Chapter V: Front Matter (5)

Chelsea was noted at different periods for two famous places of entertainment, Ranelagh (q.v.) in the second half of the 18th century, and Cremorne Gardens (q.v.) in the middle of the 19th. Don Saltero's museum, which formed the attraction of a popular coffee-house, was formed of curiosities from Sir Hans Sloane's famous collections. It was Sloane who gave to the Apothecaries' Company the ground which they had leased in 1673 for the Physick Garden, which is still extant, but ceased in 1902 to be maintained by the Company. At Chelsea Sir John Danvers (d. 1655) introduced the Italian style of gardening which was so greatly admired by Bacon and soon after became prevalent in England. Chelsea was formerly famous for a manufacture of buns; the original Chelsea bun-house, claiming royal patronage, stood until 1839, and one of its successors until 1888. The porcelain works existed for some 25 years before 1769, when they were sold and removed to Derby. Examples of the original Chelsea ware (see CERAMICS) are of great value.

Of buildings and institutions the most notable is Chelsea Royal Hospital for invalid soldiers, initiated by Charles II. (according to tradition on the suggestion of Nell Gwynne), and opened in 1694. The hospital itself accommodates upwards of 500 men, but a system of out-pensioning was found necessary from the outset, and now relieves large numbers throughout the empire. The picturesque building by Wren stands in extensive grounds, which include the former Ranelagh Gardens. A theological college (King James's) formerly occupied the site; it was founded in 1610 and was intended to be of great size, but the scheme was unsuccessful, and only a small part of the buildings was erected. In the vicinity are the Chelsea Barracks (not actually in the borough). The Royal Military Asylum for boys, commonly called the Duke of York's school, founded in 1801 by Frederick, duke of York, for the education of children connected with the army, was removed in 1909 to new quarters at Dover. Other institutions are the Whitelands training college for school-mistresses, in which Ruskin took deep interest; the St Mark's college for school-masters; the Victoria and the Cheyne hospitals for children, a cancer hospital, the South-western polytechnic, and a public library containing an excellent collection relative to local history.

The parliamentary borough of Chelsea returns one member, and includes, as a detached portion, Kensal Town, north of Kensington. The borough council consists of a mayor, 6 aldermen and 36 councillors. Area, 659.6 acres.

CHELSEA, a city of Suffolk county, Massachusetts, U.S.A., a suburb of Boston. Pop. (1890) 27,909; (1900) 34,072, of whom 11,203 were foreign-born; (1910) 32,452. It is situated on a peninsula between the Mystic and Chelsea rivers, and Charlestown and East Boston, and is connected with East Boston and Charlestown by bridges. It is served by the Boston & Maine and (for freight) by the Boston & Albany railways. The United States maintains here naval and marine hospitals, and the state a soldiers' home. Chelsea's interests are primarily industrial. The value of the city's factory products in 1905 was $13,879,159, the principal items being rubber and elastic goods ($3,635,211) and boots and shoes ($2,044,250.) The manufacture of stoves, and of mucilage and paste are important industries. Flexible tubing for electric wires (first made at Chelsea 1889) and art tiles are important products. The first settlement was established in 1624 by Samuel Maverick (c. 1602-c. 1670), the first settler (about 1629) of Noddle's Island (or East Boston), and one of the first slave-holders in Massachusetts; a loyalist and Churchman, in 1664 he was appointed with three others by Charles II. on an important commission sent to Massachusetts and the other New England colonies (see NICOLLS, RICHARD), and spent the last years of his life in New York. Until 1739, under the name of Winnisimmet, Chelsea formed a part of Boston, but in that year it was made a township; it became a city in 1857. In May 1775 a British schooner in the Mystic defended by a force of marines was taken by colonial militia under General John Stark and Israel Putnam,--one of the first conflicts of the War of Independence. A terrible fire swept the central part of the city on the 12th of April 1908.

See Mellen Chamberlain (and others), _History of Chelsea_ (2 vols.,
Boston, 1908), published by the Massachusetts Historical Society.

CHELTENHAM, a municipal and parliamentary borough of Gloucestershire, England, 109 m. W. by N. of London by the Great Western railway; served also by the west and north line of the Midland railway. Pop. (1901) 49,439. The town is well situated in the valley of the Chelt, a small tributary of the Severn, under the high line of the Cotteswold Hills to the east, and is in high repute as a health resort. Mineral springs were accidentally discovered in 1716. The Montpellier and Pittville Springs supply handsome pump rooms standing in public gardens, and are the property of the corporation. The Montpellier waters are sulphated, and are valuable for their diuretic effect, and as a stimulant to the liver and alimentary canal. The alkaline-saline waters of Pittville are efficacious against diseases resulting from excess of uric acid. The parish church of St Mary dates from the 14th century, but is almost completely modernized. The town, moreover, is wholly modern in appearance. Assembly rooms opened in 1815 by the duke of Wellington were removed in 1901. A new town hall, including a central spa and assembly rooms, was opened in 1903. There are numerous other handsome buildings, especially in High Street, and the Promenade forms a beautiful broad thoroughfare, lined with trees. The town is famous as an educational centre. Cheltenham College (1842) provides education for boys in three departments, classical, military and commercial; and includes a preparatory school. The Ladies' College (1854), long conducted by Miss Beale (q.v.), is one of the most successful in England. The Normal Training College was founded in 1846 for the training of teachers, male and female, in national and parochial schools. A free grammar school was founded in 1568 by Richard Pate, recorder of Gloucester. The art gallery and museum may be mentioned also. The parliamentary borough returns one member. The municipal borough is under a mayor, 6 aldermen and 18 councillors. Area, 4726 acres. The urban district of Charlton Kings (pop. 3806) forms a south-eastern suburb of Cheltenham.

