Empirical and Molecular Formula

Full Notes

A chemical formula tells us the types and number of atoms in a substance. Some substances are made up of individual molecules (like H₂O or C₆H₁₂O₆), while others consist of ions or atoms in fixed proportions, like NaCl or Fe₂O₃.

Empirical vs Molecular Formula

The empirical formula gives the simplest whole number ratio of elements in a compound.

The molecular formula shows the actual number of atoms of each element in one molecule of the compound.

ExampleHydrogen peroxide has the molecular formula H₂O₂, but its empirical formula is HO. Glucose has the molecular formula C₆H₁₂O₆, and its empirical formula is CH₂O.

Law of Definite Proportions

According to this law, every pure compound has the same elements in the same fixed mass ratio. So even if we have different samples of a compound, the mass ratios will always be the same.

Example Water (H₂O) always contains 2 grams of hydrogen for every 16 grams of oxygen — a ratio of 1:8 by mass.

Determining the Empirical Formula from Mass Data

To find the empirical formula from mass or percentage composition, follow these steps:

Step 1: Convert each element’s mass (or percentage) to moles
If given %, treat the total as 100 g
Use: moles = mass ÷ molar mass
Divide mole amounts by the smallest value
Multiply up to get only whole numbers if needed (i.e. x everything by 2)

Ex

Worked Example

Find the empirical formula for a compound with a composition by mass of C 52.2%, H 13.0% and O 34.8%.

1. Assume 100 g total
   C = 52.2 g → 52.2 ÷ 12.01 = 4.35 mol
   H = 13.0 g → 13.0 ÷ 1.008 = 12.9 mol
   O = 34.8 g → 34.8 ÷ 16.00 = 2.18 mol
2. Divide by smallest mole value (2.18)
   C = 4.35 ÷ 2.18 = 2.00
   H = 12.9 ÷ 2.18 = 5.92 ≈ 6.00
   O = 2.18 ÷ 2.18 = 1.00
3. Write empirical formula
   C₂H₆O

Finding the Molecular Formula

If the molar mass of the compound is known, you can find the molecular formula:

• Calculate the molar mass of the empirical formula
• Divide the compound’s molar mass by the empirical molar mass
• Multiply subscripts in the empirical formula by that number

Ex

Worked Example

The empirical formula of a compound is CH₂O and its molar mass is 180 g/mol. Find the molecular formula.

1. Calculate the empirical formula mass
   (1 × 12.0) + (2 × 1.0) + (1 × 16.0) = 30.0 g/mol
2. Find n
   n = 180 ÷ 30.0 = 6
3. Multiply empirical formula by n
   6 × CH₂O = C₆H₁₂O₆

Matt’s exam tip

Always check that your final empirical formula makes chemical sense. It should use whole numbers and reflect what’s possible based on the elements involved. If your ratio gives 1.5 or 1.33, multiply all ratios to clear the decimal.

Summary

• The empirical formula shows the simplest ratio of atoms in a compound, while the molecular formula shows the actual number of atoms in a molecule.
• Using mass or percentage composition, we can calculate the empirical formula by converting to moles and simplifying the ratio.
• If we also know the compound’s molar mass, we can determine the molecular formula.
• Key steps to remember:
  • Convert mass or % to moles
  • Divide by the smallest mole value
  • Adjust to whole numbers
  • Compare to molar mass if finding molecular formula