S1.1 Introduction to the particulate nature of matter

Chemistry explains the properties of materials in terms of the particles they are made of. Ice, liquid water and steam contain the same molecules, ${{\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{O}}}$, yet one is hard, one flows and one fills any container; the difference lies only in how those molecules are arranged and how fast they move. The particle model also explains how mixtures such as seawater and crude oil can be separated into pure substances.

Elements, compounds and mixtures

The particles that make up matter are atoms, molecules and ions. An atom is the smallest particle of an element that can take part in a chemical reaction. A molecule is a group of two or more atoms held together by covalent bonds, such as ${{\mathrm{O}{\vphantom{X}}_{\smash[t]{2}}}}$ or ${{\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{O}}}$

About 118 elements are known, 94 of which occur naturally; they are listed in the periodic table. The particles of an element may be separate atoms, as in helium, ${{\mathrm{He}}}$, and the other noble gases, or molecules, as in oxygen, ${{\mathrm{O}{\vphantom{X}}_{\smash[t]{2}}}}$, nitrogen, ${{\mathrm{N}{\vphantom{X}}_{\smash[t]{2}}}}$

Compounds

Water is a compound: every water molecule contains two hydrogen atoms bonded to one oxygen atom, so the ratio of hydrogen to oxygen atoms is always 2 : 1, wherever the water comes from. This fixed ratio means that a compound has a fixed composition by mass; any sample of pure water is 11.2% hydrogen and 88.8% oxygen by mass. The formula of a compound, such as ${{\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{O}}}$, ${{\mathrm{CO}{\vphantom{X}}_{\smash[t]{2}}}}$

A compound has properties that are completely different from those of the elements it is made from. Sodium is a soft, silvery metal that reacts violently with water, and chlorine is a toxic, pale green gas. Sodium chloride, ${{\mathrm{NaCl}}}$, formed when they react, is a white crystalline solid that is safe to eat in small amounts. Forming a compound is a chemical change: new bonds form, a new substance is made and energy is usually released or absorbed.

Because the atoms in a compound are chemically bonded, the compound can be broken down into its elements only by a chemical reaction, for example by electrolysis or by heating strongly. Passing an electric current through acidified water decomposes it into hydrogen and oxygen gases in a 2 : 1 ratio by volume.

Mixtures

Air is a mixture of mainly nitrogen and oxygen, with smaller amounts of argon, carbon dioxide and water vapour. Its composition varies: the air in a crowded room contains more carbon dioxide and water vapour than air over the ocean. In a mixture each component keeps its own properties, because its particles are unchanged. The oxygen in air supports burning exactly as pure oxygen does, only more slowly because it is diluted.

Iron and sulfur show the difference between a mixture and a compound clearly. Iron filings stirred with yellow sulfur powder form a mixture in any proportion; a magnet pulls the iron out, and the sulfur dissolves in a suitable solvent while the iron does not. When the mixture is heated, the elements react to form iron(II) sulfide, a black solid with properties of its own: it is not attracted by a magnet and the iron and sulfur can no longer be separated physically.

Elements and compounds are both pure substances: a pure substance contains only one kind of particle and has a fixed composition. A pure substance melts and boils at sharp, fixed temperatures, and these temperatures are the same for every pure sample. A mixture usually melts and boils over a range of temperatures, and its melting point is lower than that of the pure main component. Measuring a melting point is therefore a simple test of purity: a sharp melting point that matches the literature value shows that a solid is pure.

Particle diagrams show the difference at the level of the particles. In each diagram of five samples, every circle is an atom and circles that touch are bonded.

Homogeneous and heterogeneous mixtures

A phase is a region of a sample with uniform composition and properties, separated from other regions by a boundary. A homogeneous mixture has only one phase. A solution of salt in water is homogeneous: the dissolved ions are spread evenly among the water molecules, and every drop has the same concentration. Air, vinegar (ethanoic acid in water) and the alloy brass (copper and zinc) are homogeneous too. The particle diagrams compare a solution with oil floating on water.

