Part 56

Law of Mass Action.—Berthollet about the beginning of the last century was the first chemist to study the effect of mass, or more correctly, the concentration of substances on chemical action. His views summarized by himself are as follows: “The chemical activity of a substance depends upon the force of its affinity and upon the mass which is present in a given volume.” The development of this idea, which is fundamentally correct, was greatly hindered by the fact that Berthollet drew the incorrect conclusion that the composition of chemical compounds depended upon the masses of the substances combining to produce them, a conclusion in direct contradiction to the law of definite proportions, and since this view was soon disproved by Proust and others, Berthollet’s law in its other applications received no immediate attention. Mitchell, however, pointed out in the Journal (=16=, 234, 1829) the importance of Berthollet’s work, and Heinrich Rose in 1842 again called attention to the effect of mass, mentioning as one illustration the effect of water and carbonic acid in decomposing the very stable natural silicates. Somewhat later several other chemists made important contributions to the question of the influence of concentration upon chemical action, but it was the Norwegians, Guldberg and Waage, who first formulated the law of mass action in 1867.

This law has been of enormous importance in chemical theory, since it explains a great many facts upon a mathematical basis. It applies particularly to equilibrium in reversible reactions, where it states that the product of the concentrations on the one side of a simple reversible equation bears a constant relation to the products of the concentrations on the other side, provided that the temperature remains constant. In cases of this kind where two gases or vapors react with two solids, the latter if always in excess may be regarded as constant in concentration, and the law takes on a simpler aspect in applying only to the concentrations of the gaseous substances. For example, in the reversible reaction

3Fe + 4H{2}O ⇄ Fe{3}O{4} + 4H{2},

which takes place at rather high temperatures, a definite mixture of steam and hydrogen at a definite temperature will cause the reaction to proceed with equal rapidity in both directions, thus maintaining a state of equilibrium, provided that both iron and the oxide are present in excess. If, however, the relative concentrations of the hydrogen and steam are changed, or even if the temperature is changed, the reaction will proceed faster in one direction than in the other until equilibrium is again attained.

The principle of mass action also explains why it is sometimes possible for a reversible reaction to become complete in either direction. For instance, in connection with the reaction that has just been considered, if steam is passed over heated iron and if hydrogen is passed over the heated oxide, the gaseous product in each case is gradually carried away, and the reaction continually proceeds faster in one direction than in the other until it is complete, according to the equations

3Fe + 4H{2}O → 3Fe{3}O{4} + 4H{2}, and

Fe{3}O{4} + 4H{2} → 3Fe + 4H{2}O.

Many other well-known and important facts, both chemical and physical, depend upon this law. It explains the circumstance that a vapor-pressure is not dependent upon the amount of the liquid that is present; it also explains the constant dissociation pressure of calcium carbonate at a given temperature, irrespective of the amounts of carbonate and oxide present; in connection with the ionic theory, it furnishes the reason for the variable solubility of salts due to the presence of electrolytes containing ions in common; and it elucidates Henry’s law which states that the solubilities of gases are proportional to their pressures.

Ostwald, more than any other chemist, has been instrumental in making general applications of this law, and he made particularly extensive use of it in connection with analytical chemistry in a book upon this subject which he published.

The Phase Rule.—In 1876 Willard Gibbs of Yale published a paper in the Proceedings of the Connecticut Academy of Science on the “Equilibrium of Heterogeneous Substances,” and two years later he published an abstract of the article in the Journal (=16=, 441, 1878). He had discovered a new law of nature of momentous importance and wide application which is called the “Phase-Rule” and is expressed by a very simple formula.

The application of this great discovery to chemical theory was delayed for ten years, partly, perhaps, because it was not sufficiently brought to the attention of chemists, but largely it appears because it was not at first understood, since its presentation was entirely mathematical.

It was Rooseboom, a Dutch chemist, who first applied the phase-rule. It soon attracted profound attention, and the name of Willard Gibbs attained world-wide fame among chemists. When Nernst, who is perhaps the most eminent physical chemist of the present time, was delivering the Silliman Memorial Lectures at Yale a few years ago, he took occasion to place a wreath on the grave of Willard Gibbs in recognition of his achievements.

To understand the rule, it is necessary to define the three terms, introduced by Gibbs, phase, degrees of freedom and component.

By the first term, is meant the parts of any system of substances which are mechanically separable. For instance, water in contact with its vapor has two phases, while a solution of salt and water is composed of but one. The degrees of freedom are the number of physical conditions, including pressure, temperature and concentration, which can be varied independently in a system without destroying a phase. The exact definition of a component is not so simple, but in general, the components of a system are the integral parts of which it is composed. Any system made up of the compound H_{2}O, for instance, whether as ice, water or vapor, contains but one component, while a solution of salt and water contains two. Letting P, F, and C stand for the three terms, the phase-rule is simply

F = C + 2 − P

that is, the number of degrees of freedom in a system in equilibrium equals the number of components, plus two, minus the number of phases. The rule can be easily understood by means of a simple illustration. In a system composed of ice, water and water vapor, there are three phases and one component and therefore

F = 1 + 2 − 3 = 0

Such a system has no degrees of freedom. This means that no physical condition, pressure or temperature can be varied without destroying a phase, so that such a system can only exist in equilibrium at one fixed temperature, with a fixed value for its vapor-pressure.

