Chapter 49

Footnotes:[1]Under favourable circumstances (by taking all the requisite precautions), the weight of the equivalent may be accurately determined by this method. Thus Reynolds and Ramsay (1887) determined the equivalent of zinc to be 32·7 by this method (from the average of 29 experiments), whilst by other methods it has been fixed (by different observers) between 32·55 and 33·95.The differences in their equivalents may be demonstrated by taking equal weights of different metals, and collecting the hydrogen evolved by them (under the action of an acid or alkali).[2]The most accurate determinations of this kind were carried on by Stas, and will be described in Chapter XXIV.[2 bis]The amount of electricity in one coulomb according to the present nomenclature of electrical units (seeWorks on Physics and Electro-technology) disengages 0·00001036 gram of hydrogen, 0·00112 gram of silver, 0·0003263 gram of copper from the salts of the oxide, and 0·0006526 gram from the salts of the suboxide, &c. These amounts stand in the same ratio as the equivalents,i.e.as the quantities replaced by one part by weight of hydrogen. The intimate bond which is becoming more and more marked existing between the electrolytic and purely chemical relations of substances (especially in solutions) and the application of electrolysis to the preparation of numerous substances on a large scale, together with the employment of electricity for obtaining high temperatures, &c., makes me regret that the plan and dimensions of this book, and the impossibility of giving a concise and objective exposition of the necessary electrical facts, prevent my entering upon this province of knowledge, although I consider it my duty to recommend its study to all those who desire to take part in the further development of our science.There is only one side of the subject respecting the direct correlation between thermochemical data and electro-motive force, which I think right to mention here, as it justifies the general conception, enunciated by Faraday, that the galvanic current is an aspect of the transference of chemical motion or reaction along the conductors.From experiments conducted by Favre, Thomsen, Garni, Berthelot, Cheltzoff, and others, upon the amount of heat evolved in a closed circuit, it follows that the electro-motive force of the current or its capacity to do a certain work, E, is proportional to the whole amount of heat, Q, disengaged by the reaction forming the source of the current. If E be expressed in volts, and Q in thousands of units of heat referred to equivalent weights, then E = 0·0436Q. For example in a Daniells battery E = 1·09 both by experiment and theory, because in it there takes place the decomposition of CuSO4into Cu + O together with the formation of Zn + O and ZnO + SO3Aq, and these reactions correspond to Q = 25·06 thousand units of heat. So also in all other primary batteries (e.g.Bunsen's, Poggendorff's, &c.) and secondary ones (for instance, those acting according to the reaction Pb + H2SO4+ PbO2, as Cheltzoff showed) E = 0·0436Q.[3]The chief means by which we determine the valency of the elements, or what multiple of the equivalent should be ascribed to the atom, are: (1) The law of Avogadro-Gerhardt. This method is the most general and trustworthy, and has already been applied to a great number of elements. (2) The different grades of oxidation and their isomorphism or analogy in general; for example, Fe = 56 because the suboxide (ferrous oxide) is isomorphous with magnesium oxide, &c., and the oxide (ferric oxide) contains half as much oxygen again as the suboxide. Berzelius, Marignac, and others took advantage of this method for determining the composition of the compounds of many elements. (3) The specific heat, according to Dulong and Petit's law. Regnault, and more especially Cannizzaro, used this method to distinguish univalent from bivalent metals. (4) The periodic law (seeChapter XV.) has served as a means for the determination of the atomic weights of cerium, uranium, yttrium, &c., and more especially of gallium, scandium, and germanium. The correction of the results of one method by those of others is generally had recourse to, and is quite necessary, because, phenomena of dissociation, polymerisation, &c., may complicate the individual determinations by each method.It will be well to observe that a number of other methods, especially from the province of those physical properties which are clearly dependent on the magnitude of the atom (or equivalent) or of the molecule, may lead to the same result. I may point out, for instance, that even the specific gravity of solutions of the metallic chlorides may serve for this purpose. Thus, if beryllium he taken as trivalent—that is, if the composition of its chloride be taken as BeCl3(or a polymeride of it), then the specific gravity of solutions of beryllium chloride will not fit into the series of the other metallic chlorides. But by ascribing to it an atomic weight Be = 7, or taking Be as bivalent, and the composition of its chloride as BeCl2, we arrive at the general rule given in Chapter VII., Note28. Thus W. G. Burdakoff determined in my laboratory that the specific gravity at 15°/4° of the solution BeCl2+ 200H2O = 1·0138—that is, greater than the corresponding solution KCl + 200H2O (= 1·0121), and less than the solution MgCl2+ 200H2O (= 1·0203), as would follow from the magnitude of the molecular weight BeCl2= 80, since KCl = 74·5 and MgCl2= 95.