Determining Empirical Formulas

In chemistry, an empirical formula represents the simplest whole-number ratio of atoms in a compound. Think of it as a reduced fraction. For example, while the molecular formula for glucose is $C_6H_{12}O_6$, its empirical formula is simply $CH_2O$. It tells us that for every one Carbon atom, there are two Hydrogen atoms and one Oxygen atom. This is crucial because when scientists analyze unknown substances in a lab, they usually find the ratio of elements first before they find the actual size of the molecule.

To determine an empirical formula from percent composition, we follow a reliable four-step 'rhyme': 1. Percent to Mass: Assume you have a $100g$ sample; this turns percentages directly into grams. 2. Mass to Mole: Divide the mass of each element by its molar mass ($M$) from the Periodic Table. 3. Divide by Small: Look at your mole values and divide all of them by the smallest value among them. 4. Multiply 'til Whole: If your results aren't whole numbers (like $1.5$ or $1.33$), multiply all ratios by a factor to clear the decimals.

Sometimes, step 3 leaves you with a decimal like $1.5$ or $2.33$. You cannot simply round $1.5$ to $2$. This would violate the law of definite proportions! Instead, you must multiply all numbers in the ratio by the same integer to reach a whole number. Common multipliers include: - If you see $.5$, multiply by $2$. - If you see $.33$ or $.66$, multiply by $3$. - If you see $.25$ or $.75$, multiply by $4$.