Mole, mass and number of particles

This page covers a single Form 4 content standard: mole, mass and number of particles. It is the calculation that ties the previous two standards together, relative mass (3.1) and the Avogadro constant (3.2), into one working map that lets you move freely between a mass you can weigh, an amount in moles, and an actual number of particles. Nearly every numerical question in SPM Chemistry, including the whole of stoichiometry, runs through this map, so it is the single most useful skill in the chapter.

Molar mass: attaching grams to a mole

The link between mass and moles is molar mass. The molar mass of a substance is its relative atomic mass (Ar) or relative molecular mass (Mr) expressed in grams per mole. Numerically it is the same number as the Ar or Mr, but now it carries the unit g mol⁻¹.

• The Ar of sodium is 23, so the molar mass of sodium is 23 g mol⁻¹, one mole of sodium atoms has a mass of 23 g.
• The Mr of water, H₂O, is 18, so the molar mass of water is 18 g mol⁻¹, one mole of water has a mass of 18 g.

This is why the mole is so useful: it packages the Avogadro constant of particles into a mass small enough to weigh on a balance. Remember the distinction from standard 3.1, Ar and Mr have no units, but molar mass does (g mol⁻¹).

The central formula

The relationship you use constantly is:

Number of moles (n) = mass (m) ÷ molar mass (M)

which rearranges to m = n × M and M = m ÷ n. Getting mass into and out of moles is one half of the map; the Avogadro constant from standard 3.2 is the other half.

The full conversion map

Picture three boxes in a row, with the mole in the middle:

mass (g) ⇄ moles (mol) ⇄ number of particles

• To go from mass to moles, divide by the molar mass.
• To go from moles to mass, multiply by the molar mass.
• To go from moles to particles, multiply by the Avogadro constant, The Avogadro constant is 6.02 x 10²³ mol⁻¹.
• To go from particles to moles, divide by the Avogadro constant.

You can never jump straight from mass to number of particles, you must pass through the mole in the middle. Fixing this picture in your head prevents most errors on this standard.

Worked example

Question. Calculate (a) the mass of 0.25 mol of calcium carbonate, CaCO₃, and (b) the number of formula units it contains. [Ar: Ca = 40, C = 12, O = 16; NA = 6.02 x 10²³ mol⁻¹ mol⁻¹]

Step 1, Find the molar mass. Mr of CaCO₃ = 40 + 12 + (3 × 16) = 40 + 12 + 48 = 100. So the molar mass M = 100 g mol⁻¹.

Step 2, Convert moles to mass. m = n × M = 0.25 × 100 = 25 g.

Step 3, Convert moles to number of particles. Number of formula units = n × NA = 0.25 × 6.02 x 10²³ mol⁻¹ = 1.505 × 10²³ formula units.

Answer. (a) The mass is 25 g. (b) It contains 1.505 × 10²³ formula units of CaCO₃.

Practice question

Question. How many moles are there in 8.0 g of sodium hydroxide, NaOH, and how many formula units is that? [Ar: Na = 23, O = 16, H = 1; NA = 6.02 x 10²³ mol⁻¹ mol⁻¹]

Answer. Molar mass of NaOH = 23 + 16 + 1 = 40 g mol⁻¹. Number of moles = mass ÷ molar mass = 8.0 ÷ 40 = 0.2 mol. Number of formula units = 0.2 × 6.02 x 10²³ mol⁻¹ = 1.204 × 10²³ formula units.

Exam tip

Always calculate the molar mass first and write it with its unit, g mol⁻¹; a huge share of lost marks on this standard come from a wrong Mr rather than a wrong method. Then set out the conversion in named steps, mass → moles → particles, so an examiner can follow and award method marks. Watch the units at every stage: mass in grams, molar mass in g mol⁻¹, and the answer in moles or in a plain particle count (never in grams for a number of particles). If a question gives a mass in kilograms or tonnes, convert to grams before dividing.

Reading the question for the right direction

Success on this standard is often just choosing the right direction on the map. Underline what the question gives you and what it asks for. If it gives a mass and asks for moles, you divide by the molar mass; if it gives moles and asks for a mass, you multiply. If it asks for a number of atoms, molecules or ions, take the amount to moles first and then multiply by the Avogadro constant, and if it asks for atoms of a particular element inside a compound, multiply once more by how many of that atom appear in the formula. Slowing down to label “given” and “required” turns a multi-step question into a short chain of single steps you already know.

A note on carrying units

Because this standard blends two units, g mol⁻¹ for molar mass and mol⁻¹ for the Avogadro constant, it rewards students who write units at every line. When you divide a mass in grams by a molar mass in g mol⁻¹, the grams cancel and you are left with mol, which confirms you have divided the right way round. When you multiply moles by the Avogadro constant in mol⁻¹, the moles cancel and you are left with a pure number of particles. Using the units as a check like this catches the most common slip on this standard: multiplying when you should have divided, or the reverse.

Where this fits

This is content standard 3.3, the calculating heart of the The Mole Concept, Chemical Formula and Equation chapter. It draws on relative mass and the Avogadro constant and feeds forward into gas volumes, empirical formula and stoichiometry. Practise the conversions with the worked examples and test yourself with the practice questions. In our online 1-to-1 SPM Chemistry lessons, taught in English, from RM50/hr, our teachers drill the mass–mole–particle map until choosing the right direction is automatic, because this one skill underpins the marks in every later calculation.

Quick recap

• Molar mass = Ar or Mr in grams per mole (g mol⁻¹).
• Number of moles = mass ÷ molar mass; mass = moles × molar mass.
• Map: mass ⇄ moles ⇄ particles, always pass through the mole.
• Multiply moles by The Avogadro constant is 6.02 x 10²³ mol⁻¹ to reach a particle count; use units as a check.