[4]The specific heats here given refer to different limits of temperature, but in the majority of cases between 0° and 100°; only in the case of bromine the specific heat is taken (for the solid state) at a temperature below -7°, according to Regnault's determination.The variation of the specific heat with a change of temperatureis a very complex phenomenon, the consideration of which I think would here be out of place. I will only cite a few figures as an example. According to Bystrom, the specific heat of iron at 0° = 0·1116, at 100° = 0·1114, at 200° = 0·1188, at 300° = 0·1267, and at 1,400° = 0·4031. Between these last limits of temperature a change takes place in iron (a spontaneous heating,recalescence), as we shall see in Chapter XXII. For quartz SiO2Pionchon gives Q = 0·1737 + 394t10-6- 27t210-9up to 400°, for metallic aluminium (Richards, 1892) at 0° 0·222, at 20° 0·224, at 100° 0·232; consequently, as a rule, the specific heat varies slightly with the temperature. Still more remarkable are H. E. Weber's observations on the great variation of the specific heat of charcoal, the diamond and boron:0°100°200°600°900°Wood charcoal0·150·230·290·440·46Diamond0·100·190·220·440·45Boron0·220·290·35——These determinations, which have been verified by Dewar, Le Chatelier (Chapter VIII., Note13), Moissan, and Gauthier, the latter finding for boron AQ = 6 at 400°, are of especial importance as confirming the universality of Dulong and Petit's law, because the elements mentioned above form exceptions to the general rule when the mean specific heat is taken for temperatures between 0° and 100°. Thus in the case of the diamond the product of A × Q at 0° = 1·2, and for boron = 2·4. But if we take the specific heat towards which there is evidently a tendency with a rise of temperature, we obtain a product approaching to 6 as with other elements. Thus with the diamond and charcoal, it is evident that the specific heat tends towards 0·47, which multiplied by 12 gives 5·6, the same as for magnesium and aluminium. I may here direct the reader's attention to the fact that for solid elements having a small atomic weight, the specific heat varies considerably if we take the average figures for temperatures 0° to 100°:Li = 7Be = 9B = 11C = 12Q =0·940·420·240·20AQ =6·63·82·62·4It is therefore clear that the specific heat of beryllium determined at a low temperature cannot serve for establishing its atomicity. On the other hand, the low atomic heat of charcoal, graphite, and the diamond, boron, &c., may perhaps depend on the complexity of the molecules of these elements. The necessity for acknowledging a great complexity of the molecules of carbon was explained in ChapterVIII. In the case of sulphur the molecule contains at least S6and its atomic heat = 32 × 0·163 = 5·22, which is distinctly below the normal. If a large number of atoms of carbon are contained in the molecule of charcoal, this would to a certain extent account for its comparatively small atomic heat. With respect to the specific heat of compounds, it will not be out of place to mention here the conclusion arrived at by Kopp, that the molecular heat (that is, the product of MQ) may be looked on as the sum of the atomic heats of its component elements; but as this rule is not a general one, and can only be applied to give an approximate estimate of the specific heats of substances, I do not think it necessary to go into the details of the conclusions described in Liebig's ‘Annalen Supplement-Band,’ 1864, which includes a number of determinations made by Kopp.[5]It must be remarked that in the case of oxygen (and also hydrogen and carbon) compounds the quotient of MQ/n, wherenis the number of atoms in the molecule, is always less than 6 for solids; for example, for MgO = 5·0, CuO = 5·1, MnO2= 4·6, ice (Q = 0·504) = 3, SiO2= 3·5, &c. At present it is impossible to say whether this depends on the smaller specific heat of the atom of oxygen in its solid compounds (Kopp, Note4) or on some other cause; but, nevertheless, taking into account this decrease depending on the presence of oxygen, a reflection of the atomicity of the elements may to a certain extent be seen in the specific heat of the oxides. Thus for alumina, Al2O3(Q = 0·217), MQ = 22·3, and therefore the quotient MQ/n= 4·5, which is nearly that given by magnesium oxide, MgO. But if we ascribe the same composition to alumina, as to magnesia—that is, if aluminium were counted as divalent—we should obtain the figure 3·7, which is much less. In general, in compounds of identical atomic composition and of analogous chemical properties the molecular heats MQ are nearly equal, as many investigators have long remarked. For example, ZnS = 11·7 and HgS = 11·8; MgSO4= 27·0 and ZnSO4= 28·0, &c.[6]If W be the amount of heat contained in a massmof a substance at a temperaturet, anddW the amount expended in heating it fromttot+dt, then the specific heat Q =dW(m×dt). The specific heat not only varies with the composition and complexity of the molecules of a substance, but also with the temperature, pressure, and physical state of a substance. Even for gases the variation of Q withtis to be observed. Thus it is seen from the experiments of Regnault and Wiedemann that the specific heat of carbonic anhydride at 0° = 0·19, at 100° = 0·22, and at 200° = 0·24. But the variation of the specific heat of permanent gases with the temperature is, as far as we know, very inconsiderable. According to Mallard and Le Chatelier it is =0·0006/Mper 1°, where M is the molecular weight (for instance, for O2, M = 32). Therefore the specific heat of those permanent gases which contain two atoms in the molecule (H2, O2, N2, CO, and NO) may be, as is shown by experiment, taken as not varying with the temperature. The constancy of the specific heat