Molecular Formula from Empirical Formula

Finding the molecular formula from the empirical formula is often the final step in an empirical formula question. You need two pieces of information: the empirical formula itself and the Mr of the compound.

The method

1. Calculate the Mr of the empirical formula.
2. Divide the Mr of the compound by the Mr of the empirical formula to find the multiplier (n).
3. Multiply every subscript in the empirical formula by n.

The formula

n = Mr of compound / Mr of empirical formula

Molecular formula = empirical formula x n

Worked examples

Example 1: CH2O to glucose

Question: A compound has the empirical formula CH2O and a relative molecular mass of 180. Find its molecular formula. (Ar: C = 12, H = 1, O = 16)

Working:

• Mr of CH2O = 12 + (2 x 1) + 16 = 30
• n = 180 / 30 = 6
• Molecular formula = C(1x6)H(2x6)O(1x6) = C6H12O6

Answer: C6H12O6 (glucose)

Examiner note: This is the classic example. The multiplier must be a whole number. If it is not, check your empirical formula.

Example 2: CH2 to a hydrocarbon

Question: A hydrocarbon has the empirical formula CH2 and Mr = 56. Find its molecular formula. (Ar: C = 12, H = 1)

Working:

• Mr of CH2 = 12 + 2 = 14
• n = 56 / 14 = 4
• Molecular formula = C4H8

Answer: C4H8

Examiner note: C4H8 could be butene or cyclobutane. The molecular formula alone does not tell you the structure.

Example 3: When n = 1

Question: A compound has the empirical formula C2H6O and Mr = 46. Find its molecular formula. (Ar: C = 12, H = 1, O = 16)

Working:

• Mr of C2H6O = (2 x 12) + (6 x 1) + 16 = 46
• n = 46 / 46 = 1
• Molecular formula = C2H6O

Answer: C2H6O (ethanol)

Examiner note: When n = 1, the molecular formula is the same as the empirical formula. This is a valid answer.

Example 4: From percentage composition to molecular formula

Question: A compound is 85.7% carbon and 14.3% hydrogen, with Mr = 28. Find its molecular formula. (Ar: C = 12, H = 1)

Working:

• Find empirical formula first:
  • Moles of C = 85.7 / 12 = 7.14
  • Moles of H = 14.3 / 1 = 14.3
  • Divide by smallest (7.14): C = 1, H = 2
  • Empirical formula = CH2
• Mr of CH2 = 14
• n = 28 / 14 = 2
• Molecular formula = C2H4

Answer: C2H4 (ethene)

Examiner note: This is a two-part question: first find the empirical formula from percentage data, then convert to molecular formula using Mr.

Example 5: Larger multiplier

Question: A compound has the empirical formula P2O5 and Mr = 284. Find its molecular formula. (Ar: P = 31, O = 16)

Working:

• Mr of P2O5 = (2 x 31) + (5 x 16) = 142
• n = 284 / 142 = 2
• Molecular formula = P4O10

Answer: P4O10

Examiner note: Both the P and O subscripts are multiplied by 2. This is phosphorus(V) oxide.

Common mistakes

1. Not calculating n as a whole number. If your n is not a whole number (like 1.5 or 2.3), your empirical formula is likely wrong. Go back and check.
2. Only multiplying one element. Every subscript in the empirical formula must be multiplied by n, not just the first element.
3. Confusing which Mr to use. The Mr given in the question is for the compound (molecular formula). You calculate the Mr of the empirical formula yourself.
4. Skipping the empirical formula step. When percentage data is given, find the empirical formula first before attempting the molecular formula.

When this appears

Molecular formula questions are Extended tier content and appear on Paper 4. They always follow an empirical formula calculation and rely on relative formula mass. See the stoichiometry topic for the broader context.