Part B · How stuff sticks

8 · States and solutions

Ice, water and steam are the same molecules. Salt water and sugar water are water with something hidden in it. This chapter puts chapters 6 and 7 to work on two everyday questions: when does stuff melt and boil, and where does the sugar go?

Heating ice: where does the energy go?

A pan of crushed ice sits on a steady flame. While the ice is melting, what does a thermometer in the pan show?

It stays at 0 °C until all the ice has melted. The flame keeps pouring in energy, but it all goes into pulling molecules out of the crystal (breaking hydrogen bonds), not into making them jiggle faster. The same thing happens again at 100 °C, for much longer: boiling has to pull molecules completely apart, which costs about seven times as much energy as melting.

Heating 1 g of ice from −20 °C at a steady rate. The temperature line goes flat during melting and boiling. Bars below show where the energy went. Real values: specific heats 2.1 (ice), 4.18 (water), 2.0 (steam) J/(g·K); melting 334 J/g; boiling 2257 J/g.

That hidden energy is called latent heat. It's why sweating cools you (evaporating water carries off a lot of energy), why steam burns worse than boiling water, and why a drink with ice stays at 0 °C until the last cube is gone. In chapter 7's terms: at the melting point the solid and liquid have equal free energy, so heat shifts the balance between them without changing the temperature.

A map of states: the phase diagram

Whether water is ice, liquid or vapour depends on temperature and pressure. Draw the boundaries where two states have exactly equal free energy and you get a phase diagram. Drag the dot.

Water's phase diagram. Pressure is on a logarithmic scale, from 1 Pa (near vacuum) to 200 MPa (two thousand atmospheres). The boiling curve uses the Antoine equation fitted to measured data, the sublimation curve the Clausius–Clapeyron equation, and the melting curve a smooth fit to measured points. Dashed: 1 atmosphere.

Above about 200 MPa, ice comes in many other crystal forms (more than a dozen are known), not shown here. The diagram also shows only what's stable. Pure water can be supercooled below 0 °C without freezing, because freezing has to get started somewhere (chapter 10's barriers).

Things to notice:

Boiling point depends on pressure. On Everest the air pressure is about a third of sea level, and water boils near 70 °C, too cool to cook pasta properly. A pressure cooker at about two atmospheres boils at about 120 °C, so food cooks faster.
The melting line leans backwards. For almost every other substance, squeezing favours the solid. Ice is less dense than water (chapter 6), so squeezing favours the liquid instead.
Below the triple point (611 Pa, 0.01 °C) there is no liquid at all: ice turns straight to vapour. The average pressure on Mars is right around there, so ice on Mars mostly sublimes rather than melts. That's also how freeze-drying works.
The boiling curve stops at the critical point (374 °C, 22 MPa). Beyond it, liquid and gas are no longer different: you can go from one to the other without ever boiling.

Dissolving: where the sugar goes

Stir sugar into tea and it vanishes. It hasn't been destroyed. It has broken up into separate molecules, each surrounded by water molecules, spread evenly through the cup. You can taste it, weigh it, and get it back by evaporating the water. Whether something dissolves is a contest between three attractions: solute to solute, water to water, and solute to water.

Temperature

A small crystal (orange) in a liquid (blue). Orange sticks to orange a little less strongly than blue sticks to blue. Left button: orange sticks to blue more strongly than to itself, so it dissolves (give it half a minute). Right: orange barely sticks to blue, like oil in water. "Clumped" counts orange pieces touching at least two other orange pieces; fully mixed, about 10–20% touch by chance.

These are round particles with tunable stickiness, not real water. Real dissolving involves the shapes and charges of chapter 6: water's partial charges cling to ions (each Na⁺ and Cl⁻ ends up wrapped in a shell of oriented water molecules) and hydrogen-bond to sugar. Oil can't do either.

That's the rule chemists call "like dissolves like". Polar and ionic things (salt, sugar, alcohol) dissolve in water, a polar liquid. Non-polar things (oil, wax, fat) dissolve in each other but not in water. Soap works by being both: one end is ionic and loves water, the other is a long oily tail that loves grease. Soap molecules gather around a blob of grease with their tails inside and their heads outside, and the water carries it away.

Why does dissolving happen at all, if the crystal holds together so well? Chapter 7's entropy, again. A dissolved, spread-out solute has vastly more arrangements than a neat crystal (chapter 11's mixing curve). When the attractions are about equal, entropy wins and the crystal dissolves. When the solute strongly prefers its own kind, energy wins and it stays together, up to a limit: the solubility. About 360 g of salt dissolves in a litre of water at room temperature; sugar manages about 2 kg. Hot water holds more, which is how rock candy grows: a hot, saturated syrup cools and the extra sugar has to come out as crystals.

Dissolved stuff also changes when water freezes and boils. Mixing makes the liquid more favourable (more ways to be arranged), so salt water freezes below 0 °C. That's why roads are salted in winter: salt works down to about −21 °C.

Common trap

"Dissolved sugar is gone" or "it weighs nothing now". The mass is all still there: weigh the water before and after and the difference is exactly the sugar. Another trap is mixing up melting and dissolving. Ice melts: one substance changing state because of heat. Sugar dissolves: one substance spreading out through another. Children (and adults) use the words interchangeably, so it's worth getting them right.

Physics bridge

The phase diagram is an argmin map: at each (T, P), the stable phase is the one with the lowest Gibbs free energy, and boundaries are where two are equal. Setting G₁ = G₂ along a boundary gives the Clausius–Clapeyron slope, dP/dT = ΔH/(T ΔV). Ice melting has ΔV < 0, so the slope is negative: that's the backward-leaning line.

The liquid–gas critical point is a genuine continuous phase transition, in the same universality class as the 3-D Ising model. Near it, density fluctuations become correlated over long distances. You can see this as critical opalescence: a sealed sample turns milky, because the fluctuations grow to the size of light's wavelength.

The "oil and water don't mix" story is subtler than a weak attraction. For small non-polar molecules at room temperature, the main cost is entropic: water has to arrange its hydrogen bonds into ordered cages around each non-polar molecule (the hydrophobic effect). That effect is central to how proteins fold.

Tell it to a 6-year-old

Look: A clear glass of water, a teaspoon of salt and a dark-coloured plate.
Wonder: "If we stir the salt in until we can't see it any more, is it gone?"
Try: Stir until the water is clear. Dip a clean finger in and taste: still salty! Then pour a little onto the dark plate and leave it on a sunny windowsill for a few days. Look at what's left.
True sentence: "The salt breaks into pieces too small to see and spreads out among the water pieces. It's still there: we can taste it. When the water goes off into the air, the salt is left behind."

This is dissolving, not melting: use different words for the two (ice melts, salt dissolves). The crystals that grow on the plate are often little cubes, like the salt grains in chapter 5. A quick extra: drop a sugar cube into a glass of warm water and one into cold, and see which disappears first.

Play more

PhET: States of Matter. Includes a phase diagram you can move around on.
PhET: Concentration and Molarity. Dissolve, saturate and precipitate.
Concord: Oil and water. A molecule-level version of the dissolving simulation.
Mark Miodownik, Liquid Rules.