3: Solubility

Henry's law states that, at constant temperature in the suitable dilute range, the amount of gas dissolved in a liquid is proportional to the gas's partial pressure above the liquid. Consequently, a gas-solubility value has meaning only when its pressure condition is specified. Pressure does not change the liquid's name, and gases are precisely the phase for which pressure is especially important.

Henry's law is expressed as p = K_H x for a gas dissolved in a liquid, where p is the gas partial pressure and x is its mole fraction in the solution. At fixed temperature and for a fixed gas-solvent pair, K_H is constant. Therefore, p and x are directly proportional: doubling the pressure doubles the mole fraction within the law's valid dilute range.

In the commonly used form of Henry's law, p = K_H x, a lower K_H means that a given partial pressure corresponds to a larger mole fraction of dissolved gas. Thus, under the same temperature, pressure and solvent conditions, the gas with the lower constant is more soluble. It does not mean that the gas dissolves in every liquid or that pressure has no effect.

At constant temperature, Henry's law gives x proportional to the partial pressure p of the gas. Therefore, if the pressure changes from p to 3p, the dissolved mole fraction changes from x to 3x, provided the solution remains in the ideal range. It is not squared, so nine times is incorrect; pressure independence is also incorrect.

Before opening, carbon dioxide is dissolved under the elevated pressure inside the bottle. Opening it lowers the pressure above the liquid, so the equilibrium solubility of CO2 decreases. The excess dissolved gas leaves the liquid and forms visible bubbles. No sudden solidification, mass creation or fall to zero temperature is required to explain the observation.

Hydrostatic pressure increases as a diver goes deeper. According to Henry's law, increasing the partial pressure of a gas in contact with a liquid generally increases the amount dissolved in that liquid at constant temperature. Blood and its tissues can therefore contain more dissolved gases at depth. The result is not explained by high temperature or pressure independence.

Dissolved oxygen is in equilibrium with oxygen gas above the water. Heating generally increases the kinetic energy of gas molecules and makes their escape from the liquid more favourable. Consequently, the equilibrium solubility of oxygen decreases, so warm water usually contains less dissolved oxygen than cold water. Oxygen does not become a solid, and infinite pressure is not involved.

For a gas dissolved in a liquid, higher pressure increases solubility because more gas molecules are forced into contact with the liquid. Lower temperature generally favours retention of gas because heating promotes escape from the liquid. Combining these effects gives low temperature and high pressure as the most favourable condition. The other combinations contain at least one unfavourable factor.

Gas solubility generally decreases when temperature rises because gas molecules escape more readily from the liquid. It also decreases when pressure is lowered, since fewer gas molecules are driven into solution. Thus, high temperature combined with low pressure gives the least favourable condition. The other choices include either low temperature or high pressure, both of which favour greater gas solubility.

A saturated solution contains the maximum amount of a solute that can dissolve in a specified amount of solvent at a specified temperature and pressure. It is in equilibrium with any undissolved solute, if present. More solute will not dissolve appreciably under the same conditions. Saturated does not mean solute-free, gas-only, or solvent-free.

An unsaturated solution contains less dissolved solute than the equilibrium limit at the stated temperature. Adding the same solute increases its concentration; when the saturation limit is reached, further added solute remains undissolved or dissolves only as fast as equilibrium permits. Keeping temperature constant is important because the solubility limit itself may change with temperature.

A supersaturated solution contains more dissolved solute than is normally stable at that temperature. It can remain apparently clear if undisturbed, but a scratch, shaking, impurity or seed crystal may trigger crystallisation of the excess solute. Thus it is called metastable or unstable. It still contains solvent and is not necessarily gaseous or permanently crystal-free.

A seed crystal supplies an ordered surface on which dissolved solute particles can attach and arrange into a crystal lattice. Because the solution already contains more solute than its stable saturation limit, crystallisation removes the excess until equilibrium is approached. The solvent does not all vaporise, solubility does not become infinite, and the solute is converted into a solid rather than disappearing.

