Solutions: Concentration, Solubility and Vapour Pressure

One part per million of fluoride ion in drinking water prevents tooth decay; one and a half parts per million causes mottled teeth instead; high enough concentrations turn the same fluoride ion into rat poison. Intravenous injections are always matched to the exact ionic concentration of blood plasma, and brass, German silver and bronze, all copper alloys, differ entirely in their own properties purely by composition. Almost every process inside the human body happens in some kind of liquid solution, a homogeneous mixture, meaning uniform composition and properties throughout, of a solvent, whatever component is present in the largest quantity and decides the solution's own physical state, and one or more solutes dissolved within it. Any of the three states of matter can play either role: gases dissolve in gases, liquids in gases, solids in gases, and the same three-by-three pattern repeats for liquid and solid solvents too, giving nine genuinely distinct solution types, from ordinary air, gas in gas, to a gold-copper alloy, solid in solid.

Describing a solution as merely dilute or concentrated invites confusion, so chemistry uses several precise quantitative measures instead, each suited to a different situation. Mass percentage, a component's own mass divided by the solution's total mass times 100, is standard in industrial chemistry, commercial bleaching solution holding 3.62 mass percent sodium hypochlorite; volume percentage suits solutions of liquids specifically, a 35 percent by volume ethylene glycol antifreeze solution lowering water's own freezing point to 255.4 K; mass by volume percentage, mass of solute per 100 mL of solution, is the standard in medicine and pharmacy; and parts per million, a component's own parts divided by the total parts of every component present, times ten to the sixth, suits trace concentrations specifically, seawater's own roughly 6 milligrams of dissolved oxygen per litre expressed cleanly as 5.8 ppm.

Mole fraction, a component's own moles divided by the total moles of every component present, carries the useful property that every mole fraction in a solution sums to exactly 1, and it is specifically the unit most directly connected to a solution's own vapour pressure, exactly why it recurs constantly through the rest of this chapter. Molarity, moles of solute per litre of solution, remains the single most commonly used concentration unit in the laboratory, while molality, moles of solute per kilogram of solvent, offers one genuine advantage molarity lacks: since molality is defined by mass, unaffected by temperature, rather than volume, which expands and contracts as temperature changes, molality, mass percentage, ppm and mole fraction all stay fixed regardless of temperature, while molarity alone shifts as a solution warms or cools.

Sodium chloride and sugar dissolve readily in water yet resist benzene entirely, while naphthalene and anthracene do the exact opposite, the underlying rule being that a solute dissolves best in a solvent whose own intermolecular interactions closely resemble its own, like dissolves like. Adding solid solute to a solvent starts two opposing processes at once, dissolution, solute entering solution, and crystallisation, dissolved solute particles rejoining the solid, and once these two rates match exactly, a genuine dynamic equilibrium is reached, no further net change occurring, the solution now saturated and holding the maximum solute that specific temperature allows, that fixed concentration itself defining the substance's own solubility. Since this equilibrium is dynamic, Le Chatelier's Principle applies directly: if dissolving a solid absorbs heat, an endothermic process, solubility rises with temperature; if dissolving it releases heat instead, solubility falls as temperature rises. Pressure, by contrast, has essentially no effect on a solid's own solubility in a liquid, since both solids and liquids are highly incompressible and barely respond to pressure changes at all.

Gases dissolve in liquids too, oxygen only sparingly, sustaining all aquatic life, hydrogen chloride enormously by contrast, and unlike a solid's own near-total indifference to pressure, gas solubility responds directly to it, more gas dissolving as pressure over the liquid rises. Henry established the precise quantitative relationship in what is now Henry's Law: at constant temperature, a gas's own partial pressure above a solution is directly proportional to its own mole fraction dissolved within that solution, p equals KH times x, where KH, Henry's Law constant, differs from one gas to another at any given temperature, a higher KH meaning lower solubility for the same pressure. Temperature moves gas solubility the opposite way pressure does: since dissolving a gas resembles condensation, itself exothermic, and this dissolution equilibrium likewise obeys Le Chatelier's Principle, gas solubility in a liquid falls as temperature rises, exactly why aquatic species genuinely fare better in colder water, richer in dissolved oxygen, than in warm water.