A heterogeneous mixture has two or more phases. Sand in water, oil and water, granite (visible crystals of different minerals) and smoke (solid particles in air) are all heterogeneous. Whether a mixture is homogeneous often depends on the forces between the particles of its components. Ethanol and water mix completely in any proportion because their molecules attract each other strongly through hydrogen bonds, so they are miscible. Oil and water are immiscible: water molecules attract each other much more strongly than they attract the non-polar oil molecules, so the liquids form two layers. Intermolecular forces are developed fully with covalent bonding.

Alloys show why the distinction between compounds and mixtures rests on composition. An alloy such as brass or steel contains metallic bonding throughout, yet its composition can vary continuously, for example from about 60% to 90% copper in brasses, and each metal keeps its own atoms. Alloys are therefore classed as homogeneous mixtures rather than compounds; their structure is described with the metallic model.

Separating mixtures

Because the components of a mixture are not chemically bonded, they can be separated by physical methods. Every separation technique relies on a difference in one physical property of the components: particle size, solubility, boiling point or the strength of attraction to a surface. Choosing a method starts with identifying which property differs most.

Solvation and filtration

A solution consists of a solute (the substance dissolved) and a solvent (the substance it dissolves in). A solution in water is an aqueous solution. Solvation can separate a mixture when one component dissolves in the chosen solvent and the other does not. Salt dissolves in water but sand does not, so stirring rock salt with warm water puts the sodium chloride into solution and leaves the sand as a solid. Other solvents work for other mixtures: sulfur dissolves in methylbenzene but iron does not.

Filtration then separates the insoluble solid from the liquid. The mixture is poured into a funnel lined with filter paper, whose tiny pores let water molecules and dissolved ions through but hold back solid particles. The solid left on the paper is the residue; the liquid that passes through is the filtrate. The residue is washed with a little clean solvent to remove any solution clinging to it, then dried.

Evaporation and crystallization

Heating a solution in an evaporating basin turns the solvent into vapour and leaves the dissolved solid behind. This works because the solvent is volatile (it vaporizes easily) and the solute is not. Evaporating to dryness gives the solid quickly but may decompose it, and any soluble impurities are left in the solid as well.

To obtain well-formed crystals, a solution is evaporated only until it is saturated, the point at which a drop placed on a cold glass rod forms crystals. The solution is then left to cool, and crystals form slowly as the solubility falls. This is crystallization. Copper(II) sulfate crystals are made this way: excess copper(II) oxide is stirred into warm dilute sulfuric acid, the unreacted oxide is filtered off, and the blue filtrate is concentrated and left to crystallize, giving blue crystals of ${{\mathrm{CuSO}{\vphantom{X}}_{\smash[t]{4}}\,{\cdot}\,5\,\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{O}}}$

Recrystallization

The solid product of a reaction is rarely pure: it contains small amounts of unreacted starting materials and by-products. Recrystallization purifies such a solid. It uses a solvent in which the compound is very soluble when hot but much less soluble when cold. Benzoic acid is a typical example: about 5.6 g dissolves in $100\ \text{cm}^3$ of water near $100\ ^\circ\text{C}$, but only about 0.34 g at $25\ ^\circ\text{C}$

1. The impure solid is dissolved in the minimum volume of hot solvent, so that the solution is saturated when hot and as much product as possible crystallizes on cooling.

2. The hot solution is filtered, if necessary, to remove insoluble impurities.

3. The solution is cooled slowly. As the solubility falls, the compound crystallizes. The impurities are present in such small amounts that their solutions do not become saturated, so they stay dissolved.

4. The crystals are collected by filtration, washed with a small amount of cold solvent and dried.

5. The purity is checked by measuring the melting point.

Some product is always lost, because a little remains dissolved even in cold solvent. Using too much hot solvent increases this loss, which is why the minimum volume is used. Slow cooling gives larger, purer crystals, because fast crystallization can trap solution, and with it impurities, inside the crystals.

Simple distillation

Simple distillation separates a solvent from dissolved solids, such as pure water from salt water, or two liquids whose boiling points differ by a large amount (roughly 25 °C or more). The mixture is heated in a flask; the more volatile component boils and its vapour passes into a water-cooled condenser, where it condenses and runs into a collecting flask. The non-volatile solute stays behind in the flask. The apparatus for simple distillation shows the arrangement.

