Percentage Composition by Mass
This topic covers how to determine the mass contribution of each element within a compound, expressed as a percentage of the total mass. It's a fundamental calculation in chemistry, linking a compound's formula to its mass properties.
Part of the ESAT Chemistry syllabus — revision for the Engineering and Science Admissions Test (ESAT), the UAT-UK admissions test for Cambridge, Imperial, Oxford and UCL.
Key points
- The Relative Molecular Mass (Mr) of a compound is the sum of the Relative Atomic Masses (Ar) of all atoms present in its formula.
- To find the total mass of an element in one molecule, multiply its Ar by the number of times its atom appears in the chemical formula (its subscript).
- The percentage composition is the total mass of the element divided by the total Mr of the compound, then multiplied by 100.
- The sum of the percentage compositions of all elements in a compound must equal 100%; this can be a useful way to check your work.
Formulae
% by mass = (Total Ar of element in formula / Mr of compound) × 100 To calculate the percentage by mass of an element within a compound when you know the chemical formula and relevant Ar values.
Definitions
- Percentage Composition by Mass
- The proportion of a compound's total mass that is contributed by a specific element, expressed as a percentage.
Worked example
Calculate the percentage by mass of nitrogen in urea, CO(NH2)2. [Relative atomic masses: C = 12, O = 16, N = 14, H = 1]
- 1
Step 1:
Calculate the total Relative Molecular Mass (Mr) of urea.
First, count the atoms:
C=1, O=1, N=2, H=4 - 2
Step 2:
Sum the masses of all atoms:
Mr = (1 × 12) + (1 × 16) + (2 × 14) + (4 × 1) = 12 + 16 + 28 + 4 = 60 - 3
Step 3:
Calculate the total mass contribution from nitrogen.
There are 2 nitrogen atoms, so the total mass is 2 × Ar(N) = 2 × 14 = 28.
- 4
Step 4:
Apply the percentage composition formula:
% N = (Total mass of N / Mr of urea) × 100 - 5
Step 5:
Substitute the values:
% N = (28 / 60) × 100 - 6
Step 6:
Simplify the calculation.
(28 / 60) × 100 = (28 / 6) × 10 = (14 / 3) × 10 = 140 / 3.
- 7
Step 7:
Convert the fraction to a percentage.
140 divided by 3 is 46 with a remainder of 2, so the answer is 46 and 2/3 %.
Answer: 46.7% (or 46 2/3 %)
Common mistakes
- ×Incorrectly counting atoms in formulae with brackets, such as failing to multiply atoms inside the bracket by the subscript outside (e.g., counting 2 hydrogens in Ca(OH)2 instead of 2).
- ×Using the Ar of a single atom for an element in the numerator, instead of the total mass of all atoms of that element (e.g., using 14 for N in CO(NH2)2 instead of 2*14=28).
- ×Simple arithmetic errors when summing the atomic masses to calculate the Mr, which invalidates the entire calculation.
No-calculator tips
- ✓Simplify the fraction (mass of element / Mr) as much as possible before multiplying by 100. For 28/60, cancelling a common factor of 4 gives 7/15, which is simpler to handle.
- ✓To quickly convert fractions to percentages, try to manipulate the denominator to be a factor of 100. For 7/15, you can calculate (7/15) × 100 = 700/15 = 140/3.
- ✓Estimate your answer before calculating. In urea (Mr=60), nitrogen's mass is 28. Since 28 is slightly less than half of 60, you should expect an answer slightly less than 50%.