Mass Fraction: Reading Composition from a Formula
A chemical formula tells not only which elements are present, but also how much each element contributes to the formula mass. Mass fraction turns that contribution into a part of the whole or a percentage.
1. The central idea
The mass fraction of an element is the mass contributed by that element divided by the total mass of the compound. It is written as a decimal between 0 and 1 or as a percentage between 0% and 100%. For an element (E) in a compound:
Percentage of (E): \(w(E)\times100\%\)
Here, (n(E)) is the total number of atoms of element (E) in the formula, (A_r(E)) is its relative atomic mass, and (M_r) is the relative formula mass of the complete compound. Relative masses have no unit because they are ratios to an agreed atomic mass standard.
2. A reliable four-step method
- Count atoms. Read subscripts carefully. A missing subscript means one. If brackets occur, multiply every atom inside by the outside subscript.
- Find each contribution. Multiply the number of atoms by the element's relative atomic mass.
- Find the whole. Add all contributions to obtain (M_r) of the compound.
- Divide and convert. Divide the chosen contribution by the whole; multiply by 100% when a percentage is requested.
Mini-example: water, H2O
Using (A_r(H)=1) and (A_r(O)=16): (M_r(H_2O)=2\cdot1+16=18).
Hydrogen: \(w(H)=2/18=0.111\approx11.1\%\). Oxygen: \(w(O)=16/18=0.889\approx88.9\%\).
3. Why the formula matters
The subscript belongs only to the symbol or bracketed group immediately before it. In CO2, two oxygen atoms contribute (2\cdot16=32), while one carbon atom contributes 12. In Ca(OH)2, the outside 2 gives two oxygen atoms and two hydrogen atoms. Changing a subscript changes both the element contribution and the total formula mass.