Percent by Mass: Mixtures, Solutions and Hydrates
Mass percent is the mass of one component divided by the total mass of the mixture, times 100. The same ratio answers percent composition, concentration by weight, and the classic percent-of-water-in-a-hydrate question.
The formula and its cousins
- Mass percent (w/w) = mass of component ÷ total mass × 100.
- Mass/volume (w/v) = grams of solute ÷ 100 mL of solution.
- Volume percent (v/v) = volume of component ÷ total volume × 100.
- Grams from a percentage: total mass × percent ÷ 100.
Percent water in a hydrate
Heat the hydrate to constant mass, then divide the mass lost by the mass of the original sample. From the formula instead, divide the molar mass of the water portion by the molar mass of the whole hydrate: CuSO₄·5H₂O has 90.08 of water in 249.68 total, which is 36.1% water. A measured value well below the theoretical one usually means incomplete dehydration.
Percent composition from a formula
Multiply each element's atomic mass by the number of atoms, divide by the compound's molar mass, and multiply by 100. The results must sum to 100% — a good self-check. Empirical formulae are derived by running the process in reverse: convert each percentage to moles, divide by the smallest, and scale to whole numbers.
Practical notes
- Keep both masses in the same unit; grams throughout is safest.
- w/v depends on density, so it is not interchangeable with w/w.
- Weigh the container empty and full rather than trusting a tare on a drifting balance.
- Percentages of a mixture always sum to 100 — use it to catch arithmetic slips.
Key takeaways — Percent by Mass Calculator
- Mass % = component mass ÷ total mass × 100.
- Hydrate water percent = mass lost on heating ÷ original mass × 100.
- w/w, w/v and v/v are different measures — state which you used.