The site of a British village and burying-ground, Cheltenham (_Celtanhomme_, _Chiltham_, _Chelteham_) was a village with a church in 803. The manor belonged to the crown; it was granted to Henry de Bohun, earl of Hereford, late in the 12th century, but in 1199 was exchanged for other lands with the king. It was granted to William de Longespee, earl of Salisbury, in 1219, but resumed on his death and granted in dower to Eleanor of Provence in 1243. In 1252 the abbey of Fecamp purchased the manor, and it afterwards belonged to the priory of Cormeille, but was confiscated in 1415 as the possession of an alien priory, and was granted in 1461 to the abbey of Lyon, by which it was held until, once more returning to the crown at the Dissolution, it was granted to the family of Dutton. The town is first mentioned in 1223, when William de Longespee leased the benefit of the markets, fairs and hundred of Cheltenham to the men of the town for three years; the lease was renewed by Henry III. in 1226, and again in 1230 for ten years. A market town in the time of Camden, it was governed by commissioners from the 18th century in 1876, when it was incorporated; it became a parliamentary borough in 1832. Henry III. in 1230 had granted to the men of Cheltenham a market on each Thursday, and a fair on the vigil, feast and morrow of St James. Although Camden mentions a considerable trade in malt, the spinning of woollen yarn was the only industry in 1779. After the discovery of springs in 1716, and the erection of a pump-room in 1738, Cheltenham rapidly became fashionable, the visit of George III. and the royal princesses in 1788 ensuring its popularity.

See S. Moreau, _A Tour to Cheltenham Spa_ (Bath, 1738).

CHELYABINSK, a town of Russia, in the Orenburg government, at the east foot of the Urals, is the head of the Siberian railway, 624 m. by rail E.N.E. of Samara and 154 m. by rail S.S.E. of Ekaterinburg. Pop. (1900) 25,505. It has tanneries and distilleries, and is the centre of the trade in corn and produce of cattle for the Ural iron-works. The town was founded in 1658.

CHELYS (Gr. [Greek: chelus], tortoise; Lat. _testudo_), the common lyre of the ancient Greeks, which had a convex back of tortoiseshell or of wood shaped like the shell. The word _chelys_ was used in allusion to the oldest lyre of the Greeks which was said to have been invented by Hermes. According to tradition he was attracted by sounds of music while walking on the banks of the Nile, and found they proceeded from the shell of a tortoise across which were stretched tendons which the wind had set in vibration (_Homeric Hymn to Hermes_, 47-51). The word has been applied arbitrarily since classic times to various stringed instruments, some bowed and some twanged, probably owing to the back being much vaulted. Kircher (_Musurgia_, i. 486) applied the name of _chelys_ to a kind of viol with eight strings. Numerous representations of the _chelys_ lyre or _testudo_ occur on the Greek vases, in which the actual tortoiseshell is depicted; a good illustration is given in _Le Antichita, di Ercolano_ (vol. i. pl. 43). Propertius (iv. 6) calls the instrument the _lyra testudinea_. Scaliger (on Manilius, _Astronomicon_, Proleg. 420) was probably the first writer to draw attention to the difference, between _chelys_ and _cithara_ (q.v.). (K. S.)

CHEMICAL ACTION, the term given to any process in which change in chemical composition occurs. Such processes may be set up by the application of some form of energy (heat, light, electricity, &c.) to a substance, or by the mixing of two or more substances together. If two or more substances be mixed one of three things may occur. First, the particles may be mechanically intermingled, the degree of association being dependent upon the fineness of the particles, &c. Secondly, the substances may intermolecularly penetrate, as in the case of gas-mixtures and solutions. Or thirdly they may react chemically. The question whether, in any given case, we have to deal with a physical mixture or a chemical compound is often decided by the occurrence of very striking phenomena. To take a simple example:--oxygen and hydrogen are two gases which may be mixed in all proportions at ordinary temperatures, and it is easy to show that the properties of the products are simply those of mixtures of the two free gases. If, however, an electric spark be passed through the mixtures, powerful chemical union ensues, with its concomitants, great evolution of heat and consequent rise of temperature, and a compound, water, is formed which presents physical and chemical properties entirely different from those of its constituents.

In general, powerful chemical forces give rise to the evolution of large quantities of heat, and the properties of the resulting substance differ vastly more from those of its components than is the case with simple mixtures. This constitutes a valuable criterion as to whether mere mixture is involved on the one hand, or strong chemical union on the other. When, however, the chemical forces are weak and the reaction, being incomplete, leads to a state of chemical equilibrium, in which all the reacting substances are present side by side, this criterion vanishes. For example, the question whether a salt combines with water molecules when dissolved in water cannot be said even yet to be fully settled, and, although there can be no doubt that solution is, in many cases, attended by chemical processes, still we possess as yet no means of deciding, with certainty, how many molecules of water have bound themselves to a single molecule of the dissolved substance (_solute_). On the other hand, we possess exact methods of testing whether gases or solutes in dilute solution react one with another and of determining the equilibrium state which is attained. For if one solute react with another on adding the latter to its solution, then corresponding to the decrease of its concentration there must also be a decrease of vapour pressure, and of solubility in other solvents; further, in the case of a mixture of gases, the concentration of each single constituent follows from its solubility in some suitable solvent. We thus obtain the answer to the question: whether the concentration of a certain constituent has decreased during mixing, i.e. whether it has reacted chemically.

