# Solution [chemistry]

In Chemistry, a homogeneous mixture is defined as a solution in which one or more substances are contained in a liquid or solid or gaseous phase; it contains different particles mixed and distributed evenly in the space available so that each volume of the solution has the same composition as the others. It is used to call solute (or dispersed phase) the substance (or substances) in smaller quantities, and solvent (or dispersed phase or continuous phase) the substance in greater quantities.

A solution differs from a generic dispersion because the solute is dispersed in the solvent at the level of individual molecules or ions, each of them surrounded by solvent molecules (we speak more precisely of solvation). When, in a solution, a solute is present with atoms, ions, or molecules of particularly small dimensions (less than 1 nm), invisible even with the aid of the microscope, we speak of a true solution. Otherwise, when the particle size of the solute is between 1 and 1000 nm, we speak of colloidal dispersion.

When, in a solution, a solute is present with atoms, ions or molecules of particularly small size, it is called true solution. Otherwise, when the particle size of the solute is between 1 and 1000 nm, it is called false solution, or colloidal dispersion. In a true solution the solute is dispersed in the solvent as individual molecules or ions, each surrounded by solvent molecules (this is called solvation).

For the definition of solution to be disproved, it is necessary that the particles are uniformly dispersed and their size does not exceed the molecular order of magnitude. These solutions are often called true solutions to distinguish them from colloidal solutions in which there are particles much larger than the common molecules (colloids).

The essential characteristic of the solutions is the continuous variation of the properties as the proportions of the elements that compose them vary within more or less wide, but defined limits. Considering the three states of aggregation of matter (solid, liquid, gas) can be produced solutions between two elements that are in any of these states:

• gaseous solutions: as in the case of all gaseous mixtures, gases are miscible with each other in any ratio and give rise to homogeneous systems, i.e. solutions whose components can also be separated by means of liquids that selectively dissolve them or by thermal diffusion or forced circulation through membranes or porous septa;
• solid solutions (see below): these can form between substances capable of giving mixed crystals, i.e. isomorphic, a very common case in the mineral world, especially among silicates. The composition of these systems is continuously variable, although usually within narrow limits. True solid solutions are alloys as homogeneous mixtures of two or more metals, of metals with other elements or with inter-metallic compounds. Alloys are obtained in the molten state, but diffusion between solids can also be achieved, for example that of carbon in iron (cementation).
• liquid solutions: here we can distinguish solid-liquid solutions and liquid-liquid solutions; in solid-liquid solutions the solid is the solute and the liquid is the solvent, while in liquid-liquid solutions the liquid solute must have affinity with the solvent in order to dissolve, in fact, as they say “the similar dissolves its similar”: a polar solute dissolves in a polar solvent, while a non-polar solute dissolves in a non-polar solute. Some liquids are completely miscible at all proportions, such as ethanol in water (both polar) or benzene with oil (both apolar), some are only partially miscible, such as water and ether, and some are completely immiscible, such as water in oil.

To study a solution, at least two pieces of information are needed: first, it is useful to know the qualitative composition of the solution, that is we need to know which chemical components are present, second, it is necessary to know the quantitative composition of the solution, that is we need to know the quantity or “concentration” of each component in the solution.

Solutions of a solid in a liquid are always possible, as long as the liquid solvent substance is properly chosen, in this case the solution will have a volume normally smaller than the sum of the component volumes and it will involve both a molecular disintegration work and a consequent lowering of the temperature: by consumption of heat of solution (necessary for the change of state of the solid) and heat of dilution (for the transport of the disintegrated molecules in the liquid). The ratio of the amount of solute to the amount of solvent (or solution) is called the concentration of the solution and can be expressed in various ways.

The maximum amount of a substance that can dissolve in a given amount of solvent at a given temperature is called the solubility of that substance in that solvent at that temperature, and a solution containing this maximum amount is called saturated.

