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Expressing concentration

Class 12Chemistry Ways to measure how much soluteSession 1 Free

Concentration states how much solute is in a solution. It can be given by mass, by volume or by moles. Molarity depends on the volume of the solution, so it changes with temperature; the others do not.

Solutions, solutes and solvents

A solution is a homogeneous mixture of two or more substances: its composition is the same throughout. The component present in the largest amount is the solvent. The other components are solutes. In salt water, salt is the solute and water is the solvent. This unit deals mostly with binary solutions, which have one solute and one solvent.

“Dilute” and “concentrated” do not say how much solute is present. Concentration is a number that does. There are several ways to define it, each suited to particular uses.

Measures based on mass and volume

Mass percentage (w/w): (mass of solute ÷ mass of solution) × 100. A 10% glucose solution contains 10 g of glucose in every 100 g of solution, that is, 10 g of glucose with 90 g of water.
Volume percentage (v/v): (volume of component ÷ total volume of solution) × 100. A 35% v/v solution of ethylene glycol in water contains 35 mL of ethylene glycol in every 100 mL of solution.
Mass by volume percentage (w/v): mass of solute in grams per 100 mL of solution. It is used in medicine and pharmacy.
Parts per million (ppm): (parts of solute ÷ total parts of solution) × 10⁶. It is used for very small concentrations. One litre of sea water, mass about 1030 g, contains about 6 × 10⁻³ g of dissolved oxygen: about 5.8 ppm by mass.

Measures based on moles

Chemical reactions depend on numbers of particles, so measures based on moles are the most used in chemistry.

Mole fraction (x): moles of a component ÷ total moles of all components. The mole fractions of all the components add up to 1.
Molarity (M): moles of solute ÷ volume of solution in litres. A 0.25 M NaOH solution contains 0.25 mol of NaOH in each litre of solution.
Molality (m): moles of solute ÷ mass of solvent in kilograms. A 1.00 m KCl solution contains 1.00 mol of KCl for each kilogram of water.

⚖ Compare the measures › Set the amount of solute and of water, and see the mass percentage, mole fraction, molality and molarity of the same solution side by side.

Molarity and molality are both “moles of solute per something”. What is the difference, and why does it matter?

Molarity divides by the volume of the solution. Molality divides by the mass of the solvent.

Volume changes with temperature, because most liquids expand when heated. Water expands by about 1% between 20°C and 50°C. The number of moles of solute does not change, so the molarity decreases by about 1%. Mass does not change with temperature, so the molality stays the same.

For this reason, molality is used for properties measured at different temperatures, such as the boiling-point elevation and freezing-point depression later in this unit.

Which measures depend on temperature?

Mass percentage, ppm by mass, mole fraction and molality are defined only from masses and amounts in moles. These do not change when a solution is heated or cooled, so these measures are independent of temperature.

Molarity, volume percentage and mass by volume percentage use the volume of the solution, which changes with temperature. So they depend on temperature. Of these, molarity is the one used most.

Find the mole fraction of ethylene glycol (C₂H₆O₂, molar mass 62 g/mol) in a solution containing 20% ethylene glycol by mass.

Take 100 g of solution: 20 g of ethylene glycol and 80 g of water.

Moles of ethylene glycol = 20 ÷ 62 = 0.323 mol. Moles of water = 80 ÷ 18 = 4.44 mol.

Mole fraction of ethylene glycol = 0.323 ÷ (0.323 + 4.44) = 0.323 ÷ 4.77 = 0.068.

The mole fraction is much smaller than 0.20 because a water molecule (18 g/mol) has much less mass than an ethylene glycol molecule (62 g/mol). 80 g of water is many more moles than 20 g of glycol.

Check what you have understood

1In a solution, the component present in the largest amount is the…

The solvent. The other components are solutes.

2Molarity is moles of solute per…

Molarity = moles of solute ÷ litres of solution.

3Molality is moles of solute per…

Molality = moles of solute ÷ kilograms of solvent (not of solution).

4Which of these concentration measures changes with temperature?

Molarity uses the solution’s volume, which changes with temperature.

5The mole fractions of all the components of a solution add up to ____.

1, because each is a fraction of the same total.

6Which measure is most suitable for a trace pollutant in water?

ppm gives small concentrations as convenient numbers.

Next: solubility, and Henry’s law for gases.

Next: Solubility and Henry's law ›