When a compound can be obtained in a pure state, analysis affords us an important criterion of its chemical nature, for unlike mixtures, the compositions of which are always variable within wider or narrower limits, chemical compounds present definite and characteristic mass-relations, which find full expression in the atomic theory propounded by Dalton (see ATOM). According to this theory a mixture is the result of the mutual interpenetration of the molecules of substances, which remain unchanged as such, whilst chemical union involves changes more deeply seated, inasmuch as new molecular species appear. These new substances, if well-defined chemical compounds, have a perfectly definite composition and contain a definite, generally small, number of elementary atoms, and therefore the law of constant proportions follows at once, and the fact that only an integral number of atoms of any element may enter into the composition of any molecule determines the law of multiple proportions.

Nature of chemical forces.

These considerations bring us face to face with the task of more closely investigating the nature of chemical forces, in other words, of answering the question: what forces guide the atoms in the formation of a new molecular species? This problem is still far from being completely answered, so that a few general remarks must suffice here.

It is remarkable that among the most stable chemical compounds, we find combinations of atoms of one and the same element. Thus, the stability of the di-atomic molecule N2 is so great, that no trace of dissociation has yet been proved even at the highest temperatures, and as the constituent atoms of the molecule N2 must be regarded as absolutely identical, it is clear that "polar" forces cannot be the cause of all chemical action. On the other hand, especially powerful affinities are also at work when so-called electro-positive and electro-negative elements react. The forces which here come into play appear to be considerably greater than those just mentioned; for instance, potassium fluoride is perhaps the most stable of all known compounds.

It is also to be noticed that the combinations of the electro-negative elements (metalloids) with one another exhibit a metalloid character, and also we find, in the mutual combinations of metals, all the characteristics of the metallic state; but in the formation of a _salt_ from a metal and a metalloid we have an entirely new substance, quite different from its components; and at the same time, the product is seen to be an electrolyte, i.e. to have the power of splitting up into a positively and a negatively charged constituent when dissolved in some solvent. These considerations lead to the conviction that forces of a "polar" origin play an important part here, and indeed we may make the general surmise that in the act of chemical combination forces of both a non-polar and polar nature play a part, and that the latter are in all probability identical with the electric forces.

It now remains to be asked--what are the laws which govern the action of these forces? This question is of fundamental importance, since it leads directly to those laws which regulate the chemical process. Besides the already mentioned fundamental law of chemical combination, that of constant and multiple proportions, there is the law of chemical mass-action, discovered by Guldberg and Waage in 1867, which we will now develop from a kinetic standpoint.

_Kinetic Basis of the Law of Chemical Mass-action._--We will assume that the molecular species A1, A2, ... A'1, A'2, ... are present in a homogeneous system, where they can react on each other only according to the scheme

A1 + A2 + ... <--> A'1 + A'2 + ...;

this is a special case of the general equation

n1A1 + n2A2 + ... <--> n'1A'1 + n'2A'2 + ...,

in which only one molecule of each substance takes part in the reaction. The reacting substances may be either gaseous or form a liquid mixture, or be dissolved in some selected solvent; but in each case we may state the following considerations regarding the course of the reaction. For a transformation to take place from left to right in the sense of the reaction equation, all the molecules A1, A2, ... must clearly collide at one point; otherwise no reaction is possible, since we shall not consider side-reactions. Such a collision need not of course bring about that transposition of the atoms of the single molecules which constitutes the above reaction. Much rather must it be of such a kind as is favourable to that loosening of the bonds that bind the atoms in the separate molecules, which must precede this transposition. Of a large number of such collisions, therefore, only a certain smaller number will involve a transposition from left to right in the sense of the equation. But this number will be the same under the same external conditions, and the greater the more numerous the collisions; in fact a direct ratio must exist between the two. Bearing in mind now, that the number of collisions must be proportional to each of the concentrations of the bodies A1, A2, ..., and therefore, on the whole, to the product of all these concentrations, we arrive at the conclusion that the velocity v of the transposition from left to right in the sense of the reaction equation is v = kc1c2 ..., in which c1, c2, ... represent the spatial concentrations, i.e. the number of gram-molecules of the substances A1, A2, ... present in one litre, and k is, at a given temperature, a constant which may be called the velocity-coefficient.

Exactly the same consideration applies to the molecules A'1, A'2.... Here the velocity of the change from right to left in the sense of the reaction-equation increases with the number of collisions of all these molecules at one point, and this is proportional to the product of all the concentrations. If k' denotes the corresponding proportionality-factor, then the velocity v' of the change from right to left in the sense of the reaction-equation is v' = k'c'1c'2.... These spatial concentrations are often called the "active masses" of the reacting components. Hence the reaction-velocity in the sense of the reaction-equation from left to right, or the reverse, is proportional to the product of the "active-masses" of the left-hand or right-hand components respectively.

Law of chemical statics.

Neither v nor v' can be separately investigated, and the measurements of the course of a reaction always furnish only the difference of these two quantities. The reaction-velocity actually observed represents the difference of these two partial reaction-velocities, whilst the amount of change observed during any period of time is equal to the change in the one direction, minus the change in the opposite direction. It must not be assumed, however, that on the attainment of equilibrium all action has ceased, but rather that the velocity of change in one direction has become equal to that in the opposite direction, with the result that no further total change can be observed, i.e. the system has reached equilibrium, for which the relation v - v' = 0 must therefore hold, or what is the same thing

kc1c2 ... = k'c'1c'2 ...,

this is the fundamental law of chemical statics.

