Chapter 1 โ Solutions
Dissolve something in water and the water changes: its vapour pressure drops, it boils hotter, freezes colder and pulls water through membranes. All of this depends on how many solute particles there are.
In winter, road crews in cold countries spread salt on icy roads, and the ice melts even though the air is below $0\ ^{\circ}\mathrm{C}$. In a hospital, a red blood cell placed in pure water swells and bursts, while in $0.9\%$ saline it keeps its shape. A car radiator filled with a waterโglycol mixture neither freezes in a Himalayan winter nor boils over in a Rajasthan summer. A desalination plant pushes seawater through a membrane at high pressure and fresh water comes out the other side. These four effects look unrelated. In fact one idea explains them all: a dissolved solute changes the behaviour of the solvent around it.
To make that idea quantitative we first need a precise language for "how much is dissolved" (concentration) and for how much can dissolve (solubility). Then we look at the vapour above a solution. Raoult's law says each volatile component contributes to the vapour pressure in proportion to its mole fraction. Lowering the solvent's vapour pressure leads straight to the colligative properties: boiling-point elevation, freezing-point depression and osmotic pressure. These depend on the number of solute particles, not on what they are. That makes them a tool for measuring molar masses, and for spotting solutes that split into ions or pair up.
| Question | Key relation | Section |
|---|---|---|
| How much solute, in which unit? | $x_{2}=\dfrac{n_{2}}{n_{1}+n_{2}}$, $\ m=\dfrac{n_{2}}{\text{kg solvent}}$ | 1.1 |
| How much gas dissolves? | $p=K_{H}\,x$ | 1.1 |
| What is the vapour pressure above a solution? | $p_{i}=x_{i}\,p_{i}^{\circ}$ | 1.2 |
| How far do the boiling and freezing points move? | $\Delta T_{b}=K_{b}\,m$, $\ \Delta T_{f}=K_{f}\,m$ | 1.3 |
| What pressure stops osmosis? | $\pi=CRT$ | 1.3 |
- express the concentration of a solution as mass %, volume %, w/v %, ppm, mole fraction, molarity or molality, and convert between them using the density;
- explain how temperature and pressure affect solubility, and use Henry's law for gases (fizzy drinks, scuba diving, high altitude);
- use Raoult's law to find the total vapour pressure and the vapour composition of a liquid mixture, and the vapour-pressure lowering caused by a non-volatile solute;
- tell ideal from non-ideal solutions by their deviations, $\Delta_{mix}H$ and $\Delta_{mix}V$, and recognise minimum- and maximum-boiling azeotropes;
- calculate $\Delta T_{b}$, $\Delta T_{f}$ and $\pi$, use them to find molar masses, and correct for dissociation or association with the van 't Hoff factor $i$.
Sections in this chapter
Types of Solutions, Concentration and Solubility
Nine kinds of solution, seven concentration units and their conversions, solubility of solids and gases, and Henry's law.
Vapour Pressure, Raoult's Law and Non-ideal Solutions
Vapour above liquid mixtures, ideal and non-ideal behaviour, and azeotropes.
Colligative Properties and Abnormal Molar Masses
Boiling-point elevation, freezing-point depression, osmosis and the van 't Hoff factor.