Several details of the apparatus matter. The thermometer bulb sits level with the side arm, so it measures the temperature of the vapour that is leaving, which equals the boiling point of the liquid being collected. Cooling water enters the condenser at the lower end and leaves at the upper end, so the jacket stays completely full of cold water. Anti-bumping granules in the flask give small bubbles and smooth boiling, and the apparatus is open at the receiving end so that pressure cannot build up.

Fractional distillation

Ethanol (boiling point $78\ ^\circ\text{C}$) and water ($100\ ^\circ\text{C}$) are miscible, and simple distillation of their mixture gives a distillate that still contains a lot of water. In fractional distillation a vertical column packed with glass beads or rings is fitted between the flask and the condenser. The vapour rising from the boiling mixture is richer in ethanol, the more volatile component. On the cooler beads it condenses, and the liquid formed is reheated by more vapour rising from below and evaporates again. Each time this happens the vapour becomes richer in ethanol.

The column is hottest at the bottom and coolest at the top, so the less volatile water condenses and runs back into the flask, while vapour rich in ethanol reaches the top. Ethanol and water cannot be separated completely this way: the best distillate is about 96% ethanol by mass, because a mixture of that composition boils at a constant temperature, just below the boiling point of pure ethanol. The thermometer reads about $78\ ^\circ\text{C}$ while ethanol distils; when the temperature starts to rise, the ethanol has been removed and the collecting flask is changed. The same principle, on an industrial scale, separates crude oil into fractions such as petrol, kerosene and diesel, which are mixtures of hydrocarbons with similar boiling points.

Case study: desalination of seawater

Seawater contains about 35 g of dissolved salts, mainly sodium chloride, in every kilogram. In dry regions with little fresh water, such as the Middle East and North Africa, drinking water is produced from seawater on a huge scale. A 2019 survey counted about 16 000 operating desalination plants worldwide, producing about 95 million cubic metres of fresh water per day, almost half of it in the Middle East and North Africa.

The older plants use thermal desalination, which is distillation. In multi-stage flash distillation, heated seawater flows through a series of chambers at successively lower pressures. Because the boiling point of water falls as the pressure falls, part of the water boils ("flashes") in each chamber, and the vapour condenses on tubes carrying cold incoming seawater, which pre-heats it. The salts are non-volatile, so the condensed water is almost pure. The method is reliable but uses a great deal of energy, because water must absorb a large amount of energy to vaporize.

Most new plants use reverse osmosis. Seawater is pumped at high pressure against a membrane whose pores let water molecules through but hold back the hydrated salt ions. No change of state is involved, so the energy needed is much smaller; by 2019 reverse osmosis produced about 69% of the world's desalinated water. Both methods produce a concentrated salty waste, brine, which is returned to the sea and can harm marine life near the outlet. Desalination illustrates how the choice of separation method depends on cost and energy as well as on the property that differs between the components.

Chromatography

In paper chromatography the stationary phase is the water held in the fibres of the paper and the mobile phase is a solvent that rises up the paper by capillary action. Small spots of each sample are placed on a baseline drawn in pencil (ink would itself dissolve and separate), and the bottom edge of the paper is dipped in solvent below the baseline. As the solvent moves up, each component is carried along at its own rate. A component that is more strongly attracted to the mobile phase, or more soluble in it, travels further; one that is more strongly attracted to the stationary phase lags behind.

The chromatogram of three food colourings and the colouring from a green sweet shows how the technique identifies the components of a mixture. Each pure dye gives a single spot. The green colouring gives two spots, at exactly the same heights as the blue and yellow dyes, so it is a mixture of those two dyes.

The position of a spot is described by its retardation factor, $R_\text{F}$, the distance moved by the spot divided by the distance moved by the solvent front, both measured from the baseline. Under the same conditions a given substance always has the same $R_\text{F}$ value, which is always less than 1. In thin-layer chromatography (TLC) the stationary phase is a thin layer of silica or alumina on a glass or plastic plate; it is faster and gives sharper spots. Gas chromatography and high-performance liquid chromatography use the same principle with instruments. The link between $R_\text{F}$

Choosing a separation method

A separation method is chosen by asking which physical property differs between the components and what is to be kept. If a solid product is wanted from a reaction mixture, it is separated from the liquid by filtration, purified by recrystallization and its purity checked by melting point. If the product is a liquid, it is separated by distillation and its purity checked by its boiling point. Many separations need several techniques in sequence, as with rock salt.