The conception that the equilibrium is not to be attributed to absolute indifference between the reacting bodies, but that these continue to exert their mutual actions undiminished and the opposing changes now balance, is of fundamental significance in the interpretation of changes of matter in general. This is generally expressed in the form: _the equilibrium in this and other analogous cases is not static but dynamic._ This conception was a direct result of the kinetic-molecular considerations, and was applied with special success to the development of the kinetic theory of gases. Thus with Clausius, we conceive the equilibrium of water-vapour with water, not as if neither water vaporized nor vapour condensed, but rather as though the two processes went on unhindered in the equilibrium state, i.e. during contact of saturated vapour with water, in a given time, as many water molecules passed through the water surface in one direction as in the opposite direction. This view, as applied to chemical changes, was first advanced by A.W. Williamson (1851), and further developed by C.M. Guldberg and P. Waage and others.

Law of chemical kinetics.

From the previous considerations it follows that the reaction-velocity at every moment, i.e. the velocity with which the chemical process advances towards the equilibrium state, is given by the equation

V = v - v' = kc1c2 ... - k'c1c'2 ...;

this states the fundamental law of chemical kinetics.

The equilibrium equation is simply a special case of this more general one, and results when the total velocity is written zero, just as in analytical mechanics the equilibrium conditions follow at once by specialization of the general equations of motion.

No difficulty presents itself in the generalization of the previous equations for the reaction which proceeds after the scheme

n1A1 + n2A2 + ... = n'1A'1 + n'2A'2 + ...,

where n1, n2, ..., n'1, n'2, ... denote the numbers of molecules of the separate substances which take part in the reaction, and are therefore whole, mostly small, numbers (generally one or two, seldom three or more). Here as before, v and v' are to be regarded as proportional to the number of collisions at one point of all molecules necessary to the respective reaction, but now n1 molecules of A1, n2 molecules of A2, &c., must collide for the reaction to advance from left to right in the sense of the equation; and similarly n'1 molecules of A'1, n'2 molecules of A'2, &c., must collide for the reaction to proceed in the opposite direction. If we consider the path of a single, arbitrarily chosen molecule over a certain time, then the number of its collisions with other similar molecules will be proportional to the concentration C of that kind of molecule to which it belongs. The number of encounters between two molecules of the kind in question, during the same time, will be in general C times as many, i.e. the number of encounters of two of the same molecules is proportional to the square of the concentration C; and generally, the number of encounters of n molecules of one kind must be regarded as proportional to the nth power of C, i.e. C^n.

The number of collisions of n1 molecules of A1, n2 molecules of A2 ... is accordingly proportional to C1^{n1}C2^{n2} ..., and the reaction-velocity corresponding to it is therefore

v = kC1^{n1}C2^{n2} ...,

and similarly the opposed reaction-velocity is

v' = k'C'1^{n'1}C'2^{n'2} ...;

the resultant reaction-velocity, being the difference of these two partial velocities, is therefore

V = v - v' = kC1^{n1}C2^{n2} ... - k'C'1^{n'1}C'2^{n'2} ...

This is the most general expression of the law of chemical mass-action, for the case of homogeneous systems.

Equating V to zero, we obtain the equation for the equilibrium state, viz.

C1^{n1}C2^{n2} ... / C'1^{n'1}C'2^{n'2} ... = k / k' = K;

K is called the "equilibrium-constant."

Limitations and applications of the laws.

These formulae hold for gases and for dilute solutions, but assume the system to be homogeneous, i.e. to be either a homogeneous gas-mixture or a homogeneous dilute solution. The case in which other states of matter share in the equilibrium permits of simple treatment when the substances in question may be regarded as pure, and consequently as possessing definite vapour-pressures or solubilities at a given temperature. In this case the molecular species in question, which is, at the same time, present in excess and is hence usually, called a _Bodenkorper_, must possess a constant concentration in the gas-space or solution. But since the left-hand side of the last equation contains only variable quantities, it is simplest and most convenient to absorb these constant concentrations into the equilibrium-constant; whence we have the rule: leave the molecular species present as _Bodenkorper_ out of account, when determining the concentration-product. Guldberg and Waage expressed this in the form "the active mass of a solid substance is constant." The same is true of liquids when these participate in the pure state in the equilibrium, and possess therefore a definite vapour-pressure or solubility. When, finally, we are not dealing with a dilute solution but with any kind of mixture whatever, it is simplest to apply the law of mass-action to the gaseous mixture in equilibrium with this. The composition of the liquid mixture is then determinable when the vapour-pressures of the separate components are known. This, however, is not often the case; but in principle this consideration is important, since it involves the possibility of extending the law of chemical mass-action from ideal gas-mixtures and dilute solutions, for which it primarily holds, to any other system whatever.

The more recent development of theoretical chemistry, as well as the detailed study of many chemical processes which have found technical application, leads more and more convincingly to the recognition that in the law of chemical mass-action we have a law of as fundamental significance as the law of constant and multiple proportions. It is therefore not without interest to briefly touch upon the development of the doctrine of chemical affinity.

_Historical Development of the Law of Mass-action._--The theory developed by Torbern Olof Bergman in 1775 must be regarded as the first attempt of importance to account for the mode of action of chemical forces. The essential principle of this may be stated as follows:--The magnitude of chemical affinity may be expressed by a definite number; if the affinity of the substance A is greater for the substance B than for the substance C, then the latter (C) will be completely expelled by B from its compound with A, in the sense of the equation A.C + B = A.B + C. This theory fails, however, to take account of the influence of the relative masses of the reacting substances, and had to be abandoned as soon as such an influence was noticed. An attempt to consider this factor was made by Claude Louis Berthollet (1801), who introduced the conception of chemical equilibrium. The views of this French chemist may be summed up in the following sentence:--Different substances have different affinities for each other, which only come into play on immediate contact. The condition of equilibrium depends not only upon the chemical affinity, but also essentially upon the relative masses of the reacting substances.

