Chemistry and physics are each complementary to the other: that region of inquiry in which they mutually overlap is known as physical chemistry. Its beginnings are practically contemporaneous with those of chemistry itself. Its main development has occurred, however, during the last twenty-five years. Certain of its leading features have been referred to already in connection with the establishment of the fundamental principles of chemistry, the explanation of the so-called gaseous laws, the constitution of gases, the relations of their volumes to heat and pressure, and the conditions affecting their transition to the liquid state.

As regards the molecular volumes of gases it has been shown that simple relations are obtained when quantities represented by their respective molecular weights are compared under identical conditions of temperature and pressure—that is, under circumstances in which equal numbers of molecules form the basis of comparison. The investigation of the molecular volumes of liquids is complicated by the uncertainty as to what constitutes in their case a valid condition of comparison. Kopp’s assumption that a comparable condition was the temperature at which the vapour pressures of the liquids are equal to the mean atmospheric pressure was justified by the fact that the boiling-points of liquids are approximately two thirds of their respective critical temperatures. His conclusions have been confirmed and extended by Lossen, Thorpe, and Schiff. It has been shown that the molecular volume of a liquid—that is, the product of its relative density at the boiling-point into its molecular weight—is in the main an additive function modified by constitutive influences. Definite values have thus been obtained for a number of the elements from a comparison of homologous or similarly constituted compounds; and in certain cases these are found to be practically identical with the values of the elements in the uncombined state.

Considerable light has been gained during the last two decades concerning the nature of solution. In its most comprehensive sense solution means the homogeneous mixture of two or more substances: thus the gases which exert no chemical action on each other are mutually soluble; gases, liquids, and solids may be soluble in liquids; and, lastly, solids maybe soluble in solids, forming what are known as solid solutions. The mutual solubility of gases was studied by Dalton who enunciated the law of partial pressures, which states that the total pressure of a mixture of gases is the sum of the pressures exerted by the individual components. This, like all the so-called gaseous laws, is necessarily not strictly accurate under ordinary conditions, but approximates to truth in proportion as the gases are rarefied. Van ’t Hoff pointed out that the true partial pressures of the components of a gaseous mixture might be experimentally ascertained by the use of a membrane capable of effecting their separation, and on this principle Ramsay measured the partial pressures of a mixture of hydrogen and nitrogen contained in a palladium vessel connected with a manometer. The palladium, at a sufficiently high temperature, is permeable to hydrogen to the exclusion of the nitrogen. The conditions affecting the solubility of gases in liquids were experimentally studied by Dalton and Henry, and what is known as Henry’s law implies that the volume of a gas dissolved by a definite volume of a liquid is independent of the pressure; or, in other words, the density (concentration) of the gas in solution is proportional to that in the space above the liquid. Gases are dissolved by liquids in very different amounts, but nothing definite is known as yet concerning the relation between the nature of the gas and its solubility, although certain broad generalisations are possible. Thus neutral gases—e.g., hydrogen and nitrogen—are sparingly soluble, whereas gases which show acidic or basic properties, such as the hydrogen halides, etc., ammonia, etc., are freely soluble. Easily liquefiable gases are also comparatively soluble as noted by Graham.

Comparatively little is known definitely concerning the conditions of solubility of liquids in liquids. Some liquids are wholly, others partially miscible; and temperature and pressure appear to affect the proportions in which the components form a homogeneous mixture. As regards the solubility of solids in liquids, our knowledge is more extensive, and a considerable body of literature exists on the subject, chiefly concerning solubility of solids in water. The solubility of a solid depends on the temperature of the solvent, and, as a rule, increases with the temperature until a certain amount of the solid has been dissolved, when the solution is said to be saturated. If the clear saturated solution be slowly cooled, say, to a particular temperature, it is frequently observed that more of the solid remains in solution than is normal to that temperature; such a solution is said to be supersaturated. On adding some of the solid to the supersaturated solution the excess of the solute is precipitated. In certain cases of solubility of substances in water, increase of temperature appears to diminish the amount dissolved. In nearly all such cases the difference in solubility is due to differences in the hydration of the solute. The phenomena of solid solutions have been less perfectly investigated, but the facts appear to show that such solutions in general tend to obey the laws regulating the solution of liquids in liquids. Alloys may be looked upon as solid solutions; and Roberts-Austen has shown that metals are capable of intradiffusion, like liquids and gases respectively.

