William Cecil Dampier Whetham

“ It is usual to call each part of the system of uniform composition through- out a phase; in the example given, water substance, the only component is present in two phases—a liquid phase and a vapour phase, and when the potentials of the component are the same in each phase equilibrium exists.
If in unit mass of any phase we have n components instead of one we must know the amount of n−1 components present in that unit mass before we know the exact composition of it. ”

“ When a crystal of the solid phase is present the equilibrium of a solution is given by the solubility curves we have studied. If, however, a solution be cooled slowly past its saturation point with no solid present, crystallization does not occur till some lower temperature is reached. Between the saturation point and this lower temperature, the liquid holds in solution more of the solute than corresponds with equilibrium, and is said to be supersaturated. ”

“ When the equilibria become more complex difficulties of interpretation of the experimental results often arise. It is often very difficult to distinguish between a chemical compound, for example, and the case of solid solution represented by fig. 9. All available evidence, from the freezing point curve and from other sources must be scrutinized before an opinion is pronounced. But the elucidation of the complicated phenomena of solid solutions would have been impossible without the theoretical knowledge deduced from the principle of available energy. ”

“ All the thermodynamic relations we have deduced hold on any theory of solution and favour no one theory rather than another. Whether osmotic pressure be due to physical impact or to chemical affinity it must necessarily have the gas value in a dilute solution, and be related to vapour pressure and freezing point in the way we have traced. ”

“ It will be noticed that in all these theoretical curves the points of initial fusion and solidification do not in general coincide; we reach a different curve first according as we approach the diagram from below, where all is solid, or from above, where all is liquid. Again, it will be seen that the addition of a small quantity of one component, say B, to the other, A, does not necessarily lower the melting point, as it does with systems with no solid solutions; it is quite as likely to cause it to rise. ”

“ Each particle may react in some way on the solvent in its neighbourhood, but if the solution be so dilute that each of these spheres of influence is unaffected by the rest, no further addition of solvent will change the connexion between one particle of solute and its associated solvent. The only effect of adding solvent will be to separate further from each other the systems composed of solute particle as nucleus and solvent as atmosphere; it will not affect the action of each nucleus on its atmosphere. ”

“ An engine cylinder may be imagined to possess a semi-permeable bottom and to work without friction. If it be filled with a solution and the bottom immersed in the pure solvent, pressure equal to the osmotic pressure must be exerted on the piston to maintain equilibrium. ”

“ When a solid such as salt or sugar dissolves in contact with water to form a uniform substance from which the components may be regained by evaporation the substance is called a solution. Gases too dissolve in liquids, while mixtures of various liquids show similar properties. ”

“ It follows that if the thermodynamic heat of solution be positive, that is, if heat be absorbed to keep the system at constant temperature, the solubility will increase with rising temperature, while if heat be evolved on dissolution, the solubility falls when the system is heated. ”

“ Solid Solutions.—In all the cases hitherto considered, the liquid phase alone has been capable of continuous variation in composition. The solid phases each have been of one definite substance. Crystals of ice may lie side by side with crystals of common salt, but each crystalline individual is either ice or salt; no one crystal contains both components in proportions which can be varied continuously. But, in other cases, crystals are known in which both components may enter. ”

“ Certain solids also consist of two or more components which are united so as to show' similar effects. All these cases of solution are to be distinguished from chemical compounds on the one hand, and from simple mixtures on the other. When a substance contains its components in definite proportions which can only change, if at all, by sudden steps, it may be classed as a chemical compound. When the relative quantities of the components can vary continuously within certain limits, the substance is either a solution or a mixture. ”

“ If the salt crystallizes with a certain amount of water as well as with none, we get a second point of equilibrium between four phases. Sodium sulphate, for instance, crystallizes below 32.6° as Na2SO4⋅10H2O, and above that temperature as the anhydrous solid Na2SO4. Taking the point O to denote the state of equilibrium between ice, hydrate, saturated solution and vapour, we pass along OA till a new solid phase, that of Na2SO4, appears at 32.6° ”

“ This result must hold good for any solution, but if the solution be dilute when saturated, that is, if the solubility be small, the equation shows that if there be no heat effect when solid dissolves to form a saturated solution, the solubility is independent of temperature, for, in accordance with the gas laws, the osmotic pressure of a dilute solution of constant concentration is proportional to the absolute temperature. ”

