L6szlo J. Csanyi University of Szeged Szeged, Hungary
I
Wmating Standard Oxidation Potentials
A
relation between $he electrode potentials and the oxidation potentials of ean element in various oxidation states has been proposed by Luther and Wilson (I). It is developed as follows: Let the following equilibria between the various oxidation states of an element be:
In isothermal-isobaric reversible processes the work done depends only on the initial and final states. For AFo, the free energy change, we have: AFo.i, = AFo,ic
E", = f(Zn,)
+ AFsbi.
since (c
- a)Eo.,.
AF" =
(b
=
-nFEo,
- a)Eo,is + (c
By means of this formula, when two standard oxidation potentials are known, the third related potential value can be estimated. The difficultyin the application of this rule is that in general the related potential values are not available. Further i t may be that the potentials and free energy data, respectively, are not consistent with the known .ones. Perhaps this is why the Luther-Wilson rule is so infrequently applied. .The difficulty which arises from the lack of the related potential values and from the inconsistency of some data can be eliminated when the required value is estimated by means of the following function:
; b)Eoai.
It can be shown from available consistent data that when the various standard potential values of an element are plotted against the sum of the oxidation numbers of the species which take part in the equilibria, straight lines are obtained. (See the figure for typical data so treated.) The plotting for the order of the individual potential values gives the same result as that obtained from the Luther-Wilson rule. When the
Volume 37, Number
3, March 1960 \
/
147
successive oxidation states are designated a, b, and c (i.e., a < b < c), then the value of the standard oxidation potential of the a/c transfer always lies between the potential values of a/band b/c transfers, i.e., ED.,a < E0.ic
< Ensic
4
or Eo.s
the values of Eosir,Eoa/s,EOs/s,Eogi6,Eo416,and E06/a lie on a straight line. From this straight line determined by the two known points, the required values can be estimated.
Ef
> E"ei. > E"aic
20
It can be easily proved that the above function yields the Luther-Wilson relation. Let k, 1, and m represent
U
the sum of the oxidation numbers of the species taking part in the corresponding couples:
P i
il
k=a+b,l=a+c,andm=b+c.
G
According to the linear function (Fig. 1)obtained we can write:
and substituting the values of k, 1, m, and reducing we get the Luther-Wilson rule: For the applicability of the function given, the following example is illustrative: Calculate the standard oxidation potentials of the various species obtained by the reduction of chromic acid, ie., the values of E"ai&, Eoais, Eo4i6,Eopi8. Since only Eo3i6and from Wese heimer's estimation (2) Eo61e are known (E"sis = -0.60 volt), direct calculations cannot be performed.
E;
f
o
*
/
-i,z.. Figure 2.
-I
/Am
-v'
Some exomplesof plotting Eoi as o function of Zni.
The potential values obtained are the following:
The computed values of free energy of formation of the species of Cr(IV) and Cr(V) are: Cr(OH)S+aq: -59.68 kcal HCr0.2- aq: -198.74 kcal
1 :
j ; , !
'.
k
"
zni
~i~~~~ I. tima mat ion of oxidation potentiolr.
But on the basis of the Luther-Wilson rule the following relations exist between the potentials:
and from this it follows that upon plotting the function
Eat
148
/
=
f ( W
Journal of Chemical Education
Besides the estimation of unknown potential values the Eo, = f(%) function can be applied for evaluating the consistency of tabulated data. For example, plotting the function above we had observed that for the transfer SbnOs
+ 2H20 = SbrOs + 4H+ + 4e-
the value E" = -0.692 is incorrect (9). The correct value is E" = -0.670volt. Thanks are due to Prof. Dr. Z. G. Szab6 and Dr. P. Huhn for valuable discussions. Literature Cited (1) LUTHER,R., AND WILSON,D. R., 2. Phvsik. Chem., 34, 488 (1900), andibid., 36,385 (1902). (2) WESTHEIMER, F. H., C h n . Reus., 45,419 (1949). (3) LATIMER. W. M.. "The Oxidation States of the Elements and Their ~otentiklsin Aqueous Solutions," Prentiee-Hall h e . , NewYark, 1952,p. 119.
