Empirical & Molecular Formulae

The Mole Concept: Calculations rely on the fact that chemical formulas represent ratios of moles, not masses. Therefore, the first step in any derivation is converting mass data into molar amounts using $n = \frac{m}{A_r}$.

Law of Definite Proportions: This principle states that a given chemical compound always contains its component elements in a fixed ratio by mass. This allows us to use percentage composition as a proxy for mass (assuming a 100g sample).

Step 1: Obtain Mass Data: Identify the mass of each element in the sample. If given percentages, assume a total mass of 100g so that the percentage values equal the mass in grams.

Step 2: Convert to Moles: Divide the mass of each element by its relative atomic mass ($A_r$). It is crucial to use the atomic mass of the single atom, not the molecular mass of diatomic gases (e.g., use $16.0$ for Oxygen, not $32.0$).

Step 3: Determine the Simplest Ratio: Divide all the resulting mole values by the smallest mole value obtained in Step 2. This normalizes the data to a 1:X ratio.

Step 4: Convert to Whole Numbers: If the ratios are not whole numbers (e.g., 1.5 or 1.33), multiply all ratios by a common factor (e.g., multiply by 2 for .5, or by 3 for .33) to achieve a whole-number set.

Step 1: Calculate Empirical Mass: Sum the relative atomic masses of all atoms in the empirical formula to find the 'empirical formula mass'.

Step 2: Find the Multiplier ($n$): Divide the actual relative molecular mass ($M_r$) of the compound (usually provided in the problem) by the empirical formula mass calculated in Step 1.

Step 3: Scale the Formula: Multiply the subscripts of the empirical formula by the integer $n$ to obtain the molecular formula. For example, if the empirical formula is $CH_2$ and $n=2$, the molecular formula is $C_2H_4$.

Precision in Calculation: Do not round your mole values too early in the process. Keep at least 3 significant figures until you reach the final ratio to avoid rounding errors that lead to incorrect whole numbers.

Handling Non-Integers: If you get a ratio like 1.0 : 2.5, do NOT round 2.5 to 3. This is a common mistake. Instead, recognize that 2.5 is $\frac{5}{2}$ and multiply the entire ratio by 2 to get 2:5.

Sanity Check: Always verify that your final molecular formula mass matches the $M_r$ given in the question. If it doesn't, re-check your $n$ value calculation.