Since the scale for percentages is 100, it is most convenient to CALCULATE the mass of elements present in a sample weighing 100 g. The calculation is “most convenient” because, per the definition for percent composition, the mass of a given element in grams is numerically EQUIVALENT to the element’s mass percentage. This numerical equivalence results from the definition of the “percentage” unit, whose name is derived from the Latin phrase per centum meaning “by the hundred.” Considering this definition, the mass percentages provided may be more conveniently expressed as fractions:

\(\begin{array}{lll}\\ 27.29\%\text{C}& =\hfill & \frac{27.29\text{g C}}{100\text{g compound}}\hfill \\ 72.71\%\text{O}& =\hfill & \frac{72.71\text{g O}}{100\text{g compound}}\hfill \end{array}\)

The MOLAR amounts of CARBON and HYDROGEN in a 100-g sample are calculated by dividing each element’s mass by its molar mass:

\(\begin{array}{lll}\\ 27.29\text{g C}\left(\frac{\text{mol C}}{12.01\text{g}}\right)& =\hfill & 2.272\text{mol C}\hfill \\ 72.71\text{g O}\left(\frac{\text{mol O}}{16.00\text{g}}\right)& =\hfill & 4.544\text{mol O}\hfill \end{array}\)

Coefficients for the tentative empirical formula are derived by dividing each molar amount by the lesser of the two: