The chemical identity of a compound is expressed using two primary formulas: the empirical formula and the molecular formula. The empirical formula provides the simplest whole-number ratio of atoms, while the molecular formula reveals the exact number of atoms in a single molecule. Converting the simplified empirical ratio into the compound’s actual molecular structure requires a specific piece of experimental data: the molecular molar mass. This mass acts as the scaling factor needed to complete the conversion.
Distinguishing Empirical and Molecular Formulas
The molecular formula communicates the actual count of each type of atom present in a single molecule of a compound. For example, the sugar glucose has the molecular formula \(\text{C}_6\text{H}_{12}\text{O}_6\).
The empirical formula expresses the simplest whole-number ratio of those atoms. To find the empirical formula for glucose, the subscripts in \(\text{C}_6\text{H}_{12}\text{O}_6\) are divided by their greatest common divisor (six), yielding the empirical formula \(\text{CH}_2\text{O}\). For some compounds, like water (\(\text{H}_2\text{O}\)) or methane (\(\text{CH}_4\)), the molecular and empirical formulas are identical because their subscripts are already in the simplest whole-number ratio.
The Critical Role of Molecular Molar Mass
Converting the simplified empirical formula into the actual molecular formula requires a reference point that provides the necessary scale. This reference is the molecular molar mass, which is the mass of one mole of the compound, typically expressed in grams per mole (\(\text{g/mol}\)). This mass is usually provided or determined experimentally.
The empirical formula alone cannot determine the total number of atoms because many different compounds can share the same empirical formula. For example, both acetylene (\(\text{C}_2\text{H}_2\)) and benzene (\(\text{C}_6\text{H}_6\)) share the empirical formula \(\text{CH}\). By comparing the known molecular molar mass to the mass of the empirical unit, the calculation determines how many empirical units fit into the actual molecule. This comparison provides the integer multiplier needed to scale the simplest ratio.
Step-by-Step Derivation of the Molecular Formula
The derivation of a molecular formula from an empirical formula is a three-step mathematical process that uses the molecular molar mass as the scaling factor. The first step involves calculating the Empirical Formula Mass (EFM). This is done by summing the average atomic masses of all the atoms represented in the empirical formula, using values found on the periodic table. For instance, if the empirical formula is \(\text{NO}_2\), the EFM is calculated by adding the mass of one nitrogen atom and two oxygen atoms.
The second step is to determine the whole-number multiplier, often denoted as ‘n’, which represents how many empirical units are contained within the molecular unit. This value is found by dividing the given Molecular Molar Mass by the calculated Empirical Formula Mass. The formula for this relationship is \(n = \frac{\text{Molecular Molar Mass}}{\text{Empirical Formula Mass}}\). The result of this division must be a whole number, since a molecule must contain a whole number of empirical units.
For a compound with the empirical formula \(\text{NO}_2\) and a known molecular molar mass of \(92.0\ \text{g/mol}\), the EFM is approximately \(46.0\ \text{g/mol}\). Dividing the molecular mass by the EFM (\(92.0 / 46.0\)) yields a multiplier (\(n\)) of 2.
The final step is to multiply every subscript in the empirical formula by this integer multiplier, ‘n’, to obtain the molecular formula. Multiplying the subscripts in \(\text{NO}_2\) by 2 results in the molecular formula \(\text{N}_2\text{O}_4\).