GUEST AUTHOR Karol J. Mysels2
University of Southern California LOS Angeles, 90007
I I
Textbook Errors
Miscellanea NO. 5
Units in Thermodynamics
A number expressions are be in treatments of chemical thermodynamics in various closely related forms. Among these let us list
Suggestions of material suitable for this cohmn and guest columns suitable for publication directly should be sent with as many details as possible, and particularly with references tn modern textbooks, t o W. H. Eberhardt. School of Chemistrv, .. Georgia Institute of Technology, ~ t l s n t s Gs., ; 30332. Since the purpose of this column is to prevent the spread and the eontimmtion of errors and not the evaluation of individual texts, the sources of errors discussed will not be cited. In order to be presented an error must occur in st least two independent recent standard books.
44 / Journol o f Chemical Education
which mav be found in various texts.' Professor B. D. SHAHMA of Oregon State University points out that the units in these expressions never seem to be completely &fany texts take ~ l ~ of ~ten ~ apples" a problem which has been discussed a t some length in THIS JOURNALby BoggsS and by C ~ p l e y . ~ Others seem to change units in the middle of the stream which certainly has little to recommend it. Still others come out with energies per mole that apply to a specific number of moles, a point which is not immediatelv clear to most readers. Still others fail to specify . . theknits a t the m i n t when these become most, interesting. The Textbook Errors Column generally points out errors and also the, or at least a, correct way to treat t,he subiect, " , but here the author and Professor Sharma were not able co agree on any consistent approach Present address: Research Department, R. J. Reynolds Tobacco Co., Winston-Salem, N. C. 27102. BOGGS,J. E., J. CHEM.ED., 35.30 (1958). ' COPLEY,G. N., J. CEEM.ED.35,366 (1958).
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or to find one in the literature. Hence the errors are called to the attention of the readers hut the correct treatment is left to his initiative. Any reader wishing t,o share his preferred way with others is invited to submit his ideas to the editor of this column for possible publication in a future article. Submissions should include equations of the types listed above and should be explicit about the meaning and unit,s of all symbols. Equivalent Conductivity
Professor SCOTTL. KITTSLEYof Marquette University points out that in some textbooks incorrect units are given for equivalent conductivity. I n others, any mention of units is avoided. Actually, the units are simply ohm-' cm2equiv-' as follows for the fact that conductance is expressed in ohm-', specific conductanre or conductivity, K in ohm -' cm-' and equivalent conrentration either in equiv l i t e r 1 (C) or to keep uuits consistent in equiv ~ m (c). - ~ Equivalent conductiv~ty, A, is then defined either as As I03/C has the same dimensions as c the units :we ohm-'cm-'/equiv em-= = ohm-'cm2 equiv-'. I t may be noted that A is somet,imes called equivalent conductance and somet,imes equivalent conductivit,y with no clear cut preference or authority t,o follow. The latter seems more consistent with the general usage of t,he ending ance (resistance, conductance) for t,he directly measured property of an object and of ity (resist,ivity, conductivity) for the specific property of the material (corrected for the geometric fact,ors influencing the properties of the object). As A corrects not only for t,he concentration but also for these geometric factors and is derived directly from conductivity it seems t,hat it should also be called equivalent condurtivity. Mr. JAMES R. BARDof Edgewood Arsenal, Md., calls attention to the fact that ionic mobility and the ionic equivalent conductivity X are sometimes confused due t,o t,he fact that they are directly proportional to each ot,her for ions of similar valency. The situation is complicated by the fact that one has t,o distinguish between the electrophoretic or electrical mobility u' of an ion which is its velocity in unit electrir field (cm secrl/volt cm-') and it,s "ahsolute" mobility u which is its velocity under unit force (em ser1/dyne). There is also often uncert,ainty whether the ordinary internat,ional volt (v) or the electrostatic cgs unit or statvolt (V = 300v) are used in defining u'. The former is always used in reporting electrophoretic measure merits but the latt,er is often used in calcnlat,ions of transport processes. Since X represents the flux of electricity in unit field prr equivalent of ious in unit volume on one hand and on the other the total elect,ric charge carried by these ions is F and their flux is u', we oht,ain simply X = Fu'
for the relat,ion between ionic equivalent conductance and electrophoret,ic mobility. By definition an esu of charge in a field of 1V/cm is subject to a force of 1 dyne and an ion carries a charge ze where z is its valence and e the elementary charge (4.80 X esu). This gives u
= U'
(cmZ sec-'V-')/ze
=
u'(cm2 sec-'v-')/3OOze
for the relation between the absolute and electrophoretic mobilities of an ion depending on the units used in the definition of the lat,ter. Polarographic Oscillations
I n a polarographic experiment, as the droplet of mercury grows until it detaches itself, the current flowing through it increases continuously. This produces periodic oscillations of the measured current which are generally more or less damped out by the measuring system and ignored in the interpretation of the record. Their magnitude increases with the average current flowing through the drop. The most interesting part of this current is that due to the materials being analyzed it varies markedly with the applied potential over a certain range. I n the absence of such materials, a.n important part is played by the current required to charge the drop to its equilibrium potential. As the potent,ial reaches that of the electrocapillary minimum this current vanishes and it is therefore sometimes stated' that thepscillations also are minimized at this pot,ential. Dr. AKE BRESLEof Skellefteham, Sweden, points out however that this is not completely true because of the unavoidahle presence of easily reducible impurities such as traces of oxygen and of mercury (I) ions which give rise to a small diffusion current. Hence, the oscillations become minimum when the algebraic sum of these current is near zero which will not be exactly at the electrocapillary minimum. Furthermore, t,he residual diffusion current varies wit,h the 1/6 power of the age of the drop whereas the charging current varies with the power. Hence, the potential of minimum oscillation should vary with drop size and under certain circumstances it should be possible to observe oscillations crossing the zero line and not only positive and negative ones. Homogeneous Catalysis
I n a lengthy article on this subject Dr. J. A. LEISTENL deals with a number of items which are frequently incorrectly treated in textbooks1 such as definitions of a cat,alyst inconsistent with common examples of homogeneously catalyzed reactions, statement,s that catalysts always lower the activation energy of a reaction or that t,he rate is proportional to the concentration of the cat,alyst,,and the distinction between mass and medium effect,^. He also offers definite suggestions for a consistent t,reat,mentof t,hesubject. "LEISTEN, J. A,, J . Chem. Ed. 41, 23 (1964).
Volume 44, Number
I,
January
1967
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45
