Relative molecular mass

Relative molecular mass, written Mr, is the natural next step after relative atomic mass, and it is needed in almost every mole calculation in SPM Chemistry. Our online one-to-one teachers make sure you can build it accurately from a formula, because a single slip in the Mr sends every later step off course.

When you use it

You need Mr whenever a calculation involves a compound rather than a single atom, turning mass into moles, finding a concentration in g per dm cubed, or working out a percentage composition. Get comfortable reading a formula and adding up its atoms, and the rest of the chapter becomes routine.

The definition and the formula

The relative molecular mass of a substance is the average mass of one molecule compared with one-twelfth of the mass of a carbon-12 atom. In practice you find it by adding the relative atomic masses of all the atoms in the formula:

Mr = sum of ( number of each atom x its Ar )

For ionic compounds, which are not made of molecules, the identical sum is called the relative formula mass, the working is exactly the same.

Units

Mr has no unit, because it is a ratio of masses just like Ar. (Ar values used here: H = 1, C = 12, N = 14, O = 16, Na = 23, S = 32, Ca = 40, Cu = 64.)

Worked example 1 (easy), water

Water is H₂O: two hydrogen atoms and one oxygen atom.

• Step 1: 2 x Ar(H) = 2 x 1 = 2.
• Step 2: 1 x Ar(O) = 1 x 16 = 16.
• Step 3: add them: 2 + 16 = 18.

Mr of water = 18 (no unit).

Worked example 2 (medium), sulfuric acid

Sulfuric acid is H₂SO₄.

• Step 1, hydrogen: 2 x 1 = 2.
• Step 2, sulfur: 1 x 32 = 32.
• Step 3, oxygen: 4 x 16 = 64.
• Step 4, total: 2 + 32 + 64 = 98.

Mr of sulfuric acid = 98. The most common error here is forgetting to multiply the four oxygens.

Worked example 3 (SPM level), a hydrated salt

Find the relative formula mass of hydrated copper(II) sulfate, CuSO₄.5H₂O.

• Step 1, the anhydrous part CuSO₄: 64 + 32 + (4 x 16) = 64 + 32 + 64 = 160.
• Step 2, the water of crystallisation, 5H₂O: 5 x 18 = 90.
• Step 3, add both parts: 160 + 90 = 250.

Relative formula mass of CuSO₄.5H₂O = 250. The five water molecules must be included, leaving them out is the classic SPM slip.

Common traps

• Forgetting to multiply through a bracket. In Ca(OH)₂ there are two oxygens and two hydrogens: 40 + 2(16 + 1) = 74.
• Dropping the water of crystallisation in a hydrated salt.
• Writing a unit after Mr; it has none.
• Using the wrong Ar for a metal (for example writing Cu as 63.5 in one line and 64 in another); pick one value and keep it.
• Adding instead of multiplying when a subscript is present.

How we help

Our teachers drill the “read the formula, count every atom, multiply the brackets” routine until it is automatic, then push you straight into hydrated salts and bracketed formulae, the exact places SPM Chemistry sets traps. Lessons are one-to-one, taught in English, from RM50 per hour, with a paid one-hour trial so you can see how we work before deciding. Once your Mr is reliable, moles from mass, concentration and percentage composition all follow with almost no extra effort.