How much of each element?
A bag of urea fertilizer is labeled “nitrogen ≥ 46%,” and an iron supplement lists how many milligrams of iron are in each tablet. You can calculate numbers like these straight from the formula.
Mass ratio of elements
The mass ratio of the elements in a compound equals the ratio of “relative atomic mass × number of atoms” for each element.
Example: in , H : O = (1 × 2) : (16 × 1) = 2 : 16 = 1 : 8.
Mass percent of an element
Example: the mass percent of oxygen in = 16 ÷ 18 × 100% ≈ 88.9%.
From the mass of a compound to the mass of an element
Mass of an element = mass of the compound × mass percent of that element.
Example: 36 g of water contains 36 g × 2/18 = 4 g of hydrogen.
🔧 Math tool card · Ratios & PercentagesSkip it if you already know this
Simplifying a ratio: divide both numbers by their greatest common factor, so 2 : 16 = 1 : 8 (both divided by 2). If there’s a decimal, first multiply both by 2 or 10 to get whole numbers: 1 : 35.5 = 2 : 71.
Finding a percentage: part ÷ whole × 100%, so 16 ÷ 18 × 100% ≈ 88.9%.
Simplify 12 : 32 to the lowest whole-number ratio.
The greatest common factor of 12 and 32 is 4. Dividing both by 4 gives 3 : 8.
The calculator below shows each element’s mass percent and the mass ratio. Change the mass of the substance to see how many grams of each element it contains:
Urea, , comes out at 46.7% nitrogen, which matches the “≥ 46%” on the fertilizer bag.
Example 1: Nitrogen in ammonium nitrate
Find the mass percent of nitrogen in . (N = 14, H = 1, O = 16)
- Count the atoms. There are 2 N (one in ammonium, one in nitrate), 4 H, and 3 O.
- Find the relative formula mass. 14 × 2 + 1 × 4 + 16 × 3 = 80.
- Find the mass percent. 14 × 2 ÷ 80 × 100% = 35%.
Example 2: Carbon in carbon dioxide
How many grams of carbon are in 88 g of carbon dioxide? (C = 12, O = 16)
- Find carbon’s share. 12 ÷ 44 (no need to turn it into a percentage yet).
- Find the mass of carbon. 88 g × 12/44 = 24 g.
- It works backward too. To get 12 g of carbon, you need 12 g ÷ (12/44) = 44 g of carbon dioxide.
Common mistakes
Mistake 1: Missing atoms. has 2 N atoms. Counting only one gives 17.5%.
Mistake 2: Treating the atom ratio as the mass ratio. In , the atom ratio H : O is 2 : 1, but the mass ratio is 1 : 8.
Mistake 3: Using the wrong denominator. Mass percent divides by the whole relative formula mass. Oxygen in is 16 ÷ 18, not 16 ÷ 2.
Quick check
What is the mass percent of iron in ? (Fe = 56, O = 16)
56 × 2 ÷ (56 × 2 + 16 × 3) × 100% = 112 ÷ 160 × 100% = 70%.
What is the mass ratio of carbon to oxygen in ? (C = 12, O = 16)
12 : (16 × 2) = 12 : 32 = 3 : 8. A is the atom ratio, and D forgets to multiply by the number of oxygen atoms.
Summary
- Mass ratio of elements = the ratio of “relative atomic mass × number of atoms” for each element.
- Mass percent of an element = relative atomic mass × number of atoms ÷ relative formula mass × 100%.
- Mass of an element = mass of the compound × its mass percent. You can also work backward to the mass of the compound.
On to AP (for later)
AP topic 1.3 runs this in reverse: from the measured masses or mass percents of the elements, you work out a substance’s empirical (simplest) formula. Topic 1.4 extends it to finding how much of a component is in a mixture.