5.8C - Calculating molar concentration

Meaning of mol dm-3

A solution is made when a solute dissolves in a solvent. For concentration calculations, the volume used is the final volume of the solution, not just the volume of water added.

Concentration in mol dm-3 means the amount of solute, in moles, in each $1\,\mathrm{dm}^{3}$ of solution.

For example, a sodium chloride solution with concentration 0.200 mol dm-3 contains 0.200 mol of sodium chloride in every $1\,\mathrm{dm}^{3}$ of solution.

This is different from concentration in g dm-3:

The same solution can be described in either unit if you know the relative formula mass, Mr, of the solute. A mole-based concentration is especially useful when the dissolved substance reacts, because balanced equations use moles.

Calculate concentration

The concentration equation in moles is:

where:

• c is concentration in mol dm-3
• n is amount of solute in mol
• V is volume of solution in $\mathrm{dm}^{3}$

The volume must be in $\mathrm{dm}^{3}$ before you use this equation.

1000 cm3 = 1 dm3
volume in dm3 = volume in cm3 / 1000

Worked example:

A solution contains 0.0125 mol of sodium hydroxide in $250\,\mathrm{cm}^{3}$ of solution. Calculate its concentration in mol dm-3.

V = 250 / 1000 = 0.250 dm3
c = n / V
c = 0.0125 / 0.250
c = 0.0500 mol dm-3

The most common error is to divide by 250 instead of 0.250. That gives an answer that is 1000 times too small.

Now try the same route.

Rearranging concentration

The same relationship can be rearranged if a question asks for the amount of solute or the volume of solution.

c = n / V
n = c x V
V = n / c

Use these only with V in $\mathrm{dm}^{3}$.

Worked example:

Calculate the amount, in moles, of sodium hydroxide in $40.0\,\mathrm{cm}^{3}$ of 0.200 mol dm-3 sodium hydroxide solution.

V = 40.0 / 1000 = 0.0400 dm3
n = c x V
n = 0.200 x 0.0400
n = 0.00800 mol

Notice that $\mathrm{mol}\,\mathrm{dm}^{-3} \times \mathrm{dm}^{3}$ gives mol. The $\mathrm{dm}^{3}$ units cancel, leaving amount in moles.

Convert between concentration units

To convert between g dm-3 and mol dm-3, use the relative formula mass of the solute. The molar mass in g mol⁻¹ has the same numerical value as Mr; Mr itself has no unit.

[DIAGRAM: asset_name: concentration_conversion_route: Concentration calculation route map - diagram 1; asset_slug: 127_5_8c_concentration_of_solutions_in_mol_dm3_and_convert_concentration_in_g_dm3_i_diagram1; file: diagram_assets/127_5_8c_concentration_of_solutions_in_mol_dm3_and_convert_concentration_in_g_dm3_i_diagram1.png; recommended_method: deterministic_drawn; description: Exact monochrome route map for Edexcel 5.8C. It shows c = n / V with V in dm3, the cm3 to dm3 conversion by dividing by 1000, and the two concentration-unit conversions: mol dm-3 times Mr gives g dm-3, while g dm-3 divided by Mr gives mol dm-3. Deterministic drawing is required because units, formula direction and operations are assessed calculation content.]

If you know concentration in mol dm-3: