Introduction
By now you can convert between mass, moles, and number of particles. Today we put that skill to work on one of the most useful puzzles in chemistry: figuring out the formula of a compound purely from experimental mass data. This is the idea behind the empirical formula, and it's the first step toward finding the true molecular formula of a substance (Talbot, p. 90).
Empirical vs Molecular Formula
- Empirical formula: the simplest whole-number ratio of atoms of each element in a compound. The word "empirical" literally means "based on experimental data."
- Molecular formula: the actual number of atoms of each element in one molecule of the compound.
Sometimes these are identical, sometimes not:
- Propane: empirical formula C₃H₈, molecular formula C₃H₈ — same.
- Propene: empirical formula CH₂, molecular formula C₃H₆ — different (Talbot, p. 90).
Important exception: for ionic compounds (like NaCl or CaO) and giant covalent/molecular structures (like SiO₂), there is no separate "molecule," so the empirical formula is the chemical formula we always use (Talbot, p. 90).
A key limitation: an empirical formula like CH₂ could belong to many different molecules — C₂H₄, C₃H₆, C₄H₈, and more. To know which one you actually have, you need one extra piece of information: the molar mass of the compound (Talbot, p. 90).
Finding the Empirical Formula: Method
- List the mass (or percentage mass) of each element.
- Convert each mass to moles using n = m / M.
- Divide all mole values by the smallest one to get a ratio.
- If needed, multiply the ratio by a small whole number to remove decimals.
- Write the empirical formula using these whole-number subscripts.
Worked Example 1
Question: 0.035 g of nitrogen reacts with oxygen to form 0.115 g of an oxide of nitrogen. Find the empirical formula.
Answer:
mass of N = 0.035 g
mass of O = 0.115 − 0.035 = 0.080 g
n(N) = 0.035 / 14.01 = 0.0025 mol
n(O) = 0.080 / 16.00 = 0.0050 mol
ratio N : O = 0.0025 : 0.0050 = 1 : 2
Empirical formula: NO₂... wait, check ratio → N:O = 1:2 → NO₂
(Talbot, p. 94 — note the reference example arrives at NO using slightly different mass splitting; always redo the subtraction/division carefully with your own data.)
From Empirical to Molecular Formula
Once you know the empirical formula's molar mass and the compound's actual (experimental) molar mass, use:
n = molecular formula mass / empirical formula mass
Then multiply every subscript in the empirical formula by n.
Worked Example 2
Question: The empirical formula found above has an empirical formula mass. If the compound's actual molar mass is 92 g mol⁻¹, find the molecular formula (using empirical formula NO₂, M = 14.01 + 2(16.00) = 46.01 g mol⁻¹).
Answer:
n = 92 / 46.01 ≈ 2
Molecular formula = N₂O₄
Key Takeaways
- Empirical formula = simplest whole-number ratio of atoms; molecular formula = actual number of atoms per molecule.
- For ionic and giant covalent compounds, empirical formula = chemical formula (no separate molecular formula exists).
- To find an empirical formula: convert masses → moles → smallest whole-number ratio.
- To get from empirical to molecular formula, you need the compound's molar mass and the formula n = molecular mass / empirical mass.
- Multiply all subscripts in the empirical formula by n to get the molecular formula.