Simplest Formula from Percent Composition

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Problem

Vitamin C contains three elements: carbon, hydrogen, and oxygen. Analysis of pure vitamin C indicates that the elements are present in the following mass percentages:

C = 40.9
H = 4.58
O = 54.5

Use the data to determine the simplest formula for vitamin C.

Solution

We want to find the number of moles of each element in order to determine the ratios of the elements and the formula. To make the calculation easy (i.e., let the percentages convert directly to grams), let's assume we have 100 g of vitamin C. If you are given mass percentages, always work with a hypothetical 100 gram sample. In a 100 gram sample, there are 40.9 g C, 4.58 g H, and 54.5 g O. Now, look up the atomic masses for the elements from the Periodic Table. The atomic masses are found to be:

H is 1.01
C is 12.01
O is 16.00

The atomic masses provide a moles per gram conversion factor. Using the conversion factor, we can calculate the moles of each element:

moles C = 40.9 g C x 1 mol C / 12.01 g C = 3.41 mol C
moles H = 4.58 g H x 1 mol H / 1.01 g H = 4.53 mol H
moles O = 54.5 g O x 1 mol O / 16.00 g O = 3.41 mol O

The numbers of moles of each element are in the same ratio as the number of atoms C, H, and O in vitamin C. To find the simplest whole number ratio, divide each number by the smallest number of moles:

C: 3.41 / 3.41 = 1.00
H: 4.53 / 3.41 = 1.33
O: 3.41 / 3.41 = 1.00

The ratios indicate that for every one carbon atom there is one oxygen atom. Also, there are 1.33 = 4/3 hydrogen atoms. (Note: converting the decimal to a fraction is a matter of practice! You know the elements must be present in whole number ratios, so look for common fractions and become familiar with the decimal equivalents for fractions so you can recognize them.) Another way to express the atom ratio is to write it as 1 C : 4/3 H : 1 O. Multiply by three to obtain the smallest whole-number ratio, which is 3 C: 4 H : 3 O. Thus, the simplest formula of vitamin C is C₃H₄O₃.

Answer

C₃H₄O₃

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