Dissolution is favoured when solute–solvent attractions can compensate for the attractions broken within the pure solute and solvent. Substances with similar polarity or intermolecular-force character often interact favourably, which is summarised by “like dissolves like.” This is a useful guideline, not an absolute rule, because lattice energy, hydrogen bonding and entropy also matter. Mass and physical state do not vanish.

Stirring continually brings fresh solvent into contact with the solute surface and removes the concentrated layer near that surface. As a result, mass transfer improves and the solute generally dissolves faster. At fixed temperature and pressure, however, stirring does not alter the equilibrium constant or the final saturated concentration. It changes the rate of reaching equilibrium, not the equilibrium limit.

Vigorous shaking creates nucleation sites and renews the liquid surface, allowing dissolved gas to gather into bubbles. Because the container is open, the bubbles can escape and the gas is gradually lost to the atmosphere. Shaking does not create infinite solubility or automatically raise the pressure; in a sealed container the pressure response would be different. The liquid need not freeze.

Atmospheric pressure generally decreases with altitude. For water exposed to the atmosphere, the partial pressure of atmospheric gases above the surface is consequently lower, and Henry's law predicts lower equilibrium dissolved concentrations when other conditions are comparable. Temperature and water chemistry can also matter, but the pressure change is the intended main reason. High pressure would favour, not reduce, dissolution.

For the same solvent and temperature, use p = K_H x, or x = p/K_H. At the same pressure, the gas with the smaller Henry constant gives the larger dissolved mole fraction. Therefore the first gas is more soluble. Both gases can still dissolve to some extent, and their solubilities remain pressure-dependent; a lower constant does not imply unlimited solubility.

Solubility is an equilibrium quantity, and changing temperature can change the balance between dissolved and undissolved particles. Many solids become more soluble on heating, some become less soluble, and gases generally become less soluble. Therefore a numerical solubility value without its temperature is incomplete or ambiguous. Colour and the name of the solute do not supply the missing thermodynamic condition.

At constant temperature, Henry's law states that the amount or mole fraction of gas dissolved in a liquid is proportional to the gas partial pressure, within the law's applicable range. Thus changing pressure changes the equilibrium solubility, so a gas-solubility value must be tied to a pressure condition. Pressure does not merely rename the solvent, and it certainly affects gases rather than only solids.

Carbon dioxide is dissolved in a sealed drink because the internal CO2 pressure is relatively high. After opening, the gas above the liquid is no longer maintained at that pressure, so the equilibrium solubility falls. CO2 gradually diffuses out and escapes as bubbles until the drink approaches equilibrium with the atmosphere. The loss of fizziness is therefore a pressure-and-equilibrium effect, not formation of new gas or freezing.

Many aquatic animals obtain oxygen directly from water through gills or other respiratory surfaces. When dissolved oxygen falls, aerobic respiration becomes more difficult, reducing activity, growth and survival; severe depletion can cause stress or death. Warmer water often holds less oxygen, so temperature can contribute to this environmental problem. The effect is biological respiration, not solidification or colour change.

Oxygen is a gas, and the solubility of most gases in water decreases as temperature rises. At lower temperature, gas molecules have less tendency to escape from the liquid, so the equilibrium concentration of dissolved oxygen is relatively higher. Boiling drives dissolved gases out very strongly. The solubility is not zero at every temperature; it is finite and temperature-dependent.

At the stated temperature, a saturated solution already contains the maximum equilibrium concentration of the salt's ions. Adding a little more solid cannot increase that equilibrium concentration; the extra solid usually remains undissolved, with dissolution and crystallisation continuing at equal rates. Ksp is fixed for that salt and temperature, and simply adding solid does not make the solution unsaturated or force all the added material to dissolve.

Henry's law states that, at constant temperature and for a given solvent, the concentration or mole fraction of a dissolved gas is proportional to its partial pressure above the liquid, within the applicable dilute range. Thus multiplying the pressure by a factor multiplies the dissolved amount by the same factor. The relation is not inverse or pressure-independent, and solvent colour is irrelevant to this law.