THE PRINCIPLE OF THE CHEMICAL PROBLEM PAULV. MCKINNEY, THECOLLEGE OF WOOSTER, WOOSTER, OHIO
Problems based upon the chemical equation often cause high-school and college students greater difficulty than their complexity warrants. Confused by the yet unfamiliar chemical formula they neglect to master the mathematical principle. During several years of teaching the principle of the proportion after the manner
A : B : : C : D it was discovered that mathematicians advised considering i t as an equality of two ratios, which it is generically. Then all composition and division of proportion were to be discarded and the expression solved as an equality of two fractions. Finally, i t was taught that the establishment of a single ratio was all that was necessary in any given problem. Two years' experience has proved the value of this method. The establishment of a ratio which has a definite physical significance is then of fundamental importance. A familiar example is that of density, which is the ratio of mass to volume (M/V). In a comparison of two objects of the same material, since their densities are equal, the ratios of their respective mass and volume are equal, M,/V, = MJV*. The principle of proportion would allow the statement of the ratio in the following manner: M I / M ~ = V I / V ~ . The last two ratios M,/M2 and VI/VZ do not have a physical existence and have no constant value. They are confusing, for the fact that they are equal is not immediately observable, but is rather a matter of induction. The chemical problem as well involves one fundamental ratio only, a ratio whose value is definite and constant irrespective of the units in which it is expressed, providing in a given case that both terms are in the same unit. Consider the chemical reaction expressed in the equation, CuO
+ Hz -+ Cu + H20.
It is desired to know the theoretical amount of water produced by the reduction of 5 grams of CuO. The fundamental ratio is that of the amount of water to the amount of the oxide reduced, Wt' - The numerical wt. CuO value of this ratio may be determined once for all problems from the atomic weight table, for these weights themselves have been determined mol. wt. H20 = constant (chemical by the use of this very principle, mol. wt. CuO x g. Hz0 formed = confactor). In this particular problem the ratio is 5 e. CuO reduced stant. The constants are certainly the same (law of definite composition).
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Therefore, since the two fractions express anidentical ratio (the one known molecular values, the other from this specific problem) they are equal. Mol. wt. HzO x g. H 2 0 formed Mol. wt. CuO 5 g. CuO reduced The value of this ratio has a chemical significance and is the "chemical factor" of quantitative analysis whose value is listed in tables in handbooks of chemistry. Any term of the chemical equation has just such a relation to every other component used or obtained in the reaction. In the chemical problem also one may choose a second method of comwt. CuO used The quotient is numerically the number of parison, i. e., mol. wt. CUO' mole quantities of CuO entering into the reaction. And since by the equation the number of mole quantities of H20 produced are the same, then wt. H20 produced wt. CuO used mol. wt. CuO mol. wt. H 2 0 This method is confusing for i t will give a different value for every new amount of CuO used and furthermore it has no commonly used meaning if the calculations involve such other units of weight as tons, etc. Of course, one may postulate a ton-mole as well as the gram-mole if one desires and ton-molecular-weights instead of gram-molecular-weights. Perhaps i t might be illuminating to the student to do so. This ratio, since it does give the number of mole quantities, when multiplied by 22.4 will give the volume in liters of any term if the weight is expressed in grams and the substance is a gas. An example will illustrate the simplicity of this method of calculation. In the decomposition of potassium chlorate
i t is desired to know the theoretical amount of oxygen produced from 2 grams of the salt. It is evident that oxygen has been formed from the mol. wt. 302 , and in actual weight it has decomposition in the ratio, mol. wt. 2KC102 x g. Oxygen been produced in the ratio, . Therefore, mol. wt. 302 2 g. Chlorate mol. wt. 2KC103 x g. oxygen produced 2 P. chlorate used I n such problems there is no more pernicious habit among students than that of writing numbers without any designation of their character. An abstract number, without the name of its kind of unit or what i t is the
measure of, is valueless. Only in theoretical mathematics can abstract numbers have any excuse for existence. Emphasis is placed upon the necessity of establishing simple ratios which have a definite chemical meaning in working problems based upon the chemical equation.
