Illustrated Physics
physics, drawn
Concept

Raoults law — where it appears

The rule that a solvent's vapour pressure over an ideal solution equals the pure solvent's multiplied by its mole fraction. It explains why dissolved substances lower the freezing point and raise the boiling point, and it fails in concentrated salt solutions, where hydrated ions lower the vapour pressure further still.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

How a solute moves both ends of the liquid range. The molar chemical potential of water against temperature near its freezing point (left) and its boiling point (right): liquid (blue), ice (green), vapour (red), each a line whose slope is minus its entropy, drawn relative to the liquid at the transition. A solute at mole fraction 0.05 — about 2.9 mol/kg — lowers the liquid's line by RTx (dashed) and leaves the ice and the vapour unchanged. The crossings move: the freezing point down by RTx divided by the entropy of melting, 5.16 K, the boiling point up by RTx divided by the entropy of boiling, 1.42 K. The same vertical shift moves the freezing crossing 3.6 times as far, because ice's line is nearly parallel to the liquid's — melting changes the entropy by 22.0 J/mol K — while the vapour's line crosses steeply, with 109 J/mol K between them. Lowering the liquid makes it the winner over a wider range of temperature at both ends: the solution is liquid from below 0 °C to above 100 °C.

The degree a spoonful of solute buys

Dissolve anything in water and the water freezes lower and boils higher. The two shifts come from one cause — the solute lowers the liquid water's chemical potential, so the liquid wins against ice and against vapour over a wider range — but they are not the same size. For every mole of particles per kilogram the freezing point falls 1.86 degrees and the boiling point rises only 0.51, three and a half times less, and the reason is in the entropies: ice and water are so alike that a small push moves their crossing a long way. The same arithmetic says salting pasta water does nothing a cook could notice, weighed molecules for a century of chemistry, and in 1887 showed that salts in water are made of ions.

thermodynamics · Chemical potential Salt that takes in water from the air at three-quarters humidity. The water held by a crystal of common salt, in grams per gram of salt, against the relative humidity of the air around it at 25 °C, with the humidity rising (solid) and falling (dashed). Rising, the crystal stays dry until 75.2 per cent and then dissolves at once into a drop holding 2.79 g of water per gram — the saturated solution — which goes on drinking as the air gets damper: 4.24 g at 85 per cent, 11.5 g at 95. Falling, the drop does not crystallise at 75 per cent. It sheds water along the same curve, becomes supersaturated, and stays liquid down to about 45 per cent before a crystal finally nucleates and it dries out at once.

The salt that dissolves in the air's own water

Leave a dish of salt in a bathroom and it does not just clump; on a humid enough day it turns into a puddle, though no water was poured on it. Above 75 per cent humidity, common salt pulls water out of the air until it has dissolved itself. The number is not a property of salt's attraction for water in any vague sense. It is the vapour pressure of a saturated salt solution, read as a fraction of pure water's: wherever the air holds more water than that, the solution is the state with the lower chemical potential. Bring the humidity back down, and the puddle does not turn back into salt until the air is far drier — about 45 per cent.

thermodynamics · Chemical potential

Named alongside it

The objects these essays reach for when they reach for this one.

Chemical potentialBoiling point elevationColligative propertiesDeliquescenceEntropyFreezing point depressionHysteresisIdeal solutionLatent heatNucleationRelative humiditySupersaturation

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