Percent Composition of Water

Easy

Problem

What is the percent by mass of hydrogen and of oxygen in water (H2O)? Show that the two percentages add up to 100%.

Given

Formula: H2O (2 H atoms, 1 O atom)
Atomic weights: H = 1.008 u, O = 15.999 u
Molar mass of H2O: M = 18.015 g/mol

Find

The mass percent of H and of O in H2O.

Principle

Percent composition reports each element's share of a compound's total mass. Divide the total mass contributed by all atoms of one element by the compound's molar mass, then multiply by 100. It is the same idea as percent composition of a mixture, except the ratios are fixed by the formula.

Formula

\%\,E = \frac{n_E \times A_E}{M_{\mathrm{compound}}} \times 100

% element = (atoms x atomic weight / molar mass) x 100

Solution

Total mass from hydrogen: 2 x 1.008 = 2.016 u.
Percent hydrogen: (2.016 / 18.015) x 100 = 0.11190 x 100 = 11.19%.
Total mass from oxygen: 1 x 15.999 = 15.999 u.
Percent oxygen: (15.999 / 18.015) x 100 = 0.88809 x 100 = 88.81%.
Check: 11.19% + 88.81% = 100.00%, confirming no element was missed.

11.19% H and 88.81% O by mass.

Unit check

Both the numerator (element mass) and denominator (compound mass) carry the same unit, which cancels to leave a pure percentage. Summing to exactly 100% confirms the parts account for the whole.

What this means physically

Water is overwhelmingly oxygen by mass — nearly nine-tenths — because one oxygen atom outweighs two hydrogens about eight to one. This is why percent composition is not obvious from the formula alone; atom counts and masses are different things.

Common mistake

Students divide the single atom's mass (1.008) by the molar mass without multiplying by the subscript 2, getting 5.60% hydrogen. The subscript must be applied before dividing.