When teaching the method for converting percentage composition to an empirical formula, I have devised the following rhyme:
Percent to mass
Mass to mole
Divide by small
Multiply 'til whole
Here's an example of how it works. A compound consists of 72.2% magnesium and 27.8% nitrogen by mass. What is the empirical formula?
(1) Percent to mass:
Assume 100 g of the substance, then 72.2 g magnesium and 27.8 g nitrogen.
(2) Mass to moles:
for Mg: 72.2 g Mg x (1 mol Mg/24.3 g Mg) = 2.97 mol Mg
for N: 27.8 g N x (1 mol N/14.0 g N) = 1.99 mol N
(3) Divide by small:
for Mg: 2.97 mol / l.99 mol = 1.49
for N: 1.99 mol / l.99 mol = 1.00
(4) Multiply 'til whole:
for Mg: 2 x 1.49 = 2.98 (i.e., 3)
for N: 2 x 1.00 = 2.00
and the formula of the compound is Mg3N2.
Students enjoy this device and have discovered that they have both the rhyme and reason for working chemistry problems of this type.
The above article is copyright © 1988 by the Division of Chemical Education of the American Chemical Society, Inc.
ChemTeam comments on the article:
The assumption of 100 grams in part 1 is purely for convenience sake. This means that the percentages transfer directly into grams. If you assumed that 36.7 grams were present, you would have to multiply 36.7 by each percentage. Assuming 100 grams makes it much easier.
In part 3, make sure you divide ALL answers from #2 by the smallest value. This may seem obvious, but the ChemTeam has had students who neglect to divide the smallest value by itself to get one.
In part 4, multiply ALL values from #3 by the same factor. This factor is selected so as to produce ALL whole numbers as answers. Often this factor is chosen by trial-and-error.