The kinetic molecular theory

The kinetic molecular theory is a model that explains the physical properties of solids, liquids and gases, and the changes between them, in terms of the behaviour of particles. Its main statements are:

• All matter is made of very small particles (atoms, molecules or ions).

• The particles are in constant, random motion. In a solid they vibrate about fixed positions; in liquids and gases they also move from place to place.

• There are forces of attraction between the particles. The closer the particles are, the stronger the attractions between them.

• The particles have kinetic energy because they move. The higher the temperature, the faster they move on average.

• Collisions between particles, and between particles and the walls of a container, are elastic: the total kinetic energy of the colliding particles is unchanged.

The three states of matter differ in how closely the particles are packed, how they are arranged, how strongly they attract each other and how they move. The particle diagrams of a solid, a liquid and a gas show these differences.

The properties in the table follow from the model. A solid keeps its shape because its particles cannot leave their positions in the lattice. A liquid flows because its particles can slide past one another, but it is almost incompressible because the particles are already touching. A gas is easily compressed because about 99.9% of its volume is empty space; the pressure of a gas comes from the collisions of its particles with the walls of the container, an idea developed with the ideal gas model.

Water is an unusual exception to the density pattern: ice is less dense than liquid water, so it floats. The hydrogen bonds between water molecules hold them in an open arrangement in the solid, which collapses partly when the ice melts.

Evidence for moving particles

The particles themselves are far too small to see, but their motion has visible effects. Diffusion is the net movement of particles from a region of higher concentration to a region of lower concentration, caused by their random motion. A crystal of purple potassium manganate(VII) dropped into still water slowly colours the whole beaker without stirring, and a few drops of brown liquid bromine placed in a gas jar fill it with brown vapour within minutes. Diffusion is much faster in gases than in liquids, because gas particles move faster and are further apart, so they travel further between collisions.

Brownian motion gives more direct evidence. Under a microscope, smoke particles in air, or pollen grains in water, jiggle about randomly. They are being struck unevenly from all sides by the invisible, fast-moving molecules of the air or water around them.

Changes of state

A change of state is a physical change: the particles are the same before and after, only their arrangement, spacing and motion change. The six changes of state form three pairs of opposites.

Why some changes absorb energy and others release it

To melt, vaporize or sublime, the particles must move further apart, which means overcoming some or all of the attractions between them. Overcoming an attraction requires energy, so these changes absorb energy from the surroundings: they are endothermic. When particles come closer together in freezing, condensation or deposition, new attractions form between them and energy is released to the surroundings: these changes are exothermic. The energy absorbed when a substance melts is exactly equal to the energy released when the same amount freezes.

These energy changes have everyday consequences. Steam at $100\ ^\circ\text{C}$ causes worse burns than water at $100\ ^\circ\text{C}$, because the steam releases a large amount of energy as it condenses on the skin before it starts to cool. Fruit growers spray water on crops on frosty nights: as the water freezes it releases energy, which keeps the plant tissue at about $0\ ^\circ\text{C}$

What is overcome depends on the structure of the substance. When a molecular substance such as water or iodine melts or boils, only the forces between molecules (intermolecular forces) are overcome; the covalent bonds inside the molecules are not broken. Boiling water produces gaseous ${{\mathrm{H}{\vphantom{X}}_{\smash[t]{2}}\mathrm{O}}}$ molecules, not hydrogen and oxygen. In a giant structure such as diamond or sodium chloride, melting or subliming means breaking the strong covalent or ionic bonds that hold the whole structure together, which is why such substances melt at much higher temperatures.

Evaporation and boiling

Evaporation and boiling are both kinds of vaporization, but they differ. Even below the boiling point, some particles in a liquid have more kinetic energy than average. If one of these fast particles is at the surface and moving outwards, it can escape the attractions of its neighbours and enter the gas phase. This is evaporation. It happens at any temperature, only at the surface, and more quickly when the liquid is warmer, has a larger surface area or has a draught over it.

