Short on time? This page is the recap. For explanations and worked examples, use the full study guide.
Recap
- A solution (homogeneous mixture) has the same macroscopic properties throughout. It can be a gas (air), a liquid (sugar in water) or a solid (brass).
- A heterogeneous mixture has properties that depend on where you sample it: layers, settling solids, visible grains.
- Molarity is the lab’s main concentration unit: moles of solute per litre of solution, written M (mol L⁻¹).
- An ionic solute separates into ions. Each ion’s concentration = salt concentration × number of that ion in the formula. Polyatomic ions stay whole.
- Dilution and mixing change the volume; the moles of each solute species are unchanged.
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| M = n ÷ V | M in mol L⁻¹, n in mol, V in L of solution | find molarity, or rearrange: n = M × V, V = n ÷ M |
| [ion] = M(salt) × subscript | e.g. 0.25 M CaCl₂ → 0.50 M Cl⁻ | find ion concentrations |
| M₁V₁ = M₂V₂ | moles before = moles after; any volume unit, if the same on both sides | dilution |
| M(mix) = (n₁ + n₂) ÷ (V₁ + V₂) | add moles of the same species | mixing solutions that do not react |
| N = M × V × N_A | N_A = 6.022 × 10²³ mol⁻¹ | count solute particles |
Assumptions behind the numbers
- The solute dissolves completely and does not react with anything else present.
- When two dilute aqueous solutions are mixed, the volumes add. This is close to true, not exact.
- The solution is homogeneous, so any portion has the same molarity as the whole.
Mistakes to avoid
- Millilitres in M = n ÷ V. Convert to litres first.
- Litres of water instead of litres of solution. Make the solution up to the final volume.
- Forgetting ion counts. 0.10 M Al(NO₃)₃ is 0.30 M NO₃⁻.
- Averaging concentrations when mixing. Add moles; divide by total volume.
- Thinking a portion is weaker. Pouring some out changes moles, not molarity.
- Calling a coloured liquid heterogeneous. Colour is not the test; uniformity is.
Quick self-check
- How many moles of solute are in 50.0 mL of a 0.120 M solution? (0.00600 mol)
- What is [NO₃⁻] in 0.040 M Ca(NO₃)₂? (0.080 M)
- 20.0 mL of 1.00 M HCl is diluted to 250.0 mL. What is the new concentration? (0.0800 M)
- A salad dressing of oil and vinegar has separated into two layers. Solution or heterogeneous mixture? (Heterogeneous: a sample from the top layer differs from one taken from the bottom layer.)
Next: practice questions.