The salt that dissolves in the air's own water

The degree a spoonful of solute buys found that a dissolved substance lowers the vapour pressure of the water it is dissolved in, and with it the freezing point, by an amount that depends on how many particles are dissolved rather than on what they are. The frost that lifts by drinking found water moving through frozen soil towards a growing ice lens because ice and thin films of water at the same temperature have different chemical potentials, so that water flows from where its chemical potential is high to where it is low. Both essays were about water’s chemical potential being lowered — by solute in one, by contact with ice and soil in the other. This essay is about the same lowering seen from the air.

The air always holds some water vapour, and its relative humidity is the vapour’s pressure as a fraction of what pure water would have in equilibrium with it at the same temperature. That fraction is also the vapour’s chemical potential, measured from pure water’s: humidity 100 per cent means air in equilibrium with liquid water, and lower humidities mean water that would rather be somewhere else. Anything whose water has a lower chemical potential than the air’s will take water from the air. A salt crystal, it turns out, can become such a thing — all at once, at one humidity, and then it dissolves itself.

Water that escapes less readily from a solution #

The chemical potential of water in a solution is measured by its activity, the ratio of the solution’s vapour pressure to pure water’s. For an ideal solution, Raoult’s law makes the activity the fraction of the molecules that are water. Sodium chloride dissolves into two ions per formula unit, so a solution of $m$ moles of salt per kilogram of water has an ideal activity of $1/(1 + 2mM_w)$, with $M_w$ the molar mass of water.

Real salt solutions are not ideal. At low concentration they follow Raoult’s law, but as the ions crowd together they bind water in their hydration shells and interact with one another, and the water’s activity falls faster than the count of particles predicts. The figure computes the real activity from Kenneth Pitzer’s model of electrolyte solutions, which adds to the ideal law a long-range term for the ions’ electrostatic screening and short-range terms for their pairwise interactions, with coefficients fitted to measurements. At saturation, where no more salt will dissolve, the solution holds 6.144 moles per kilogram of water, and its water activity is 0.752; Raoult’s law would have said 0.819. The measured value is 0.753.

That number is the whole of deliquescence. A saturated solution of common salt has the vapour pressure of air at 75.3 per cent relative humidity. In air drier than that, a saturated solution evaporates and the salt comes out of it. In air wetter than that, water condenses onto the solution, which dilutes it, and fresh salt dissolves to re-saturate it, and the process continues until either the air dries or the salt has gone.

A crystal that dissolves itself #

A dry salt crystal in rising humidity takes up almost nothing — a molecular film on its surface — until the humidity reaches 75 per cent. Then, over a fraction of a percentage point, it takes up nearly three times its own weight of water and becomes a drop of saturated solution. The transition is sharp because it is a phase change: at the deliquescence humidity, crystal and saturated solution have the same chemical potential for water, and just above it the solution is the stable state for any amount of salt the air can supply water to.

Above deliquescence the drop goes on drinking. Its water activity must match the humidity, and the only way to raise its activity is to dilute it, so at 85 per cent humidity it holds more than four grams of water per gram of salt and at 95 per cent more than eleven. A drop of brine on a cold window, in air saturated with water, would go on growing without limit.

The curve is a precise version of something seen every day in a kitchen. Salt kept in a damp place cakes because each humid spell turns the surfaces of its grains into a film of saturated solution, which bridges neighbouring grains; each drier spell recrystallises the bridges into solid necks that cement the grains together. Rice grains in a salt shaker are there to absorb the water first.

Why the threshold is a single number #

The deliquescence humidity is sharp for a reason that phase diagrams make plain. At a fixed temperature, a salt crystal sitting in its saturated solution under moist air is three phases — solid salt, solution, vapour — made of two substances, salt and water. Gibbs’s phase rule counts the freedom such a system has: the number of substances minus the number of phases plus two, less one for the temperature that has been fixed, which leaves none. There is nothing left to vary. The composition of the solution, its vapour pressure and therefore the humidity are all fixed, and they are fixed at the same value whatever the amounts of salt and water present. That is the same counting why the triple point is a point used to show that ice, water and vapour can coexist at only one temperature and pressure.