Essentially, Berthollet's idea is to-day the guiding principle of the doctrine of affinity. This is especially true of our conceptions of many reactions which, in the sense of Bergman's idea, proceed to completion, i.e. until the reacting substances are all used up; but only for this reason, viz. that one or more of the products of the reaction is removed from the reaction mixture (either by crystallization, evaporation or some other process), and hence the reverse reaction becomes impossible. Following Berthollet's idea, two Norwegian investigators, C.M. Guldberg and Peter Waage, succeeded in formulating the influence of the reacting masses in a simple law--the law of chemical mass-action already defined. The results of their theoretical and experimental studies were published at Christiania in 1867 (_Etudes sur les affinites chimiques_); this work marks a new epoch in the history of chemistry. Even before this, formulae to describe the progress of certain chemical reactions, which must be regarded as applications of the law of mass-action, had been put forward by Ludwig Wilhelmy (1850), and by A.G. Vernon-Harcourt and William Esson (1856), but the service of Guldberg and Waage in having grasped the law in its full significance and logically applied it in all directions, remains of course undiminished. Their treatise remained quite unknown; and so it happened that John Hewitt Jellett (1873), J.H. van't Hoff (1877), and others independently developed the same law. The thermodynamic basis of the law of mass-action is primarily due to Horstmann, J. Willard Gibbs and van't Hoff.

_Applications._--Let us consider, as an example of the application of the law of mass-action, the case of the dissociation of water-vapour, which takes place at high temperatures in the sense of the equation 2H2O = 2H2 + O2. Representing the concentrations of the corresponding molecular species by [H2], &c., the expression [H2]^2 [O2] / [H2O]^2 must be constant at any given temperature. This shows that the dissociation is set back by increasing the pressure; for if the concentrations of all three kinds of molecules be increased by strong compression, say to ten times the former amounts, then the numerator is increased one thousand, the denominator only one hundred times. Hence if the original equilibrium-constant is to hold, the dissociation must go back, and, what is more, by an exactly determinable amount. At 2000 deg. C. water-vapour is only dissociated to the extent of a few per cent; therefore, even when only a small excess of oxygen or hydrogen be present, the numerator in the foregoing expression is much increased, and it is obvious that in order to restore the equilibrium state, the concentration of the other component, hydrogen or oxygen as the case may be, must diminish. In the case of slightly dissociated substances, therefore, even a relatively small excess of one component is sufficient to set back the dissociation substantially.

_Chemical Kinetics._--It has been already mentioned that the law of chemical mass-action not only defines the conditions for chemical equilibrium, but contains at the same time the principles of chemical kinetics. The previous considerations show indeed that the actual progress of the reaction is determined by the difference of the reaction-velocities in the one and the other (opposed) direction, in the sense of the corresponding reaction-equation. Since the reaction-velocity is given by the amount of chemical change in a small interval of time, the law of chemical mass-action supplies a differential equation, which, when integrated, provides formulae which, as numerous experiments have shown, very happily summarize the course of the reaction. For the simplest case, in which a single species of molecule undergoes almost complete decomposition, so that the reaction-velocity in the reverse direction may be neglected, we have the simple equation

dx/dt = k(a-x)

and if x = 0 when t = 0 we have by integration

k = t^{-1}log{a/(a-x)}.

Theory of explosive combustion

We will now apply these conclusions to the theory of the ignition of an explosive gas-mixture, and in particular to the combustion of "knallgas" (a mixture of hydrogen and oxygen) to water-vapour. At ordinary temperatures knallgas undergoes practically no change, and it might be supposed that the two gases, oxygen and hydrogen, have no affinity for each other. This conclusion, however, is shown to be incorrect by the observation that it is only necessary to add some suitable catalyst such as platinum-black in order to immediately start the reaction. We must therefore conclude that even at ordinary temperatures strong chemical affinity is exerted between oxygen and hydrogen, but that at low temperatures this encounters great frictional resistances, or in other words that the reaction-velocity is very small. It is a matter of general experience that the resistances which the chemical forces have to overcome diminish with rising temperature, i.e. the reaction-velocity increases with temperature. Therefore, when we warm the knallgas, the number of collisions of oxygen and hydrogen molecules favourable to the formation of water becomes greater and greater, until at about 500 deg. the gradual formation of water is observed, while at still higher temperatures the reaction-velocity becomes enormous. We are now in a position to understand what is the result of a strong local heating of the knallgas, as, for example, by an electric spark. The strongly heated parts of the knallgas combine to form water-vapour with great velocity and the evolution of large amounts of heat, whereby the adjacent parts are brought to a high temperature and into a state of rapid reaction, i.e. we observe an ignition of the whole mixture. If we suppose the knallgas to be at a very high temperature, then its combustion will be no longer complete owing to the dissociation of water-vapour, whilst at extremely high temperatures it would practically disappear. Hence it is clear that knallgas appears to be stable at low temperatures only because the reaction-velocity is very small, but that at very high temperatures it is really stable, since no chemical forces are then active, or, in other words, the chemical affinity is very small.

The determination of the question whether the failure of some reaction is due to an inappreciable reaction-velocity or to absence of chemical affinity, is of fundamental importance, and only in the first case can the reaction be hastened by catalysts.

