Calculating relative formula mass and percentage by mass

Chemistry · Percentage by mass

Methane, CH₄, is one carbon atom (12) and four hydrogen atoms (4 × 1), so its relative formula mass is 12 + 4 × 1 = 16. The whole bar is that 16. Drag the handle to count atoms: stop where it covers every hydrogen atom and read off their share.

Predict, then check

Calcium carbonate, CaCO₃, has Mr = 40 + 12 + 3 × 16 = 100. Heat it and it decomposes into calcium oxide, CaO (Mr = 56), and carbon dioxide, CO₂.

CaCO₃ → CaO + CO₂. For mass to be conserved, what must the relative formula mass of the carbon dioxide be?

What you need to know

• Think of a formula as a shopping list of atoms: each symbol is an item and its subscript says how many.
• Relative atomic mass (Ar) is the mean mass of an atom compared to 1/12 of a carbon-12 atom, and the periodic table shows it.
• Use the relative atomic mass, not the atomic number. The key that comes with the periodic table tells you which number is the mass.
• Have a goSam adds up atomic numbers to get a relative formula mass, 'because they're right there in the box'. What should Sam use instead?

  The relative atomic mass, the number the key to the periodic table labels as the mass.

  Relative formula mass is a sum of relative atomic masses, so Sam needs the number the key identifies as the mass, and the atomic number is the other number.

• Relative formula mass (Mr) is the sum of the relative atomic masses of all the atoms in the formula.
• If an element has a subscript, multiply its relative atomic mass by it. The number one is never written.
• Have a goFill the gaps: in C₂H₆, carbon's relative atomic mass is multiplied by ___ and hydrogen's is multiplied by ___.

  2 and 6.

  Each subscript counts the atoms of the element it follows, so each relative atomic mass is multiplied by its own subscript and never by the other element's.

• From a displayed formula, count the atoms of each element, write the formula, then add up the masses.
• Different molecules can share a relative formula mass: carbon dioxide and propane both come to 44.
• Have a goMo is sure it's a mistake: 'CO₂ and propane are totally different molecules, so one of those 44s has to be wrong.' What do you tell Mo?

  Neither is wrong: different atoms can add up to the same total.

  Mr is just a total of relative atomic masses, so two different formulas can land on the same number without being the same molecule.

• In a balanced equation mass is conserved, so reactant and product Mr totals match, each multiplied by its coefficient.
• Percentage by mass of an element = (relative mass of the element in the compound / Mr of the compound) × 100.
• Count every atom of the element when you find its relative mass in the compound, because the subscript is easy to miss.

The big picture

A relative formula mass (Mr) is the sum of the relative atomic masses of all the atoms in a formula, so each subscript multiplies its element's relative atomic mass. Once you have it, mass conservation in a balanced equation and an element's percentage by mass both follow: the percentage is the element's relative mass in the compound, counting every atom of it, divided by Mr and multiplied by 100.

⚠ Watch out

Treating every symbol as one atom's mass. When a symbol has a subscript, it stands for several atoms, and each one has to be counted, whether you are adding up Mr or finding an element's share of it.

Memory hook

Shopping list: read each symbol, price it with its relative atomic mass, multiply by the subscript, total the bill. Then ask what share of the bill one element paid, and remember the bill counts every item of it.

Check yourself

Cover the page. Which periodic-table number do you add up, and what do you do with a subscript? Then write the percentage by mass equation and say what its top must include.