that BrOH is an acid even if the instructor wrote the formula incorrectly." Apparently the latter student thought the formula HBrO was correct. Isn't it ironic that we rush ahead with new concepts and yet cling to the Arrhenius theory of acids and bases when writing formulas? With comments such as those given above one has to ask the question, can students understand the concept of antibonding molecular orbitals when they have diiculty understanding the difference between an acid and a base? I would like to raise one final question, and then suggest a starting point for discussion. Could it be that no matter how noble our goal, we are missing a large number of students in our pel1 me11 dash to cover more and more material on a more sophisticated level? Perhaps it is time to back track part way. It may well be that some fundamental principles and their application to important problems of the day, such as pollution, are just as important as a concept like free energy. I have not attempted to propose a complete answer to the current conflict as the problem is complex. However, it is my hope that in raising these questions a dialogue can be established and a happy medium between conventional freshman material and physical chemistry topics can be realized.
like a completion to the given rule. When the author, for inequality discussions, uses the equation [HzO+] = (K.C.
valid for a solution containing two monobasic weak acids, I would raise the equation to the second power and express the result as follows [RINCBOM, A., "Complexation in Analytical Chemistry," John Wiley & Sons, Inc., New York, 1963, pp. 163, 1381: When a solution contains several weak acids, the hydrogen ion concentrations separately calculated for various acids are not additive, but the squares ofthe separately calculated hydrogen i o n concentrations of all weak acids in the solution are additive. Also water is considered an acid. A corresponding rule is valid for bases. The rule can also be used for solubilities, i.e., the equation IAgf]
T o the Editor: I n the November issue of THIS JOURNAL [44, 658 (1967)l James A. Goldman, in a paper, "Le Chatelier's Principle and Rigorous Ionic Equilibria Equations," discusses the difference between rigorous and approximate expressions for equilibrium calculations. His conclusion is that "the equilibrium concentration is always less than the sum of the individually calculated concentrations from the consideration of each individual equilibrium in the absence of others. Furthermore, the equilibrium concentration is always greater than the average of the individually oalculated concentrations." It is certainly useful to know which of two compared quantities is larger and which is smaller, and as an illustration to Le Chatelier's principle the rule offers some interest. However, I cannot help feeling that equalities are more useful than inequalities, and therefore I should
442 / lournal of Chemical Education
=
(KIi KC,)'/'
given by the author for silver halide solutions, can be stated as follows: If a solution is saturated with several binary salts containing a common ion, the individually calculated concentrations of this ion (equal to the individual molar solubilities) are not additive, but their squares are additive. The suggested formulation facilitates memorizing and-although not a rigorously valid r u l e i t is useful in many connections. As an example we may take the case that two metals, MI and MII, are titrated complexometrically with a ligand, L. Then, the additivity-ofsquares rule states that a t the equivalence point, when both metals have reacted to 111Land 1\111L,respectively, [L].,=
Le Chalelier and Ionic Equilibria
+ KbCb + KW)'/*
=
+
[ L I I ~ ILII?
Instead of [L]I and [L]IIthe corresponding metal ion concentrations, [MI] and (MII]can also be used according to the individually valid equation, where CMis the total concentration of metal and KMLis the stability constant of the metal complex. A condition for the use of the rule given above is that the individually calculated quantities are proportional to the square roots of the concentrations. If [H30+]or some other quantity is proportional to the concentration (as in solutions of strong acids or buffer solutions) the additivity-of-square rule can not be applied. More details of the suggested approach can be found in the book referred to above, where fairly complicated systems are also considered.
