Calculation of Empirical Formula from Percent Composition

2 Calculation of Empirical Formula from Percent Composition 

The conversion of experimental composition data to empirical formula is an important step in determining the identity of a substance. Suppose that we have a sample of a heavy, pale yellow, crystalline material that has the composition 59.0% Ba, 13.5% S, and 27.4% O. We need to convert this percent composition data to an empirical formula, which will 

We could choose any amount of the substance and convert it to the mass of each of the elements. If we choose 100 grams of the substance, it makes the problem a little easier because we can do the first part of the math in our heads. For example, if we have a 100 g sample of the substance and it contains 59.0% barium, the mass of barium present is 

Likewise, in this same sample we have 13.5g sulfur and 27.4 g oxygen. In order to convert these masses to moles we divide each by their atomic mass  

We could at this point write the empirical formula as Bao.430So.421O1.71, but we know that the empirical formula should be expressed in whole numbers. Consequently, we divide each of the subscripts by the smallest one (0.421), which gives us subscripts of 1.02,1.00, and 4.06. These still are not whole numbers, but because these numbers have been derived from experimental data, which contain errors, we cannot expect the numbers to come out to exact whole numbers. The numbers appear close enough to 1, 1, and 4 to allow us to safely round them off. Hence, the empirical formula of the substance is BaS04. 

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