Why does ice melt at 0 degrees and a diamond not at 3,000?
Read phase diagrams and relate structure to the properties of liquids and solids.
ExperimentsEscaping moleculesVapour pressure, boiling, and the staircase of heat.
Experiment 1 · Dalton, 1801; Clapeyron, 1834
When does a liquid boil?
Water evaporates from a puddle on a cold day, though it is nowhere near 100 degrees. What decides how much escapes, and what is 'boiling' then?
In 1801 John Dalton measured the pressure of water vapour over water at many temperatures and found that it depended on the temperature alone, however much air was in the vessel. In 1834 Émile Clapeyron, and later Rudolf Clausius, tied its steep rise to the heat needed to vaporize the liquid. Choose a liquid, warm it, and watch its vapour pressure climb to meet the pressure outside; then use two points of the curve to find the heat of vaporization.
Pressure outside
Vapour pressure 3.54 kPa vs outside 101.3 kPa: no bubbles yet
Still too cold: the vapour pressure is below the outside pressure.
Step 1 of 2 · Find three boiling points of waterChoose water. For each outside pressure, raise the temperature until the vapour pressure meets it, and mark where it starts to boil: 0 of 3.
Vapour pressure3.54 kPa
Boils at (outside)100.0 °C
Boiling points found0 / 3
The maths
A liquid boils when its vapour pressure equals the outside pressure. Clausius–Clapeyron: ln(P₂/P₁) = −(ΔH_vap / R)(1/T₂ − 1/T₁).
Water at 300.0 K (26.9 °C): vapour pressure 3.54 kPa = 0.035 atm. Outside: 1 atm → it does not boil.
Water boils at 100.0 °C when the pressure is 1 atm.
Water: ΔH_vap = R ln(27.18 ÷ 3.54) ÷ (1/300 − 1/340) = 43.2 kJ/mol. Tabulated near the boiling point: 40.68 kJ/mol.
Questions you might have (3)Why does a pressure cooker cook faster?
It holds the steam in, so the pressure rises to about 2 atm and the boiling point to about 120 °C. Food cooks faster at the higher temperature, because chemical reactions go faster when it is hotter. (Our table of water stops at 100 °C, but the curve keeps rising.)
Why does a wet floor dry if the water is nowhere near boiling?
Evaporation happens at any temperature: some molecules always have enough energy to escape, and in open air the vapour is blown away, so more keep leaving. Boiling is different: it is evaporation inside the liquid, possible only when the vapour can push back the surrounding pressure.
Why do ethanol and acetone feel cold on the skin?
They evaporate quickly because their vapour pressure is high, and each molecule that leaves takes energy with it, so the liquid and your skin cool. It is the heat of vaporization at work, and the same reason sweating cools you.
Run the experiment to see what it showed.
Experiment 2 · Black, 1760s
The staircase of heat
Heat a block of ice steadily. The temperature climbs, stops, climbs, stops, and climbs again. What is the heat doing while the thermometer stands still?
In the 1760s Joseph Black in Glasgow noticed that when ice melts it takes in a great deal of heat without getting any warmer, and that boiling water does the same. He called it latent heat. Here is 100 g of ice at −20 °C on a steady heater. Add heat and watch where the temperature climbs and where it stops, then work out how much heat each stage took.
Stage: warm the ice.
Step 1 of 2 · Heat the iceAdd heat in steps. Watch where the temperature stops rising. Go on until the water starts to boil.
Heat added0.0 kJ
Temperature-20.0 °C
Answers right0 / 3
The maths
Rising stretches: q = m c ΔT. Plateaus: q = n ΔH_fus (melting) and q = n ΔH_vap (boiling). n = 100 g ÷ 18.015 g/mol = 5.551 mol.
Heat so far: 0.0 kJ → -20.0 °C, stage: warm the ice.
warm the ice: 100 × 2.035 × 20 = 4.1 kJ
melt the ice: 5.551 mol × 6.01 = 33.4 kJ
warm the liquid: 100 × 4.179 × 100 = 41.8 kJ
boil it: 5.551 mol × 40.68 = 225.8 kJ
warm the steam: 100 × 2.026 × 20 = 4.1 kJ
Questions you might have (3)Why does boiling need so much more heat than melting?
Melting only loosens the molecules so they can slide past one another: most of the attractions remain. Boiling must tear each molecule completely free of the others, and it must also push back the atmosphere to make room for the vapour. Per mole, boiling water takes about 6.8 times the heat that melting ice does.