Many chemical compounds behave like knallgas. Acetylene is stable at ordinary temperatures, inasmuch as it only decomposes slowly; but at the same time it is explosive, for the decomposition when once started is rapidly propagated, on account of the heat evolved by the splitting up of the gas into carbon and hydrogen. At very high temperatures, however, acetylene acquires real stability, since carbon and hydrogen then react to form acetylene.

Explosion-waves.

Many researches have shown that the combustion of an inflammable gas-mixture which is started at a point, e.g. by an electric spark, may be propagated in two essentially different ways. The characteristic of the slower combustion consists in this, viz. that the high temperature of the previously ignited layer spreads by conduction, thereby bringing the adjacent layers to the ignition-temperature; the velocity of the propagation is therefore conditioned in the first place by the magnitude of the conductivity for heat, and more particularly, in the second place, by the velocity with which a moderately heated layer begins to react chemically, and so to rise gradually in temperature, i.e. essentially by the change of reaction-velocity with temperature. A second entirely independent mode of propagation of the combustion lies at the basis of the phenomenon that an explosive gas-mixture can be ignited by strong compression or--more correctly--by the rise of temperature thereby produced. The increase of the concentrations of the reacting substances consequent upon this increase of pressure raises the reaction-velocity in accordance with the law of chemical mass-action, and so enormously favours the rapid evolution of the heat of combustion.

It is therefore clear that such a powerful compression-wave can not only initiate the combustion, but also propagate it with extremely high velocity. Indeed a compression-wave of this kind passes through the gas-mixture, heated by the combustion to a very high temperature. It must, however, be propagated considerably faster than an ordinary compression-wave, for the result of ignition in the compressed (still unburnt) layer is the production of a very high pressure, which must in accordance with the principles of wave-motion increase the velocity of propagation. The absolute velocity of the explosion-wave would seem, in the light of these considerations, to be susceptible of accurate calculation. It is at least clear that it must be considerably higher than the velocity of sound in the mass of gas strongly heated by the explosion, and this is confirmed by actual measurements (see below) which show that the velocity of the explosion-wave is from one and a half times to double that of sound-waves at the combustion temperature.

We are now in a position to form the following picture of the processes which follow upon the ignition of a combustible gas-mixture contained in a long tube. First we have the condition of slow combustion; the heat is conveyed by conduction to the adjacent layers, and there follows a velocity of propagation of a few metres per second. But since the combustion is accompanied by a high increase of pressure, the adjacent, still unburnt layers are simultaneously compressed, whereby the reaction-velocity increases, and the ignition proceeds faster. This involves still greater compression of the next layers, and so if the mixture be capable of sufficiently rapid combustion, the velocity of propagation of the ignition must continually increase. As soon as the compression in the still unburnt layers becomes so great that spontaneous ignition results, the now much more pronounced compression-waves excited with simultaneous combustion must be propagated with very great velocity, i.e. we have spontaneous development of an "explosion-wave." M.P.E. Berthelot, who discovered the presence of such explosion-waves, proved their velocity of propagation to be independent of the pressure, the cross-section of the tubes in which the explosive gas-mixture is contained, as well as of the material of which these are made, and concluded that this velocity is a constant, characteristic of the particular mixture. The determination of this velocity is naturally of the highest interest.

In the following table Berthelot's results are given along with the later (1891) concordant ones of H.B. Dixon, the velocities of propagation of explosions being given in metres per second.

+-------------------------------------+---------------------+
| | Velocity of Wave in |
| Reacting Mixture. | Metres per second. |
| +-----------+---------+
| | Berthelot.| Dixon. |
+-------------------------------------+-----------+---------+
|Hydrogen and oxygen, H2+O | 2810 | 2821 |
|Hydrogen and nitrous oxide, H2+N2O | 2284 | 2305 |
|Methane and oxygen, CH4+4O | 2287 | 2322 |
|Ethylene " " C2H4+6O | 2210 | 2364 |
|Acetylene " " C2H2+5O | 2482 | 2391 |
|Cyanogen " " C2N2+4O | 2195 | 2321 |
|Hydrogen and chlorine, H2+Cl2 | .. | 1730 |
| " " " 2H2+Cl2 | .. | 1849 |
+-------------------------------------+-----------+---------+

The maximum pressure of the explosion-wave possesses very high values; it appears that a compression of from 1 to 30-40 atmospheres is necessary to produce spontaneous ignition of mixtures of oxygen and hydrogen. But since the heat evolved in the path of the explosion causes a rise of temperature of 2000 deg.-3000 deg., i.e. a rise of absolute temperature about four times that directly following upon the initial compression, we are here concerned with pressures amounting to considerably more than 100 atmospheres. Both the magnitude of this pressure and the circumstance that it so suddenly arises are peculiar to the very powerful forces which distinguish the explosion-wave from the slow combustion-wave.

_Nascent State._--The great reactive power of freshly formed or nascent substances (_status nascens_)may be very simply referred to the principles of mass-action. As is well known, this phenomenon is specially striking in the case of hydrogen, which may therefore be taken as a typical example. The law of mass-action affirms the action of a substance to be the greater the higher its concentration, or, for a gas, the higher its partial-pressure. Now experience teaches that those metals which liberate hydrogen from acids are able to supply the latter under extremely high pressure, and we may therefore assume that the hydrogen which results, for example, from the action of zinc upon sulphuric acid is initially under very high pressures which are then afterwards relieved. Hence the hydrogen during liberation exhibits much more active powers of reduction than the ordinary gas.

