The EQUILIBRIUM
CONSTANT EQUATION A Concrete Solution of
a ~ e a c h i nD@culty ~'
WILLIAM A. DOW Grand Rapids Junior College, Grand Rapids, Michigan
total molecular concentration raised to that power represented by the coefficient standing before its formula in the balanced equation. Let 0 represent a hydrogen iodide molecule. Taking four molecules, it can easily he shown (by Figure 1) that the total number of chances of collision per unit of time is six. Molecule No. 1 2 No.ofcollisions= 3 + 2 f
3 4 1 + O= 6
Another diagram (Figure 2) is drawn for a molecular concentration of eight molecules representing the number of chances of collision per unit of time as twentyeight.
Therefore, for x molecules of hydrogen iodide the chance of collision will be ( x - 1) ( x - 2) ( x - 3) . . . 1. The general formula of such a series is,
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HOGNESS nm JORNSON, "Qualitative analysis and chemical N THE mathematical expression of the Law of equilibrium," Henry Holt and Co., New York City, 1937, Part I, Chemical Equilibrium, it has been generally difficult p. 51.
I
for the student of elementary college chemistry to understand clearly why it is necessary'to use the total concentration of a reactant raised to some power, e. g.,
The student cannot readily understand why [HI] in the above expression must represent the total concentration. I believe this can be explained simply and clearly without sacrificing either mathematical principles or chemical theory. It may be presented to a class by starting with the assumption that the velocity of the reaction to the right is proportional to the number of collisions between the hydrogen iodide molecules per unit of time, explaining that on the average only a certain per cent of the total contacts will result in chemical change, since the molecules have different kinetic energies a t any instant and only those at an energy level above a certain point are capable of reaction. Then proceed by means of drawings to show that the number of chances of collision is proportional to the velocity of the reaction and to the
Testing this formula, using the second illustration (Figure 2) above where x = 8
molecular concentration of the reactant, hydrogen iodide, i t follows that the velocity of the reaction to the right is proportional to the total concentration of the = 28 chances of collision 2 hydrogen iodide raised to the second power. Since the number of chances per unit of time is proAlthough the above reaction represents a specific portional to the number of actual collisions, i t follows type, other types lead to modified general mathematical that the number of collisions is also proportional to formulas all pointing to the same conclusion, namely, (x - 1)x, where x represents the number of molecules of that the total concentration of each reactant must be hydrogen iodide in the system. For all practical sys- used and that this total concentration must be raised to tems x would represent a very large number of mole- that power represented by the coefficient standing hecules, so (x - 1) may be considered equal to x, and fore the formula of the substance in the balanced (x - l)x equal to xz. Since x represents the total equation.
