Percentage by mass
Once you have the Mr, the share belonging to one element is a fraction of it.
percentage by mass of an element = (number of atoms × Ar) ÷ Mr × 100
- Nitrogen in ammonium nitrate, NH₄NO₃ (Ar: N = 14, H = 1, O = 16)
- Mr = 14 + 4 + 14 + 48 = 80
- mass of N in the formula = 2 × 14 = 28
- percentage = 28 ÷ 80 × 100 = 35%
The same fraction scales up. If 35% of ammonium nitrate is nitrogen, a 20 kg bag holds 20 × 28 ÷ 80 = 7 kg of nitrogen. For water in a hydrate, the "element" is the water: 5 × 18 = 90 out of 249.5 in CuSO₄.5H₂O, which is 36.1%.
Count every atom of the element. Fe₂O₃ has two iron atoms, so use 2 × 56 = 112, not 56.
Concentration in g/dm³
A concentration tells you how much solute is dissolved in each cubic decimetre (dm³) of solution. 1 dm³ is the same as 1000 cm³ (one litre).
concentration (g/dm³) = mass of solute (g) ÷ volume of solution (dm³)
All boards: recall this one. Rearrange it for mass (concentration × volume) or volume (mass ÷ concentration).
- 6.0 g of copper(II) sulfate made up to 250 cm³
- 250 cm³ = 250 ÷ 1000 = 0.25 dm³
- concentration = 6.0 ÷ 0.25 = 24 g/dm³
The classic trap: dividing by 250 instead of 0.25 gives 0.024, a thousand times too small. Change cm³ to dm³ first, every time.
More solute or less water
A solution gets more concentrated if you dissolve more solute in the same volume, or the same solute in less solution. Doubling the mass doubles the concentration; doubling the volume halves it.
Check a percentage with the calculator
Open the Molar Mass Calculator and type NH4NO3. Work out the percentage by mass of nitrogen yourself (it should be 35%), then compare it with the percentage column in the calculator's table. Try Fe2O3 next and check the iron.
Your first percentage
Find Mr first, then the fraction that is the element.