of perfect gases forms one of the fundamental propositions of the whole theory of heat and on it depends the determination of temperatures by means of gas-thermometers containing hydrogen, nitrogen, or air. Le Chatelier (1887), on the basis of existing determinations, concludes that the molecular heat—that is, the product MQ—of all gases varies in proportion to the temperature, and tends to become equal (= 6·8) at the temperature of absolute zero (that is, at -273°); and therefore MQ = 6·8 +a(273 +t), whereais a constant quantity which increases with the complexity of the gaseous molecule and Q is the specific heat of the gas under a constant pressure. For permanent gasesaalmost = 0, and therefore MQ = 6·8—that is, the atomic heat (if the molecule contains two atoms) = 3·4, as it is in fact (Chapter IX., Note17 bis. As regards liquids (as well as the vapours formed by them), the specific heat always rises with the temperature. Thus for benzene it equals 0·38 + 0·0014t. R. Schiff (1887) showed that the variation of the specific heat of many organic liquids is proportional to the change of temperature (as in the case of gases, according to Le Chatelier), and reduced these variations into dependence with their composition and absolute boiling point. It is very probable that the theory of liquids will make use of these simple relations which recall the simplicity of the variation of the specific gravity (Chapter II., Note34), cohesion, and other properties of liquids with the temperature. They are all expressed by the linear function of the temperature,a+bt, with the same degree of proximity as the property of gases is expressed by the equationpv=Rt.As regards the relation between the specific heats of liquids (or of solids) and of their vapours, the specific heat of the vapour (and also of the solid) is always less than that of the liquid. For example, benzene vapour 0·22, liquid 0·38; chloroform vapour 0·13, liquid 0·23; steam 0·475, liquid water 1·0. But the complexity of the relations existing in specific heat is seen from the fact that the specific heat of ice = 0·502 is less than that of liquid water. According to Regnault, in the case of bromine the specific heat of the vapour = 0·055 at (150°), of the liquid = 0·107 (at 30°), and of solid bromine = 0·084 (at -15°). The specific heat of solid benzoic acid (according to experiment and calculation, Hess, 1888) between 0° and 100° is 0·31, and of liquid benzoic acid 0·50. One of the problems of the present day is the explanation of those complex relations which exist between the composition and such properties as specific heat, latent heat, expansion by heat, compression, internal friction, cohesion, and so forth. They can only be connected by a complete theory of liquids, which may now soon be expected, more especially as many sides of the subject have already been partially explained.[7]According to the above reasons the quantity of heat, Q, required to raise the temperature of one part by weight of a substance by one degree may be expressed by the sum Q = K + B + D, where K is the heat actually expended in heating the substance, or what is termed the absolute specific heat, B the amount of heat expended in the internal work accomplished with the rise of temperature, and D the amount of heat expended in external work. In the case of gases the last quantity may be easily determined, knowing their coefficient of expansion, which is approximately = 0·00368. By applying to this case the same argument given at the end of Note11, Chapter I., we find that one cubic metre of a gas heated 1° produces an external work of 10333 × 0·00368, or 38·02 kilogrammetres, on which 38·02/424 or 0·0897 heat units are expended. This is the heat expended for the external work produced by one cubic metre of a gas, but the specific heat refers to units of weight, and therefore it is necessary in order to know D to reduce the above quantity to a unit of weight. One cubic metre of hydrogen at 0° and 760 mm. pressure weighs 0·0896 kilo, a gas of molecular weight M has a density M/2, consequently a cubic metre weighs (at 0° and 760 mm.) 0·0448M kilo, and therefore 1 kilogram of the gas occupies a volume 1/0·0448M cubic metres, and hence the external work D in the heating of 1 kilo of the given gas through 1° = 0·0896/0·0448M, or D = 2/M.Taking the magnitude of the internal work B for gases as negligible if permanent gases are taken, and therefore supposing B = 0, we find the specific heat of gases at a constant pressure Q = K + 2 M, where K is the specific heat at a constant volume, or the true specific heat, and M the molecular weight. Hence K = Q - 2/M. The magnitude of the specific heat Q is given by direct experiment. According to Regnault's experiments, for oxygen it = 0·2175, for hydrogen 3·405, for nitrogen 0·2438; the molecular weights of these gases are 32, 2, and 28, and therefore for oxygen K = 0·2175 - 0·0625 = 0·1550, for hydrogen K = 3·4050 - 1·000 = 2·4050, and for nitrogen K = 0·2438 - 0·0714 = 0·1724. These true specific heats of elements are in inverse proportion to their atomic weights—that is, their product by the atomic weight is a constant quantity. In fact, for oxygen this product = 0·155 × 16 = 2·48, for hydrogen 2·40, for nitrogen 0·7724 × 14 = 2·414, and therefore if A stand for the atomic weight we obtain the expression K × A = a constant, which may be taken as 2·45. This is the true expression of Dulong and Petit's law, because K is the true specific heat and A the weight of the atom. It should be remarked, moreover, that the product of the observed specific heat Q into A is also a constant quantity (for oxygen = 3·48, for hydrogen = 3·40), because the external work D is also inversely proportional to the atomic weight.In the case of gases we distinguish the specific heat at a constant pressurec′(we designated this quantity above by Q), and at a constant volumec. It is evident thatthe relation between the two specific heats, k, judging from the above, is the ratio of Q to K, or equal to the ratio of 2·45n+ 2 to 2·45n. Whenn= 1 this ratiok= 1·8; whenn= 2,k= 1·4, whenn= 3,k= 1·3, and with an exceedingly large numbern, of atoms in the molecule,k= 1. That is, the ratio between the specific heats decreases from 1·8 to 1·0 as the number of atoms,n, contained in the molecule increases. This deduction is verified to a certain extent by direct experiment. For such gases as hydrogen, oxygen, nitrogen, carbonic oxide, air, and others in whichn= 2, the magnitude ofkis determined by methods described in works on physics (for example, by the change of temperature with an alteration of pressure, by the velocity of sound, &c.) and is found in reality to be nearly 1·4, and for such gases as carbonic anhydride, nitric dioxide, and others it is nearly 1·3. Kundt and Warburg (1875), by means of the approximate method mentioned in Note29, Chapter VII., determinedkfor mercury vapour whenn= 1, and found it to be = 1·67—that is, a larger quantity than for air, as would be expected from the above.It may be admitted that the true atomic heat of gases = 2·43, only under the condition that they are distant from a liquid state, and do not undergo a chemical change when heated—that is, when no internal work is produced in them (B = 0). Therefore this work may to a certain extent be judged by the observed specific heat. Thus, for instance, for chlorine (Q = 0·12, Regnault;k= 1·33, according to Straker and Martin, and therefore K = 0·09, MK = 6·4), the atomic heat (3·2) is much greater than for other gases containing two atoms in a molecule, and it must be assumed, therefore, that when it is heated some great internal work is accomplished.In order to generalise the facts concerning the specific heat of gases and solids, it appears to me possible to accept the following general proposition:the atomic heat(that is, AQ or QM/n, where M is the molecular weight andnthe number of molecules) issmaller(in solids it attains its highest value 6·8 and in gases 3·4),the more complex the molecule(i.e.the greater the number (n) of atoms forming it)and so much smaller, up to a certain point(in similar physical states)the smaller the mean atomic weight M/n.[8]As an example, it will be sufficient to refer to the specific heat of nitrogen tetroxide, N2O4, which, when heated, gradually passes into NO2—that is, chemical work of decomposition proceeds, which consumes heat. Speaking generally, specific heat is a complex quantity, in which it is clear that thermal data (for instance, the heat of reaction) alone cannot give an idea either of chemical or of physical changes individually, but always depend on an association of the one and the other. If a substance be heated fromt0tot1it cannot but suffer a chemical change (that is, the state of the atoms in the molecules changes more or less in one way or another) if dissociation sets in at a temperaturet1. Even in the case of the elements whose molecules contain only one atom, a true chemical change is possible with a rise of temperature, because more heat is evolved in chemical reactions than that quantity which participates in purely physical changes. One gram of hydrogen (specific heat = 3·4 at a constant pressure) cooled to the temperature of absolute zero will evolve altogether about one thousand units of heat, 8 grams of oxygen half this amount, whilst in combining together they evolve in the formation of 9 grams of water more than thirty times as much heat. Hence the store of chemical energy (that is, of the motion of the atoms, vortex, or other) is much greater than the physical store proper to the molecules, but it is the change accomplished by the former that is the cause of chemical transformations. Here we evidently touch on those limits of existing knowledge beyond which the teaching of science does not yet allow us to pass. Many new scientific discoveries have still to be made before this is possible.[9]As if NaH = Mg and KH = Ca, which is in accordance with their valency. KH includes two monovalent elements, and is a bivalent group like Ca.[10]Sodium carbonate and other carbonates of the alkalis give acid salts which are less soluble than the normal; here, on the contrary, with an excess of carbonic anhydride, a salt is formed which is more soluble than the normal, but this acid salt is more unstable than sodium hydrogen carbonate, NaHCO3.[11]The formation of dolomite may be explained, if only we imagine that a solution of a magnesium salt acts on calcium carbonate. Magnesium carbonate may be formed by double decomposition, and it must be supposed that this process ceases at a certain limit (ChapterXII.), when we shall obtain a mixture of the carbonates of calcium and magnesium. Haitinger heated a mixture of calcium carbonate, CaCO3, with a solution of an equivalent quantity of magnesium sulphate, MgSO4, in a closed tube at 200°, and then a portion of the magnesia actually passed into the state of magnesium carbonate, MgCO3, and a portion of the lime was converted into gypsum, CaSO4. Lubavin (1892) showed that MgCO3is more soluble than CaCO3in salt water, which is of some significance in explaining the composition of sea water.