It is possible to affirm, therefore, that as every liquid has, for a certain value of temperature, its own vapor pressure which is opposed by the external pressure, so every substance has, for a given solvent, a certain solution tension, which is a function of temperature, which is opposed by the osmotic pressure (osmosis); when the solution tension and the osmotic pressure are equal, the solution becomes saturated, i.e. a dynamic equilibrium is established for which as many as the solute particles are dispersed, as many as the solute particles are redeposited. Therefore, as a vapor is saturated in the presence of its liquid, so is saturated the solution of a solid in a liquid when a part of the solute is present undissolved, as a background body.

Changes in solubility as a function of temperature can be represented, for each substance in a given solvent, by solubility curves. Since the solution of a substance in a solvent is accompanied by thermal changes, it can be predicted whether the solubility increases or decreases with temperature: it increases for substances that dissolve with heat absorption, decreases for those that dissolve with heat development. In liquid mixtures, when the solubility is limited (for example case of water and ether) two layers are formed consisting of mutually saturated solutions (ether in water, heavier, and water in ether, lighter). Gases dissolve in liquids with the development of heat, so their solubility increases with decreasing temperature, as well as with increasing pressure (Henry’s law).

The solution of a crystalline substance can be brought, by cautious evaporation of the solvent, to a higher concentration than the saturation level: so we obtain over-saturated solutions, unstable, from which, by simple agitation for the addition of a small fragment (germ) of solute, the part dissolved in excess is separated.

From a physical point of view, besides the temperature, other factors affect the solubility of a substance, in particular the type and intensity of the forces that interact between the particles of solvent and solute; in the study of the phenomenon, the particles that are considered can be molecules (in which is present, or not, an electric dipole), ions and metal atoms.

In general we can say that solubility is high when the electrical properties of solvent and solute molecules are similar; for example water, a polar substance, is a good solvent of polar substances and ionic compounds, such as salts, as electrostatic interactions are established between the dipoles represented by water molecules and the molecules or ions of the solute, with formation of solvates.

For non-polar substances, such as hydrocarbons, which are miscible with each other in any ratio, solubility is due to quantum-mechanical interactions between the electronic systems of the molecules (London forces); these interactions do not depend on temperature, but on the number and mobility of the electrons of the individual molecules.

A very dilute solution, in which the interactions between solute and solvent molecules can be neglected, is called ideal solution; in this case it is assumed that the mixing of solute and solvent molecules occurs without changes in volume and thermal content.

For ideal solutions are valid the so-called colligative properties, which do not depend on the nature of the solute, but only on the number of particles in the solution. One of these properties is the osmotic pressure for which Van’t Hoff’s law applies. This is based on Avogadro’s principle, stated for ideal gases: equal volumes of solution, under equal conditions of temperature and osmotic pressure, contain an equal number of molecules.

Based on this law, πV = nRT, is similar to the equation of state of ideal gases: PV = nRT, we can also determine the molecular weights of solutes. In fact, the reaction g/PM expresses the number of moles of the nondissociable solute, and thus the molecular weight PM can be calculated from the relation:

$\textrm{PM} =\dfrac{gRT}{\pi V}$

In fact, the equations describing systems in solution should refer more properly to activities than to solute concentration. The term activity refers not so much to the species of the solute, ions or molecules, present in solution, but to the active species of the solute, that is, those that generate the effect that can be measured experimentally.

The relationship between activity a and concentration c of the solute is given by a = αc, where α is the activity coefficient, which is equal to 1 only for concentrations less than 0.01 M. This means that solutions with unit activity coefficient have behavior close to ideal solutions. Real solutions are studied by applying the laws valid for ideal solutions and comparing the results with values obtained by experimental measurements of colligative properties.

## Solid Solutions

A solid solution is essentially a crystalline phase that can have varying composition. As in the case of doped materials, simple solid solutions can be of two types: substitutional or interstitial. From these two basic types, much more complex types of solid solutions can be derived, which are simultaneously substitutional and interstitial, or which contain ions of different charge than the originals, and so on. Many solid solutions have considerable technological interest.