For instance, if the system is heated above the fixed temperature, ice disappears and if the pressure is raised, vapor is condensed. If this same system of water alone contains but two phases, for instance, liquid and vapor, F = 1 + 2 − 2 = 1, or there is one degree of freedom. In such a system, one physical condition such as temperature can be varied independently, but only one, without destroying a phase. For instance, the temperature may be raised or lowered, but for every value of temperature there is a corresponding value for the vapor-pressure. One is a function of the other. If both values are varied independently, one phase will disappear, either vapor condensing entirely to water or the reverse. Finally if the system consists of one phase only, as water vapor, F = 2, or the system is divariant, which means that at any given temperature it is possible for vapor to exist at varying pressures.

The illustration which has been given relates to physical equilibrium, but the rule is applicable to cases involving chemical changes as well. In comparing the phase-rule with the law of mass action, it will be noticed that both have to do with equilibrium. The great advantage of the former is that it is entirely independent of the molecular condition of the substances in the different phases. For instance, it makes no difference so far as the application of the rule is concerned, whether a substance in solution is dissociated, undissociated or combined with the solvent. In any case, the solution constitutes one phase. On the other hand, the rule is purely qualitative, giving information only as to whether a given change in conditions is possible. The law of mass action is a quantitative expression so that when the value of the constant is once known, the change can be calculated which takes place in the entire system if the concentration of one substance is varied. The law, however, requires a knowledge of the molecular condition of the reacting substances, which may be uncertain or unknown, and chiefly on this account it has, like the phase-rule, often only a qualitative significance.

The phase rule has served as a most valuable means of classifying systems in equilibrium and as a guide in determining the possible conditions under which such systems can exist. As illustrations of its practical application, van’t Hoff used it as an underlying principle in his investigations on the conditions under which salt deposits have been formed in nature, and Rooseboom was able by its means to explain the very complicated relations existing in the alloys of iron and carbon which form the various grades of wrought iron, steel and cast iron.

Thermochemistry.—This branch of chemistry has to do with heat evolved or absorbed in chemical reactions. It is important chiefly because in many cases it furnishes the only measure we have of the energy changes involved in reactions. To a great extent, it dates from the discovery by Hess in 1840 of a fundamental law which states that the heat evolved in a reaction is the same whether it takes place in one or in several stages. This law has made it possible to calculate the heat values of a large number of reactions which cannot be determined by direct experiment.

Thermochemistry has been developed by a comparatively few men who have contributed a surprisingly large number of results. Favre and Silbermann, beginning shortly after 1850, improved the apparatus for calorimetric determinations, which is called the calorimeter, and published many results. At about the same time Julius Thomsen, and in 1873 Berthelot, began their remarkable series of publications which continued until recently. Thomsen’s investigations were published in 1882 in =4= volumes. It is probably safe to say that the greater part of the data of thermochemistry was obtained by these two investigators. The bomb calorimeter, an apparatus for determining heat values by direct combustion, was developed by Berthelot. The recent work of Mixter at Yale, published in the Journal, and of Richards at Harvard should be mentioned particularly. Mixter’s work in this field began in 1901 (=12=, 347). Using an improved bomb calorimeter, he has developed a method of determining the heats of formation of oxides by combustion with sodium peroxide. By this same method as well as by direct combustion in oxygen, he has obtained results which appear to equal or excel in accuracy any which have ever been obtained in his field of work. Richards’s work has consisted largely of improvements in apparatus. He developed the so-called adiabatic calorimeter which practically eliminates one of the chief errors in thermal work caused by the heating or cooling effect of the surroundings. This modification is being generally adopted where extremely accurate work is required.

Organic Chemistry.

One hundred years ago qualitative tests for a few organic compounds were known, the elements usually occurring in them were recognized, and some of them had been analyzed quantitatively, but organic chemistry was far less advanced than inorganic, and almost the whole of its enormous development has taken place during our period.

Berzelius made a great advance in the subject by establishing the fact, which had been doubted previously, that the elements in organic compounds are combined in constant, definite proportions. In 1823 Liebig brought to light the exceedingly important fact of isomerism by showing that silver fulminate had the same percentage composition as silver cyanate, a compound of very different properties. Isomeric compounds with identical molecular weight as well as the same composition have since been found in very many cases, and they have played a most important part in determining the arrangements of atoms in molecules. They have been found to be very numerous in many cases. For instance, three pentanes with the formula C{5}H{12}are known, all that are possible according to theory, and in each case the structure of the molecule has been established. On theoretical grounds it has been calculated that 802 isomeric compounds with the formula C{13}H{28} are possible, while with more complex formulas the numbers of isomers may be very much greater.

A particularly interesting case of isomerism was observed by Wöhler in 1828, when he found that ammonium cyanate changes spontaneously into urea

(NH{4}CNO → N{2}H_{4}CO).