[12]The undoubted action of lime in increasing the fertility of soils—if not in every case, at all events, with ordinary soils which have long been under corn—is based not so much on the need of plants for the lime itself as on those chemical and physical changes which it produces in the soil, as a particularly powerful base which aids the alteration of the mineral and organic elements of the soil.[13]Sodium and potassium only decompose magnesium oxide at a white heat and very feebly, probably for two reasons. In the first place, because the reaction Mg + O develops more heat (about 140 thousand calories) than K2+ O or Na2+ O (about 100 thousand calories); and, in the second place, because magnesia is not fusible at the heat of a furnace and cannot act on the charcoal, sodium, or potassium—that is, it does not pass into that mobile state which is necessary for reaction. The first reason alone is not sufficient to explain the absence of the reaction between charcoal and magnesia, because iron and charcoal in combining with oxygen evolve less heat than sodium or potassium, yet, nevertheless, they can displace them. With respect to magnesium chloride, it acts on sodium and potassium, not only because their combination with chlorine evolves more heat than the combination of chlorine and magnesium (Mg + Cl2gives 150 and Na2+ Cl2about 195 thousand calories), but also because a fusion, both of the magnesium chloride and of the double salt, takes place under the action of heat. It is probable, however, that a reverse reaction will take place. A reverse reaction might probably be expected, and Winkler (1890) showed that Mg reduces the oxides of the alkali metals (Chapter XIII., Note42).[14]Commercial magnesium generally contains a certain amount of magnesium nitride (Deville and Caron), Mg3N2—that is, a product of substitution of ammonia which is directly formed (as is easily shown by experiment) when magnesium is heated in nitrogen. It is a yellowish green powder, which gives ammonia and magnesia with water, and cyanogen when heated with carbonic anhydride. Pashkoffsky (1893) showed that Mg3N2is easily formed and is the sole product when Mg is heated to redness in a current of NH3. Perfectly pure magnesium may be obtained by the action of a galvanic current.[15]Hydrogen peroxide (Weltzien) dissolves magnesium. The reaction has not been investigated.[16]A special form of apparatus is used for burning magnesium. It is a clockwork arrangement in which a cylinder rotates, round which a ribbon or wire of magnesium is wound. The wire is subjected to a uniform unwinding and burning as the cylinder rotates, and in this manner the combustion may continue uniform for a certain time. The same is attained in special lamps, by causing a mixture of sand and finely divided magnesium to fall from a funnel-shaped reservoir on to the flame. In photography it is best to blow finely divided magnesium into a colourless (spirit or gas) flame, and for instantaneous photography to light a cartridge of a mixture of magnesium and chlorate of potassium by means of a spark from a Ruhmkorff's coil (D. Mendeléeff, 1889).[17]According to the observations of Maack, Comaille, Böttger, and others. The reduction by heat mentioned further on was pointed out by Geuther, Phipson, Parkinson and Gattermann.[18]This action of metallic magnesium in all probability depends, although only partially (seeNote13), on its volatility, and on the fact that, in combining with a given quantity of oxygen, it evolves more heat than aluminium, silicon, potassium, and other elements.[19]Davy, on heating magnesia in chlorine, concluded that there was a complete substitution, because the volume of the oxygen was half the volume of the chlorine; it is probable, however, that owing to the formation of chlorine oxide (Chapter XI., Note30) the decomposition is not complete and is limited by a reverse reaction.[20]Even a solution of ammonium chloride gives this salt with magnesium sulphate. Its sp. gr. is 1·72; 100 parts of water at 0° dissolve 9, at 20° 17·9 parts of the anhydrous salt. At about 130° it loses all its water.[21]This is an example of equilibrium and of the influence of mass; the double salt is decomposed by water, but if instead of water we take a solution of that soluble part which is formed in the decomposition of the double salt, then the latter dissolves as a whole.[22]If an excess of ammonia be added to a solution of magnesium chloride, only half the magnesium is thrown down in the precipitate, 2MgCl2+ 2NH4.OH = Mg(OH)2+ Mg.NH4Cl3+ NH4Cl. A solution of ammonium chloride reacts with magnesia, evolving ammonia and forming a solution of the same salt, MgO + 3NH4Cl = MgNH4Cl3+ H2O + 2NH3.Among the double salts of ammonium and magnesium, the phosphate, MgNH4PO4,6H2O, is almost insoluble in water (0·07 gram is soluble in a litre), even in the presence of ammonia. Magnesia is very frequently precipitated as this salt from solutions in which it is held by ammonium salts. As lime is not retained in solution by the presence of ammonium salts, but is precipitated nevertheless by sodium carbonate, &c., it is very easy to separate calcium from magnesium by taking advantage of these properties.[23]In order to see the nature and cause of formation of double salts, it is sufficient (although this does not embrace the whole essence of the matter) to consider that one of the metals of such salts (for instance, potassium) easily gives acid salts, and the other (in this instance, magnesium) basic salts; the properties of distinctly basic elements predominate in the former, whilst in the latter these properties are enfeebled, and the salts formed by them bear the character of acids—for example, the salts of aluminium or magnesium act in many cases like acids. By their mutual combination these two opposite properties of the salts are both satisfied.