Simplest Formula From Percent Composition

This is a worked example chemistry problem to calculate the simplest formula from the percent composition. Simplest Formula from Percent Composition 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 40.9H 4.58O 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), lets 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 1.01C is 12.01O 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 Cmoles H 4.58 g H x 1 mol H / 1.01 g H 4.53 mol Hmoles 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 1.00H: 4.53 / 3.41 1.33O: 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 Second Example This is another  worked example chemistry problem to calculate the simplest formula from the percent composition. Problem The mineral cassiterite is a compound of tin and oxygen. Chemical analysis of cassiterite shows that the mass percentages of tin and oxygen are 78.8 and 21.2, respectively. Determine the formula of this compound. 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), lets assume we have 100 g of cassiterite. In a 100 gram sample, there are 78.8 g Sn and 21.2 g O. Now, look up the atomic masses for the elements from the  Periodic Table. The atomic masses are found to be: Sn is 118.7O 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 Sn 78.8 g Sn x 1 mol Sn / 118.7 g Sn 0.664 mol Snmoles O 21.2 g O x 1 mol O / 16.00 g O 1.33 mol O The numbers of moles of each element are in the same ratio as the number of atoms Sn and O in cassiterite. To find the simplest whole number ratio, divide each number by the smallest number of moles: Sn: 0.664 / 0.664 1.00O: 1.33 / 0.664 2.00 The ratios indicate that there is one  tin atom for every two  oxygen atoms. Thus, the  simplest formula  of cassiterite is SnO2. Answer SnO2