A molecular formula provides the exact count of each type of atom present in a single molecule of a substance. This differs from an empirical formula, which represents the simplest whole-number ratio of atoms within a compound. This article explains how to determine a molecular formula from an empirical formula.
Distinguishing Empirical and Molecular Formulas
The distinction between empirical and molecular formulas lies in their level of detail regarding atomic composition. An empirical formula expresses the most reduced whole-number ratio of elements in a compound. For instance, glucose has a molecular formula of C₆H₁₂O₆, indicating six carbon atoms, twelve hydrogen atoms, and six oxygen atoms. Its empirical formula, however, is CH₂O, which represents the 1:2:1 ratio of carbon, hydrogen, and oxygen atoms.
The relationship between these two formulas is direct: the molecular formula is always a whole-number multiple of the empirical formula. This multiplier is denoted by ‘n’. The molecular formula can therefore be expressed as (Empirical Formula) \ n. This ‘n’ value is determined by comparing the compound’s known molecular mass to the calculated mass of its empirical formula.
The Calculation Method
Determining the molecular formula from an empirical formula involves a series of structured steps. The first step requires obtaining the empirical formula for the compound. This formula is typically provided or would have been previously determined through elemental analysis.
The next step involves calculating the empirical formula mass (EFM). This is achieved by summing the atomic masses of all atoms present in the empirical formula. For example, if the empirical formula is CH₂O, you would add the atomic mass of one carbon atom, two hydrogen atoms, and one oxygen atom.
Following this, the molecular mass of the compound needs to be known. This value is usually provided as part of the problem or can be determined experimentally using techniques like mass spectrometry.
The fourth step calculates the whole-number multiple, ‘n’. This is found by dividing the molecular mass of the compound by its empirical formula mass. The formula for this calculation is n = Molecular Mass / Empirical Formula Mass. The resulting value for ‘n’ should be a whole number, or very close to a whole number, allowing for slight variations due to rounding of atomic masses.
Finally, to determine the molecular formula, each subscript in the empirical formula is multiplied by the calculated ‘n’ value. This multiplication scales the simplest ratio of atoms to their actual numbers in the molecule, yielding the complete molecular formula.
Practical Examples
Consider glucose, with an empirical formula of CH₂O. Its molecular mass is known to be 180.16 g/mol.
First, calculate the empirical formula mass (EFM) for CH₂O. Using atomic masses (Carbon ≈ 12.01 g/mol, Hydrogen ≈ 1.008 g/mol, Oxygen ≈ 16.00 g/mol), the EFM is 12.01 + (2 × 1.008) + 16.00 = 30.026 g/mol. Next, determine the whole-number multiple ‘n’ by dividing the molecular mass by the EFM. This yields n = 180.16 g/mol / 30.026 g/mol ≈ 6.00.
Since ‘n’ is approximately 6, the final step involves multiplying each subscript in the empirical formula (CH₂O) by 6. This results in C₁ₓ₆H₂ₓ₆O₁ₓ₆, which simplifies to C₆H₁₂O₆.