Chapter 5: States of Matter

Matter is anything that has mass and occupies space. Its particles can be arranged in different ways. These arrangements help explain its different physical states.

Particles move and attract one another. Temperature and pressure affect their arrangement. These factors help decide the state. Kinetic energy is energy of motion. At one temperature, some particles move faster than others.

A particle is not always a molecule. Depending on the substance, it may be an atom, a molecule or an ion.

A gas has many tiny particles. There are large spaces between them.

The particles keep moving in random directions. Between collisions, they move in straight lines.

Particles hit one another and the container walls. In an ideal gas, these collisions are elastic: the total kinetic energy stays the same during each collision.

The ideal-gas model treats particles as very small compared with the container. It ignores attractions between them except during collisions.

The average kinetic energy of straight-line particle motion depends only on temperature in kelvin. Higher kelvin temperature means higher average kinetic energy.

Moving particles hit the walls. Each hit transfers momentum and produces a force. The force on each unit of wall area gives gas pressure.

Real particles take up space and attract one another. The ideal-gas model works best at low pressure and high temperature, when the gas is not close to becoming liquid.

Diffusion is the net spreading of particles from higher concentration to lower concentration due to random motion, until the mixture becomes more uniform.

Effusion is the escape of gas through a tiny opening into a lower-pressure region, ideally with the opening smaller than the molecular mean free path.

A gas may escape through a tiny hole in a balloon or tyre.

Rate of effusion ∝ 1 / √(molar mass). Thus, rate₁ / rate₂ = √(M₂ / M₁). This simple relation is most accurate for ideal gases effusing through small openings.

Example: Hydrogen gas (M = 2) effuses four times as fast as oxygen gas (M = 32), since √(32/2) = √16 = 4.

Graham’s simple law works best for effusion through very small openings. Diffusion in air also depends on collisions and mixing, so this law alone may not predict its rate.

The average distance a gas molecule travels between successive collisions.

Pressure = force acting at right angles to a surface / area, or P = F/A. Its SI unit is pascal (Pa), where 1 Pa = 1 N/m².

A barometer measures atmospheric pressure.

A manometer compares gas pressure with a known pressure, often the pressure of the air.

Heating gas in a rigid container usually raises its pressure. The particles hit the walls harder and transfer more momentum.

Large gaps make a gas easy to squeeze into less space. Compression brings the same particles closer. At the same temperature, pressure increases.

Gas particles move freely, which allows gases to flow, expand and mix easily.

Density is mass divided by volume: ρ = m/V. Gas density is usually much lower than the density of a liquid or solid.

At the same pressure, heating a fixed amount of gas increases its volume. Its density falls because the same mass occupies more space. Cooling has the opposite effect.

Gas density depends on temperature and pressure. Check both conditions before comparing values.

For a fixed amount of gas at constant temperature, volume is inversely proportional to absolute pressure.

V ∝ 1/P → PV = constant → P₁V₁ = P₂V₂.

Write P₁, V₁, P₂ and V₂ with units.

Convert pressures to the same unit and volumes to the same unit.

Use P₁V₁ = P₂V₂, rearrange and substitute.

Check whether the answer makes physical sense.

For a fixed amount of gas at constant pressure, its volume is directly proportional to its absolute temperature.

V ∝ T → V/T = constant → V₁/T₁ = V₂/T₂. Always use temperature in kelvin.

T(K) = t(°C) + 273.15. For school-level mental calculations, +273 is a common approximation.

Absolute zero is 0 K, or −273.15 °C. Extending the ideal-gas graph reaches zero volume there. A real gas changes into liquid or solid before it can reach this predicted state.

Convert each Celsius temperature to kelvin before applying the formula.

Identify V₁, V₂, T₁ and T₂.

Rearrange V₁/T₁ = V₂/T₂ and substitute.

If the required answer is °C, convert back at the end.

For both laws, keep the amount of gas fixed. For Boyle’s law, also keep temperature fixed. For Charles’s law, keep pressure fixed.

Expansion alone does not tell us whether gas temperature rises or falls. It depends on how the gas expands and whether heat enters or leaves. Charles’s law applies when pressure stays fixed.

Gas-law ratios need kelvin temperature. Celsius starts from a different zero. Convert Celsius to kelvin before putting temperatures into the formula.

A liquid has nearly fixed volume but no fixed shape. It flows and takes the shape of the lower part of its container.

Liquid particles are close together. They can slide past one another.

Liquids are hard to squeeze into less space because their particles are already close.

Attractions hold liquid particles together. The particles are still free to change places.

Under similar conditions, particles usually spread more slowly through liquids than through gases.

A liquid flows because its particles can change places. It keeps nearly the same volume and usually has a surface. A gas spreads to fill all the space available.

Faster, higher-energy molecules are more likely to escape. The liquid left behind can have lower average kinetic energy and become cooler. Heat then flows in from the surroundings.

Examples: sweating cools the skin; wet clothes dry in air.

Higher temperature usually makes evaporation faster.

A larger exposed surface lets more molecules escape each second.

Moving air carries vapour away. More liquid can then evaporate.