“ But, if no solid be present initially, or if the cooling be rapid, the liquid of composition x becomes supersaturated and may cool till the supersaturation curve is reached at b, and a cloud of A crystals comes down. The temperature may then rise and the concentration of B increase in the liquid in a manner represented by some such line as b f. The conditions may then remain those of equilibrium along the curve / E, but before reaching / the solution may become supersaturated with B and deposit B crystals spontaneously. The eutectic point may never be reached. ”

“ The physical investigation of osmotic pressure, and its correlation by Van't Hoff with the pressure of a gas, brought forward a new aspect of the phenomena, and suggested an identity of physical modus operandi as well as of numerical value. On this view, the function of the solvent is to give space for the solute to diffuse, and the pressure on a semi-permeable membrane is due to the excess of solvent molecules entering over those leaving in conse- quence of the smaller number which impinge on the membrane from the side of the solution ”

“ Graham named the solids formed by the setting or coagulation of these liquids hydrogels. Solutions of colloids in solvents such as water and alcohol seem to be divisible into two classes. Both mix with warm water in all proportions, and will solidify in certain conditions. One class, represented by gelatin, will redissolve on warming or diluting, while the other class, containing such substances as silica, albumen, and metallic, hydrosulphides, will solidify on heating or on the addition of electrolytes to form a solid “gel” which cannot be redissolved. ”

“ Artificial membranes are seldom or never perfectly semi-permeable — some leakage of solute nearly always occurs, but the imperfections of actual membranes need no more prevent our use of the ideal conception than the faults of real engines invalidate the theory of ideal thermodynamics founded on the conception of a perfect, reversible, frictionless, heat engine. ”

“ If the temperature at which this dense spontaneous shower of crystals is found be determined for different concentrations of solution, we can plot a " supersolubility curve," which is found generally to run roughly parallel to the " solubility curve " of steady equilibrium between liquid and already existing solid. When two substances are soluble in each other in all proportions, we get solubility curves like those of copper and silver shown in fig. ”

“ If each mole- cule of the solute combines with a certain number of molecules of the solvent in such a way as to render them inactive for evapora- tion, we get a lowering of vapour pressure. Let us assume that the ratio pjp' of the vapour pressures of the solvent and solution is equal to the ratio of the number of free molecules of solvent to the whole number of molecules in the solution. Each molecular complex, formed by solution and solvent, is treated as a single molecule. ”

“ Whatever view, if any, be adopted as to the nature of a solu- tion, the thermodynamic relations we have investigated equally hold good. It is the strength and weakness of thermodynamic methods that they are independent of theories of constitution. ”

“ In the limit of dilution when n is very small compared with N this gives Raoult's experimental law that the relative lowering is w/N, which we deduced from the osmotic law, and conversely from which the osmotic law follows, while for more concentrated solutions agreement is obtained by assigning arbitrary values to a, which, as we have seen, is 5 in the case of cane-sugar. ”

“ A quantity of gas measured by its molecular weight in grammes when confined in a volume of one litre exerts a pressure of 22-2 atmospheres, and thus the osmotic pressure of a dilute solution divided by its concentration in gramme-molecules per litre has a corresponding value. But we have seen that the depression of dT of the freezing poinjt of a dilute solution is measured by TPdv/h. ”

“ The solution will thus gain solvent,, and will grow more and more dilute. Its volume will also increase, and thus its upper surface will rise in the vessel. But as we ascend in an atmosphere the pressure diminishes; hence the pressure of the vapour in the chamber is less the higher we go, and thus eventually w T e reach a state of equilibrium where the column of vapour is in equilibrium at the appropriate level both with solvent and solution. ”

“ Fig. 16.
of crystals of the solute, crystals will dissolve as solvent enters, and the solution remains saturated throughout. By an imaginary cycle of operations we may then justify the application to solutions of the latent heat have already assumed as applicable. \/T (v2â€"i>i) , P is the osmotic pressure, ture and X the heat of solution of when dissolving to form a volume equation which we In the equation dP/dT = T the absolute temperaunit mass of the solute of saturated solution in an osmotic cylinder. ”