Percentage by mass and concentration in g/dm³

Once you have the M_r, the share belonging to one element is a fraction of it.

percentage by mass of an element = (number of atoms × Ar) ÷ Mr × 100

1. Nitrogen in ammonium nitrate, NH₄NO₃ (Ar: N = 14, H = 1, O = 16)
2. Mr = 14 + 4 + 14 + 48 = 80
3. mass of N in the formula = 2 × 14 = 28
4. 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.

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).

1. 6.0 g of copper(II) sulfate made up to 250 cm³
2. 250 cm³ = 250 ÷ 1000 = 0.25 dm³
3. 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.

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.

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.