Drier air usually allows faster evaporation. Humidity tells us how much water vapour is in the air.

Under similar conditions, weaker attractions let particles escape more easily.

Evaporation happens at the surface and can occur below the boiling point. Boiling makes vapour bubbles throughout the liquid. It begins when vapour pressure matches the pressure outside.

At first, some liquid particles escape into the space above the liquid.

Vapour builds up. More vapour particles then return to the liquid. This return is condensation.

Eventually, particles leave and return at equal rates. Both processes continue. This is dynamic equilibrium.

Higher temperature gives a higher equilibrium vapour pressure.

At the same temperature, stronger attractions usually give a lower vapour pressure.

Molecular size also affects attractions. Polarity alone cannot tell us how easily a liquid evaporates.

At 100 °C, water's equilibrium vapour pressure is 760 mmHg (1 atm), its normal boiling point. At 0 °C the saturation pressure over liquid water is about 4.6 mmHg.

At a fixed temperature, the equilibrium vapour pressure stays the same while some liquid remains. Adding more of that liquid does not raise the equilibrium vapour pressure.

The boiling point is the temperature at which vapour pressure becomes equal to external pressure. Vapour bubbles can then grow throughout the liquid.

Higher outside pressure raises the boiling point. This is why water boils at a higher temperature in a pressure cooker.

Lower outside pressure lowers the boiling point. On high mountains, water boils below 100 °C.

Among similar liquids, stronger attractions usually give a higher boiling point.

At standard atmospheric pressure (1 atm), water boils near 100 °C; ethanol near 78 °C; bromine near 59 °C; diethyl ether near 35 °C; acetic acid near 118 °C; mercury near 357 °C.

The freezing point is the temperature where a liquid and its solid can coexist in equilibrium at a specified pressure. A pure substance has the same equilibrium freezing and melting point at that pressure.

Changing pressure has a large effect on boiling point. Its effect on ordinary freezing points is usually much smaller.

Some dissolved impurities lower a solvent’s freezing point. Salt added to ice water is an example.

Particle arrangement and attractions help determine melting and freezing points.

Examples of freezing points: water 0 °C; benzene 5.5 °C; acetic acid 16.6 °C; ethanol −114 °C; bromine −7.2 °C; mercury −38.8 °C.

At the freezing point, solid and liquid can remain together without an overall change from one into the other. This balance is called phase equilibrium.

Diffusion is the net spreading of particles from a region of greater concentration to a region of lower concentration due to random motion. A drop of ink gradually spreads through still water.

Temperature: higher temperature usually speeds up diffusion.

Viscosity describes resistance to flow. Particles usually move more slowly through a more viscous liquid.

Under similar conditions, smaller particles can spread faster. Particle shape also matters.

A concentration difference gives an overall spread from the more concentrated region towards the less concentrated region.

Mobility is how easily particles can move. Molecules in a warmer or less viscous liquid are often more mobile.

Density (ρ) = mass (m) / volume (V). Liquids are generally denser than gases and much less compressible.

Most liquids expand when heated. Their density therefore falls. Water is unusual between 0 and 4 °C: it is densest near 4 °C.

Approximate water densities: 0 °C = 0.99984 g/cm³; 30 °C = 0.99565 g/cm³; 60 °C = 0.9832 g/cm³; 90 °C = 0.9653 g/cm³.

Under usual conditions, pressure changes a liquid’s density only slightly.

Solids have definite shape and volume.

Particles vibrate near fixed positions. They do not stop moving.

Most solids are hard to compress. They do not flow like liquids.

Pure crystalline solids often have a sharp melting point.

The melting point is the temperature at which solid and liquid coexist in equilibrium at a fixed pressure. Added heat changes particle arrangement rather than increasing temperature during the phase transition of a pure material.

Ice melts near 0 °C at atmospheric pressure; sodium chloride near 801 °C.

Particles in a solid cannot easily change neighbours. The solid therefore resists a change in shape. Its particles still vibrate.

Density = m/V. Many solids are denser than corresponding liquids, but ice is less dense than liquid water.

Approximate solid densities in g/cm³: aluminium 2.70; iron 7.87; gold 19.3; sodium chloride 2.16; sucrose 1.59.

Mercury is liquid at room temperature. Its melting point is −38.8 °C.

Particles are arranged in a regular, repeating three-dimensional pattern (long-range order). Pure crystals commonly have a sharp melting point. Some split along particular flat surfaces called cleavage planes.

Examples include sodium chloride, diamond, quartz and ice.

Particles have no long-range periodic order. Many amorphous substances soften over a range of temperatures rather than melting sharply.

Ordinary glass and many plastics are examples. Some polymers contain both ordered and disordered regions.

A crystal has a repeating structure. It often melts at a sharp temperature. Some properties depend on direction. This is called anisotropy.

An amorphous solid lacks a long-range repeating pattern. It often softens over a range of temperatures. Its properties are usually the same in different directions. This is called isotropy.

Some crystals split along particular flat surfaces, called cleavage planes. Amorphous solids do not have regular cleavage planes.

Crystals are not all made of molecules. NaCl contains ions. Diamond contains covalently bonded carbon atoms.

