Empirical formula

The empirical formula question tests whether you can turn masses into a mole ratio, and it appears often in SPM Chemistry, including in the classic magnesium oxide and copper oxide experiments. Our online one-to-one teachers give you a fixed, reliable method so a decimal ratio never leaves you stuck.

When you use it

Use this whenever a question gives the masses, or the percentage composition, of the elements in a compound and asks for a formula. It is also the first half of a molecular-formula question, so the method carries straight over.

The method

1. Write the mass of each element (if given a percentage, treat it as the mass in a 100 g sample).
2. Divide each mass by that element’s relative atomic mass (Ar) to get moles.
3. Divide every mole value by the smallest of them.
4. If the ratio is not yet whole numbers, multiply all of it by a small factor (2, 3, …) to clear the fraction.
5. Write the ratio as subscripts.

Units

Masses are in grams and Ar has no unit, so the mole values are in mol. The final ratio is a set of whole numbers with no unit.

Worked example 1 (easy), magnesium oxide

2.4 g of magnesium combines with 1.6 g of oxygen. Find the empirical formula. (Ar: Mg = 24, O = 16.)

• Step 1, moles: Mg = 2.4 / 24 = 0.1; O = 1.6 / 16 = 0.1.
• Step 2, divide by the smallest (0.1): Mg = 1, O = 1.
• Step 3, empirical formula = MgO.

Worked example 2 (medium), a carbon-hydrogen-oxygen compound

A compound is 40 % carbon, 6.7 % hydrogen and 53.3 % oxygen by mass. Find the empirical formula. (Ar: C = 12, H = 1, O = 16.)

• Step 1, moles (per 100 g): C = 40 / 12 = 3.33; H = 6.7 / 1 = 6.7; O = 53.3 / 16 = 3.33.
• Step 2, divide by the smallest (3.33): C = 1, H = 2, O = 1.
• Step 3, empirical formula = CH₂O.

Worked example 3 (SPM level), an iron oxide with a half-ratio

An iron oxide contains 70 % iron and 30 % oxygen by mass. Find the empirical formula. (Ar: Fe = 56, O = 16.)

• Step 1, moles (per 100 g): Fe = 70 / 56 = 1.25; O = 30 / 16 = 1.875.
• Step 2, divide by the smallest (1.25): Fe = 1, O = 1.5.
• Step 3, clear the half by multiplying by 2: Fe = 2, O = 3.
• Step 4, empirical formula = Fe₂O₃.

The 1.5 is the trap: you must multiply up rather than round it to 2.

Common traps

• Multiplying by the Ar instead of dividing by it.
• Rounding a value like 1.5 to a whole number instead of scaling the whole ratio up.
• Not dividing by the smallest, so the ratio never simplifies.
• Forgetting that percentages can be treated as grams in a 100 g sample.
• Rounding the mole values too early, which hides the true ratio.

How we help

Our teachers give you ratios that come out cleanly and ones that need the x2 or x3 step, so you recognise instantly when to scale up rather than round. Lessons are one-to-one, taught in English, from RM50 per hour, with a paid one-hour trial so you can test the method first. Because the empirical formula is the first stage of a molecular-formula question, mastering it here makes the next topic almost automatic.