[24]Carnallite has been mentioned in Chapter X. (Note4) and in ChapterXIII. These deposits also contain muchkainite, KMgCl(SO4),3H2O (sp. gr. 2·13; 100 parts of water dissolve 79·6 parts at 18°). This double salt contains two metals and two haloids. Feit (1889) also obtained a bromide corresponding to carnallite.[25]The component parts of certain double salts diffuse at different rates, and as the diffused solution contains a different proportion of the component salts than the solution taken of the double salt, it shows that such salts are decomposed by water. According to Rüdorff, the double salts, like carnallite, MgK2(SO4)2,6H2O, and the alums, all belong to this order (1888). But such salts as tartar emetic, the double oxalates, and double cyanides are not separated by diffusion, which in all probability depends both on the relative rate of the diffusion of the component salts and on the degree of affinity acting between them. Those complex states of equilibrium which exist between water, the individual salts MX and NY, and the double salt MNXY, have been already partially analysed (as will be shown hereafter) in that case when the system is heterogeneous (that is, when something separates out in a solid state from the liquid solution), but in the case of equilibria in a homogeneous liquid medium (in a solution) the phenomenon is not so clear, because it concerns that very theory of solution which cannot yet be considered as established (Chapter I., Note9, and others). As regards the heterogeneous decomposition of double salts, it has long been known that such salts as carnallite and K2Mg(SO4)2give up the more soluble salt if an insufficient quantity of water for their complete solution be taken. The complete saturation of 100 parts of water requires at 0° 14·1, at 20° 25, and at 60° 50·2 parts of the latter double salt (anhydrous), while 100 parts of water dissolve 27 parts of magnesium sulphate at 0°, 36 parts at 20°, and 55 parts at 60°, of the anhydrous salt taken. Of all the states of equilibrium exhibited by double salts the most fully investigated as yet is the system containing water, sodium sulphate, magnesium sulphate, and their double salt, Na2Mg(SO4)2, which crystallises with 4 and 6 mol. OH2. The first crystallo-hydrate, MgNa2(SO4)2,4H2O, occurs at Stassfurt, and as a sedimentary deposit in many of the salt lakes near Astrakhan, and is therefore calledastrakhanite. The specific gravity of the monoclinic prisms of this salt is 2·22. If this salt, in a finely divided state, be mixed with the necessary quantity of water (according to the equation MgNa2(SO4)2,4H2O + 13H2O = Na2SO4,10H2O + MgSO4,7H2O), the mixture solidifies like plaster of Paris into a homogeneous mass if the temperature bebelow22° (Van't Hoff und Van Deventer, 1886; Bakhuis Roozeboom, 1887); but if the temperature be above thistransition-pointthe water and double salt do not react on each other: that is, they do not solidify or give a mixture of sodium and magnesium sulphates. If a mixture (in equivalent quantities) of solutions of these salts be evaporated, and crystals of astrakhanite and of the individual salts capable of proceeding from it be added to the concentrated solution to avoid the possibility of a supersaturated solution, then at temperatures above 22° astrakhanite is exclusively formed (this is the method of its production), but at lower temperatures the individual salts are alone produced. If equivalent amounts of Glauber's salt and magnesium sulphate be mixed together in a solid state, there is no change at temperatures below 22°, but at higher temperatures astrakhanite and water are formed. The volume occupied by Na2SO4,10H2O in grams = 322/1·46 = 220·5 cubic centimetres, and by MgSO4,7H2O = 246/1·68 = 146·4 c.c.; hence their mixture in equivalent quantities occupies a volume of 366·9 c.c. The volume of astrakhanite = 334/2·22 = 150·5 c.c., and the volume of 13H2O = 234 c.c., hence their sum = 380·5 c.c., and therefore it is easy to follow the formation of the astrakhanite in a suitable apparatus (a kind of thermometer containing oil and a powdered mixture of sodium and magnesium sulphates), and to see by the variation in volume that below 22° it remains unchanged, and at higher temperatures proceeds the more quickly the higher the temperature. At the transition temperature the solubility of astrakhanite and of the mixture of the component salts is one and the same, whilst at higher temperatures a solution which is saturated for a mixture of the individual salts would be supersaturated for astrakhanite, and at lower temperatures the solution of astrakhanite will be supersaturated for the component salts, as has been shown with especial detail by Karsten, Deacon, and others. Roozeboom showed that there are two limits to the composition of the solutions which can exist for a double salt; these limits are respectively obtained by dissolving a mixture of the double salt with each of its component simple salts. Van't Hoff demonstrated, besides this, that the tendency towards the formation of double salts has a distinct influence on the progress of double decomposition, for at temperatures above 31° the mixture 2MgSO4,7H2O + 2NaCl passes into MgNa2(SO4)2,4H2O + MgCl2,6H2O + 4H2O, whilst below 31° there is not this double decomposition, but it proceeds in the opposite direction, as may be demonstrated by the above-described methods. Van der Heyd obtained a potassium astrakhanite, K2SO4MgSO4,4H2O, from solutions of the component salts at 100°.From these experiments on double