Concentration in g/dm³ and mol/dm³

Quantitative chemistry

GCSE Chemistry (8462) · 4.3.2.5 & 4.3.4 · Higher

ORIGINAL

Convert cm³ to dm³ first; mass ÷ volume gives g/dm³, moles ÷ volume gives mol/dm³ (the mol/dm³ half is Higher, chemistry only).

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Question

A student dissolves 4.00 g of sodium hydroxide, NaOH, in water and makes the solution up to 250 cm³. Calculate the concentration of the solution in g/dm³ and in mol/dm³.

A_r

: Na = 23, O = 16, H = 1.

Every step worked, with the reasoning.

1
$250\ \text{cm}^3 = \dfrac{250}{1000} = 0.250\ \text{dm}^3$
Concentration is measured per dm³, and 1 dm³ = 1000 cm³. Common error: dividing by 250 instead of 0.250 — that gives 0.016, a value 1000 times too small.
2
$\text{concentration} = \dfrac{4.00\ \text{g}}{0.250\ \text{dm}^3} = 16.0\ \text{g/dm}^3$
Mass concentration = mass ÷ volume in dm³.
3
$M_r(\mathrm{NaOH}) = 23 + 16 + 1 = 40$ , so $n = \dfrac{4.00}{40} = 0.100\ \text{mol}$
For mol/dm³ you need the amount in moles, not the mass.
4
$\text{concentration} = \dfrac{0.100\ \text{mol}}{0.250\ \text{dm}^3} = 0.400\ \text{mol/dm}^3$
Moles ÷ volume in dm³. Check: 16.0 g/dm³ ÷ $M_r$ of 40 = 0.400 mol/dm³ too.

Answer: $16.0\ \text{g/dm}^3$ and $0.400\ \text{mol/dm}^3$ (3 s.f.)

Question

Stuck on concentration of solutions?