Elemental Composition Of Pure Substances

Silicon dioxide is a covalent network solid, so SiO₂ is a formula unit representing the simplest ratio of silicon to oxygen atoms in the extended lattice. Discrete SiO₂ molecules do not exist under ordinary conditions.

Sodium chloride is an ionic compound in which Na⁺ and Cl⁻ ions are arranged in a continuous three-dimensional lattice held together by electrostatic forces. The formula NaCl reports the 1 : 1 ratio of cations to anions in the lattice, not a discrete molecular unit.

According to the law of definite proportions, every formula unit of CO₂ contains one carbon atom and two oxygen atoms. Because the atomic masses of carbon and oxygen are fixed, the mass ratio of carbon to oxygen is always the same in any pure sample, regardless of origin.

The chemist would conclude that the sample is either impure (contaminated with another substance) or is not magnesium oxide. The law of definite proportions requires that any pure sample of MgO has the fixed mass ratio of 60.3% Mg to 39.7% O, so a deviation indicates the sample does not consist solely of MgO.

The empirical formula represents only the lowest whole-number ratio of atoms. Different compounds can have molecular formulas that are different whole-number multiples of the same simplest ratio. For example, CH₂O, C₂H₄O₂, and C₆H₁₂O₆ all reduce to a 1 : 2 : 1 carbon-to-hydrogen-to-oxygen ratio, so they share the empirical formula CH₂O despite being distinct substances.

The percent composition by mass gives the mass of each element per 100 g of compound. Converting these masses to moles using each element’s molar mass and simplifying to the lowest whole-number mole ratio directly yields the empirical formula. This works because the law of definite proportions guarantees that the mass ratio — and therefore the mole ratio — is fixed for any pure compound.

Step 1 — Assume 100.00 g sample: $${m}_{\text{K}}=26.57\text{ g}$$ $${m}_{\text{Cr}}=35.36\text{ g}$$ $${m}_{\text{O}}=38.07\text{ g}$$ Step 2 — Convert to moles: Equation used: $$n=\frac{m}{M}$$ Potassium: $${n}_{\text{K}}=\frac{26.57}{39.10}$$ $${n}_{\text{K}}=0.6795\text{ mol}$$ Chromium: $${n}_{\text{Cr}}=\frac{35.36}{52.00}$$ $${n}_{\text{Cr}}=0.6800\text{ mol}$$ Oxygen: $${n}_{\text{O}}=\frac{38.07}{16.00}$$ $${n}_{\text{O}}=2.379\text{ mol}$$ Step 3 — Divide by the smallest mole value (0.6795 mol): $$\text{K}:\frac{0.6795}{0.6795}=1.00$$ $$\text{Cr}:\frac{0.6800}{0.6795}=1.00$$ $$\text{O}:\frac{2.379}{0.6795}=3.50$$ Step 4 — Multiply all ratios by 2 to obtain whole numbers: $$\text{K}:1.00\times 2=2$$ $$\text{Cr}:1.00\times 2=2$$ $$\text{O}:3.50\times 2=7$$ The empirical formula is: $$\text{Empirical formula}={\text{K}}_{2}{\text{Cr}}_{2}{\text{O}}_{7}$$