Calculating percentage composition

When using chemical formula it is possible to calculate the percentage composition of the chemical. This can be useful when extracting metals from ores or when making fertilisers for specific plants.

The following formula is used to calculate percentage mass:

\( percentage \, mass = \frac{mass \, of \, desired \, elements}{gfm} \times 100 \% \)

Example one

Calculate the percentage mass of iron in iron (III) oxide.

Step one

Write the formula for the compound:

\( Fe_{2}O_{3}\)

Step two

Calculate the gram formula mass for the compound

\(gfm \, Fe_{2}O_{3} = (2 \times 56) + (3 \times 16) = 112 + 48 = 160\)

Step three

Finally, divide the gram formula mass for iron by the total gram formula mass of iron (III) oxide and convert to a percentage.

\(percentage \, mass \, Fe = \frac{(56 \times 2)}{160} \times 100\% = \frac{112}{160} \times 100\% = 70\% \, Fe\)

Example two

Calculate the percentage composition of ammonium nitrate fertilizer.

For this question you are calculating the percentage of each element.

Step one

Write the formula for the compound.

Step two

Calculate the gram formula mass of the compound.

\( gfm \ NH_{4}NO_{3} = 14 + (4 \times 1) + 14 + (3 \times 16) = 14 + 4 + 14 + 48 = 80\)

Step three

Calculate the percentage mass of each element in turn.

\(percentage \, mass \, N= [\frac{(14 \times 2)}{80}] \times 100\% = [\frac{28}{80}] \times 100\% = 0.35 \times 100\% = 35\% \, N\)

\(percentage \, mass \, H = [\frac{(1 \times 4)}{80}] \times 100\% = [\frac{4}{80}] \times 100\% = 0.05 \times 100\% = 5\% \, H\)

\( Percentage \, mass \, O = [\frac{(16 \times 3)}{80}] \times 100\% = [\frac{48}{80}] \times 100\% = 0.06 \times 100\% = 60\% \, O\)

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Revise: Balanced equationsCalculating percentage composition