### Substitutional solid solutions

In metal alloys formed by substitutional solid solution, ions of another metal replace as many ions in the crystal lattice of the main metal; for this to happen, the ions of the two metals must be of similar size; this is the case, for example, of brass, a copper-zinc alloy.

To form a simple substitutional solid solution there are conditions that must be verified:

1. The substituting ions must have the same charge. Otherwise, other structural changes occur, with formation of vacancies and interstitial species to maintain electroneutrality.
2. The substituting ions must be of very similar size. From experimental data on metal alloys, it is believed that the upper limit for substitution of dissimilar metals is around 15% of the metal radius. For non-metallic solid solutions the limiting difference in size appears to be a little over 15% but it is difficult to quantify precisely mainly because of uncertainties about ionic radii and because the formation of solid solutions is very much temperature dependent. In fact, often several solid solutions can be formed at high temperatures while at lower temperatures the formation of the same can be very reduced or practically impossible. In general the formation of solid solutions is thermodynamically favored by high temperatures (as the TDS term increases).
3. An important factor is the crystal structure of the two component salts. For systems that exhibit complete solid solution behavior, it is essential that the two extreme members be isostructural. The reverse is not true, of course, i.e., it is not enough for two phases to be isostructural to form solid solutions (e.g., LiF and CaO both have rock salt structure but do not form solid solutions).

### Interstitial solid solutions

In metal alloys formed by interstitial solid solution, small atoms are placed in the lattice cavities of the main metal. A typical example is steel, an alloy in which carbon atoms are present among the iron ions, in a percentage varying from 0.2% to 1.5%.

### More complex solid solutions: aliovalent substitution

Considering solid solutions in a more general perspective, we can distinguish them into two broad classes: those obtained by homovalent substitutions and those obtained by heterovalent or aliovalent substitutions.

In the first case the ions are replaced by others with the same charge (as in the examples seen so far), while in the second case the ions are replaced by others of different charge. Consequently, in this case, other changes are required to achieve electrical neutrality, either by an ionic mechanism of the “vacancy or interstitial” type (ionic compensation), or by an electronic mechanism of “electrons or holes” (electronic compensation).

#### Ionic compensation

There are four possibilities for cation substitution, as with non-stoichiometric compounds:

1. substitution with higher-charge cations > creation of cation vacations: if the substituent cation has a higher charge, cation vacations can be created to preserve electroneutrality. For example NaCl can dissolve a small amount of CaCl2 by substituting two Na+ ions with one Ca2+ ion leaving one Na site vacant.
2. Substitution with higher charged cations > creation of interstitial anions: the other mechanism, if the substituting cation has a higher charge, is to create interstitial anions. This is not very common because in many structures there are not large enough interstitial sites to accommodate extra anions. Only in certain cases can fluorite type structures function in this way.
3. substitution with less charged cations > creation of anionic vacancies: if the cation to be substituted has a higher charge than the one being replaced, the charge balance can be maintained by creating anionic vacancies or interstitial cations. The best known example is still with the structure of fluorite, in oxides such as zirconia, ZrO2. These materials are very important in modern technology, both as ceramic materials and as solid electrolytes (with oxide ions as conductors).
4. substitution with lower charged cations > creation of interstitial cations: this is a common mechanism of solid solution formation, although the most important structural examples (some aluminosilicates) are quite complex.

A similar pattern is possible for anionic substitution, but this is much less common in solid solutions.

## Hypotonic, isotonic and hypertonic solutions

Taking two solutions with different molar concentration (different number of particles dissolved in them), we define:

• hypotonic solution the solution with lower molar concentration (in other words it is the solution that has a lower osmotic pressure than another solution to which it is compared, and consequently the solvent will tend to diffuse towards the hypertonic solution with higher concentration);
• hypertonic solution the solution with a higher molar concentration (in other words it is the solution that has a higher osmotic pressure than another solution to which it is compared, and consequently the solvent will tend to diffuse towards the hypotonic solution with lower concentration);
• isotonic solution when two solutions have the same molar concentration of solute (they are also called equimolar); in other words the two solutions have the same osmotic pressure value.