DAT General Chemistry: Percent Composition

DAT High-Yield Concept

Percent Composition Definition: The percentage by mass of each constituent element in a chemical compound.
Subscript Multipliers: Always multiply the element's atomic mass by its subscript in the chemical formula when calculating theoretical mass percent.
Mass Conservation: The sum of all elemental mass percentages in a pure compound must equal exactly 100%.
Intensive Property: Percent composition depends only on chemical identity, not on total sample size. It serves as the primary stepping stone to determining empirical formulas (covered in depth in its own lesson).

Mass Percent of an Element: The ratio of the total mass contributed by a specific element to the overall molar mass (or sample mass) of the compound, multiplied by 100%.

Percent Composition from a Formula

When given a chemical formula, the mass percent of an element is calculated using its theoretical mole ratio and atomic masses from the periodic table:

\text{Mass \% of Element} = \frac{n \times \text{Atomic Mass of Element}}{\text{Molar Mass of Compound}} \times 100\%

where $n$ is the subscript of that element in the chemical formula.

Worked Example 1: Formula-Based Calculation

Problem: Calculate the mass percent of oxygen in calcium carbonate, $\ce{CaCO3}$ .

Step 1: Identify atomic masses.
$\ce{Ca} = \pu{40.08 g/mol}$ , $\ce{C} = \pu{12.01 g/mol}$ , $\ce{O} = \pu{16.00 g/mol}$

Step 2: Calculate the compound's molar mass.
$\text{Molar Mass of } \ce{CaCO3} = \pu{40.08 g/mol} + \pu{12.01 g/mol} + 3(\pu{16.00 g/mol}) = \pu{100.09 g/mol}$

Step 3: Calculate the mass contribution of oxygen.
$\text{Mass of Oxygen} = 3 \times \pu{16.00 g/mol} = \pu{48.00 g/mol}$

Step 4: Compute mass percent.
$\text{Mass \% O} = \frac{\pu{48.00 g/mol}}{\pu{100.09 g/mol}} \times 100\% = 47.96\%$

Common Exam Trap: Forgetting the subscript multiplier! A frequent DAT distractor divides a single atom's mass (

\pu{16.00 g/mol}

) by the total molar mass, yielding

15.99\%

instead of

47.96\%

. Always multiply by

n

Percent Composition from Experimental Data

In laboratory analysis, percent composition is determined directly from measured masses of elements recovered from a sample of known total mass:

\text{Mass \% of Element} = \frac{\text{Mass of Element in Sample}}{\text{Total Mass of Sample}} \times 100\%

Worked Example 2: Experimental Data Calculation

Problem: A $\pu{12.00 g}$ sample of an unknown hydrocarbon is decomposed in the lab, yielding $\pu{9.60 g}$ of carbon and $\pu{2.40 g}$ of hydrogen. Determine the percent composition of hydrogen in the compound.

Step 1: Identify measured component and total masses.
$\text{Mass of } \ce{H} = \pu{2.40 g}$
$\text{Total Sample Mass} = \pu{12.00 g}$

Step 2: Apply mass percent formula.
$\text{Mass \% H} = \frac{\pu{2.40 g}}{\pu{12.00 g}} \times 100\% = 20.0\%$

Step 3: Verify total composition.
$\text{Mass \% C} = \frac{\pu{9.60 g}}{\pu{12.00 g}} \times 100\% = 80.0\%$
$80.0\% + 20.0\% = 100.0\%$

Common Exam Trap: Dividing the elemental mass by the mass of another element rather than the total compound mass. Always place total sample mass in the denominator.

Comparison: Formula vs. Experimental Determination

Feature	Formula-Based Method	Experimental Data Method
Starting Information	Known chemical formula and periodic table atomic masses	Measured laboratory mass values from analysis or combustion
Equation	$\frac{n \times \text{Atomic Mass}}{\text{Molar Mass}} \times 100\%$	$\frac{\text{Mass of Element}}{\text{Total Mass of Sample}} \times 100\%$
Primary Application	Calculating theoretical composition of known structures	Determining elemental ratios to derive empirical formulas

DAT Memory Aid: Part over Whole times 100 gives Percent (P/W × 100 = %). Ensure the "Part" includes all atoms of that element in the chemical formula unit!

Critical Thinking Questions

Why does carbon dioxide, $\ce{CO2}$ , have a higher mass percentage of oxygen than carbon monoxide, $\ce{CO}$ , even though both consist solely of carbon and oxygen?
If a hydrated salt sample $\ce{MgSO4 \times 7H2O}$ is heated to drive off water, how would you calculate the mass percent of anhydrous $\ce{MgSO4}$ remaining in the original hydrate?
How would an unevaporated water impurity in an experimental sample affect the calculated mass percent of carbon in a hydrocarbon?

References

Sources returned by Google Search grounding during lesson verification.

6.7: Mass Percent Composition from a Chemical Formula - Chemistry LibreTexts — chem.libretexts.org
Percent Composition Of Compounds - Stoichiometry - MCAT Content - Jack Westin — jackwestin.com

Percent Composition

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