Disproportionation Reaction
Taikyue Rae University of Utah salt Lake City, 84112
in Electrochemistry
Recently, disproportionation reactions have been widely treated in textbooks of freshman chemistry. The briefness of the description, however, causes a great confusion among students. Here we point out the facts by yhich they are confused and propose how to avoid their confusion. For the purpose mentioned above, we first state the characteristic points of the disproportionation reactions. An example of the latter is shown in the following 3HNOdaq) = N O a - ( 4
+ 2NOW + H Y w ) + HLW)
(1)
The reduction potentials of the half-reactions (acidic solution) involved in reaction (1) are showq by the Latimer potential diagram1 096
I n reaction (I), HN02, in which N is of oxidation state 3, transforms into NOa-(aq) and NO(g) where the oxidation states of the N-atoms are 5 and 2, respectively. This is the first characteristic point of disproportionation reactions, i.e., an atom with an intermediate oxidation state oxidizes into an oxidation state higher than the original (reactant) state whereas it also reduces to a lower oxidation state. Generally the cell potentials Aco for disproportionation reactions are not uniquely determined from eO's for the half-cell reactions involved. This is the second characteristic point, since it is not the case for other cell reactions. For example, AcO for the cell reaction Cu2+(aq) Zn(s) = Cu(s) Zn2+, the value of Aeo (1.10 V) is uniquely determined from the values of cO's, -0.763 and 0.34, for the half-reactions, Znz+(aq) 2e- = Zn(s) and Cuz+(aq) 2e- = Cu(s), respectively. The non-uniqueness in the determination of AsD for disproportionation reactions is readily shown by using reaction (1). By combining reactions (2) and (3), the value. Aco = 0.06. is obtained for the cell reaction (1) w h e r e i t h e combinations of (2) . . with (4) . . and (4) with (3) yield AcD = 0.02 and A t o = 0.04, respectively. The student's cmfusion arises from the multivalues of Aco, i.e., their questions are: why is Aro not uniquely determined, and which of the Aco's is the true value of the disproportionation reaction? These questions should be answered clearly, othemise they will lose interest in electrochemistry.
+
+
Here the number between two substances connected by a line indicates the reduction potential of a half-cell reaction r o (in volts); i.e. NO3-(aq)
+ 3H+(aq) + 2c-
=
HNOdaq)
+ HzO
H N O & ~ )+ H + ( ~+ ~ e) = NO(^) + H,O NOS-(aq)
+ 4Hi(aq) + 30-
=
NO(g)
e" =
0.94 (2)
r* =
1.00 (3)
e'
0.96 (4)
+ 2HzO =
' LATIMER, W. M., "The Oxidation States of the Elements and Their Potenti& in Aqueous solutionsz2 (znd d . ) , Inc., NewYorlc, 1952, pp. 13,104.
+
+
Volume 48,
Number 7, July 1971
/
467
The first question is answered below. For generality, let a, b, and c be the half-reactions between the highest and the medium, the medium and the lowest, and the highest and the lowest oxidation states, respectively; these reactions correspond to half-reactions (2), ( 3 , and (4) for the disproportionation reaction (1). We can construct three cells by colnhining three half-cell reactions, i.e., a - b, a - c, and c - b, which correspond to the combinations of reactions (2) - (3), (2) - (4), and (4) - (3), respectively. These cells should have differentAto's since each cell has a different combination of two electrodes (half-cell reactions). This is the reason why Aro for a disproportionation system is not uniquely determined. In a t e x t h o ~ l t , ~ the multi-values of Ato of a disproportionation system have been pointed out. Before answering the second question, we should note that the students misunderstand Aro as a state function. This prejudice is based on a partial similarity which exists between the calculation of A t D for chemical cells (i.e., simple subtraction of so's) and that of AH0 for all chemical reactions from Ho's of the reactants and products. Thus, we should emphasize to them that Ato is not a state function, but the Gibhs free-energy change, AGO = -nFAeo, is, where n is the number of electrons transferred from one electrode to the other, and F is the Faraday constant, 23.06 kcal/V equivalent. For reaction (I), one obtains AGO = -0.12 F by combining half-reactions (2) and (3), where Aro = 0.06 and n = 2; the comhinations of reactions (2) - (4) and (4) - (3) yield the same value of AGO, because in the former, n = 6, A c O = 0.02, and in the latter, n = 3, Aro = 0.04. Thus, AGo for cell reaction (1) is constant irrespective of the values of Ato, i.e., AGO is a state function. Since Aro depends on the electrodes producing the cell-reaction (I), it is not a state function. Thps Aeo corresponds to W (work) which depends on the path (process) by which the state attained. The answer to the second question is: all of the multi-values of Ato is true provided that for each of A t o , the half-reactions are shown. Note that cell reaction (1) does not show unequivocally the half-cell reactions since there are three half-cell reactions involved as previously mentioned. This is quite contrary to ordinary cell reactions, e.g., the Daniel1 cell reaction, Cu2+ Zn(s) = Cu(s) Zn2+, automatically indicates the halfreactions involved in it. Although there are three valves of Ato, if we choose one as a representative of he's for a disproportionation
+
+
system by con~ention,~ it will greatly simplify the description and reduce the confusion. As "the representative potential," we propose to use Ato of the cell, a - b, corresponding to the combination of halfreactions (2) and (3) for cell reaction (1). This is due to the fact that the representative potential is often used as the criterion for the possibility of occurrence of a disproportionation reaction. Thus the chemical equation of a disproportionation reaction attached with the representative potential A t a , enables one to understand its electrode reactions and to obtain the t o values of the latter from a table of standard electrode potentials in the case of ordinary chemical cells. One should also note that to,, the value of to for the half-reaction c, is readily obtained if to's of halfreactions a and b are known and that by using t o , two values of At0 other than Ato, are calculated if necessary. In the above, we have pointed out that a disproportionation reaction has generally three values of Ato. I n special cases, however, it has only two values of AE". For example, in the copper series
The combination of half-reactions a - b, a - c, and c - b give the values of Ae", 0.36, 0.18, and 0.18, respectively, i.e., there are twovalues of Aeo. Theoretically there will be no single value of Ato for a disproportionation reaction. The reason is as follows: The a - b combination of half-cell reactions, which produces Ato,, is a path with the least number of electrons (a,)transferred (or the maximum value of Ar0) according to AGO = - n F A t O ; if the comhinations, a - c and c - b, produces the same value of Aro as AcO,, the values of n should be equal to n,; this is impossible since the a - c and c - b comhinations require more electrons transferred than the a - b combination because of half-reaction c which accompanies the maximum number of transferring electrons. In concluding this note, the author wishes to express his thanks to the students in the class who raised the questions and discussed the answers previously mentioned with great enthusiasm. 1 ANDREWS, D. H., AND KOKES, R J , "Fundamental Chemistry," John Wiley & Sons, New York, 1962, p. 460. far as we know, there is no agreement concerning the representative potential [[e.f., the report of International Union of Pure and Applied Chemistry, see also J. Amer. Chern. Soe., 82, 5517 (1960)J.
In Odwald's ouramid of the sciences. sociolorm stands on the anez. It mav be counted as me of
and sympathetic mutual co-operatian.
.. .Taken from "The Present State of the Natural Sciences," a Cornell-Baker Lecturer given by Alfred Stock at Cornell University, 1932.
468
/
Journal of Chemical Educotion