salts we see that there is as close a dependence between the temperature and the formation of substances as there is between the temperature and a change of state. It is a case of Deville's principles of dissociation, extended in the direction of the passage of a solid into a liquid. On the other hand, we see here how essential arôlewater plays in the formation of compounds, and how the affinity for water of crystallisation is essentially analogous to the affinity between salts, and hence also to the affinity of acids for bases, because the formation of double salts does not differ in any essential point (except the degree of affinity—that is, from a quantitative aspect) from the formation of salts themselves. When sodium hydroxide with nitric acid gives sodium nitrate and water the phenomenon is essentially the same as in the formation of astrakhanite from the salts Na2SO4,10H2O and MgSO4,7H2O. Water is disengaged in both cases, and hence the volumes are altered.[26]This salt, and especially its crystallo-hydrate with 7H2O, is generally known as Epsom salts. It has long been used as a purgative. It is easily obtained from magnesia and sulphuric acid, and it separates on the evaporation of sea water and of many saline springs. When carbonic anhydride is obtained by the action of sulphuric acid on magnesite, magnesium sulphate remains in solution. When dolomite—that is, a mixture of magnesium and calcium carbonates—is subjected to the action of a solution of hydrochloric acid until about half of the salt remains, the calcium carbonate is mostly dissolved and magnesium carbonate is left, which by treatment with sulphuric acid gives a solution of magnesium sulphate.[27]The anhydrous salt, MgSO4(sp. gr. 2·61), attracts moisture (7 mol. H2O) from moist air; when heated in steam or hydrogen chloride it gives sulphuric acid, and when heated with carbon it is decomposed according to the equation 2MgSO4+ C = 2SO2+ CO2+ 2MgO. The monohydrated salt (kieserite), MgSO4,H2O (sp. gr. 2·56), dissolves in water with difficulty; it is formed by heating the other crystallo-hydrates to 135°. The hexahydrated salt is dimorphous. If a solution, saturated at the boiling-point, be prepared, and cooled without access of crystals of the heptahydrated salt, then MgSO4,6H2O crystallises out inmonoclinicprisms (Loewel, Marignac), which are quite as unstable as the salt, Na2SO4,7H2O; but if prismatic crystals of the cubic system of the copper-nickel salts of the composition MSO4,6H2O be added, then crystals of MgSO4,6H2O are deposited on them as prisms of thecubicsystem (Lecoq de Boisbaudran). The common crystallo-hydrate, MgSO4,7H2O, Epsom salts, belongs to therhombicsystem, and is obtained by crystallisation below 30°. Its specific gravity is 1·69. In a vacuum, or at 100°, it loses 5H2O, at 132° 6H2O, and at 210° all the 7H2O (Graham). If crystals of ferrous or cobaltic sulphate be placed in a saturated solution,hexagonalcrystals of the heptahydrated salt are formed (Lecoq de Boisbaudran); they present an unstable state of equilibrium, and soon become cloudy, probably owing to their transformation into the more stable common form. Fritzsche, by cooling saturated solutions below 0°, obtained a mixture of crystals of ice and of a dodecahydrated salt, which easily split up at temperatures above 0°. Guthrie showed that dilute solutions of magnesium sulphate, when refrigerated, separate ice until the solution attains a composition MgSO4,24H2O, which will completely freeze into a crystallo-hydrate at -5·3°. According to Coppet and Rüdorff, the temperature of the formation of ice falls by 0·073° for every part by weight of the heptahydrated salt per 100 of water. This figure gives (Chapter I., Note49)i= 1 for both the heptahydrated and the anhydrous salt, from which it is evident that it is impossible to judge the state of combination in which a dissolved substance occurs by the temperature of the formation of ice.The solubility of the different crystallo-hydrates of magnesium sulphate, according to Loewel, also varies, like those of sodium sulphate or carbonate (seeChapter XII., Notes7and18). At 0° 100 parts of water dissolves 40·75 MgSO4in the presence of the hexahydrated salt, 34·67 MgSO4in the presence of the hexagonal heptahydrated salt, and only 26 parts of MgSO4in the presence of the ordinary heptahydrated salt—that is, solutions giving the remaining crystallo-hydrates will be supersaturated for the ordinary heptahydrated salt.All this shows how many diverse aspects of more or less stable equilibria may exist between water and a substance dissolved in it; this has already been enlarged on in ChapterI.Carefully purified magnesium sulphate in its aqueous solution gives, according to Stcherbakoff, an alkaline reaction with litmus, and an acid reaction with phenolphthalein.The specific gravity of solutions of certain salts of magnesium and calcium reduced to 15°/4° (see my work cited, Chapter I., Note 119), are, if water at 4° = 10,000,MgSO4:s= 9,992 + 99·89p+ 0·553p2MgCl2:s= 9,992 + 81·31p+ 0·372p2CaCl2:s= 9,992 + 80·24p+ 0·476p2

Footnotes:

[1]Under favourable circumstances (by taking all the requisite precautions), the weight of the equivalent may be accurately determined by this method. Thus Reynolds and Ramsay (1887) determined the equivalent of zinc to be 32·7 by this method (from the average of 29 experiments), whilst by other methods it has been fixed (by different observers) between 32·55 and 33·95.The differences in their equivalents may be demonstrated by taking equal weights of different metals, and collecting the hydrogen evolved by them (under the action of an acid or alkali).

