The concentration of a solution is measured in g dm-3 or mol dm-3

The concentration of a solution refers to the amount of solute that is dissolved per unit volume of solution. It is a way to express how much solute is present in a given amount of solution.

• Concentration is measured in g dm^-3 or mol dm⁻³.
• Using mass or moles accounts for the number of particles present.
• Measuring per dm³ (or per litre) accounts for the volume of solution.
• Square brackets [ ] are used to denote concentration. For example, [H⁺] represents the concentration of hydrogen ions in a solution.

The equation linking mass, volume and concentration is:

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

Where:

• c = concentration of solution (g dm^-3)
• m = mass in solution (g)
• V = volume of solution (dm³)

The equation linking moles, volume and concentration is:

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

Where:

• c = 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 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

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

Calculating concentration of solutions

The concentration of a solution can be determined using:

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

The following worked examples illustrate how to calculate the concentration of a solution in both mol dm^-3 and g dm^-3.

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.

Worked example 2 - Calculating mass of product

Calculate the mass of hydrogen that forms when an excess of magnesium is added to 175 cm³ of 1.80 mol dm^-3 hydrochloric acid. The equation for the reaction is:

Mg_(s) + 2HCl_(aq) ➔ MgCl_2(aq) + H_2(g)

Give your answer to 3 significant figures.

Step 1: Conversion of cm³ to dm³

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

175 cm³ = 0.175 dm³

Step 2: Calculate number of moles of HCl

$\text{n }=\text{ c }\times \text{ V }=1.80\times 0.175=0.315\text{ mol}$

Step 3: Calculate number of moles of H₂

HCl: H₂ mole ratio = 2:1

${\text{Moles of H}}_2=\frac{0.315}{2}=0.1575\text{ mol}$

Step 4: Calculate mass of H₂

m = n x M_r = 0.1575 x 2.0 = 0.315 g

Calculating concentrations in ppm

Concentrations of solutions can be expressed in parts per million (ppm). This unit is often used for very dilute solutions, such as trace pollutants in water or gases in air.

For solutions, we use the following equation to calculate concentration in ppm:

$\text{concentration in ppm }=\frac{\text{mass of solute }\times \mathrm{1,000,000}}{\text{total mass of solution}}$

The masses must be in the same units (usually g or mg).

For gases in the atmosphere, we use a similar equation, but with volumes instead of masses:

$\text{concentration in ppm }=\frac{\text{volume of gas }\times \mathrm{1,000,000}}{\text{total volume of air}}$

The volumes must be in the same units (usually dm³ or cm³).

The following worked examples demonstrate how to calculate the concentration of solutions and gases in ppm.

Worked example 3 - Calculating concentration in ppm

A water sample contains 37 mg of dissolved copper sulfate in 650 g of water.

Calculate the concentration of copper sulfate in ppm. Give your answer to 2 significant figures.

Step 1 - Convert from mg into g

To convert from mg into g, divide by 1,000

37 mg = 0.037 g

Step 2 - Equation

$\text{concentration in ppm }=\frac{\text{mass of solute }\times \mathrm{1,000,000}}{\text{total mass of solution}}$

Step 3 - Substitution and correct evaluation

$\text{concentration in ppm }=\frac{0.037\times \mathrm{1,000,000}}{650}=57\text{ ppm}$

Worked example 4 - Calculating concentration in ppm

A sample of air with a volume of 2,500 dm³ contains carbon monoxide with a concentration of 150 ppm.

Calculate the volume of carbon monoxide in this sample of air. Give your answer to 2 significant figures,

Step 1 - Equation

$\text{concentration in ppm }=\frac{\text{volume of gas }\times \mathrm{1,000,000}}{\text{total volume of air}}$

Step 2 - Rearrange equation

$\text{volume of gas }=\frac{\text{concentration in ppm }\times \text{ total volume of air}}{\mathrm{1,000,000}}$

Step 3 - Substitution and correct evaluation

$\text{volume of gas }=\frac{150\times \mathrm{2,500}}{\mathrm{1,000,000}}=0.375{\text{ dm}}^3$