Percentage composition by mass

Percentage composition tells you how much of a compound’s mass comes from each element, and it appears in SPM Chemistry on its own and as part of fertiliser and purity questions. Our online one-to-one teachers make sure you build both parts of the fraction correctly, because a mistake in either the top or the bottom loses the mark.

When you use it

Use this whenever a question asks what percentage of a compound is a given element, or the percentage of water of crystallisation in a hydrated salt. It is a favourite for comparing the nitrogen content of fertilisers, which is a common application question.

The formula

percentage by mass of an element = ( total mass of that element in the formula / relative molecular mass ) x 100 %

where the total mass of the element = number of its atoms x its Ar, and the relative molecular mass is the sum of the Ar values of every atom in the formula.

Units

The masses and the Mr are relative (unit-less), so the answer is a percentage. As a check, the percentages of all the elements in a compound add up to about 100 (allowing for rounding).

Worked example 1 (easy), oxygen in water

Find the percentage by mass of oxygen in water, H₂O. (Ar: H = 1, O = 16.)

• Step 1, Mr of H₂O: (2 x 1) + 16 = 18.
• Step 2, mass of oxygen: 1 x 16 = 16.
• Step 3, percentage: (16 / 18) x 100 = 88.9 %.

Worked example 2 (medium), nitrogen in ammonium nitrate

Find the percentage by mass of nitrogen in ammonium nitrate, NH₄NO₃. (Ar: N = 14, H = 1, O = 16.)

• Step 1, Mr: (2 x 14) + (4 x 1) + (3 x 16) = 28 + 4 + 48 = 80.
• Step 2, mass of nitrogen: 2 x 14 = 28.
• Step 3, percentage: (28 / 80) x 100 = 35 %.

Note that there are two nitrogen atoms in the formula, one in the ammonium ion and one in the nitrate ion.

Worked example 3 (SPM level), water of crystallisation

Find the percentage by mass of water in hydrated copper(II) sulfate, CuSO₄.5H₂O. (Ar: Cu = 64, S = 32, O = 16, H = 1.)

• Step 1, relative formula mass: CuSO₄ = 64 + 32 + (4 x 16) = 160; plus 5H₂O = 5 x 18 = 90; total = 250.
• Step 2, mass of water: 5 x 18 = 90.
• Step 3, percentage: (90 / 250) x 100 = 36 %.

The five water molecules must be counted both in the water mass and in the total.

Common traps

• Forgetting to multiply the Ar by the number of atoms of the element.
• Using the wrong Mr on the bottom, especially by leaving out water of crystallisation.
• Writing the fraction upside down (compound over element).
• Dropping the per-cent sign or the “x 100” step.
• Rounding early so the element percentages no longer add up to about 100.

How we help

Our teachers give you elements, ions with repeated atoms, and hydrated salts, so you always build the top and bottom of the fraction correctly and check that the parts sum to about 100. Lessons are one-to-one, taught in English, from RM50 per hour, with a paid one-hour trial so you can try the method first. Because percentage composition uses the same Mr skill as empirical formula and molar mass, getting it right reinforces the whole mole chapter at once.