A deeper insight into the relations prevailing here is offered from the atomistic point of view. From this we are bound to conclude that the hydrogen is in the first instance evolved in the form of free atoms, and since the velocity of the reaction H + H = H2 at ordinary temperatures, though doubtless very great, is not practically instantaneous, the freshly generated hydrogen will contain a remnant of free atoms, which are able to react both more actively and more rapidly. Similar considerations are of course applicable to other cases.

_Ion-reactions._--The application of the law of chemical mass action is much simplified in the case in which the reaction-velocity is enormously great, when practically an instantaneous adjustment of the equilibrium results. Only in this case can the state of the system, which pertains after mixing the different components, be determined merely from knowledge of the equilibrium-constant. This case is realized in the reactions between gases at very high temperatures, which have, however, been little investigated, and especially by the reactions between electrolytes, the so-called ion-reactions. In this latter case, which has been thoroughly studied on account of its fundamental importance for inorganic qualitative and quantitative analysis, the degrees of dissociation of the various electrolytes (acids, bases and salts) are for the most part easily determined by the aid of the freezing-point apparatus, or of measurements of the electric conductivity; and from these data the equilibrium-constant K may be calculated. Moreover, it can be shown that the state of the system can be determined when the equilibrium constants of all the electrolytes which are present in the common solution are known. If this be coupled with the law that the solubility of solid substances, as with vapour-pressures, is independent of the presence of other electrolytes, it is sufficient to know the solubilities of the electrolytes in question, in order to be able to determine which substances must participate in the equilibrium in the solid state, i.e. we arrive at the theory of the formation and solution of precipitates.

Strength of acids and bases.

As an illustration of the application of these principles, we shall deal with a problem of the doctrine of affinity, namely, that of the relative strengths of acids and bases. It was quite an early and often repeated observation that the various acids and bases take part with very varying intensity or avidity in those reactions in which their acid or basic nature comes into play. No success attended the early attempts at giving numerical expression to the strengths of acids and bases, i.e. of finding a numerical coefficient for each acid and base, which should be the quantitative expression of the degree of its participation in those specific reactions characteristic of acids and bases respectively. Julius Thomsen and W. Ostwald attacked the problem in a far-seeing and comprehensive manner, and arrived at indisputable proof that the property of acids and bases of exerting their effects according to definite numerical coefficients finds expression not only in salt-formation but also in a large number of other, and indeed very miscellaneous, reactions.

When Ostwald compared the order of the strengths of acids deduced from their competition for the same base, as determined by Thomsen's thermo-chemical or his own volumetric method, with that order in which the acids arrange themselves according to their capacity to bring calcium oxalate into solution, or to convert acetamide into ammonium acetate, or to split up methyl acetate into methyl alcohol and acetic acid catalytically, or to invert cane-sugar, or to accelerate the mutual action of hydriodic on bromic acid, he found that in all these well-investigated and very miscellaneous cases the same succession of acids in the order of their strengths is obtained, whichever one of the above chemical processes be chosen as measure of these strengths. It is to be noticed that all these chemical changes cited took place in dilute aqueous solution, consequently the above order of acids refers only to the power to react under these circumstances. The order of acids proved to be fairly independent of temperature. While therefore the above investigations afforded a definite qualitative solution of the order of acids according to strengths, the determination of the quantitative relations offered great difficulties, and the numerical coefficients, determined from the separate reactions, often displayed great variations, though occasionally also surprising agreement. Especially great were the variations of the coefficients with the concentration, and in those cases in which the concentration of the acid changed considerably during the reaction, the calculation was naturally quite uncertain. Similar relations were found in the investigation of bases, the scope of which, however, was much more limited.

These apparently rather complicated relations were now cleared up at one stroke, by the application of the law of chemical mass-action on the lines indicated by S. Arrhenius in 1887, when he put forward the theory of electrolytic dissociation to explain that peculiar behaviour of substances in aqueous solution first recognized by van't Hoff in 1885. The formulae which must be made use of here in the calculation of the equilibrium-relations follow naturally by simple application of the law of mass-action to the corresponding ion-concentrations.

The peculiarities which the behaviour of acids and bases presents, and, according to the theory of Arrhenius, must present--peculiarities which found expression in the very early distinction between neutral solutions on the one hand, and acid or basic ones on the other, as well as in the belief in a polar antithesis between the two last--must now, in the light of the theory of electrolytic dissociation, be conceived as follows:--

The reactions characteristic of acids in aqueous solution, which are common to and can only be brought about by acids, find their explanation in the fact that this class of bodies gives rise on dissociation to a common molecular species, namely, the positively charged hydrogen-ion (+H). The specific chemical actions peculiar to acids are therefore to be attributed to the hydrogen-ion just as the actions common to all chlorides are to be regarded as those of the free chlorine-ions. In like manner, the reactions characteristic of bases in solution are to be attributed to the negatively charged hydroxyl-ions (-OH), which result from the dissociation of this class of bodies.

A solution has an acid reaction when it contains an excess of hydrogen-ions, and a basic reaction when it contains an excess of hydroxyl-ions. If an acid and an alkaline solution be brought together mutual neutralization must result, since the positive H-ions and the negative OH-ions cannot exist together in view of the extremely weak conductivity of pure water and its consequent slight electrolytic dissociation, and therefore they must at once combine to form electrically neutral molecules, in the sense of the equation

[+H] + [-OH] = H2O.

In this lies the simple explanation of the "polar" difference between acid and basic solutions. This rests essentially upon the fact that the ion peculiar to acids and the ion peculiar to bases form the two constituents of water, i.e. of that solvent in which we usually study the course of the reaction. The idea of the "strength" of an acid or base at once arises. If we compare equivalent solutions of various acids, the intensity of those actions characteristic of them will be the greater the more free hydrogen-ions they contain; this is an immediate consequence of the law of chemical mass-action. The degree of electrolytic dissociation determines, therefore, the strength of acids, and a similar consideration leads to the same result for bases.

