Relative formula mass with brackets

Quantitative chemistry

GCSE Chemistry (8462) · 4.3.1.2 · Foundation & Higher

ORIGINAL

Multiply out the bracket before you add — the formula mass every mole calculation starts from.

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Question

Calculate the relative formula mass,

M_r

, of aluminium sulfate,

\mathrm{Al_2(SO_4)_3}

. Relative atomic masses,

A_r

: Al = 27, S = 32, O = 16.

Every step worked, with the reasoning.

1
Atoms: $\mathrm{Al} = 2$ , $\mathrm{S} = 1 \times 3 = 3$ , $\mathrm{O} = 4 \times 3 = 12$
The 3 outside the bracket multiplies everything inside it: each sulfate has one S and four O, and there are three sulfates.
2
$\mathrm{Al}: 2 \times 27 = 54$
Multiply each atom count by that element's $A_r$ .
3
$\mathrm{S}: 3 \times 32 = 96$ and $\mathrm{O}: 12 \times 16 = 192$
The same rule for each element.
4
$M_r = 54 + 96 + 192 = 342$
Add the contributions. $M_r$ is a ratio of masses, so it has no unit. Common error: multiplying only the oxygen by 3 (one S, twelve O) gives 278, not 342.

Answer: $M_r = 342$ (no unit)