Assume a 100 g sample, convert each element's mass into moles, divide all mole values by the smallest value, and simplify the results to the smallest whole-number ratio. That ratio gives the empirical formula.
This method is assessed at both SL and HL in Structure 1.4: Counting particles by mass.
where is the amount in moles, is mass, and is molar mass. 3. Divide every mole value by the smallest mole value. 4. If necessary, multiply all ratios by the same integer until they are close to whole numbers. 5. Use these whole numbers as subscripts in the empirical formula.
The conversion works because chemical formulas compare numbers of atoms, and mole amounts are proportional to numbers of particles through Avogadro constant. Dividing by the smallest amount normalizes the data without changing the proportions. If a ratio is close to 1.50, multiply every ratio by 2; if it is close to 1.33, multiply every ratio by 3 before writing subscripts.
A compound contains 40.0% carbon, 6.7% hydrogen, and 53.3% oxygen.
Assuming 100 g:
Divide by the smallest value, 3.33:
Therefore, the empirical formula is .
A common misconception is to use percentage values directly as subscripts. Percentages represent relative masses, not particle ratios, so they must first be converted to moles. Also, do not confuse the empirical formula with the molecular formula, which may be a whole-number multiple of it.
For a calculate question, show the percentage-to-mass assumption, each mole calculation, the division by the smallest value, and the final formula. Avoid rounding intermediate ratios too early; values near 1.5 or 1.33 usually require whole-number scaling.
