W. H. Eberhardt
Georgia Institute of Technology Atlanta, Georgia 30332
I
I
Miscellanea NO. 6
Cell Electromotive Forces and Disproportionation Reactions
Several individuals have called attention to the fact that, in the case of disproportionation reactions, it is possible to devise different electrochemical cells in which the same chemical reaction occurs but with different values of E". The reason for the difference is that although the chemical reaction requires the same value for the change in Gibbs Energy, AG" = -Eon5, cells may have different values of n. An example cited by B. D. Costley and J. A. Sandbach of The Polytechnic, Wolverhampton, England, involves the overall cell reaction 2 TI
+ TI'+ = 3 Tlf
For this reaction, AGO (25°C) = -3.185 joules. The relevant standard electrode potentials are Tl'f, T1 Eo
=
0.72 V
TI+, TI E o = -0.34 V Tlat, TI+'
Eo = 1.25 V
which lead to three possible cells with the same chemicalreaction
D. J. Jenkins and D. J. Marks of Harris College, Preston, England have published a note1 on this topic with examples involving Hg, Fe, and Cu. Although these comments may not come under the heading of conventional Textbook Errors, they do call attention to the value of describing chemical reactions in terms of AGO rather thanE0 alone. Partially Miscible Liquids and Upper Consolute Temperatures
Discussions of solutions and phase equilibria involving partially miscible liquids generally indicate that an increase in mutual solubility with temperature frequently gives rise to complete miscibility above a
certain temperature. Professor Irvin M. ICrieger of Case Western Reserve University points out that the example cited frequently, that of nicotine and water, is often presented inaccurately. This system exhibits both an upper consolute temperature at 208°C and a lower consolute temperature a t 61°C. Measurements on this system were made by C. S. Hudson2 using sealed tubes of a special Jena glass. Several prominent textbooks reproduce Hudson's nicotine-water phase diagram asserting that it represents the system's behavior at 1 a t m pressure. Since the vapor pressure of the two-phase system at all temperatures significantly above 100°C must exceed 1 atm, the cited pressure is in error and arguments based on the phase rule assuming constant pressure must he modified accordingly. The gas phase is always present and the actual pressure is the vapor pressure of the system at each temperature. Enthalpy and Free Energy of Formation
Dr. L. F. Koons of Tuslcegee Institute stresses the need for increasing emphasis on the concept of standard states particularly as reflected in the use of tabulated thermodynamic data. For example, he points out in the presentation of the concept, enthalpy of formation, the statement is often made that the enthalpies of the elements are arbitrarily set equal to zero. The enthalpy of one element in a given state could, of course, be called zero, hut it is unlikely that any two elements, let alone all of them, a t standard conditions have the same enthalpy. Actually the standard enthalpy of formation of a pure substance is the difference between the enthalpy of that substance in the standard state and the enthalpies of the component elements in their corresponding standard states. Thus for CIHz(g), %H; = H & H ~- a 2 H 6 HR,, or for CsHs(l),AH; = H c a ~-* 6Hk - ~ H H , . The enthal~vchance that accomnanies the change in state, I ) he determined by tKe subtrac~ C ~ H & ) C ~ H ~ (can tion of three times the molar enthalpy of formation of acetylene from the molar enthalpy of formation of benzene
-
AH,",,e
Suggestions of material suitable for this column and guest columns suitable for ~ublicationdirectlv should he sent with as many details as possible, and particularly with reference t o modern textbooks, t o W. H. Eberhardt, School of Chemistry, Georgia Institute of Technology, Atlanta, Georgia 30332. Since the purpose of this column is to prevent the spread and continuation of errors and not the evaluation of individual texts, the sources of errors discussed will not be cited. I n order to be presented, an error must occur in a t least two independent recent standard books.
'JENKINS, D. A,,
-
AND
MARKS,D. J., Edue. C h m . , 2 , 213
I -l Q - M.,i. \
2
H
~C.S., ~ Z . ~Phy8.~ Chm., ~ 47, , 113 (1904)
107
Textbook Errors:
- 3AH; 2,2,
=
H&-
6Hg
- 3Hk,
-
3(H& - 2HE - H&) = H&
- 3H&
Thus when enthalpies (actually enthalpy changes) of reactions are calculated from enthalpies of formation in the usual manner, the enthalpies of the elements cancel, and it does not matter that these enthalpies are neither zero nor have values that can be determined. It is trivially true that the enthalpies of formation of the elements are zero since, e.g., AH;", = HR, - HK,; but AH;=, = 0 is.quite a d i e r e n t statement from the claim that Hk, = 0. In any event if we are to insist on Volume
48, Number 12, December 1971
/
829
some measure of precision in the expressions of our students, we ourselves should avoid such statements as "The enthalpy of an element in its standard state is set equal to zero." Exactly similar comments pertain to Gibbs Energies, but of course, an absolute entropy is definable and generally measurable. Magnetic Momenl:
A Question of Dimensions
Dr. S. F. A. Kettle of SheffieldUniversity, England, calls attention to the common practice of misidentifying units associated with the magnetic moment. This quantity is of special interest and is measured frequently in investigations on transition metal compounds. In many studies, the paramagnetic susceptibility is determined and a quantity is calculated by the definition3
830
/
lournol of Chemkol Education
where X M is the molar magnetic susceptibility, N is Avogadro's number, and P is the Bohr Magneton, eh/4amc. The quantity, we,,, is dimensionless and has been referred to as the effective Bohr mugneton n ~ r n b e r . ~ Thus, it is correct to say that "the effective magnetic moment of a molecule is @,I, Bohr magnetons," hut incorrect to say that "w, has units of Bohr magnetons." The essential distinction is that the effective magnetic moment of a system does have dimensions and units whereas the quantity defined by pendoes not; i t is simply a number.
'VAN VLECK,J. H., "The Theory of Electric and Magnetic Susceptibility,'' Oxford University Press, 1932.