Henry's Law is far from an abstract classroom relationship: soda water bottles are sealed under high pressure specifically to force extra carbon dioxide into solution, and opening that bottle drops pressure sharply, driving dissolved CO2 back out as visible fizz, exactly the reverse process. Scuba divers face a genuinely dangerous version of the same physics: breathing pressurised air underwater dissolves more nitrogen into the blood than usual, and surfacing too quickly drops that pressure faster than the body can safely release the excess gas, forming nitrogen bubbles that block capillaries, the painful and dangerous condition called the bends, avoided in practice by diluting a diver's own breathing air with helium instead of nitrogen. At high altitude, the same law works in the opposite, still-dangerous direction: lower atmospheric pressure means lower dissolved oxygen in the blood, causing the weakness and impaired thinking of anoxia in climbers and high-altitude residents alike.

When two volatile liquids share a closed container, both evaporate until vapour and liquid phases reach equilibrium, and Raoult established the quantitative relationship governing that equilibrium: each component's own partial vapour pressure is directly proportional to its own mole fraction in the liquid, p1 equals x1 times p1 standard, p2 equals x2 times p2 standard, and total pressure, by Dalton's Law, simply sums both partial pressures together. Working through chloroform mixed with dichloromethane at 298 K shows this directly: total vapour pressure comes out to 347.9 mm Hg from the two components' own mole fractions and pure vapour pressures, and the resulting vapour phase composition, calculated from each partial pressure divided by the total, comes out genuinely richer in dichloromethane, the more volatile of the two, than the liquid phase itself is, a completely general result: the vapour above any liquid mixture is always enriched in whichever component evaporates more readily.

Comparing Raoult's Law, p equals x times p standard, directly against Henry's Law, p equals x times KH, reveals they share the exact same mathematical form, differing only in which proportionality constant is used, meaning Raoult's Law is genuinely just the specific case of Henry's Law where that constant happens to equal the pure liquid's own vapour pressure. Dissolving a non-volatile solid into a liquid solvent lowers the solvent's own vapour pressure too, for a directly visualisable reason: a pure liquid's entire surface is occupied by solvent molecules alone, but once solute particles occupy part of that same surface, fewer solvent molecules remain able to escape into vapour, and this lowering depends purely on how much solute is present, not on what the solute actually is, dissolving one mole of sucrose or one mole of urea into the same mass of water producing nearly identical vapour pressure drops.

A solution obeying Raoult's Law across its entire concentration range is genuinely ideal, and this behaviour traces back to molecular interactions: if the attraction between unlike molecules A and B matches the attraction each has for its own kind closely enough, mixing costs no extra energy, enthalpy of mixing exactly zero, and volumes simply add, n-hexane with n-heptane and benzene with toluene both nearly reaching this ideal. A non-ideal solution deviates from Raoult's Law in one of two directions: positive deviation, vapour pressure higher than predicted, arises when A-B attraction is weaker than A-A or B-B, ethanol mixed with acetone breaking apart some of ethanol's own hydrogen bonds and letting molecules escape more easily; negative deviation, vapour pressure lower than predicted, arises when A-B attraction is genuinely stronger instead, chloroform forming a fresh hydrogen bond directly with acetone, or phenol with aniline, holding molecules in more tightly than usual. Large enough deviations produce an azeotrope, a mixture whose liquid and vapour share identical composition and which therefore cannot be separated further by ordinary fractional distillation at all: strong positive deviation gives a minimum-boiling azeotrope, ethanol-water fermentation stalling at roughly 95 percent ethanol by volume no matter how much further distillation is attempted, while strong negative deviation gives a maximum-boiling azeotrope instead, nitric acid and water locking at roughly 68 percent acid.