Below the threshold, only the crystal and the vapour can coexist, and the crystal holds essentially no water. Above it, only the solution and the vapour can coexist, and the solution adjusts its concentration to the humidity. At exactly the threshold all three coexist, and adding water vapour simply dissolves more crystal while the humidity stays put — which is exactly why a saturated salt solution with excess crystals makes a humidity standard. It is the humid-air version of what a boiling point is a pressure found for water boiling: a phase change pins the variable that would otherwise move.

The way down is different #

The salt does not reverse the path. Lower the humidity, and the drop gives up water along the same curve, becoming more and more concentrated — but at 75 per cent, where a saturated solution should start to crystallise, nothing happens. To form a crystal, the solution must first nucleate one, and the barrier a new phase has to climb found that a new phase cannot appear exactly at its equilibrium point, because its first tiny nucleus costs surface energy it has not yet earned. The drop goes on losing water, becoming supersaturated, until at about 45 per cent humidity — for a sodium chloride drop with no impurities to seed it — the supersaturation is enough for a crystal to form somewhere in the drop, and then the whole drop dries out in seconds.

Between 45 and 75 per cent humidity, then, a salt particle may be solid or liquid, and which it is depends on its history: solid if it was last dry, liquid if it was last wet. That hysteresis matters wherever humidity cycles. It is the same supercooling that the supercooled water that only partly freezes found keeping water liquid below its freezing point, here acting on a solution that should be precipitating.

On a coast where the humidity never falls below about half, a salt crust that has once deliquesced stays liquid for days, though the air is drier than 75 per cent every afternoon: it never gets dry enough to recrystallise. Inland, where the afternoon air falls to a third, the crust dissolves every night and recrystallises every afternoon. Each cycle draws salt solution into the pores of whatever the salt sits on — stone, brick, concrete — and crystallises it there. A salt crystal growing in a pore from supersaturated solution can exert a pressure of tens of atmospheres on the pore walls, enough to break most stone, and repeated cycles of dissolution and crystallisation are the main way salt weathers buildings and carves the honeycomb hollows called tafoni into seaside rocks.

Eleven salts and the humidities they keep #

Every soluble salt has its own deliquescence humidity, set by how much it lowers water’s activity when saturated, and the range is enormous. Lithium chloride, extremely soluble and strongly hydrating, dissolves in air at 11 per cent humidity, which is why it is used to dry air in industrial dehumidifiers. Magnesium chloride, present as a trace in unrefined sea salt, dissolves at 33 per cent, and that trace is why sea salt turns damp and clumps in weather in which pure salt stays dry. Potassium sulphate, only modestly soluble, does not dissolve until 97 per cent.

Read the other way, the table is a set of humidity standards. A sealed box containing a saturated solution of one of these salts, with excess crystals so that it stays saturated, holds the air above it at that salt’s humidity, whatever water evaporates or condenses, because any change is absorbed by crystals dissolving or forming. Laboratories calibrate hygrometers this way, and museums keep the air round fragile objects at a chosen humidity with trays of saturated salt solution. The same principle lets a dish of salt, in a box, act as a humidity buffer.

A grain of sea salt in damp air #

The same physics works on the smallest scale in the atmosphere. Breaking waves throw billions of droplets of seawater into the air, and as they dry they leave tiny particles of sea salt, a few tenths of a micrometre to a few micrometres across, drifting inland. In dry air they are crystals. When the humidity rises past 75 per cent they deliquesce and grow to nearly twice their dry diameter at once, and keep growing as the air approaches saturation, to five times their dry diameter at 99 per cent. A particle that scatters light in proportion to roughly the square of its diameter scatters many times more light when swollen, and that is part of why coastal haze thickens on damp evenings and clears in the afternoon.

The largest of these drops are where clouds begin. The ice that grows by stealing from the droplets followed what happens once a cloud has formed; before that, water vapour needs something to condense on, and a deliquesced salt particle is ideal, because its water activity is already below one. For very small particles the curvature of the drop raises the vapour pressure again, and the balance between the salt lowering it and the curvature raising it sets the humidity at which a particle can grow into a cloud droplet — a little above saturation, by a fraction of a per cent, for a typical sea-salt particle.