Because the most energetic particles leave, the average kinetic energy of the particles left behind falls, and the liquid cools. Sweating cools the body in this way, and a drop of ethanol feels cold on the skin because it evaporates quickly.

Boiling happens at one particular temperature, the boiling point, when bubbles of vapour form throughout the liquid, not just at its surface. Bubbles can form only when the pressure of the vapour inside them is high enough to push back the pressure of the atmosphere above the liquid. The boiling point therefore depends on the external pressure. At the summit of Mount Everest, where atmospheric pressure is about a third of that at sea level, water boils at only about $70\ ^\circ\text{C}$; in a pressure cooker the higher pressure raises the boiling point to about $120\ ^\circ\text{C}$, so food cooks faster. Boiling points listed in data tables are measured at standard atmospheric pressure, $101.325\ \text{kPa}$

Sublimation and deposition

Some solids turn straight into gas without melting at atmospheric pressure. Solid carbon dioxide, "dry ice", sublimes at $-78.5\ ^\circ\text{C}$, which is why it leaves no liquid behind and is used to keep food and medical samples cold during transport. Iodine is a shiny grey-black solid that gives off violet vapour when warmed gently; the vapour turns straight back into crystals on a cold surface. The reverse change, gas to solid, is deposition. Frost forms by deposition when water vapour in the air meets surfaces colder than $0\ ^\circ\text{C}$.

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State symbols

Chemical equations show the state of each substance with a state symbol in brackets after its formula:

• (s) solid

• (l) liquid, including a pure substance that has been melted, such as molten sodium chloride, ${{\mathrm{NaCl}\mskip2mu (\mathrm{l})}}$

• (g) gas

• (aq) aqueous: dissolved in water

The symbol (aq) is used only for a substance dissolved in water. Ethanol is a liquid, ${{\mathrm{C}{\vphantom{X}}_{\smash[t]{2}}\mathrm{H}{\vphantom{X}}_{\smash[t]{5}}\mathrm{OH}\mskip2mu (\mathrm{l})}}$

Temperature and the kinetic energy of particles

The particles in a sample do not all move at the same speed: collisions constantly speed some up and slow others down, so at any instant there is a spread of kinetic energies. Temperature is a measure of the average kinetic energy of the particles. When a substance is heated and its temperature rises, its particles move faster on average.

Two important consequences follow. First, at the same temperature the particles of all substances have the same average kinetic energy, whether they are in a solid, a liquid or a gas, and whatever their mass. Second, because kinetic energy depends on both mass and speed ($E_\text{k} = \tfrac{1}{2}mv^2$

The diffusion of ammonia and hydrogen chloride shows this. Cotton wool soaked in concentrated ammonia solution is placed at one end of a long glass tube and cotton wool soaked in concentrated hydrochloric acid at the other. Ammonia and hydrogen chloride gases diffuse along the tube, and where they meet they react to form a white ring of solid ammonium chloride.

The ring forms nearer the hydrochloric acid end. Both gases are at the same temperature, so their molecules have the same average kinetic energy; ammonia molecules ($M_\text{r} = 17.04$) are lighter than hydrogen chloride molecules ($M_\text{r} = 36.46$), so they move faster and cover a greater distance in the same time. The spread of kinetic energies at a given temperature is shown by the Maxwell–Boltzmann distribution, which explains how temperature affects the rate of reactions.

The Kelvin scale

On the Celsius scale, $0\ ^\circ\text{C}$ is the melting point of ice and $100\ ^\circ\text{C}$ is the boiling point of water at standard atmospheric pressure. These reference points are convenient, but they have nothing to do with the energy of the particles, so negative Celsius temperatures are common. The Kelvin scale is the absolute temperature scale and the SI scale of temperature. Its zero, absolute zero ($0\ \text{K} = -273.15\ ^\circ\text{C}$

The kelvin has the same size as the Celsius degree, so the two scales differ only in where they start. Converting between them means adding or subtracting 273.15 (usually rounded to 273):

Because the degrees are the same size, a temperature change has the same value in both units: a rise from $20\ ^\circ\text{C}$ to $35\ ^\circ\text{C}$ is a rise of $15\ \text{K}$. Temperatures in kelvin are written without a degree sign ($298\ \text{K}$

Heating and cooling curves

A heating curve is a graph of temperature against time for a substance heated at a constant rate. The heating curve of water, starting from ice at $-20\ ^\circ\text{C}$, has five parts: three sloping parts, where one state is being heated, and two flat parts, or plateaus, where the substance is changing state.