In diamond, each carbon bonds to 4 others in a three-dimensional network. Diamond is very hard. Pure diamond does not conduct electricity.

In graphite, carbon atoms form layers of hexagonal rings. Some electrons move along the layers, so graphite conducts electricity.

Graphene is one layer of bonded carbon atoms in a hexagonal pattern. It is very thin, strong and electrically conductive.

In fullerenes, carbon atoms form closed cages. C₆₀ is one example.

Plasma contains free-moving charged particles, including positive ions and electrons. The particles affect one another and respond to electric and magnetic fields. Plasma is often called the fourth state of matter.

Examples: lightning, plasma globes, the Sun, fluorescent tubes and neon signs.

Adding enough energy to a gas can remove electrons and form plasma. Not every plasma is extremely hot.

Fusion researchers study ways to control very hot plasma.

A Bose–Einstein condensate (BEC) can form when a suitable gas is cooled to extremely low temperatures near absolute zero. Many particles then share the same lowest-energy quantum state. Bosons are the kind of particles that can share the same quantum state in this way. A quantum state describes a particle’s allowed energy and other features of its motion.

Bose and Einstein developed the ideas in 1924–1925. Cornell, Wieman and their team made the first dilute-gas BEC in 1995. Ketterle also carried out important early experiments.

BEC depends on particle wave behaviour at very low temperatures. It is not ordinary condensation from gas to liquid.

Absolute zero is 0 K, or −273.15 °C. It does not mean that every kind of motion stops. Some quantum motion, called zero-point motion, can remain.

Melting: solid → liquid and absorbs energy. Freezing: liquid → solid and releases energy.

Vaporization: liquid → gas and absorbs energy. Condensation: gas → liquid and releases energy.

Sublimation: solid → gas without first becoming liquid. Deposition: gas → solid.

Ionization forms charged particles in a gas. During recombination, electrons can rejoin ions.

At fixed pressure, a pure substance stays at nearly the same temperature while melting or boiling. Energy changes the state during this time.

A simple energy ladder can help compare familiar changes of state. It does not fully describe plasma or BEC.

Boiling point: temperature where liquid vapour pressure equals external pressure. Melting point: temperature where solid and liquid coexist in equilibrium. Freezing point: temperature where liquid solidifies in equilibrium with solid.

Heating generally expands a liquid and lowers its density; higher pressure slightly raises density. Water has maximum density near 4 °C.

Scientists cool a suitable gas until many of its particles can share the same lowest-energy state. Their wave behaviour then becomes important and a BEC can form. Their motion does not completely stop.

Solid: particles vibrate near fixed positions. Liquid: nearby particles move past one another. Gas: particles are far apart, move randomly and spread to fill the container.

Gas particles move constantly and have relatively large spaces between them, leading to rapid mixing.

For a fixed amount of gas at constant pressure, cooling reduces its volume, so density m/V rises.

Liquid particles remain close to one another and interact strongly, making long-distance movement slower than gas mixing in common conditions.

More energetic molecules escape first, reducing the average energy of the remaining liquid; energy is absorbed from its surroundings.

Higher pressure raises water's boiling point, allowing food to be heated above 100 °C.

In a closed container at fixed temperature, evaporation and condensation continue at equal rates.

Absolute zero is 0 K or −273.15 °C, the lowest temperature on the kelvin scale. Some quantum motion can remain even at this temperature.

Evaporation is surface vaporization below the boiling point. It requires energy, often causing cooling. Its rate generally rises with temperature, exposed surface area and airflow and falls with humidity. Liquids with weaker intermolecular attractions are usually more volatile under similar conditions.

For fixed gas amount and temperature, pressure and volume vary inversely: PV = constant, so P₁V₁ = P₂V₂. Example: 1 atm × 4 L = 2 atm × 2 L. A pressure increase makes volume smaller.

Crystalline solids have long-range repeating order, often sharp melting points and directional properties. Amorphous solids lack long-range order and commonly soften over a temperature range. Examples: NaCl crystal versus ordinary glass.

At constant pressure for a fixed quantity of gas, V ∝ T(K), so V₁/T₁ = V₂/T₂. Example: 300 K and 2 L become 600 K and 4 L at constant pressure.

In a liquid, particles move randomly. Overall, more particles move from a region of higher concentration to one of lower concentration. The change in concentration over a distance is called a concentration gradient.

Diffusion is usually faster at higher temperature and slower in more viscous liquids. Viscosity is resistance to flow. Particle size and shape also affect diffusion.

A liquid boils when its vapour pressure reaches external pressure. Higher external pressure raises boiling point; lower pressure lowers it. Stronger intermolecular attractions generally cause a higher boiling point for similar molecules; composition can also alter it.

Equilibrium vapour pressure is the pressure of vapour in contact with its liquid when evaporation equals condensation at a fixed temperature. This saturated dynamic equilibrium is most readily established and maintained in a closed container; vapour still exists above an open liquid.

An ideal gas is a model that ignores particle volume and attractions between particles. Real gas particles have size and attract one another. Real gases behave more like ideal gases at low pressure and high temperature.