Double Disproportionations Mario E. Cardinali Chemistry Department of the University, via Eice di Sotto, 10 06100 Perugia, ltaiy Claudio ~ i o m i n i ' ,Giancarlo Marrosu iCMMPM Department, via dei Castro Laurenziano, 7 001 61 Rome, ltaiy The assignment of the stoichiometric coefficients to the species involved in the (unbalanced) redox reaction P21, + P,
+ H 2 0 + PH41 + H3P0,
(1)
has been recognized as a somewhat troublesome task, if methods are employed which rely upon the oxidation number and related co&epts. The reasin why, in this case, the oxidation number method may fail is that phosphorus, the only element undergoing oxidation or reduction, is present in two chemical species among the reactants and also in two chemical species among the products, exhibiting four different oxidation states, so that "it is not clear which product is beine formed from which reactant'' (1). . . Various procedures have been used (1, and quotations therein) to balance this eauation. Here. we would mesent a further way; it does not give up the oxidation number concept. Two simple observations can be made:
cies HI. (This combination amounts to imposing the condition that the two disproportionations are no more free of proceeding a t rates independent from each other). In other words, the coefficients in reaction (2) have to be multiplied by 5 , and those in (3) by 13, and the two chemical equations, thus modified, have to be summed, to give
whence, upon simplification, the correct balancing of reaction (1)is finally achieved:
-
1. The oxidation numhers of phosphorus in the reactants (+2 and 01 are intermediate with respect to those in the products (-3 and +51, so that the reaction could be intemreted as a double disproportionation, in which both of the products are being formed from each of the reactants; 2.
The number of iodine atoms per phosphorus atom in P21, is twice as high as the same number in PHJ, so that the disproportionation of P214would imply HI as ca-product,
while, for the disproportlonatian of elementary phasphorus, HI would be needed as ea-reactant in order to yield the iodinated product PHJ. On the basis of these observations, the following two disproportionations can be written. and easilv balanced.. bv" ihe;sual methods: 4P214
+ 20H20 + 3PH41 + 5H3P0, + 1 3 ~ 1 '
2P4 + 12H20
+ 5HI + 5PHJ + 3H3P0,
(2)
(3)
The above disproportionations can then be combined according to coeff~cientsthat ~ l out e the "extraneous" spe-
716
Journal of Chemical Education
Further examples of (unbalanced) double (direct or inverse) disproportionations can be found in the following list (241: (NH,)2S,03 + (NH,),S,O,+
(NH&304+
S
The task of balancing these equations is left to the interested readers, by introducing suitable "extraneous" species as co-reactants and co-products, along the guidelines provided in this paper. Literature Cited 1. linlb. D.J. Cliem. Educ 1919.56, 181-184. 2. Remy, H. %dine on hzolpnic Wernirrq: Elsevier:Amsterdam. 1956;Val. I. p 616. 3. Mellnrh Compmhsnsiue Tkatise nn Irrommir and Theorrlicnl Chernirrq; Longmans: London. 1962:Vol.11. Supplement I. p 522. 4. Cotton, F A . ;Wllkinron.G.Aduon~edIn~~rpn!~ir Ckrmisfq, 3rded.:Interscience: New York. 1972;p 362.
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