Lesson 7: Solutions, Concentration, and Solubility

Dissolving is a competition: the attractions holding a solute together versus the attractions between solute and solvent. When a solid dissolves, its particles disperse evenly through the solvent to form a solution; how much dissolves, and how fast, decides everything from making squash to absorbing medicine. This lesson quantifies concentration, explains saturation and solubility, and uses solubility rules to predict the precipitates that form when solutions meet.

Concentration and molarity

Concentration in molarity counts moles of solute per litre of solution: c = n ÷ V, with V in litres. Chemists also use g/L, percent by mass, and parts per million (ppm) for very dilute solutions — 1 ppm = 1 mg of solute per litre of water, roughly.

Worked example 1: preparing and diluting solutions

(a) Molarity: 5.85 g of NaCl (Mr = 58.44) in 500.0 mL of solution: n = 5.85 ÷ 58.44 = 0.1001 mol; c = 0.1001 ÷ 0.5000 = 0.200 mol/L. (b) Dilution: what volume of 6.00 mol/L HCl stock makes 250.0 mL of 0.100 mol/L? Dilution adds solvent only, so moles are conserved: c₁V₁ = c₂V₂ → V₁ = (0.100 × 250.0) ÷ 6.00 = 4.17 mL. A sanity check matters: the stock is 60 times more concentrated, so the volume needed should be about 250 ÷ 60 ≈ 4.2 mL. ✓ (c) Fluoride in drinking water at 1.0 ppm means 1.0 mg per litre = 0.0010 g ÷ 19.00 g/mol ≈ 5.3 × 10⁻⁵ mol/L — a useful reminder that "trace" quantities are still astronomically many particles.

Saturation and solubility curves

A saturated solution holds the maximum dissolved solute at that temperature; its concentration defines the solute's solubility, often plotted against temperature. Most solids grow more soluble when hot (KNO₃ dramatically so: 13 g per 100 g water at 0 °C, 247 g at 100 °C), while gases always grow less soluble — warm soda goes flat as CO₂ escapes. Cooling a hot saturated solution slowly can produce a supersaturated solution, holding more than equilibrium allows until a seed crystal triggers sudden crystallisation — the trick inside reusable hand warmers (sodium ethanoate).

Predicting precipitates

When two solutions mix, a precipitate forms if the mixture contains an insoluble compound. Solubility rules summarise the patterns: all nitrates are soluble; all Group 1 and ammonium salts are soluble; most chlorides are soluble except AgCl and PbCl₂; most sulfates are soluble except BaSO₄, PbSO₄ and CaSO₄ (sparingly); most carbonates and hydroxides are insoluble except Group 1 and ammonium ones. Mix AgNO₃ with NaCl and AgCl precipitates: Ag⁺(aq) + Cl⁻(aq) → AgCl(s). The Na⁺ and NO₃⁻ are spectator ions — present, soluble, unchanged.

Worked example 2: mass of precipitate

50.0 mL of 0.200 mol/L AgNO₃ is mixed with excess NaCl solution. Moles of Ag⁺ = 0.200 × 0.0500 = 0.0100 mol. The ionic equation is 1 : 1, so n(AgCl) = 0.0100 mol; mass = 0.0100 × 143.32 = 1.43 g. Had the chloride been limiting, the same three-step method (to moles, across the ratio, to mass) with the chloride's amount would give the answer — always check which ion is in smaller supply.

In the lab: measuring a solubility curve

To map KNO₃ solubility, students dissolve a known mass in 10.0 g of water, heat until it just dissolves, then cool slowly and record the temperature at which crystals first appear. The measurement uncertainty hides in that phrase "first appear": crystal onset is a judgement call worth ±2 °C between observers, and if the tube is cooled too fast the solution overshoots into supersaturation before crystallising, recording a temperature several degrees too low — a systematic bias that grows with cooling rate. Stirring and a slow water bath reduce it. The thermometer itself reads to ±0.5 °C (school grade) and the balance to ±0.01 g; plotting class results typically scatters ±3 °C around the published curve, teaching a durable lesson: the limiting uncertainty in most school practicals is the human criterion for the endpoint, not the instrument precision. Repeating the cooling three times and taking the middle value is the standard defence.

Chemistry in the real world

Kidney stones are unwanted precipitation: calcium oxalate crystallising where it should stay dissolved, which is why hydration (dilution) is the first-line prevention. In water treatment, alum is added to precipitate suspended solids as a gelatinous hydroxide floc. And oceanographers track how warming seas hold less dissolved CO₂ and O₂ — solubility curves with planetary stakes.

Common mistakes

• "Insoluble" read as "zero dissolved". Insoluble means very sparingly soluble; tiny equilibrium concentrations still exist and matter (Lesson 11).
• Using the volume of solvent instead of the volume of solution in molarity. Making 500.0 mL of solution is not adding 500.0 mL of water — dissolve, then make up to the mark.
• Precipitate equations with spectator ions left in. Write the ionic equation with only the ions that form the solid; state symbols included.
• ppm treated as percent. They differ by 10⁴; conflating them in a dosing calculation is dangerous, not just wrong.

