Chemistry · Solutions and electrolytes · Grade 11

Solutions and solubility

Why does more sugar dissolve in hot tea, while fizzy water quickly goes flat when warm?

The situation

At a teahouse, nabat — rock sugar — is dropped into hot tea and dissolves quickly. A bottle of fizzy water taken from the fridge hisses slowly when opened, while one warmed in the sun froths over the moment it is opened. Why do many solids dissolve better in hot water, but gases the opposite — less? How much salt can water hold, where do the crystals come from when it is cooled, and what is “hot ice”?

Topic

Solutions and solubility. Tea, sugar and fizzy water: solubility curves, saturated and supersaturated solutions (“hot ice”)

Key ideas

Solubility curve
Saturated and supersaturated solutions
Solubility of gases

Formulas

s = \frac{m (substance)}{m (water)} \cdot 100 g

Solubility coefficient: the mass of dissolved substance per 100 g of water in a saturated solution.

ω = \frac{s}{100 + s}

Mass fraction of a saturated solution.

m (crystals) = m_{1} (salt) - m (water) \cdot \frac{s_{2}}{100}

The crystals that separate when a saturated solution of an anhydrous salt is cooled from $t_{1}$ to $t_{2}$ .

c = k_{H} p

Henry's law: the solubility of a gas is proportional to its partial pressure; $k_{H}$ falls as the temperature rises.

CuSO_{4} + 5 H_{2} O \overset{}{\to} CuSO_{4} \cdot 5 H_{2} O

Crystalline hydrate: white anhydrous copper(II) sulfate turns into blue copper(II) sulfate pentahydrate (blue vitriol).

Theory

Solutions and disperse systems (§12)

A solution is a homogeneous system of two or more substances: a solvent (most often water) and a solute. Any system in which particles of one substance are spread through another is a disperse system: the substance that is spread is the disperse phase, and the medium it is spread in is the dispersion medium. By particle size: true solutions (molecules and ions, < 1 nm) — clear, they do not settle and pass through a filter; colloidal solutions (1–100 nm; the IUPAC limit goes up to 1 µm) — they look almost clear, but when lit from the side the path of the light is visible (the Tyndall effect); coarse disperse systems (> 100 nm): a suspension (solid particles in a liquid — chalk, clay) settles, and an emulsion (droplets of one liquid in another — milk, oil and water) separates into layers.

Dissolving — a physico-chemical process

When a crystal dissolves, the lattice is broken — this takes energy; the ions and molecules are surrounded by water molecules (hydration) — this releases energy. Whichever is greater decides whether the solution cools or warms. At 25 °C, on dissolving 1 mol, $NH_{4} NO_{3}$ absorbs 25.7 kJ (the solution cools — a “cold pack”), NaCl absorbs 3.9 kJ (hardly noticeable), and NaOH releases 44.5 kJ (the solution heats up). The temperature change is $Δ T = - n Δ H / (m c)$ . Water of hydration can also stay in the crystal: white anhydrous $CuSO_{4}$ combines with water to form blue blue vitriol $CuSO_{4} \cdot 5 H_{2} O$ — a crystalline hydrate. “Like dissolves like”: ionic and polar substances dissolve well in water, while non-polar ones (fat, iodine) dissolve well in non-polar solvents such as petrol.

Solubility (§13)

Solubility (the solubility coefficient) is the greatest mass of a substance that can dissolve in 100 g of solvent at a given temperature. A solution containing that much dissolved substance is saturated: crystals and solution are in equilibrium, and extra salt does not dissolve; one with less dissolved is unsaturated. The solubility of most solids rises with temperature, but differently for each: the curve for $KNO_{3}$ is steep (31.6 g at 20 °C, 110 g at 60 °C, 246 g at 100 °C), that of table salt is almost horizontal (35.9 → 39.0 g), and that of copper sulfate is moderate (20.1 → 77.0 g). So when a hot saturated $KNO_{3}$ solution is cooled, a lot of crystals fall out — the purification of substances by recrystallisation is based on this. Some substances, such as $Ca (OH)_{2}$ , dissolve less well when hot. A point on the solubility curve is a saturated solution, a point below the curve is unsaturated, and a point above it is supersaturated.

