The molecular formula of a compound indicates the exact number of atoms for each element present within a single molecule. This representation offers insight into a compound’s true composition.
Empirical Formula as a Starting Point
Before determining a compound’s molecular formula, chemists first establish its empirical formula, which represents the simplest whole-number ratio of atoms. This initial step uses percent composition data, detailing the mass percentage of each element. To derive the empirical formula, assume a 100-gram sample. This converts percentage values directly into grams for each element.
Once the mass of each element is known, convert these masses into moles by dividing by each element’s atomic mass. These mole values represent the relative number of atoms. To find the simplest whole-number ratio, divide each mole value by the smallest calculated mole value. If the resulting ratios are not whole numbers, multiply them by a small integer (e.g., 2, 3, or 4) to convert them into the smallest possible whole numbers, yielding the empirical formula.
The Role of Molar Mass
The molar mass of a compound is the mass of one mole of that substance, expressed in grams per mole (g/mol). This value is important for transitioning from an empirical formula to a molecular formula. While the empirical formula shows the simplest ratio of atoms, it does not necessarily represent the actual number of atoms in a molecule. The molecular formula is always a whole-number multiple of the empirical formula.
The compound’s molar mass determines this whole-number multiple. The empirical formula mass, calculated by summing the atomic masses of the atoms in the empirical formula, provides a reference. By comparing the compound’s molar mass to its empirical formula mass, the scaling factor needed to convert the empirical formula into the molecular formula is identified.
Calculating the Molecular Formula
With the empirical formula and the compound’s molar mass established, determine the empirical formula mass (EFM). This is the sum of the atomic masses of all atoms present in the empirical formula unit.
Next, divide the compound’s known molar mass by the calculated empirical formula mass. The result should be a whole number or very close to a whole number, representing the multiplier for the empirical formula. Finally, to obtain the molecular formula, multiply each subscript in the empirical formula by this whole-number factor.
Worked Examples
Consider a compound with a percent composition of 40.0% carbon, 6.7% hydrogen, and 53.3% oxygen, and a molar mass of 180.16 g/mol. To find its molecular formula, begin by assuming a 100-gram sample, yielding 40.0 g C, 6.7 g H, and 53.3 g O. Converting these masses to moles gives approximately 3.33 mol C (40.0 g / 12.01 g/mol), 6.63 mol H (6.7 g / 1.008 g/mol), and 3.33 mol O (53.3 g / 16.00 g/mol).
Dividing each mole value by the smallest (3.33) yields a ratio of 1:2:1 for C:H:O, resulting in an empirical formula of CH₂O. The empirical formula mass for CH₂O is approximately 30.03 g/mol (12.01 + 2(1.008) + 16.00). Dividing the compound’s molar mass (180.16 g/mol) by the empirical formula mass (30.03 g/mol) gives a multiplier of approximately 6. Multiplying the subscripts in CH₂O by 6 produces the molecular formula C₆H₁₂O₆.