Exam Experience

1. Which pair of solutions produces a precipitate when mixed? A) NaCl + KNO₃ B) AgNO₃ + NaCl C) NaOH + KCl D) NH₄Cl + Na₂SO₄ Answer: B. AgCl is insoluble; every other combination contains only soluble salts (all nitrates, Group 1 and ammonium salts are soluble).

2. A solution contains 0.250 mol of glucose in 2.00 L. Its concentration is: A) 0.500 mol/L B) 0.125 mol/L C) 2.00 mol/L D) 8.00 mol/L Answer: B. c = 0.250 ÷ 2.00 = 0.125 mol/L. A multiplies instead of divides.

3. A gas's solubility in water decreases when: A) pressure of the gas increases B) the water is heated C) the water is stirred D) more gas is added Answer: B. Heating drives dissolved gas out (thermal energy overcomes solute–solvent attraction); A would increase solubility (Henry's law).

Constructed response (5 marks). A technician needs 500.0 mL of 0.0500 mol/L CuSO₄ (Mr = 159.61) from solid crystals. (a) Calculate the mass of CuSO₄ to weigh out. (b) Describe the correct procedure for making the solution in a volumetric flask, including how the final volume is set. (c) The technician instead adds the solid to 500.0 mL of water. Explain why the resulting concentration is slightly less than 0.0500 mol/L. Scoring guide: (a) 1 mark: n = 0.0500 × 0.5000 = 0.0250 mol; 1 mark: mass = 0.0250 × 159.61 = 3.99 g. (b) 1 mark: dissolve in less than the final volume of water (beaker), transfer quantitatively with rinsings; 1 mark: make up to the graduation mark with the meniscus on the line at eye level, then mix by inversion. (c) 1 mark: dissolving increases the total volume beyond 500.0 mL, so the same moles occupy more volume — concentration = n ÷ V falls. Answers referring to undissolved solid earn nothing here.

Colligative properties: counting particles, not identities

Some solution properties depend only on how many solute particles are present, not on what they are. Freezing-point depression is the school-accessible one: dissolved particles disrupt crystal formation, so solutions freeze below the solvent's freezing point by ΔTf = Kf × m, where m is molality (moles of solute per kilogram of solvent) and Kf for water is 1.86 °C·kg/mol. Worked example 3. A solution of 0.50 mol of glucose in 1.00 kg of water (0.50 mol/kg) freezes at −(1.86 × 0.50) = −0.93 °C. Replace the glucose with 0.50 mol of NaCl and the depression nearly doubles, to about −1.86 °C, because each NaCl unit releases two particles (Na⁺ and Cl⁻) — colligative properties count particles, so ionic solutes multiply their effect by their ion count (the van 't Hoff factor). This is why salt grit melts ice (the mixture's freezing point drops below the road temperature, though it stops working near −21 °C, the eutectic limit), why CaCl₂ is used on colder roads, and why antifreeze (ethane-1,2-diol, covalent, one particle per molecule) needs molal quantities to protect an engine to −20 °C. It is also how molar masses were measured before mass spectrometry: freeze, measure ΔTf precisely, and invert the formula.

Molality versus molarity

Notice the solvent-based definition: molality uses kilograms of solvent and does not change with temperature, whereas molarity uses litres of solution and drifts as the liquid expands. Kineticists and colligative-property work prefer molality for exactly that stability; bench chemists prefer molarity because volumetric glassware is faster. Converting between them requires the solution's density — one more reminder (with Lesson 7's common mistakes) that "500 mL of solution" and "500 g of solvent" are different recipes that happen to rhyme.

A first look at solubility product, Ksp

"Insoluble" salts still dissolve microscopically until the ion product reaches a constant, the solubility product Ksp. For AgCl, Ksp = [Ag⁺][Cl⁻] = 1.8 × 10⁻¹⁰. In pure water, let the solubility be s: then [Ag⁺] = [Cl⁻] = s, so s² = 1.8 × 10⁻¹⁰ and s = 1.3 × 10⁻⁵ mol/L — about 2 mg per litre. Tiny, yet real enough to matter in photography chemistry and in the common-ion effect: in 0.10 mol/L NaCl, the solubility collapses to s = 1.8 × 10⁻¹⁰ ÷ 0.10 = 1.8 × 10⁻⁹ mol/L, because the chloride already present pushes the equilibrium left (Lesson 11 arriving early). Ksp is equilibrium's foothold inside this lesson: every precipitate in Lesson 7's rules is a Ksp too small to see past, and every "will it precipitate?" question is a Q-versus-Ksp comparison.

Hard water and ion exchange: precipitation prevented

Hard water carries Ca²⁺ and Mg²⁺ ions that precipitate soap as scum and fur kettles with CaCO₃ when heated (the Lesson 11 equilibrium CaCO₃(s) ⇌ Ca²⁺ + CO₃²⁻ driven by CO₂ loss). Water softeners run an ion-exchange resin: Na⁺ ions held on the resin swap two-for-one with Ca²⁺ ions in the water (charge balance demands the ratio), releasing harmless Na⁺ instead. The resin is regenerated by flooding it with concentrated brine — mass action (Le Châtelier) pushing the exchange backwards. The same equilibrium logic, industrialised, deionises the water for laboratories and power-station boilers, where a millimetre of scale on a heating surface wastes measurable percent of fuel: solubility equilibria running a utility bill.