Solutions & Concentration
High SchoolDissolving, 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:
On dilution the amount of solute is unchanged, only the volume grows, giving the dilution relation:
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.
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.
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?
- Convert volume to litres: 250 mL = 0.250 L.
- Find moles of solute: n = c × V = 0.200 × 0.250 = 0.0500 mol.
- Convert to mass: m = n × M = 0.0500 × 40.0 = 2.00 g.
- 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?
- Use c₁V₁ = c₂V₂. Solve for V₂ = c₁V₁ / c₂.
- Substitute: V₂ = (0.200 × 25.0) / 0.0500 = 100 mL.
- 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.
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.)
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.
The key facts, visualised
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.
- Molarity = moles / volume in liters.
- M = 0.50 mol / 2.0 L.
- 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?
- Use C1V1 = C2V2, solve for V1 = C2V2 / C1.
- V1 = (0.50 x 500) / 2.0.
- Compute: 250 / 2.0 = 125 mL of stock, then top up to 500 mL.
Now you try
Work each one out first, then tap to reveal the worked answer.