Percent composition Knowledge-Based Study

Study notes

1. What is Percent Composition?

   The percent composition by mass of a compound represents the percentage of each element present relative to the total mass of the compound. Because matter is conserved and chemical compounds consist of atoms bonded in fixed whole-number ratios (the Law of Definite Proportions), every pure sample of a given compound always exhibits the exact same percentage by mass of each constituent element regardless of sample size.

   Understanding percent composition allows chemists to verify the purity of synthesized substances and serves as a fundamental bridge between laboratory mass measurements and chemical formulas.

   The General Formula

   To determine the percent composition of an element from its chemical formula, use the molar mass of the compound and the atomic mass of each element:

   $$\%\text{ of element} = \frac{n \times (\text{atomic mass of element})}{\text{molar mass of compound}} \times 100\%$$

   Here, n represents the number of moles of atoms of that element in one mole of the compound (given by the subscript in the chemical formula).

   Step-by-Step Example: Water (H2O)

   • Step 1: Find molar mass of the compound.
     Hydrogen: 2 × 1.008 g/mol = 2.016 g/mol
     Oxygen: 1 × 16.00 g/mol = 16.00 g/mol
     Total molar mass = 18.016 g/mol
   • Step 2: Divide the total mass of each element by the molar mass and multiply by 100%.
     $\%\text{ H} = \frac{2.016\text{ g/mol}}{18.016\text{ g/mol}} \times 100\% \approx 11.19\%$
     $\%\text{ O} = \frac{16.00\text{ g/mol}}{18.016\text{ g/mol}} \times 100\% \approx 88.81\%$
   • Step 3: Verify that the sum of the percentages equals 100% (within rounding tolerances): 11.19% + 88.81% = 100.00%.

   Experimental Mass Measurements

   When a compound is synthesized or decomposed in the laboratory, the masses of the individual elements forming the sample can be directly measured. In this case, percent composition is calculated directly from measured masses:

   $$\%\text{ of element} = \frac{\text{mass of element in sample}}{\text{total mass of sample}} \times 100\%$$

   Worked Example

   A 2.500 g sample of an iron-oxygen compound is analyzed and found to contain 1.748 g of iron.

   • Mass of iron (Fe): 1.748 g
   • Mass of oxygen (O): 2.500 g - 1.748 g = 0.752 g
   • Percent Fe: $\frac{1.748\text{ g}}{2.500\text{ g}} \times 100\% = 69.92\%$
   • Percent O: $\frac{0.752\text{ g}}{2.500\text{ g}} \times 100\% = 30.08\%$

   Determining Mass from Percent Composition

   Percent composition can also be used as a conversion factor to determine the absolute mass of an element present in a known quantity of a compound.

   For example, to calculate how many grams of nitrogen are in 50.0 g of ammonium nitrate, $\text{NH}_4\text{NO}_3$:

   • Molar mass of $\text{NH}_4\text{NO}_3$:
     N: 2 × 14.01 = 28.02 g/mol
     H: 4 × 1.008 = 4.032 g/mol
     O: 3 × 16.00 = 48.00 g/mol
     Total = 80.05 g/mol
   • Percent Nitrogen: $\frac{28.02}{80.05} \times 100\% \approx 35.00\%$
   • Mass of Nitrogen: $50.0\text{ g} \times 0.3500 = 17.5\text{ g}$ of N

   Mastery of percent composition forms the essential basis for determining empirical and molecular formulas of unknown compounds.