The sloping parts

While the ice is warming from $-20\ ^\circ\text{C}$ to $0\ ^\circ\text{C}$, the energy supplied makes the water molecules vibrate faster about their positions: their average kinetic energy increases, so the temperature rises. The same happens to the liquid between $0\ ^\circ\text{C}$

The plateaus

At $0\ ^\circ\text{C}$ the temperature stops rising even though energy is still being supplied. All of this energy is used to overcome the attractions holding the molecules in the solid arrangement, so it increases the potential energy of the particles, not their kinetic energy. Because the average kinetic energy does not change, the temperature stays constant until all the ice has melted. The two states, solid and liquid, are present together throughout the plateau. The plateau at $100\ ^\circ\text{C}$ is explained in the same way: energy is used to separate the molecules completely as the water boils.

The boiling plateau is much longer than the melting plateau. Melting only loosens the arrangement of the particles, which stay close together, whereas boiling separates them completely, overcoming nearly all the attractions between them. For water, about 6.0 kJ is needed to melt one mole of ice at $0\ ^\circ\text{C}$, but about 41 kJ to boil one mole of water at $100\ ^\circ\text{C}$, almost seven times as much.

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Cooling curves and purity

A cooling curve shows the same changes in reverse. A common experiment uses lauric acid (dodecanoic acid), which melts at about $44\ ^\circ\text{C}$. A boiling tube of solid lauric acid is melted in a beaker of hot water, then placed in a beaker of water at room temperature with a thermometer or temperature probe in the liquid. The temperature is recorded every 30 seconds, ideally with a data logger, while the acid is stirred gently until it sets.

As the liquid cools, its temperature falls until it reaches the freezing point. The temperature then stays constant while the liquid solidifies, because the attractions forming between the particles release energy that balances the energy lost to the surroundings. Once all the acid is solid, the temperature falls again. The freezing point read from the plateau of a pure substance is the same as its melting point.

An impure sample behaves differently: it starts to freeze at a lower temperature and its temperature keeps falling slowly as it solidifies, so there is no sharp plateau. This is the basis of using melting points to judge purity. The main sources of error in the experiment are energy lost or gained through the walls of the tube, uneven temperature in an unstirred sample, and the response time of the thermometer.

Applying the ideas in exam questions

Paper 1A: an equation for a change of state

Paper 1A: properties of mixtures

Paper 1A: temperature and kinetic energy

Paper 1B: the cooling curve of stearic acid

A student melted a sample of stearic acid (octadecanoic acid) and recorded its temperature every minute as it cooled in air. Thermometer uncertainty: $\pm 0.5\ ^\circ\text{C}$.

Paper 2: purifying a solid product

Paper 2: the heating curve of a substance

Self-check

• To do:

  I can define element, compound and mixture, and give an example of each.

• To do:

  I can distinguish between the properties of elements, compounds and mixtures, including how each can be separated or decomposed.

• To do:

  I can explain why a pure substance has a sharp melting point and a mixture melts over a range.

• To do:

  I can classify particle diagrams as elements, compounds or mixtures.

• To do:

  I can distinguish homogeneous from heterogeneous mixtures and give examples of each.

• To do:

  I can state what solvation, filtration, evaporation, recrystallization, distillation, fractional distillation and chromatography separate and the property each relies on.

• To do:

  I can describe the steps of recrystallization and give the reason for each.

• To do:

  I can describe and explain the apparatus for simple and fractional distillation.

• To do:

  I can choose and justify a method to separate a mixture or purify the product of a reaction.

• To do:

  I can state the main ideas of the kinetic molecular theory and use them to explain the properties of solids, liquids and gases.

• To do:

  I can name all six changes of state and say whether each is endothermic or exothermic.

• To do:

  I can distinguish evaporation from boiling and explain why boiling point depends on pressure.