Solubility of gases and Henry's law

Gases dissolve less in hot water: dissolving a gas releases heat, so heating drives the gas out of the solution. At a pressure of 101.3 kPa, $CO_{2}$ dissolves to ≈ 1.7 g/L at 20 °C, and almost twice as much at 0 °C. From the oxygen in the air, ≈ 9 mg/L passes into water at 20 °C and ≈ 14.6 mg/L at 0 °C — which is why fish lack oxygen in a warm pond in summer. Henry's law (William Henry, 1803): at constant temperature the solubility of a gas is proportional to its partial pressure, $c = k_{H} p$ . Fizzy water is kept in a closed container under $CO_{2}$ at a pressure above atmospheric; when it is opened the pressure drops, the solution becomes supersaturated and the gas comes out as bubbles. If a diver surfaces too quickly, the nitrogen dissolved in the blood can form bubbles in the same way (decompression sickness).

Supersaturated solution and crystallisation

A carefully cooled saturated solution may not give up the excess substance immediately — it stays supersaturated: more substance is dissolved than the solubility allows, but there is no crystallisation centre. This state is unstable: a single crystal or a speck of dust sets crystallisation off, and it spreads through the whole solution. Sodium acetate trihydrate $CH_{3} COONa \cdot 3 H_{2} O$ “melts” in its own water of crystallisation at 58 °C; if a crystal is dropped into the cooled solution, it freezes solid like “ice”, but hot: ≈ 264–289 kJ/kg of heat is released on crystallisation. Chemical hand warmers work on this basis and are reused by heating them in boiling water. Nabat (rock sugar) is also grown as crystals on strings from a hot, thick sugar syrup as it cools and becomes supersaturated (sucrose: 201.9 g dissolves at 20 °C, 476 g at 100 °C).

Problems (§14), safety and the model

In a saturated solution $ω = s / (100 + s)$ . In $m$ g of solution saturated at $t_{1}$ the salt is $m s_{1} / (100 + s_{1})$ and the water $100 m / (100 + s_{1})$ g. On cooling to $t_{2}$ , $x = m_{salt} - m_{water} s_{2} / 100$ g of crystals separate for an anhydrous salt. A crystalline hydrate ( $CuSO_{4} \cdot 5 H_{2} O$ ) carries water away with it: $(m_{salt} - k x) / (m_{water} - (1 - k) x) = s_{2} / 100$ , where $k = M (CuSO_{4}) / M (CuSO_{4} \cdot 5 H_{2} O)$ = 0.639. Safety: when NaOH dissolves, the solution gets very hot and may spatter — wear safety goggles; if alkali touches the skin, wash it off with plenty of water. Hold hot vessels with tongs; copper sulfate is poisonous — never taste any substance. Model: solubility is linearly interpolated between table points; the heat capacity of the solution in the calorimeter is taken as that of water and no heat is lost; the times of dissolving, crystallisation, heating and cooling and gas release are shortened; the 50–58 °C part of the sodium acetate curve is interpolated and the heat capacity of the flask is approximate; for gases, the Henry constants (Sander) and the van 't Hoff relation are used; the colours of the colloid, suspension and emulsion are illustrative.

Did you know?

Reusable hand warmers contain a supersaturated solution of sodium acetate: bending the metal disc sets off crystallisation, and the heat released warms the hand. If the warmer is heated in boiling water until the crystals dissolve and then cooled slowly, it can be used again.
The proportionality of the solubility of gases to pressure was established in 1803 by the English chemist William Henry. If a diver rises quickly from depth, the nitrogen dissolved in greater amounts in the blood can form bubbles and lead to decompression sickness.

Inside the experiment

The experiment starts from a real-life situation: you predict the result, change the controls, run the experiment and draw a conclusion. Inside are missions, theory, a quiz and a guided tour in which the camera moves and explains the key points.

More experiments in this section

Acids and metals — Grade 7
Acids, bases and indicators — Grade 7
Water purification and softening — Grade 7
Electrolytic dissociation — Grade 9
Hydrolysis of salts and the medium — Grade 9
Concentration of a solution — Grade 11
Raoult's law, distillation and osmosis — Year 1