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We read with interest "How Do I Balance
Thee?...Let Me Count the Ways!" (J. Chem.
Educ. 1996, 73, 1129). The author points out an interesting dilemma in
balancing equations, namely, situations in which the number of
variables (in this case, the number of coefficients of the
species involved) is more than the number of independent
constraints (in most cases, the number of elements to be
balanced) plus one. This situation has been described
previously in this Journal (1991,
68, 984; 1994, 71, 490;
1995, 72, 894). It results in an infinite number of
algebraically balanced equations, each of which is a combination of
two equations. One such pair of equations is
4HCl + ClO2 ->
2H2O + 2.5Cl2
2KClO3 +
1.5Cl2 -> 2KCl +
3ClO2
Ferguson correctly points out that the number of
degrees of freedom in choosing a balanced equation for
this system is two, and that one way to choose these degrees
of freedom is to set the coefficients of
KClO3 and ClO2. From these, all other coefficients are uniquely determined.
[Note: There were two misprints in the table of
coefficients in Ferguson's paper. Line 3 should have
coefficients 4, 16, 4, 8, 7, 2 and line 5 should have 5, 22, 5, 11,
10, 2.]
However, in his final paragraph, he goes one step
too far and incorrectly implies that only one of the equations obtained in this way is actually correct, and that the
others can somehow be "negated". The fact is that all of the
equations that he presents are correctly balanced, and that
none can be negated on this basis. He suggests that there is
a constraint beyond the balancing of atomsthat is, the
balancing of the transfer of electrons. However, if charge is
balanced (it is in all these cases), and if each of the atom
types in the equation is correctly balanced (they are), then
the number of electrons in the equation is trivially balanced.
Based on the mathematics of equation balancing,
none of these equations is more correct than any of the
others. There is frequently more than one correct answer to
any given question, and often new insights into a problem
come from the "unconventional" answer. To answer the
question of what ratios of reactant and product masses are
actually obtained requires experimental data that are not part of
the algebraic equation-balancing theory.
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