Let us suppose that we have just created a new procedure to make glucose, the simplest of all sugars, and we'd like to publish our findings in the Journal of Organic Chemistry. The Journal requires that we properly identify the substance, partly by including an elemental analysis. If we really made glucose, the elemental analysis had better be consistent with glucose's empirical formula.
The elemental analysis can answer the question, "Are the elements present in the correct ratios?" If they aren't, we didn't really make glucose. The correct ratios are given by the empirical formula. So our first step is to determine the empirical formula of glucose so we know what ratios between elements to expect from our elemental analysis. To do this, we need to determine the empirical formula from the molecular formula.
To determine the empirical formula of a known substance, such as glucose, we take the subscripts of the molecular formula (C6H12O6) and reduce then to the simplest whole number ratios. If we divide this by 6, we get C1H2O1. (We don't usually write the 1's, so this would be CH2O.)
Now that we know the empirical formula of glucose, we know what the "correct ratios" from elemental analysis should be if we really made glucose. In this case, we have 6 carbons, 12 hydrogens and 6 oxygens, and the ratios are one carbon and oxygen for every two hydrogens. If the elemental analysis of our sample shows a ratio of one carbon and one oxygen for every two hydrogens, then the analysis is consistent with glucose.
Remember that a number of different molecules may have the same empirical formula, so this does not prove that we made glucose. On the other hand, if the elemental analysis is not consistent with the empirical formula of glucose, then that certainly means that we did not make glucose. For example, let's say we found one carbon for every three oxygens. That would not be consistent with the formula of glucose, and so the elemental analysis would prove that we failed in our attempt to make glucose.
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