The critical humidity in a warehouse #

Industry calls the deliquescence humidity the critical relative humidity, and it governs how a great many dry products have to be stored. Fertilisers are the classic case: ammonium nitrate has a critical humidity of about 60 per cent at room temperature, so in a humid climate it draws water, cakes into blocks and must be coated or bagged. Sugar, citric acid and many soluble drugs behave the same way, each with its own threshold, and a powder that is free-flowing on a dry day can set solid in a damp week. Tablets are packed with sachets of desiccant whose job is to keep the air inside the package below the critical humidity of whatever is most soluble in them.

Mixtures make it worse, because, as the last section of this essay explains, a mixture of salts deliquesces at a humidity below either component’s own. A blend of two fertiliser salts that are each safe at 70 per cent humidity can turn damp at 55. The lowering of water’s chemical potential by everything dissolved in it adds up, and the threshold for a mixture is set by the saturated solution of all of them together.

The same lowering, everywhere water meets something #

Deliquescence is one of several ways water condenses from air that is not saturated. The pore that fills from dry air found water condensing in a fine pore below saturation because a concave meniscus lowers the vapour pressure; the salt does it because dissolved ions lower it. In both, a lowered chemical potential of water in some confined state lets that state draw water from unsaturated air. In living things the same physics holds water in cells: a cell’s water activity is lowered by everything dissolved in it, and organisms in salty or dry environments survive by making their water activity match their surroundings’.

The driest places on Earth show it most plainly. In the Atacama Desert in Chile, rocks of almost pure halite — natural rock salt — deliquesce at night when the coastal fog raises the humidity past 75 per cent, and the brine held in their pores supports colonies of microorganisms in a desert where no liquid water otherwise exists. Perchlorate salts, which dissolve at much lower humidities and freeze at much lower temperatures, have been found in the soil of Mars, and droplets seen on the legs of the Phoenix lander in 2008 were interpreted by some as perchlorate brine formed by deliquescence. Whether liquid brines form this way on Mars often enough to matter is debated.

Bulk solutions, a fixed temperature and a clean crystal #

The figures use Pitzer’s model for sodium chloride at 25 °C, which reproduces measured water activities to a few parts in a thousand up to saturation and beyond into mild supersaturation, where it is extrapolated. The deliquescence humidity changes little with temperature for sodium chloride but strongly for some other salts, and the figures fix the temperature throughout. The efflorescence humidity, 45 per cent, is a typical measured value for pure particles; it depends on particle size, on impurities that seed nucleation and on how long the drop is held, and a dish of salt on a dusty surface may recrystallise well above it. The swelling figure assumes particles large enough that the curvature of their surface has no effect, which holds above about a tenth of a micrometre; smaller particles deliquesce at slightly lower humidity and grow less. The humidity cycles are idealised sine waves. The domain is single salts, at room temperature, in air between about 30 and 99 per cent humidity.

Still open: what happens in mixtures #

Real salt is rarely one salt. Sea spray carries chloride, sulphate, magnesium, calcium and potassium; the dust on a monument carries whatever pollution and soil have left. A mixture of two salts deliquesces at a humidity below either one’s own — at the “eutonic” composition, where both are saturated together — and then dissolves progressively as the humidity rises, with each component’s solid disappearing at its own point. Predicting the behaviour of a real mixture needs the water activity of a concentrated solution of many ions at once, which models such as Pitzer’s can provide only with many fitted coefficients, and measurements are sparse for the concentrated mixtures that matter. How a real deposit of mixed salts in a stone wall, or a particle of mixed sea salt and organic matter in the air, takes up and gives up water through a day is still often measured rather than predicted.

The single salt comes down to one equality. A salt crystal in air dissolves when the relative humidity exceeds the water activity of its saturated solution — 0.752 for sodium chloride by Pitzer’s model, measured 0.753, against Raoult’s ideal 0.819 — and the drop then takes up water until its activity matches the air, 2.79 g per gram at deliquescence and 11.5 at 95 per cent; going down, it stays liquid until nucleation lets it crystallise near 45 per cent, so between the two it is wet or dry according to its history. The air’s own water, at three-quarters of saturation, is enough to dissolve the salt, because the salt makes the water want to stay.