, SA" and sB", are defined by the mass action law in the case of chemical interaction, but they may be explicitly described when physical interactions operate, only if the precise nature of the hydrodynamic forces involved is known. Nevertheless, in both cases the modified or constituent velocities must vary monotonically with concentration and it is this correlation which permits the behavior of interacting systems of both kinds to be viewed in conjunction.8 If the A constituent moves faster than the B constituent in a transport experiment, leaving pure B behind in the Pphase, a relation expressing the conservation of B across the a@boundary may be written as
Equation 1 is the Johnston-Ogston expression' describing the effect of physical interaction where VB@ and SB" are numerically different. Moreover, with the terminology adopted it is also the moving boundary equation frequently applied to the study of chemically interacting systems.a~6It might be noted that in the ,&phase, where B exists alone, EBB = CB' and SB' = OB'. Equation 1 is generally visualized as applying to sedimentation velocity,' to the descending side in electroph~resis,~~~ and to the trailing edge of a zone moving down a column while preserving a plateau regi~n.~ An analogous expression may be written for the corresponding ascending side in terms of the A constituent which does not disappear across the boundary separating the mixture and pure A (termed the ab boundary3), with the caution that in chemically reacting systems the model selected involving the separation of B alone on the descending side and A alone on the ascending need not necessarily apply in all (1) J. P. Johnston and A. G. Ogston, Trans. Faraduy SOC.,42, 789
(1946). (2) G. A. Gilbert and R. C. L. Jenkins, Proc. Roy. SOC.(London), A253,420 (1959). (3) L.W.Nichol and D. J. Winzor, J. Phys. Chem., 68,2455 (1964). (4) A. Tiselius, Nova A& Regrim? SOC. Sci., Upsdiemis, [4] 7 , 1 (1930). (5) L. G. Longsworth' in "Electrophoresis, Theory, Methods and Applications," M. Bier, Ed., Academic Press, New York, N. Y., 1959,p. 91. (6) M. Davies, L. W. Nichol, and A. G. Ogston, Bwchim. Bwphys. Acta, 75,436 (1963).
