The molar concentration of a solution is measured in mol dm^-3

The molar concentration of a solution refers to the amount of solute (in moles) that is dissolved per unit volume of solution. It is a way to express how many moles of solute are present in a given amount of solution.

The amount of solute can be expressed in terms of mass or moles to give concentration units of g dm^-3 or mol dm^-3, respectively. Concentration in units of mol dm^-3 is referred to as molar concentration or molarity.

Square brackets [ ] are used to denote molar concentration. For example, [H⁺] represents the molar concentration of hydrogen ions in a solution.

The equation for the molar concentration of a solution is:

$\text{c }=\frac{\text{n}}{\text{V}}$

Where:

• c = molar concentration of solution (mol dm^-3)
• n = number of moles in solution (mol)
• V = volume of solution (dm³)

Converting units of volume

To convert cm³ to dm³:

Divide the volume in cm³ by 1,000

For example, 50 cm³ = 0.05 dm³

To convert dm³ to cm³:

Multiply the volume in dm³ by 1,000

For example, 0.05 dm³ = 50 cm³

Converting units of concentration

To convert mol dm^-3 to g dm^-3:

Multiply the concentration in mol dm^-3 by the M_r of the solute

For example, a 2.00 mol dm^-3 solution of NaCl (M_r = 58.5) = 117 g dm^-3

To convert g dm^-3 to mol dm^-3:

Divide the concentration in g dm^-3 by the M_r of the solute

For example, a 58.5 g dm^-3 solution of NaCl (M_r = 58.5) = 1.00 mol dm^-3

Calculating molar concentration of solutions

The molar concentration of a solution can be determined using:

1. The number of moles of dissolved solute.
2. The total volume of solution.

The following worked examples illustrate how to calculate molar concentration.

Worked example 1 - Calculating concentration using moles and volume

Calculate the concentration, in mol dm^-3, of a sodium chloride (NaCl) solution prepared by dissolving 5.85 g of NaCl in enough water to make 250 cm³ of solution. The molar mass of NaCl is 58.5 g mol^-1.

Step 1: Calculate number of moles of NaCl

$\text{n }=\frac{\text{mass}}{\text{M}_\text{r }}=\frac{5.85}{58.5}=0.100\text{ mol}$

Step 2: Conversion of cm³ to dm³

To convert from cm³ into dm³, divide by 1,000

250 cm³ = 0.250 dm³

Step 3: Calculate concentration of NaCl

$\text{c }=\frac{\text{n}}{\text{V}}=\frac{0.100}{0.250}=0.400\text{ mol dm}^{-3}$

The concentration of the NaCl solution is 0.400 mol dm^-3.

Calculating molar concentration in reactions

Titration experiments can also be used to determine the molar concentration of a solution.

Here are the steps:

1. Write a balanced equation for the reaction.
2. Use the titration volumes and a known molar concentration to calculate the moles of one reactant.
3. Use stoichiometry to relate moles of this reactant to the moles of the reactant whose concentration is unknown.
4. Divide the moles by the volume to calculate the unknown molar concentration.

Worked example 2 - Calculating concentration from a titration

30.0 cm³ of 0.100 mol dm^-3 NaOH neutralises 20.0 cm³ of HCl.

Calculate the concentration of the HCl solution.

Step 1: Write the balanced equation

NaOH_(aq) + HCl_(aq) ➔ NaCl_(aq) + H₂O_(l)

Step 2: Conversion of cm³ to dm³

To convert from cm³ into dm³, divide by 1,000

30.0 cm³ = 0.0300 dm³

20.0 cm³ = 0.0200 dm³

Step 3: Calculate number of moles of NaOH

$\text{n }=\text{ c }\times\text{ V }=0.100\times0.0300=3.00\times10^{-3}\text{ mol} $

Step 4: Calculate number of moles moles of HCl

HCl : NaOH mole ratio = 1:1

Moles of HCl = 3.00 x 10^-3 mol

Step 5: Calculate concentration of HCl

$\text{c }=\frac{\text{n}}{\text{V}}=\frac{3.00\times10^{-3}}{0.0200}=0.150\text{ mol dm}^{-3}$

The concentration of the HCl solution is 0.150 mol dm^-3.

The next example covers a more complex reaction stoichiometry.

Worked example 3 - Calculating concentration from a titration

25.0 cm³ of 0.200 mol dm^-3 H₂SO₄ neutralises 50.0 cm³ of KOH.

Calculate the concentration of the KOH solution.

Step 1: Write the balanced equation

H₂SO_4(aq) + 2KOH_(aq) ➔ K₂SO_4(aq) + 2H₂O_(l)

Step 2: Conversion of cm³ to dm³

To convert from cm³ into dm³, divide by 1,000

25.0 cm³ = 0.0250 dm³

50.0 cm³ = 0.0500 dm³

Step 3: Calculate number of moles of H₂SO₄

$\text{n }=\text{ c }\times\text{ V }=0.200\times0.0250=5.00\times10^{-3}\text{ mol}$

Step 4: Calculate number of moles of KOH

KOH : H₂SO₄ mole ratio = 2:1

Moles of KOH = 2 x 5.00 x 10^-3 = 0.0100 mol

Step 5: Calculate concentration of KOH

$\text{c }=\frac{\text{n}}{\text{V}}=\frac{0.0100}{0.0500}=0.200\text{ mol dm}^{-3}$

The concentration of the KOH solution is 0.200 mol dm^-3.

A similar method can also calculate the volume of one reagent needed to completely react with a certain amount of another reagent.

Worked example 4 - Calculating volume from a titration

Calculate the volume (in dm³) of 0.250 mol dm^-3^ Na₂CO₃ solution required to completely neutralise 40.0 cm³ of 0.100 mol dm^-3 HCl.

Step 1: Write the balanced equation

Na₂CO_3(aq) + 2HCl_(aq) ➔ 2NaCl_(aq) + H₂O_(l) + CO_2(g)

Step 2: Conversion of cm³ to dm³

To convert from cm³ into dm³, divide by 1,000

40.0 cm³ = 0.0400 dm³

Step 3: Calculate number of moles of HCl

$\text{n }=\text{ c }\times\text{ V }=0.100\times0.0400=4.00\times10^{-3}\text{ mol}$

Step 4: Calculate number of moles of Na₂CO₃

Na₂CO₃ : HCl mole ratio = 1:2

$\text{Moles of Na}_2\text{CO}_3\text{ }=\frac{4.00\times10^{-3}}{2}=2.00\times10^{-3}\text{ mol}$

Step 5: Calculate volume of Na₂CO₃

$\text{V }=\frac{\text{n}}{\text{c}}=\frac{2.00\times10^{-3}}{0.250}=8.00\times10^{-3}\text{ dm}^{-3}$