Percent Composition and Empirical Formulas

A compound always breaks down into its elements in the same mass ratio, no matter how much of it you have. That fixed ratio is a fingerprint. If you know the percent by mass of each element, you know something fixed about the compound itself, not just about your particular sample. The trick is that mass ratios and atom ratios are not the same thing, because atoms of different elements have different masses. To get from mass to a ratio of atoms, you have to convert through moles, since moles count particles directly.

Here is the mechanism. Assume a 100 gram sample, so each percent becomes grams directly. Divide each element's mass by its molar mass to get moles of each element. Then divide every mole value by the smallest one in the set, which scales the ratio down so the smallest element becomes 1. Round the results to whole numbers, and those whole numbers are the subscripts in the empirical formula. Sometimes rounding fails because a ratio lands on something like 1.5 instead of 1 or 2. When that happens, you cannot round, since x.5 never rounds cleanly. Instead multiply every ratio in the set by 2, which turns 1.5 into 3 and preserves the correct proportions.

This topic sets up everything that follows in the unit. Once you can find an empirical formula, the next step is finding the actual molecular formula, which requires knowing the compound's molar mass and seeing how many empirical units fit inside it. Percent composition also connects backward to the mole concept: without a reliable way to convert mass to moles, none of this arithmetic works.