SOLUBILITY EXPLAINED B y A. G. S HARPE , l\1.A., PH .D., F.R.I.C. Lect~t1·e1· in In01·ganic Ghemist1·y, Gamb1··idge Unive;rsity A solution is a homogeneous mixture of t wo with which the chemist, especially in t he (or more) components. In t his context, early stages of his training, is most concerned. homogeneity denotes not merely uniformity The general principles on which solubility is under observation by the eye, but incapability discussed apply, however, to all types of of separation into constituents by any solution, and the aim of this account is to mechanical means: in a true solution the provide a brief introduction which , although particles of both constit uents are separate reasonably self-contained, will serve as an molecules or ions, though there is sometimes introduction to a more advanced under­ quite strong interaction between one molecule standing of the whole field of solubility. No or ion and a small number of others in its part of this, it is interesting to note, is more immediate environment. It is common difficult to treat quantitatively t han t he practice to discuss solubility in terms of a solubility of salts in water, the subject with solvent and one (or more) solutes; t he which the student usually makes his fu·st solvent is the component that dissolves the acquaintance with solubility phenomena. sol~de , i .e. retains its own physical state after Most pairs of substances (other than pairs addit ion of the solute. In some instances, of gases) are only partially miscible. When however, it is not clear which component is sucrose (ordinal'y sugar) is stirred with water the solvent and which the solute. Such a at 25°, for example, the concentration of t he case exists for two liquids such as ethanol solution event ually reaches a consta,nt value; and water, which are miscible in all propor­ t he solution is then said to be saturated, and tions; the distinction is of no real importance its concentration is the solubility of sucrose in these circumstances, but it is conventional in water at this temperature. This solubility to refer to the component present in greater may be expressed in several ways. From a amount as the solvent. physicochemical viewpoint , the most funda­ Solutions are often classified on the basis of mental of these is in terms of t he ratio of the t heir physical state (gaseous, liquid, or solid) number of gram-molecules, or moles, of and t he physical state of the pur e solute at the sucrose to t he total number of gram-molecules ordinary temperature. There are then nine (of sucrose and water) in the liquid phase­ types of solution, and these are listed, with the mole j?-action of sucrose. Also in common an example of each , in the table. use are molm·ity (the number of moles per litre of solution), molality (number of moles per 1,000 g of solvent) and weight peT cent (number of grams of solute per 100 g of Solution E xample solution) as units of solubility; the second of Gas in gas Air t hese is especially widely used in dealing with L iq uid in gas .. ·w ater (vP.pou r) in nitrogen solutions of electrolytes, where the term Solid in gas .. Iodine (vapour) in nit.-ogen Gas in liquid .. Carbon dioxide in water (sod a- 'gram-formula-weight' replaces 'gram-mole­ water ) cule.' F or solutions of gases in liquids t he Liquid in liq uid Ethanol in water absorption coefficient (the volume of gas, Solid in liqu id Sodium chloride in wate r Gas in solid . H ych·ogen in palladium reduced to 0°0 at l atm, dissolved by one L iquid in solid Morcury in silve1.· (amalgam) volume of solvent at the temperature of the Sol id in solid . Copper in nickel (coinage alloy) experin1ent under a partial pressure of the gas of l atm) is the unit most frequently This article is concerned mainly with employed. solutions of gases, liquids and different t ypes The equilibrium which exists in a saturated of solid in liquids, since these are the solutions solution is, lilce all other equilibria, a dynamic 75 76 EDUCATION IN CHEMISTRY one, as may be shown by isotopic tracer to the division of the total heat content (H) at experiments: the rate of dissolution of the absolute temperature T of a system into two solute is equal to its rate of separation from parts: that part which can be converted into the solution. The position of equilibrium is other forms of energy without change of affected by heat and pressure in accordance temperature is ]mown as j?-ee ene1·gy (G), with Le Chatelier's principle, and the solu­ whilst the part which is not convertible bility of a non-electrolyte is, in fact, an (H - G) is defined as the product of the equilibrium constant. F or substances which absolute temperature and a quantity called yield ions in solution, such as salts of formula the ent1·opy (S) of the system. Thus l\fX, the equilibrium is of the form H = 0 + TS MX (solid) ~ :M+ (in soln) + X- (in soln) or, for a change taking place at constant and the equilibrium constant is the product temperature T , of the activities {approximately, of the con­ D.H = D.G + T 6S centrations) of M+ and X- in solution, t he activities of solids being taken arbitrarily as The quantity S may also be looked at in unity; this equilibrium constant is known as another way, as a measure of the degree of the solubility prod1tct of l\fX at the tem­ randomness of the system. This aspect may perature chosen. For a salt of formula l\1X2, be illustrated by considering what happens if 2 the solubility product is [M+] [X-] , and so we m.i...-.,;: equal quantities of hot and cold on. Since [M+] and [X- ] are proportional to water : the resulting liquid all has the same the amount of dissolved salt, we see that the temperature, and instead of there being relation between solubility and solubility molecules describable as belonging to one product depends on the formula of the salt of two different categories, all are now mixed concerned. up-the randomness of the system has One feature of discussions of solubility increased. At the same time, although no which calls for particular comment is the use heat has been gained or lost, the possibility of the term 'insoluble.' )fost chemists tend of using the system to obtain electrical energy to describe as 'insoluble' any substance by putting thermocouples in the water at which dissolves in a liquid to the extent of different temperatw-es has disappeared. Gain less than about l g in 1,000 g of solvent. in entropy is therefore accompanied by a Silver chloride and cupric sulphide, for corresponding loss in free energy if there is example, are by this criterion insoluble in no change in the total heat content of the water. Their solubilities, l 0- 5 and 10- 22 system. Just as every substance has a g-formula-weight per litt·e, and solubility standard heat offormation, it has also a stan­ products, 10- 1 0 and I0- 44 (g-ionflitre)2, at dard free energy of formation and a 25°, however, are very different, and (as will standard entropy, and from tables of such be seen later) from the point of view of the quantities (which may be determined inde­ energy change which would be involved in pendently by a variety of methods) it is getting a g-formula-weight of solute into possible to compute changes in them for aqueous solution there is very much more different reactions. difference between silver chloride and copper The very existence of endothermic (heat­ sulphide than between silver chloride and absorbing) processes which take place spon­ sodium chloride, the solubility of which is taneously (e.g. the dissolution of most 0·62 g-formula-weight per litre at 25°. substances in water) is a proof that it is not ·we must now see why it is important to the change in heat content (t:JJ) which know something about such energy changes. determines how far a reaction goes, i .e. it s. It is well known that there are several forms equilibrium constant. This quantity is the of energy, such a,'3 mechanical, electrical, free-energy change, which is therefore a chemical and thermal energy. All forms of quantity of the greatest importance through­ energy can be converted into heat, but the out chemistry. It is not essential in obtainij1g converse is not always t rue, and this has led some understanding of the significance of the SOLUBILITY EXPLAINED 77 concept of free energy in chemistry to master tion or liberation of heat (if 6.H = 0, MJ. = the numerical form of all the relationships -T6.S). Usually, however, it will be involved, but one such relationship is of out­ necessary to consider heat terms as well as standing importance: if a reaction is carried entropy terms, and to what extent a solute A out on a very small scale (say, one-millionth will dissolve in a solvent B will then be deter­ gram-formula quantities) in the presence of mined la.rgely by the difference between the all the reactants and products at unit energy of interaction of A with B and the activity, and the free-energy change is energies of interaction of A with A, and B with multiplied (in t his case by a million) to give B.