Types of solutions

What makes a mixture a "solution." A solution is a homogeneous mixture — uniform in composition and properties throughout, down to the molecular scale — of two or more chemically non-reacting substances. "Homogeneous" is the key word: unlike a suspension or a colloid, you cannot see separate phases even under a microscope, and the composition can be varied continuously within limits without the mixture separating out. The component present in the larger amount is conventionally the solvent; the component(s) in smaller amount are the solute(s). A solution built from exactly two components is a binary solution, the type this whole chapter deals with.

Classification by physical state. Since matter exists in three states — solid, liquid, gas — a solute and a solvent can in principle combine in nine ways. Not all nine are common, but the syllabus expects you to recognise the standard set: gas-in-gas (air), gas-in-liquid ($CO_2$ in soda water), liquid-in-liquid (ethanol in water), solid-in-liquid (sugar in water), solid-in-solid (alloys such as brass), gas-in-solid ($H_2$ adsorbed in palladium), and liquid-in-solid (mercury in amalgams). The figure below lays these out against the two axes of solute state and solvent state.

Focus of the chapter. Almost every equation you will meet later in the Solutions chapter concerns a liquid solvent, further split by the state of the solute: gas in liquid is governed by Henry's law (dissolved oxygen, carbonated drinks); liquid in liquid is governed by Raoult's law and may be ideal or show positive or negative deviation, sometimes forming an azeotrope; solid in liquid is the setting for the four colligative properties — relative lowering of vapour pressure, boiling-point elevation, freezing-point depression and osmotic pressure — most often with a non-volatile solid dissolved in a volatile liquid.

Volatile vs non-volatile. A volatile solute has an appreciable vapour pressure of its own and contributes to the total vapour pressure above the solution — this matters for Raoult's law in liquid-liquid mixtures, where both components evaporate. A non-volatile solute has essentially zero vapour pressure; it only lowers the solvent's vapour pressure without adding any of its own, which is exactly the assumption behind all four colligative-property formulae.

Dilute/concentrated vs saturated/unsaturated. These are two independent axes, not synonyms. Dilute and concentrated describe how much solute is present relative to solvent — a purely quantitative comparison. Saturated and unsaturated describe whether the solution has reached its solubility limit at that temperature: a saturated solution holds the maximum solute that can dissolve (in equilibrium with any undissolved excess), while an unsaturated one can still dissolve more. A solution can be concentrated yet still unsaturated, and a dilute solution of a very insoluble substance can already be saturated. Most colligative-property equations assume dilute solutions, where solute-solute interactions are negligible.

This topic has no single formula to derive — it is a classification scheme, and the reasoning worth internalising is why the chapter draws its boundaries where it does, so that later formulae attach to the right kind of mixture without you having to re-derive the logic each time. The state-based classification exists because the physics that governs a mixture depends on the physical states involved, not on some arbitrary label. A gas dissolving in a liquid is controlled by how strongly gas molecules are attracted into the liquid phase against the pressure pushing them out — the territory of Henry's law. Two liquids mixing is controlled by how the escaping tendency (vapour pressure) of each liquid changes as it is diluted by the other — the territory of Raoult's law. A solid dissolving in a liquid, when the solid itself does not evaporate, is controlled by how the solute particles disrupt the solvent's own escaping tendency and phase-change temperatures — the territory of colligative properties. Sorting solutions by physical state is therefore not bookkeeping; it is sorting them by which physical law applies. The volatile/non-volatile distinction follows the same logic one level down. Colligative-property formulae (relative lowering of vapour pressure, $\Delta T_b$, $\Delta T_f$, osmotic pressure $\Pi$) are all derived on the assumption that only the solvent escapes into the vapour phase — if the solute also evaporates, those formulae simply do not apply, and you would need the two-volatile-component version of Raoult's law instead. Recognising volatility up front tells you, before any calculation, which family of equations is even in play. Finally, dilute/concentrated and saturated/unsaturated are kept separate because they answer different questions: "how much solute is here" versus "could more solute still dissolve." Confusing them leads to real errors later — for instance, assuming a concentrated solution must be near saturation, when solubility limits depend on the solute-solvent pair, not on how much you happen to have added.

A student is asked to design an experiment to find the molar mass of an unknown protein using a colligative-property method, given that the solution is solid protein dissolved in water and is extremely dilute. Which colligative property should they choose, and why?

Step 1. Classify the solution first, since the chapter's logic (above) says the physics depends on this. Protein in water is a solid dissolved in a liquid, and protein has no meaningful vapour pressure of its own, so it is a non-volatile solid-in-liquid solution — exactly the setting where all four colligative properties are candidates.

Step 2. Note the practical constraint: proteins have very large molar mass $M$. For a fixed, measurable mass of protein dissolved, the molar concentration $n_2/V$ (or molality $n_2/w_1$) is very small, because $n_2 = \text{mass}/M$ shrinks as $M$ grows.

Step 3. Check how each property scales with that small concentration. Freezing-point depression $\Delta T_f$ and boiling-point elevation $\Delta T_b$ are both directly proportional to molality; at protein-level dilution the resulting temperature changes are a small fraction of a degree — too small to read reliably off an ordinary thermometer.

Step 4. Compare with osmotic pressure, $\Pi = MRT$ (M here is molarity, not molar mass). Because $R$ and $T$ multiply even a tiny molarity into a workable, measurable pressure, $\Pi$ stays comfortably detectable at concentrations where $\Delta T_f$ and $\Delta T_b$ have become unreadable.

The osmotic-pressure method is the right choice. For high-molar-mass, dilute solutes such as proteins, $\Pi = MRT$ gives an easily measurable signal where the temperature-based colligative properties do not — which is exactly why osmotic pressure, not freezing-point depression, is the standard method for measuring protein and polymer molar masses in practice.

• Assuming "solution" always means a solid dissolved in a liquid — air (gas-in-gas) and alloys like brass (solid-in-solid) are solutions too, and both can appear in classification questions.
• Treating "dilute" and "unsaturated" as the same idea — a solution can be concentrated yet still unsaturated, or dilute yet already saturated if the solute is only sparingly soluble.
• Assuming every solute is non-volatile — liquid-liquid mixtures governed by Raoult's law (e.g. benzene-toluene, ethanol-water) typically have a volatile solute, which rules out the colligative-property formulae entirely.
• Forgetting that "solute" and "solvent" are labels of convenience — for the major and minor components — so in a near-50:50 mixture the assignment can be arbitrary or context-dependent, not a fixed chemical property.

Ask the tutor: want to practise classifying a batch of everyday mixtures by solute-solvent state and volatility before moving on to Henry's law and Raoult's law?