Introduction to the particulate nature of matter

📚The chemistry

Elements, compounds and mixtures

An element is a substance that cannot be chemically broken down into anything simpler; there are about 118 of them and they are what the periodic table lists. A compound contains atoms of different elements chemically bonded in a fixed ratio. A mixture contains more than one element or compound in no fixed ratio, not chemically bonded, and therefore separable by physical means.

Three consequences follow, and questions test all three:

• A compound’s properties bear no necessary relation to those of its elements. Sodium is a metal that explodes in water; chlorine is a poisonous green gas; sodium chloride is table salt. A mixture, by contrast, keeps the properties of its components — iron filings mixed with sulfur are still magnetic.
• A compound has a fixed composition by mass. Water is 11.2% hydrogen whether it came from a tap or a comet. A mixture can be any proportion you like.
• Separating a compound requires a chemical change (electrolysis, thermal decomposition); separating a mixture requires only a physical one.

Mixtures are homogeneous if the composition is uniform throughout and there is a single phase — salt water, air, an alloy, a solution of ethanol in water. They are heterogeneous if the composition varies and separate phases are visible — sand in water, oil and water, granite.

Choosing a separation technique

Every separation technique exploits a difference in a physical property. Naming the property is what earns the mark; naming the technique alone rarely does.

• Solvation (dissolving) — difference in solubility in a chosen solvent. Add water to a salt/sand mixture and only the salt dissolves.
• Filtration — difference in particle size, separating an insoluble solid from a liquid. The solid caught in the paper is the residue; the liquid that passes is the filtrate.
• Evaporation — recovers a dissolved solid by removing the solvent. Only works if you want the solid and the solid is thermally stable.
• Distillation — difference in boiling point. Simple distillation recovers a solvent from a solution; fractional distillation separates two liquids whose boiling points differ, using a fractionating column so that the mixture repeatedly condenses and re-evaporates up its length.
• Recrystallization — difference in how solubility varies with temperature. Dissolve the impure solid in the minimum volume of hot solvent, then cool: the product crystallises out while the impurities, present in much smaller amounts, stay in solution. This is the standard purification step in any organic preparation, and the purity of what you get is judged by a sharp melting point.
• Paper chromatography — difference in relative attraction to a mobile and a stationary phase. Treated fully in S2.2, because the attractions involved are intermolecular forces.

The kinetic molecular theory

The kinetic molecular theory is a model: matter consists of particles in constant motion, and the state of a substance is decided by the balance between the kinetic energy of those particles and the forces of attraction between them.

• Solid (s) — particles closely packed in a fixed arrangement, vibrating about fixed positions. Fixed shape, fixed volume, essentially incompressible.
• Liquid (l) — particles still close together but free to move past one another. Fixed volume, takes the shape of the container, very slightly compressible.
• Gas (g) — particles far apart, moving rapidly and randomly, with negligible attraction between them. No fixed shape or volume, highly compressible.

The fourth state symbol, (aq), is not a state of matter at all: it means dissolved in water. Getting state symbols right matters more than it looks — whether a species is (aq) or (s) decides whether it appears in an equilibrium expression (R2.3) and whether it can conduct electricity (S2.1).

The six changes of state

Evaporation and boiling are not the same thing. Evaporation happens at any temperature, only at the surface, and only for those particles in the high-energy tail of the distribution that have enough energy to escape the attractions holding them in the liquid — which is why evaporation cools what is left behind. Boiling happens at one specific temperature, throughout the bulk of the liquid, when its vapour pressure equals the external pressure.

Heating curves and the temperature plateaus

Heat a pure solid steadily and plot temperature against time. The graph rises, then holds flat at the melting point, rises again, holds flat at the boiling point, then rises. The flat sections are the part that gets examined:

During a change of state the energy supplied does not raise the temperature, because it is being used to overcome the forces of attraction between particles rather than to increase their average kinetic energy. Since temperature measures average kinetic energy, the temperature cannot change while the potential energy is changing. The plateau at boiling is longer than the plateau at melting, because separating particles completely takes far more energy than merely freeing them to move past each other.

Temperature and the Kelvin scale

Temperature, in kelvin, is a measure of the average kinetic energy of the particles in a sample. Not the total energy, and not the energy of any individual particle — at any instant the particles have a wide spread of speeds (see the Maxwell–Boltzmann distribution in R2.2).

The kelvin is the SI unit and has the same size increment as the degree Celsius, so the conversion is an offset with no scaling:

Zero kelvin, absolute zero, is the temperature at which particles would have minimum kinetic energy. Because the Kelvin scale starts there, kelvin temperatures are proportional to average kinetic energy: doubling the kelvin temperature doubles the average kinetic energy, which is untrue of Celsius. That is exactly why every gas equation in S1.5 demands kelvin.