The general question of solution was greatly developed in 1885 by Van ’t Hoff, by specially considering the case of dilute solutions. The gaseous laws are capable of their simplest expression when the gases are rarefied to such an extent that their molecules exert no sensible mutual influence. The case of dilute solutions is analogous. If the solute is present only in very small amount, the mutual influence of its molecules is practically negligible. Under such conditions it obeys the laws hitherto supposed to be applicable only to matter in the gaseous state.

It may be desirable to explain how this fundamental fact was recognised. It has long been known to the physiologist that certain membranes are semi-permeable—that is, they allow of the passage of certain liquids, and of substances in solution, to the exclusion of others. This phenomenon is termed osmosis, and is of great biological significance. It was first studied by plant-physiologists, notably by Traube and Pfeffer. Many such semi-permeable membranes can be formed artificially, but the most generally convenient is found to be one consisting of copper ferrocyanide deposited on the walls of a porous vessel.

If a vessel so prepared be filled with a solution of sugar, and be then placed in water, the water is found to pass through the membrane, but the membrane is impermeable to the sugar. In consequence pressure, termed osmotic pressure, is found to occur within the pot, and may be measured by suitable means. These osmotic pressures may at times be very large: thus a 1 per cent. solution of sugar may exert a pressure of half an atmosphere, and in the case of a solution of potassium nitrate of the same concentration it may amount to a couple of atmospheres.

Pfeffer determined the relation of the osmotic pressures to the concentration of solutions of these substances, measuring the pressures in centimetres of mercury by a manometer attached to the closed porous vessel. His results in the case of sugar were as follows:

It will be seen from these numbers that the ratio P/C is practically constant—that is, the osmotic pressure varies directly as the concentration. It was further found that the osmotic pressure exerted by a solution of uniform strength increases with the temperature.

The importance, of these observations in relation to the general theory of solution was first recognised by Van ’t Hoff. Osmotic pressure was regarded by him as analogous to gaseous pressure. Since P/C is constant for any one substance, and since for a definite weight of the solute the concentration is inversely as the volume of the solution, we obtain an equation analogous to the statement of Boyle’s law, PV = constant. Van ’t Hoff also found that the osmotic pressure is proportional to the absolute temperature, like the gaseous pressure. From these results, in conjunction with Avogadro’s hypothesis, it follows that the osmotic pressure exerted by any substance in solution is the same as it would exert if present as gas in the same volume as that occupied by the solution, provided that the solution is so dilute that the volume occupied by the solute is negligible in comparison with that occupied by the solvent. Another important consequence is that solutes, when present in the ratio of their molecular weights in equal volumes of the same solvent, exert the same osmotic pressure. Such solutions are said to be isomotic or isotonic. It can be proved by thermodynamical reasoning that depression of the vapour pressure and freezing-point of a solution is proportional to its osmotic pressure. The significance of this relation in connection with the determination of the molecular weight of a soluble substance has already been referred to.6

Determinations of molecular freezing-point depressions by Raoult and others showed that certain substances exerted only about half the osmotic pressure calculated from their known formulæ, whereas others have abnormally high osmotic pressures. The explanation of the discrepancies in the latter case was given in 1887 by Arrhenius, who pointed out that only those solutions which have abnormally high osmotic pressures are electrically conductive. This pregnant observation proved to be very fruitful in suggestiveness; and the connection between conductivity and Van ’t Hoff’s theory of solution was developed by Arrhenius into the doctrine of electrolytic dissociation or ionisation—one of the most important consequences of Faraday’s electrolytic laws, the work of Hittorf, and the kinetic conceptions of Williamson and Clausius to which the last quarter of a century has given rise. Arrhenius showed that not only were free ions present in an electrically conductive solution before electrolysis, as maintained by Clausius, but that the proportion of molecules dissociated into ions could be calculated from measurements of electrical conductivity, as well as from measurements of osmotic pressure. Both methods give concordant results—a strong confirmation of the validity of the theory. In a solution of common salt, containing a gramme equivalent of that substance in a litre, Arrhenius calculated that only about three tenths of the salt exists as NaCl, the remaining seven tenths being resolved into independent ions of chlorine (chloridion) and sodium (sodion): NaCl⇄[Na·] + Cl´, each moving freely in all directions, like gaseous molecules. On passing the current, electrodes placed in the solution exert a directive action on the free ions, these alone being concerned in determining the conductivity, the un-ionised molecules or the solvent itself exercising no influence. Methods of determining the migration velocity of the ions have been worked out by Hittorf, Kohlrausch, Lodge, and others.

