Percent Composition

Percent composition asks what fraction of a compound's mass each element accounts for. The arithmetic is one division per element, and almost everyone can do it on the second attempt. The reason it goes wrong on the first attempt is a misreading of the question that the arithmetic cannot catch.

Per cent of the mass, not per cent of the atoms

Water is H₂O. Two of its three atoms are hydrogen, so hydrogen is 66.7% of the atoms. Hydrogen is 11.19% of the mass.

Both numbers are true and they answer different questions. Percent composition always means the mass version unless a question explicitly says "atom percent" or "mole percent". Oxygen dominates water's mass because a single oxygen atom outweighs sixteen hydrogens; the atom count is irrelevant except as a multiplier.

The formula is:

mass % of element = (atoms of that element × its atomic weight) ÷ (molar mass) × 100

Everything above the line comes from one row of a molar mass calculation, so if you have already computed a molar mass you have already done four fifths of the work.

Worked: reading a bag of fertiliser

Fertilisers are sold on their nitrogen content, and the numbers printed on the bag are percent compositions. Working out where they come from makes the concept concrete.

Ammonium nitrate, NH₄NO₃. The formula contains two nitrogen atoms, one in the ammonium ion and one in the nitrate ion — miss the second and everything downstream halves.

• N: 2 × 14.007 = 28.014

• H: 4 × 1.008 = 4.032

• O: 3 × 15.999 = 47.997

• Molar mass: 80.043 g/mol

  %N = 28.014 ÷ 80.043 × 100 = 35.00% %H = 4.032 ÷ 80.043 × 100 = 5.04% %O = 47.997 ÷ 80.043 × 100 = 59.96%

Urea, CO(NH₂)₂. Expanding the brackets gives one carbon, one oxygen, two nitrogen, four hydrogen — molar mass 60.056 g/mol.

%N = 28.014 ÷ 60.056 × 100 = 46.65%

Ammonium sulfate, (NH₄)₂SO₄, molar mass 132.134 g/mol, also carries two nitrogens:

%N = 28.014 ÷ 132.134 × 100 = 21.20%

All three compounds contain exactly two nitrogen atoms per formula unit. Their nitrogen contents differ by more than a factor of two purely because of the mass of everything else attached. That is why urea is sold as 46-0-0 and ammonium sulfate as 21-0-0, and why the cheaper-per-tonne bag is not automatically the cheaper source of nitrogen.

Epsom salt is more than half water

Water of crystallisation is part of the compound and part of its mass, which produces figures that surprise people the first time.

Magnesium sulfate heptahydrate, MgSO₄·7H₂O. The MgSO₄ portion comes to 24.305 + 32.06 + (4 × 15.999) = 120.361. Seven waters add 7 × 18.015 = 126.105. Total molar mass: 246.466 g/mol.

% water = 126.105 ÷ 246.466 × 100 = 51.16%

So a kilogram of these crystals contains 512 g of water and 488 g of magnesium sulfate. Follow it through to the element you actually care about and the effect compounds:

%Mg = 24.305 ÷ 246.466 × 100 = 9.86%

Under a tenth of the mass is magnesium. The same calculation on the anhydrous salt gives 20.19%, which is roughly double — and is why any question involving a hydrate specifies which form it means.

The check that catches almost every error

The percentages must sum to 100. Not approximately — to within a couple of hundredths, the whole of any rounding you did on the way.

This one check catches the two commonest mistakes at once. Miscount an atom and the total drifts away from 100 by several per cent. Use the wrong molar mass in the denominator and every percentage is wrong by the same factor, so the total lands somewhere obviously wrong like 94% or 107%.

There are exactly two situations where a small honest discrepancy is fine:

• Rounding. Three compounds' worth of two-decimal figures can total 99.99% or 100.01%. Quote what you calculated; do not fudge a digit to force the total.
• Interval atomic weights. Where an element's tabulated weight is a published range rather than one number, any percentage derived from it inherits that range. The effect is real and far smaller than any arithmetic slip.

If your total is 50% or 200%, you have almost certainly divided by an element's atomic weight instead of by the molar mass.

What the percentage is actually used for

Outside homework, mass percent is the language of anything sold by composition.

Chalcopyrite, CuFeS₂, is the world's main copper mineral. Its molar mass is 183.511 g/mol and

%Cu = 63.546 ÷ 183.511 × 100 = 34.63%

That is the copper content of the mineral. The copper content of the ore dug out of the ground is a different number entirely — a large modern mine may work rock at half a per cent copper, because the chalcopyrite is scattered through worthless silicate. Confusing the composition of a compound with the grade of a mixture containing it is a mistake that appears in professional contexts, not just student ones.

The same distinction runs through pharmaceutical assay figures, alloy specifications and food labelling. A percent composition computed from a formula is a property of a pure substance and tells you nothing about how much of that substance is in the sample in front of you.

Turning a percentage into a mass

The follow-up question is usually the point of the whole exercise: not what fraction, but how much. Once you have the percentage it is a single multiplication, because the percentage is a property of the compound and does not depend on how much of it you have.

A 50 kg sack of urea at 46.65% nitrogen contains 50 × 0.4665 = 23.3 kg of nitrogen. Getting the same 23.3 kg from ammonium sulfate at 21.20% would take 110 kg of it. Work in whatever mass unit the question uses and it cancels — there is no need to convert to grams first, and doing so is a common source of a stray factor of a thousand.

One caution on wording. "Percent" attached to a solution rarely means this quantity at all: %w/w is mass of solute per mass of solution, %v/v is volume per volume, and %w/v is grams per 100 mL, a hybrid with mismatched units that survives because it is convenient. None of those are percent composition, and a question that mentions a concentration is asking about a mixture rather than about the make-up of a compound.

Proust, Berthollet, and the compounds that refuse to have a fixed composition

The whole exercise rests on an assumption worth naming: that a given compound always has the same composition by mass. That is the law of definite proportions, and it was not obvious. Between roughly 1794 and 1804, Joseph Proust and Claude Louis Berthollet argued it out in print. Proust insisted that copper carbonate made by any route had identical composition; Berthollet held that composition varied continuously with the conditions of preparation.

Proust won, and the law became one of the foundations of atomic theory. But Berthollet was not simply wrong, and the modern name for the exception honours him. Berthollide compounds — also called non-stoichiometric — genuinely do vary in composition. Iron(II) oxide, written FeO in every textbook, essentially never has that composition: the real material is iron-deficient, with a formula nearer Fe₀.₉₅O, its charge balanced by some of the iron sitting as Fe³⁺. Many transition metal oxides, sulfides and hydrides behave the same way, and the property is not a defect to be purified away — it is what makes several of them useful as semiconductors and battery materials.

A percent composition calculated from a written formula therefore describes an idealisation. For molecular compounds and ordinary salts the idealisation is essentially perfect. For a transition metal oxide it may be a per cent or two out from anything you could actually weigh, and no amount of care with the arithmetic will close that gap.

Going the other way

Everything here starts from a known formula. The far more common exam question runs backwards: you are given percentages from an analysis and asked what the compound is. That inversion has its own procedure, its own rounding trap and its own worked examples on the empirical and molecular formulas page.