A chemical formula represents the composition of a compound, indicating the types of atoms present. Chemists use two main formulas: the empirical formula and the molecular formula. The molecular formula provides the precise count of every atom within a single molecule. Determining this count requires information about both the simplest atomic ratio and the overall mass of the molecule.
Understanding Empirical and Molecular Formulas
The molecular formula shows the exact number of atoms of each element that make up a compound. For instance, the molecular formula for glucose is C6H12O6, indicating six carbon, twelve hydrogen, and six oxygen atoms in one molecule. In contrast, the empirical formula represents the simplest whole-number ratio of those atoms.
The empirical formula for glucose (C6H12O6) is found by dividing all subscripts by the largest common denominator, six, resulting in CH2O. Although different, both formulas represent the same substance and composition. To convert the empirical formula to the molecular formula, the compound’s molar mass is required. Molar mass is the weight in grams of one mole of the substance.
Determining the Empirical Formula Mass
The first step involves calculating the mass of the empirical formula unit, known as the Empirical Formula Mass (EFM). The EFM is calculated by summing the atomic weights of all atoms listed in the empirical formula. These atomic weights are readily available on the periodic table. For the empirical formula CH2O, one adds the mass of one carbon, two hydrogen, and one oxygen atom.
To perform this calculation, the atomic mass of each element is multiplied by its subscript in the empirical formula. For example, the mass contribution of hydrogen in CH2O is twice the atomic mass of hydrogen, since there are two atoms. The EFM represents the total mass of the smallest whole-number ratio of atoms in the compound and provides the necessary denominator for the next computational step.
Calculating the Whole Number Ratio
The calculated Empirical Formula Mass (EFM) is compared to the substance’s experimentally determined Molar Mass. This comparison yields a whole-number multiplier, represented by \(n\), which links the two formulas mathematically. This multiplier is calculated by dividing the Molar Mass by the EFM: \(n\) = Molar Mass / Empirical Formula Mass.
The resulting value of \(n\) indicates how many empirical formula units are contained within the full molecular structure. Since the molecular formula must contain a whole number of atoms, this ratio should always be a whole number, or extremely close to one that can be rounded. If \(n\) is 1, the empirical formula and the molecular formula are identical, such as in the case of water (H2O).
Converting to the Molecular Formula
Once the whole-number multiplier (\(n\)) has been determined, the final step is to convert the empirical formula into the molecular formula. This conversion is accomplished by multiplying every subscript in the empirical formula by the calculated value of \(n\). This action increases the number of atoms of each element by the factor \(n\), moving from the simplest ratio to the actual count.
For instance, if a compound has an empirical formula of CH2 and the calculated ratio \(n\) is 2, multiplying the subscripts by 2 yields the molecular formula C2H4. This final formula represents the true composition of a single molecule, consistent with the compound’s known molar mass. The process utilizes the simplified ratio and the overall mass to reveal the exact atomic structure.