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.
\(percentage \, mass \, N= [\frac{(14 \times 2)}{80}] \times 100\% = [\frac{28}{80}] \times 100\% = 0.35 \times 100\% = 35\% \, N\)
\(percentage \, mass \, H = [\frac{(1 \times 4)}{80}] \times 100\% = [\frac{4}{80}] \times 100\% = 0.05 \times 100\% = 5\% \, H\)
\( Percentage \, mass \, O = [\frac{(16 \times 3)}{80}] \times 100\% = [\frac{48}{80}] \times 100\% = 0.06 \times 100\% = 60\% \, O\)