Empirical Formula

• Law of Definite Proportions: This principle states that a given chemical compound always contains its component elements in a fixed ratio by mass. The empirical formula is the chemical expression of this fixed ratio.

• Mole Concept Foundation: Empirical formulas are derived from the molar ratio of elements, not their mass ratio. Because different atoms have different relative atomic masses ($A_r$), a 1:1 mass ratio does not imply a 1:1 atomic ratio.

• Ionic Lattices: For ionic compounds, the term 'molecule' is technically incorrect as they exist in giant 3D lattices. Therefore, the formula for an ionic compound (e.g., $NaCl$) is always its empirical formula, representing the simplest ratio of ions required to achieve electrical neutrality.

Calculating from Experimental Data

• Step 1: Determine Mass: Obtain the mass of each element present in a sample (often given in grams or as percentages). If given percentages, assume a 100g sample so that % equals grams.
• Step 2: Convert to Moles: Divide the mass of each element by its Relative Atomic Mass ($A_r$). This converts the 'weight' of the sample into the 'number of atoms' (moles).
• Step 3: Find the Ratio: Divide all the resulting mole values by the smallest mole value obtained in Step 2. This identifies the relative number of atoms.
• Step 4: Simplify to Whole Numbers: If the results are not whole numbers (e.g., 1.5), multiply all values by a common factor (e.g., 2) to achieve the simplest whole-number ratio.

Deducing from Molecular Formula

• To find the empirical formula from a known molecular formula, identify the Greatest Common Divisor (GCD) of all the subscripts in the molecular formula and divide each subscript by that number.

• Relationship Formula: The molecular formula is always an integer multiple ($n$) of the empirical formula, where $n = \frac{\text{Molecular Mass}}{\text{Empirical Formula Mass}}$.

• The 'Divide by Smallest' Rule: Always ensure you divide by the smallest number of moles. Students often forget this step and try to round numbers like 1.33 to 1.0, which leads to incorrect formulas.

• Handling Decimals: Recognize common fractions in your ratios. 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.

• Ionic Compound Shortcut: If an exam asks for the empirical formula of an ionic compound, simply balance the charges of the ions. For example, $Mg^{2+}$ and $Cl^-$ must combine in a 1:2 ratio to be neutral, resulting in $MgCl_2$.

• Sanity Check: Always verify that your final empirical formula cannot be simplified further. If you get $C_2H_4$, you have found a molecular formula, not an empirical one ($CH_2$).

• Mass vs. Moles: The most common error is using the mass ratio directly as the formula subscripts. You must convert to moles first because atoms have different masses.

• Rounding Too Early: Do not round intermediate mole values to the nearest whole number too aggressively. Keep at least 3 significant figures until the final ratio step to avoid losing the correct whole-number relationship.

• Diatomic Confusion: When calculating empirical formulas, use the $A_r$ of the single atom (e.g., $16$ for Oxygen), even if the element exists naturally as a diatomic molecule ($O_2$).