A. A. S. C. Machado Faculty of Science The University
of Oporto
Oporto, Portugal
The Use of Electron Balance in Ionic Equilibrium Calculations
Books dealing with the treatment of ionic equilihria ( 1 - 4 ) when treating oxidation-reduction equilihria do not
normally use the electron balance condition as thoroughly as they use the proton balance condition when treating acid-base equilibria. Indeed most books (ref (5) is an exception) do not even introduce the electron balance condition as a principle so fundamental as the proton balance condition, the total charge balance condition (rule of electroneutrality), and the conditions for mass balance. I t is the purpose of this note to show the primary importance of the electron balance condition in ionic oxidation-reduction equilibria and how to use the formal similarity of oxidation-reduction reactions to Bronsted-Lowry acid-base reactions (e.g., ref (4, 6)) to express that condition. In acid-base equilihria, since free protons do not occur in solution, the numher of protons given up by acids eqnals the numher of protons accepted hy bases. The proton halance condition is the mathematical statement of this principle (7, 8). When a solution contains more than one species which either accepts or donates protons, the total number of protons donated by acids equals the total number of protons accepted by bases. Assuming the reactions are expressed by Acidi +. . . a Base; + niH+ + and Base;
+ n,H+ + .. . s Acidj+
the mathematical statement of the proton balance condition (P.B.) is
MOH) will illustrate the formulation of E.B. and its parallel to P.B., and will show some other features of its use in the study of ionic equilibrium. Choosing C12 itself as reference species, the electron transfer reactions are Oxidations Reductions .
which yield the following E.B. Any other statement of the E.B., obtained by choosing another reference species, can be obtained from this and the total chlorine mass balance condition On the other hand, for this system, the total charge halance condition [Cl-] + [CIO-] + [CIOZ-]+ [CD-]
+ [CIOI-] + [OH-] =
[Mt] + [Ht] = cz + [Ht] (3)
is easier to write than the P.B. Equations (1)-(3) are independent since each of the last two contains a t least one variable which is missing from the first. A statement of the P.B. is rather awkward to obtain but this can be done by choosing Cln as reference species (together with H20) and considering it as an acid Acids
The electron halance'condition can be described similarly. That is, when a solution contains more than one species which either accepts or donates electrons, the total number of electrons donated by reductants equals the total number of electrons accepted by oxidants. Assuming the reactions are expressed by Redi + . . . -Ox,
+ nje + . . .
and the mathematical statement of the electron balance condition (E.B.) is
In cases where only one oxidation-reduction equilibrium is important the E.B. reduces to a simple stoichiometric condition easily obtained from the balanced reaction. Since in most oxidation-reduction systems it is possible to identify a priori the only one important reaction, this is probably the reason why so scarce attention has been given to the E.B. In contrast, when several oxidations occur simnltaneously and none is dominant, the E.B. can not be reduced to a simule stoichiometric condition and its imuortance stands 0n.t. in The treatment of the disproportionation of alkaline solution (cl M in Clz and cz M in strong base
-- CIO+ 2Ht C102+ -- C10~: + CIOn + 8Ht H20 - O H + Hi
1/2Clz
4H' 6Ht
Bases
H20
-
H+ +OH-
If the weak basic properties of CIO- are neglected the following P.B. is obtained 2[CIO-]
+ 4[C10*-] + 6[C103-] + 8[C10~-]+ [OH-] -en
=
[Ht]
(4)
This equation can be obtained by reversing eqn. (1) and adding eqn. (3) which proves that one of the balance conditions is superfluous (9).In order to constitute the system of equations to calculate all the concentrations, four independent oxidation-reduction equilibrium constants, as well as the ionic product of water, must he included together with any three of the previous four equations. Acknowledgment
This work has been supported by the Instituto de Alta Cultura, Lisbon, Portugal (Research Project PQ3). The author is indebted to Professor J. Cabral for valuable discussions and to a reviewer for helpful criticism about the manuscript. Llteralure Cited (1,
Fleet. G.
M., "Equilibria in Solutions:
Holt. Rinehart and Winston, N e w York,
1966.
Volume 53. Number 5, May 1976 / 305
(21 Blackburn, T. M., "Equilibrium. A Chnni8tlr of Solutiom,'. Holt. Rinehmt sod Winston. Near York. 1%9. (3) Dyrssen. D..Jape,, D.. and W@a. F., ‘‘Computer Cdeulstioru of Ionic Equilibria and Titration Pmeduea: Almquist and WilracU. Staekhoim. 1968. 14) Stunm. W.. and Morgan, J. J., "Aquatic Chemistry: Wilcy-lntemcienec, New York. 1910. (5) Butler, J. N., '"Ionic Equilibrium. A Mathamatid Approach." Addim-Wdey, Reading. Musachuactta. 1964,~.396.
306 I Journal of Chemical Educaflon
(61 Pacer, R.A., J. CHEM. EDUC., 50.178, (1573). 17) Bruekenltein. S., and Kolthoff, I. M., "Aeid-Bees Strength and Protolopis Curves in Water: in ~ o l t h o f fI., M., Elving, P. J., and sandell, E. B. (Editors), '"~reetise on Analytical Chemistry," Wiioy-Interseienee. N e w York, Part I, voi I. 1965, p. 421. 18) Kolthoff, I. M., Sandell, E. B..Meehan. E. J., and Bruekenstein, S., ',Quantitative Chemical Analysis," 4th Ed.. MacMillan (Collier-MacMillan). London, 1971. p. 62. (9) Dyrsscn, D..and Jsgner.D., A n d C h i m Act.. 42,338 (19681.