Why is a steam burn worse than a boiling-water burn?
Steam at 100 °C gives up not only the heat of cooling but also the heat of condensation, 40.7 kJ/mol, as it turns back to liquid on your skin. A gram of steam gives off about 2.26 kJ on condensing, enough to warm 5 g of water by 100 °C, before it even begins to cool.
Why do ice cubes keep a drink cold so well?
Because to melt a gram of ice takes 334 J, as much as to warm the same gram of water by 80 °C. The ice absorbs the heat of the drink, holding it at 0 °C until all of it has melted.
Run the experiment to see what it showed.
TheorySurfacesWhy drops are round and water climbs a tube.
Theory 1 · Young and Laplace, 1805
The skin on a liquid
A needle floats on water, drops are round, and water climbs a thin tube against gravity. What do all three have in common?
Inside a liquid every molecule is attracted by neighbours all round. At the surface, half of them are missing, so the surface is under tension, like a skin. In 1805 Thomas Young described the angle at which a liquid meets a solid and the pull of the surface, and Laplace added the mathematics of the curved surface. Dip a thin tube into water and the surface pulls the liquid up it. Change the tube and the temperature to see what controls how far.
Water at 20 °C must climb 30 mm in a thin glass tube. What radius (in mm) should the tube be?
mm
By what factor is water thinner (less viscous) at 100 °C than at 5 °C?
times
Step 1 of 2 · Play with the tubeChange the radius and the temperature. Which makes the water climb higher: a narrower tube, or a warmer liquid? Then answer the questions.
Rise29.7 mm
Surface tension72.8 mN/m
Questions right0 / 2
The maths
The pull of the surface on the rim: 2π r γ. The weight of the column: π r² h ρ g. Equal at the height h = 2γ / (ρ g r).
At 20 °C: γ = 72.75 mN/m, ρ = 998.2 kg/m³; r = 0.50 mm: h = 2 × 0.0727 ÷ (998.2 × 9.807 × 0.00050) = 29.7 mm.
Viscosity at 20 °C: 1.005 mPa·s (at 5 °C 1.519, at 100 °C 0.284).
Questions you might have (3)Why does soap lower the surface tension?
Soap molecules have a water-loving head and an oily tail, and they gather at the surface with the tails sticking out. They weaken the pull of the water molecules on one another, so the surface tension falls (to about a third). That is why soapy water spreads and wets and a bubble can be blown.
Why can a water strider walk on a pond?
Its weight is spread over legs with a waxy, water-repelling coat, and the surface tension, like a stretched skin, pushes up on the legs more than the leg weighs. A needle laid gently on water floats for the same reason; push it through the surface and it sinks.
What if the liquid does not wet the tube, as mercury does not wet glass?
Then the contact angle is more than 90°, the surface bows downward, and the liquid is pushed down the tube: capillary depression. In a mercury barometer the surface at the top of the column is convex for this reason, and good barometer tubes are wide enough that the effect is small.
Work through it to see what it shows.
ExperimentsInside a crystalOne block, repeated, and the X-rays that read it.
Experiment 3 · Bragg, 1913
How the atoms sit
A crystal looks the same all through, so its atoms must repeat. What is the repeating block, how many atoms does it hold, and how could anyone see inside?
Crystals have flat faces and fixed angles, and René-Just Haüy suggested in the 1780s that they are built of identical tiny blocks. In 1912 Max von Laue showed that X-rays pass through a crystal and diffract, and in 1913 father and son William Henry and William Lawrence Bragg used the angles of the reflections to place the atoms. Turn the three cubic cells, count what belongs to each, and then use the size of the cell to weigh the atoms.
How many atoms belong to one face-centred cubic cell?
Step 1 of 2 · Count the atomsTurn each cell, and count the share of each atom that lies inside: 0 of 3 right.
Atoms per cell4
Packing74.0 %
Touches12 neighbours
The maths
Atoms in a cell: corner atoms are shared by 8 cells (1/8 each), face atoms by 2 (1/2), the body atom by none (1). Density ρ = Z M ÷ (N_A a³).
Face-centred cubic: 8 corners × 1/8 + 6 faces × 1/2 = 4 atoms per cell; each atom touches 12 others; packing 74.0 % of the space.
