Chapter 12

Solutions & Concentration

High School
At a glance
Core ideaConcentration measures how much solute is dissolved in a solvent.
Key termMolarity — moles of solute per litre of solution.
You can…Prepare and dilute solutions with c₁V₁ = c₂V₂.
Watch out"Like dissolves like" — polar solvents dissolve polar/ionic solutes.
Theory

Dissolving, and how much

A solution is a homogeneous mixture of a solute (dissolved) in a solvent (the medium). Dissolving happens when solute–solvent attractions can replace the solute–solute and solvent–solvent attractions broken in the process — captured by the rule of thumb "like dissolves like": polar solvents dissolve polar/ionic solutes; non-polar solvents dissolve non-polar solutes.

Concentration quantifies how much solute is present. The chemist's standard is molarity:

c = n / V   mol dm⁻³ (M) = moles of solute ÷ volume of solution in litres

On dilution the amount of solute is unchanged, only the volume grows, giving the dilution relation:

c₁V₁ = c₂V₂

Colligative properties depend on the number of solute particles, not their identity: dissolving a solute raises the boiling point and lowers the freezing point of the solvent.

Explanation

Saturation, and why salt melts ice

Add solute to a solvent and it keeps dissolving until the solution is saturated — the maximum that will dissolve at that temperature. Beyond that, extra solute simply sits undissolved. Solubility usually rises with temperature for solids (hot water dissolves more sugar); for gases it falls with temperature, which is why a warm fizzy drink goes flat faster and why warm rivers hold less dissolved oxygen.

Colligative effects explain everyday chemistry. Spreading salt on icy roads works because dissolved ions depress the freezing point below 0 °C, so the ice melts. Antifreeze in a car radiator both lowers the freezing point (so coolant doesn't freeze in winter) and raises the boiling point (so it doesn't boil in summer). The magnitude depends only on how many particles dissolve — an ionic compound that splits into several ions has a bigger effect per mole than a molecular one.

Practical

Worked example — preparing and diluting a solution

(a) What mass of NaOH (M = 40.0 g mol⁻¹) is needed to make 250 mL of 0.200 M solution?

  1. Convert volume to litres: 250 mL = 0.250 L.
  2. Find moles of solute: n = c × V = 0.200 × 0.250 = 0.0500 mol.
  3. Convert to mass: m = n × M = 0.0500 × 40.0 = 2.00 g.
  4. Dissolve 2.00 g NaOH and make up to exactly 250 mL in a volumetric flask.

(b) To what volume must 25.0 mL of this 0.200 M solution be diluted to make it 0.0500 M?

  1. Use c₁V₁ = c₂V₂. Solve for V₂ = c₁V₁ / c₂.
  2. Substitute: V₂ = (0.200 × 25.0) / 0.0500 = 100 mL.
  3. So add water to the 25.0 mL sample up to a total of 100 mL — a fourfold dilution matching the fourfold drop in concentration.
Q&A
Why does oil not dissolve in water?

Water is polar and hydrogen-bonded; oil is non-polar. Water molecules attract each other far more strongly than they attract non-polar oil molecules, so mixing is energetically unfavourable — the water excludes the oil ("like dissolves like"). They form separate layers.

Calculate the molarity of a solution containing 5.85 g of NaCl (M = 58.5) in 500 mL.

n = 5.85 ÷ 58.5 = 0.100 mol. V = 0.500 L. c = 0.100 ÷ 0.500 = 0.200 M.

Why does 1 mol of NaCl lower the freezing point of water about twice as much as 1 mol of glucose?

Freezing-point depression is colligative — it depends on the number of dissolved particles. Glucose stays as one molecule per formula unit, but NaCl dissociates into two ions (Na⁺ + Cl⁻), producing roughly twice as many particles per mole and therefore about twice the effect.

How would you prepare 1.0 L of 0.10 M HCl from a 2.0 M stock?

Use c₁V₁ = c₂V₂: V₁ = (0.10 × 1.0) ÷ 2.0 = 0.050 L = 50 mL of stock. Add the 50 mL of 2.0 M HCl to water and make up to 1.0 L. (Always add acid to water, not the reverse.)

Concept mind map

How the ideas connect

Every key idea in this chapter, branching from the core concept — use it to see the whole picture at a glance.

Solute and solventMolarity mol/LDilution C1V1=C2V2SaturationSolubilityColligativeeffectsSolutions and Concentration
Infographic

The key facts, visualised

Molarity
moles of solute per liter of solution (mol/L)
C1V1=C2V2
the dilution equation for adding solvent
Saturated
solution holding the maximum dissolved solute
Solvent
the dissolving medium, often water
Solved examples

Worked problems, step by step

Follow each solution line by line, then try to reproduce it on paper before moving on.

Example 1Find the molarity of 0.50 mol NaCl dissolved to make 2.0 L of solution.

  1. Molarity = moles / volume in liters.
  2. M = 0.50 mol / 2.0 L.
  3. Divide: 0.50 / 2.0 = 0.25.

Example 2How much 2.0 M stock is needed to make 500 mL of 0.50 M solution?

  1. Use C1V1 = C2V2, solve for V1 = C2V2 / C1.
  2. V1 = (0.50 x 500) / 2.0.
  3. Compute: 250 / 2.0 = 125 mL of stock, then top up to 500 mL.
Practice problem set

Now you try

Work each one out first, then tap to reveal the worked answer.

1What is the solute when salt is dissolved in water?
The salt is the solute; water is the solvent.
2How many moles of solute are in 2.0 L of 1.5 M solution?
3.0 mol, because moles = M x V = 1.5 x 2.0.
3What does it mean for a solution to be saturated?
It holds the maximum solute that will dissolve at that temperature; extra solute stays undissolved.
4Why does salt lower the freezing point of water?
Dissolved particles disrupt ice formation, a colligative effect, so it freezes below 0 degrees C.
5If you add water to a solution, what happens to its concentration?
It decreases, because the same solute is spread through more solvent (dilution).
6How does temperature usually affect the solubility of a solid in water?
It usually increases, so more solid dissolves in hot water than cold.