The theory of ionisation affords a satisfactory explanation of many chemical phenomena. It accounts for the characteristic properties of acids, and explains why different acids have varying “strengths” and why a “weak” acid has the same “strength” as the “strong” acid at high equivalent dilutions: in each case the acid is nearly completely ionised—in other words, the “strength” of an acid depends on the concentration of its hydrogen ions. So, too, the “strength” of a base is related to the number of its hydroxyl ions. Aqueous ammonia is relatively a “weak” base—its solution contains few hydroxyl ions. On the other hand, caustic potash is a “strong” base—its solution, on moderate dilution, is almost completely ionised: KOH = K· + OH´, the positive ion being represented by one or more dots, and the negative ion by one or more dashes. The theory accounts, too, for many phenomena in analytical chemistry—such as why magnesia is precipitated by ammonia only in the absence of ammonium chloride, and why sulphuretted hydrogen throws down zinc sulphide in the absence of hydrochloric acid. It also serves to explain many thermo-chemical facts observed by Hess, Thomsen, and others, such as the fact that the heat of neutralisation of the “strong” acids and bases is independent of their nature, and has the uniform value of 13,700 calories, in agreement with the value, as calculated by Van ’t Hoff, for the reaction H· + OH´ = H₂O, deduced from Kohlrausch’s measurements of the conductivity of water at varying temperatures.

Certain phenomena relative to the effect of concentration (mass action) in determining chemical change—many of which have been studied by Ostwald and his pupils, as, for example, why two dilute solutions can be mixed together without thermal disturbance; numerous hydrolytic actions; the alkalinity and acidity of salts on solution; the behaviour of the “indicators” in analysis; such phenomena as the precipitability of common salt in aqueous solution by hydrogen chloride; the influence of an excess of a precipitant; the varying behaviour of reagents; the varying colour of salt solutions; the reason why water is formed in so many reactions; why a potential difference occurs at the surface of two electrolytic solutions, etc.—phenomena for the most part otherwise unintelligible, are all capable of explanation by means of it.

Although, in the above statement, we have been mainly concerned with aqueous solutions, it should be said that the theory of ionisation is applicable to other solvents, organic and inorganic. Moreover, it should be added, the theory has not been universally accepted as accounting for all the phenomena of solution. Many substances form definite hydrates which can be isolated, and it is a moot point whether such hydrates are capable of existing in aqueous solution, as contended by Mendeléeff, Pickering, Kahlenberg, Armstrong, and others. Such hydrates are, however, unstable compounds, affected by temperature changes, and dissociable on dilution in accordance with the law of concentration (mass action). Further, there is evidence, largely based on the work of Kohlrausch, H. C. Jones, and Lowry, to show that the ions in aqueous solutions of electrolytes are themselves hydrated.

Limitations of space preclude further attempts to deal with the development of physical chemistry during the last half-century, and many important matters must remain practically unnoticed.

The subject of thermo-chemistry is mainly the creation of the last half-century, elaborated by the labours of Hess, Andrews, Thomsen, Favre and Silbermann, and Berthelot. The work of Wenzel and Berthollet on the influence of molecular concentration on chemical change has been greatly extended by Berthelot, Guldberg and Waage, Julius Thomsen, Van ’t Hoff, Harcourt and Esson, and Le Chatelier; and the theory of mass action and the nature of reversible processes are now capable of definite expression, and can be proved independently by thermo-dynamical and kinetic reasoning. The phenomena of catalysis and the action of enzymes and of fermentation in general have received attention from many investigators. The phenomena of gaseous transpiration have been studied by Graham, Maxwell, and O. E. Meyer. Thermal dissociation has been experimentally observed by Deville, Troost, and others, and mathematically investigated by Willard Gibbs and Van der Waals; and its analogy to electrolytic dissociation has been established. The nature of gaseous explosions has been investigated by Berthelot, Le Chatelier, Abel, and Dixon. Important work has been done by Gladstone, Lorentz, Landolt, Nasini, Brühl, and others, on the connection between the nature and constitution of substances and their optical characters. Similar work has been done by Sir William Perkin as regards their magnetic rotation, and by Thorpe and Rodger with reference to their viscosity. The theory of phases, originating with Gibbs and developed by Van der Waals and Roozeboom, has been greatly extended. Sir J. J. Thomson and Sir J. Larmor have elaborated an electrical theory of the atom. Barlow and Pope have traced the relation between valency and volume, and the accurate measurements of Groth and of Tutton have extended our knowledge of the crystallographic relations of correlated substances.

Lastly, the whole subject of photo-chemistry, although originating with the observations of Ingenhousz, Scheele, and Senebier, may be said to have been studied only within our own time, notably by Bunsen and Roscoe, Pringsheim, Pfeffer, Vogel, and Abney.