Cu (fcc, a = 3.597 Å, M = 63.55 g/mol): ρ = 4 × 63.55 ÷ (6.022e+23 × (3.597×10⁻⁸ cm)³) = 9.07 g/cm³; measured 8.96 g/cm³; N_A from the cell = 6.10×10²³ per mol.
Questions you might have (3)Why is face-centred cubic called close-packed?
It is one of two ways, the other being hexagonal close-packing, of stacking layers of spheres so that each sits in the dips of the layer below with the least waste: 74.05 % of the space is filled, which is the largest possible for equal spheres (Gauss proved it for regular lattices in 1831). Gold, silver, copper, aluminium and lead all choose it.
Why is iron body-centred and not close-packed?
Packing is not the only thing that matters: the details of how the atoms' electrons bond decide, and they make the body-centred arrangement the more stable one for iron at room temperature. Iron is body-centred (ferrite) below 912 °C, becomes face-centred (austenite) between 912 and 1394 °C, and body-centred again before it melts. The change is what makes steel hardening possible.
Do salts have unit cells too?
Yes. In sodium chloride the chloride ions form a face-centred cubic array and the sodium ions fill the gaps between them, so the cell holds 4 Na⁺ and 4 Cl⁻ (four formula units). This is the arrangement for which Unit 4's Madelung constant was worked out.
Run the experiment to see what it showed.
TheoryThe mapSolid, liquid and gas on one chart.
Theory 2 · Andrews, 1869
One map for every force
Ice melts at 0 °C and diamond does not at 3,000. Is there a single chart that tells, for any substance, where it is solid, liquid or gas?
In 1869 Thomas Andrews at Queen's College Belfast pressed carbon dioxide in a strong glass tube at different temperatures. Below 31 °C it liquefied under pressure. Above it, however hard he pressed, there was no liquid, only a gas that grew denser. He had found the critical point, and with it the idea that gas and liquid are not different things but two regions of one map. Here is the map for water and for carbon dioxide, drawn from the measured data. Move the marker around, and try the tasks.
It is a liquid.
Click or drag on the diagram, or use the sliders.
1 of 5 · Water boils at 20 °C. Put the marker where that happens.
Step 1 of 2 · Find your way aroundMove the marker over the regions and watch the label. Then try the first task: water at 20 °C.
Phase at the markerliquid
Temperature300 K
Places found0 / 5
The maths
Lines: two phases in equilibrium. Triple point: all three. Above the critical point the liquid and gas are one fluid. Clapeyron: dP/dT = ΔH ÷ (T ΔV), which gives the slope of each line.
Water: triple point 273.16 K, 612 Pa; critical point 647.0 K, 22.1 MPa.
Marker: 300 K (27 °C) at 100 kPa (0.987 atm) → liquid.
Melting line slope: dT/dP is negative, because ice is less dense than water (ΔV < 0): -0.070 K per MPa.
Questions you might have (3)Why does ice skating work, if ice melts under pressure?
The idea was long taught that the skate's weight melts the ice beneath it, but the numbers say otherwise: to melt ice at −5 °C needs about 60 MPa, and a skater exerts far less. The slipperiness is now thought to come mainly from a thin film of water that is already on the surface of ice, and from friction. The backward slope is real; it just is not the main thing in skating.
What is dry ice good for, and why does it not melt?
It is solid carbon dioxide, and at atmospheric pressure it is below the triple-point pressure, so heating it takes it from solid to gas with no liquid stage: it sublimes at −78 °C. It cools without leaving a puddle, and it makes the fog on stage when the cold vapour condenses the water in the air.
Why does diamond not melt at 3,000 °C, and ice at 0?
Ice is a molecular solid: its molecules are held to one another by hydrogen bonds, which are weak next to a covalent bond. To melt diamond, every atom in the crystal has to be pulled from four others by covalent bonds, of the kind that held the molecules in Unit 5. Melting point follows from what is broken, and the map for each substance has a different scale.
Work through it to see what it shows.
PracticeProblemsNumbers from this unit, in the style of a college problem set.
Practice
Practice
Numbers from the experiments, in the style of a college problem set. Every problem has a hint and a worked solution.
Boiling and vapour pressure0 right of 0 · streak 0
Water's vapour pressure is 101.3 kPa at 100 °C, 47.4 kPa at 80 °C and 31.2 kPa at 70 °C. At about what temperature does water boil on a mountain where the pressure is 0.5 atm (50.7 kPa)? Give the answer in °C.