Now the degree of electrolytic dissociation changes with concentration in a regular manner, which is given by the law of mass-action. For if C denote the concentration of the electrolyte and a its degree of dissociation, the above law states that

C^2a^2/C(1-a) = Ca^2/(1-a) = K.

At very great dilutions the dissociation is complete, and equivalent solutions of the most various acids then contain the same number of hydrogen-ions, or, in other words, are equally strong; and the same is true of the hydroxyl-ions of bases. The dissociation also decreases with increasing concentration, but at different rates for different substances, and the relative "strengths" of acids and bases must hence change with concentration, as was indeed found experimentally. The dissociation-constant K is the measure of the variation of the degree of dissociation with concentration, and must therefore be regarded as the measure of the strengths of acids and bases. So that in this special case we are again brought to the result which was stated in general terms above, viz. that the dissociation-coefficient forms the measure of the reactivity of a dissolved electrolyte. Ostwald's series of acids, based upon the investigation of the most various reactions, should therefore correspond with the order of their dissociation-constants, and further with the order of their freezing-point depressions in equivalent solutions, since the depression of the freezing-point increases with the degree of electrolytic dissociation. Experience confirms this conclusion completely. The degree of dissociation of an acid, at a given concentration, for which its molecular conductivity is A, is shown by the theory of electrolytic dissociation to be a = A/A[oo]; A[oo], the molecular conductivity at very great dilution in accordance with the law of Kohlrausch, is u + v, where u and v are the ionic-mobilities (see CONDUCTION, ELECTRIC). Since u, the ionic-mobility of the hydrogen ion, is generally more than ten times as great as v, the ionic-mobility of the negative acid-radical, A[oo] has approximately the same value (generally within less than 10%) for the different acids, and the molecular-conductivity of the acids in equivalent concentration is at least approximately proportional to the degree of electrolytic dissociation, i.e. to the strength.

In general, therefore, the order of conductivities is identical with that in which the acids exert their specific powers. This remarkable parallelism, first perceived by Arrhenius and Ostwald in 1885, was the happy development which led to the discovery of electrolytic dissociation (see CONDUCTION, ELECTRIC; and SOLUTION).

_Catalysis._--We have already mentioned the fact, early known to chemists, that many reactions proceed with a marked increase of velocity in presence of many foreign substances. With Berzelius we call this phenomenon "catalysis," by which we understand that general acceleration of reactions which also progress when left to themselves, in the presence of certain bodies which do not change in amount (or only slightly) during the course of the reaction. Acids and bases appear to act catalytically upon all reactions involving consumption or liberation of water, and indeed that action is proportional to the concentration of the hydrogen or hydroxyl-ions. Further, the decomposition of hydrogen peroxide is "catalysed" by iodine-ions, the condensation of two molecules of benzaldehyde to benzoin by cyanogen-ions. One of the earliest known and technically most important instances of catalysis is that of the oxidation of sulphur dioxide to sulphuric acid by oxygen in the presence of oxides of nitrogen. Other well-known and remarkable examples are the catalysis of the combustion of hydrogen and of sulphur dioxide in oxygen by finely-divided platinum. We may also mention the interesting work of Dixon and Baker, which led to the discovery that a large number of gas-reactions, e.g. the combustion of carbon monoxide, the dissociation of sal-ammoniac vapour, and the action of sulphuretted hydrogen upon the salts of heavy metals, cease when water-vapour is absent, or at least proceed with greatly diminished velocity.

"Negative catalysis," i.e. the retardation of a reaction by addition of some substance, which is occasionally observed, appears to depend upon the destruction of a "positive catalyte" by the body added.

A catalyte can have no influence, however, upon the affinity of a process, since that would be contrary to the second law of thermodynamics, according to which affinity of an isothermal process, which is measured by the maximum work, only depends upon the initial and final states. The effect of a catalyte is therefore limited to the resistances opposing the progress of a reaction, and does not influence its driving-force or affinity. Since the catalyte takes no part in the reaction its presence has no effect on the equilibrium-constant. This, in accordance with the law of mass-action, is the ratio of the separate reaction-velocities in the two contrary directions. A catalyte must therefore always accelerate the reverse-reaction. If the velocity of formation of a body be increased by addition of some substance then its velocity of decomposition must likewise increase. We have an example of this in the well-known fact that the formation, and no less the saponification, of esters, proceeds with increased velocity in the presence of acids, while the observation that in absence of water-vapour neither gaseous ammonium chloride dissociates nor dry ammonia combines with hydrogen chloride becomes clear on the same grounds.

A general theory of catalytic phenomena does not at present exist. The formation of intermediate products by the action of the reacting substance upon the catalyte has often been thought to be the cause of these. These intervening products, whose existence in many cases has been proved, then split up into the catalyte and the reaction-product. Thus chemists have sought to ascribe the influence of oxides of nitrogen on the formation of sulphuric acid to the initial formation of nitrosyl-sulphuric acid, SO2(OH)(NO2), from the mixture of sulphur dioxide, oxides of nitrogen and air, which then reacted with water to form sulphuric and nitrous acids. When the velocity of such intermediate reactions is greater than that of the total change, such an explanation may suffice, but a more certain proof of this theory of catalysis has only been reached in a few cases, though in many others it appears very plausible. Hence it is hardly possible to interpret all catalytic processes on these lines.