Empirical and Molecular Formulas: Concepts and Calculations

Empirical and Molecular Formulas

Definition and Comparison

The empirical formula of a compound represents the simplest whole-number ratio of the constituent elements. In contrast, the molecular formula shows the actual number of atoms of each element in a molecule of the compound.

• Molecular Formula: Indicates the actual number of atoms of each element in a molecule. Example: C6H12O6 (glucose)

• Empirical Formula: Indicates the simplest whole-number ratio of atoms. Example: CH2O (for glucose)

By convention, any formula must contain whole numbers of each kind of atom.

Compound	Molecular Formula	Empirical Formula
Glucose	C6H12O6	CH2O
Hydrogen Peroxide	H2O2	HO
Ethylene	C2H4	CH2

Calculating the Empirical Formula

The empirical formula can be determined from the masses or percentages of elements in a compound.

1. Write down the mass (in grams) of each element present. If given percentages, assume 100 g of the compound.

2. Convert masses to moles using the molar mass of each element: $\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}$

3. Divide all mole values by the smallest number of moles to obtain the simplest ratio.

4. If necessary, multiply all ratios by a common factor to obtain whole numbers.

Example: Determine the empirical formula of a compound that is 48.6% chromium and 51.4% oxygen.

• Assume 100 g sample: 48.6 g Cr, 51.4 g O

• Convert to moles:

  • Cr: $\frac{48.6}{51.996} = 0.935$ mol

  • O: $\frac{51.4}{16.00} = 3.21$ mol

• Divide by smallest: Cr: $0.935/0.935 = 1$, O: $3.21/0.935 = 3.43$

• Multiply to get whole numbers: $1 \times 3 = 3$, $3.43 \times 3 = 10.3$ (round as appropriate)

*Additional info: If the ratio is not a whole number, multiply by the smallest integer that converts all ratios to whole numbers.

Practice Problems

• Practice 1: A compound contains 48.64% C, 8.16% H, and 43.2% O by mass. What is the empirical formula? Solution: CH2O2

• Practice 2: A sample contains 2.2 g Na, 3.8 g Cl, and 7.8 g O. What is the empirical formula? Solution: NaClO2

• Practice 3: A compound contains C, H, and Cl and 1.0 g of the compound contains 5.05% Cl. What is the empirical formula? Solution: (Detailed calculation provided in the original notes)