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The empirical formula of a compound expresses the simplest ratio of atoms among its constituent elements. It tells you which elements are present and their relative proportions, but not the exact count of atoms in a single molecule. The molecular formula, on the other hand, reveals the precise number of each atom in a molecule. Because many distinct compounds share the same empirical formula, you can only deduce a molecular formula when you also know the compound’s molar mass.

TL;DR (Too Long; Didn't Read)

Once you know the empirical formula, calculate its molar mass. Divide the actual mass of the sample by this molar mass to obtain an integer multiplier. Multiply every subscript in the empirical formula by that multiplier to get the molecular formula.

How to Determine the Empirical Formula

Chemists commonly use a combustion or titration analysis to determine the mass of each element in a known quantity of the compound. After measuring the mass of each element, divide by its atomic weight to find the number of moles. Express these mole ratios as whole numbers (or simplified fractions) to obtain the empirical formula, the most concise representation of the compound’s composition.

Deriving the Molecular Formula

Follow these steps:

1. Compute the Empirical Mass. Sum the product of each element’s atomic weight and its subscript in the empirical formula. This gives the molar mass that the empirical formula represents.
2. Measure the Sample Mass. Weigh a pure sample of the compound (ideally in grams).
3. Calculate the Multiplier. Divide the sample mass by the empirical mass. The result should be an integer (or very close to one, within experimental error).
4. Scale the Empirical Formula. Multiply each element’s subscript by the integer multiplier to obtain the molecular formula.

Illustrative Example

Step 1: Find the Empirical Formula

The compound contains 72 g of carbon (C), 12 g of hydrogen (H), and 96 g of oxygen (O). Calculate the number of moles:

• C: 72 g ÷ 12 g mol⁻¹ = 6 mol
• H: 12 g ÷ 1 g mol⁻¹ = 12 mol
• O: 96 g ÷ 16 g mol⁻¹ = 6 mol

Divide each by the smallest value (6) to get the simplest ratio: 1 : 2 : 1. The empirical formula is CH₂O, the same as formaldehyde.

Step 2: Determine the Molecular Formula

First, calculate the empirical mass: one C (12 g) + two H (2 g) + one O (16 g) = 30 g. The sample weighs 180 g, so 180 g ÷ 30 g = 6. Multiply each subscript by 6 to obtain the molecular formula: C₆H₁₂O₆, which is glucose. Although glucose and formaldehyde share the same empirical formula, they exhibit markedly different properties—glucose sweetens, while formaldehyde is a hazardous preservative.