The differences in their equivalents may be demonstrated by taking equal weights of different metals, and collecting the hydrogen evolved by them (under the action of an acid or alkali).

[2]The most accurate determinations of this kind were carried on by Stas, and will be described in Chapter XXIV.

[2 bis]The amount of electricity in one coulomb according to the present nomenclature of electrical units (seeWorks on Physics and Electro-technology) disengages 0·00001036 gram of hydrogen, 0·00112 gram of silver, 0·0003263 gram of copper from the salts of the oxide, and 0·0006526 gram from the salts of the suboxide, &c. These amounts stand in the same ratio as the equivalents,i.e.as the quantities replaced by one part by weight of hydrogen. The intimate bond which is becoming more and more marked existing between the electrolytic and purely chemical relations of substances (especially in solutions) and the application of electrolysis to the preparation of numerous substances on a large scale, together with the employment of electricity for obtaining high temperatures, &c., makes me regret that the plan and dimensions of this book, and the impossibility of giving a concise and objective exposition of the necessary electrical facts, prevent my entering upon this province of knowledge, although I consider it my duty to recommend its study to all those who desire to take part in the further development of our science.There is only one side of the subject respecting the direct correlation between thermochemical data and electro-motive force, which I think right to mention here, as it justifies the general conception, enunciated by Faraday, that the galvanic current is an aspect of the transference of chemical motion or reaction along the conductors.From experiments conducted by Favre, Thomsen, Garni, Berthelot, Cheltzoff, and others, upon the amount of heat evolved in a closed circuit, it follows that the electro-motive force of the current or its capacity to do a certain work, E, is proportional to the whole amount of heat, Q, disengaged by the reaction forming the source of the current. If E be expressed in volts, and Q in thousands of units of heat referred to equivalent weights, then E = 0·0436Q. For example in a Daniells battery E = 1·09 both by experiment and theory, because in it there takes place the decomposition of CuSO4into Cu + O together with the formation of Zn + O and ZnO + SO3Aq, and these reactions correspond to Q = 25·06 thousand units of heat. So also in all other primary batteries (e.g.Bunsen's, Poggendorff's, &c.) and secondary ones (for instance, those acting according to the reaction Pb + H2SO4+ PbO2, as Cheltzoff showed) E = 0·0436Q.

There is only one side of the subject respecting the direct correlation between thermochemical data and electro-motive force, which I think right to mention here, as it justifies the general conception, enunciated by Faraday, that the galvanic current is an aspect of the transference of chemical motion or reaction along the conductors.

From experiments conducted by Favre, Thomsen, Garni, Berthelot, Cheltzoff, and others, upon the amount of heat evolved in a closed circuit, it follows that the electro-motive force of the current or its capacity to do a certain work, E, is proportional to the whole amount of heat, Q, disengaged by the reaction forming the source of the current. If E be expressed in volts, and Q in thousands of units of heat referred to equivalent weights, then E = 0·0436Q. For example in a Daniells battery E = 1·09 both by experiment and theory, because in it there takes place the decomposition of CuSO4into Cu + O together with the formation of Zn + O and ZnO + SO3Aq, and these reactions correspond to Q = 25·06 thousand units of heat. So also in all other primary batteries (e.g.Bunsen's, Poggendorff's, &c.) and secondary ones (for instance, those acting according to the reaction Pb + H2SO4+ PbO2, as Cheltzoff showed) E = 0·0436Q.

[3]The chief means by which we determine the valency of the elements, or what multiple of the equivalent should be ascribed to the atom, are: (1) The law of Avogadro-Gerhardt. This method is the most general and trustworthy, and has already been applied to a great number of elements. (2) The different grades of oxidation and their isomorphism or analogy in general; for example, Fe = 56 because the suboxide (ferrous oxide) is isomorphous with magnesium oxide, &c., and the oxide (ferric oxide) contains half as much oxygen again as the suboxide. Berzelius, Marignac, and others took advantage of this method for determining the composition of the compounds of many elements. (3) The specific heat, according to Dulong and Petit's law. Regnault, and more especially Cannizzaro, used this method to distinguish univalent from bivalent metals. (4) The periodic law (seeChapter XV.) has served as a means for the determination of the atomic weights of cerium, uranium, yttrium, &c., and more especially of gallium, scandium, and germanium. The correction of the results of one method by those of others is generally had recourse to, and is quite necessary, because, phenomena of dissociation, polymerisation, &c., may complicate the individual determinations by each method.It will be well to observe that a number of other methods, especially from the province of those physical properties which are clearly dependent on the magnitude of the atom (or equivalent) or of the molecule, may lead to the same result. I may point out, for instance, that even the specific gravity of solutions of the metallic chlorides may serve for this purpose. Thus, if beryllium he taken as trivalent—that is, if the composition of its chloride be taken as BeCl3(or a polymeride of it), then the specific gravity of solutions of beryllium chloride will not fit into the series of the other metallic chlorides. But by ascribing to it an atomic weight Be = 7, or taking Be as bivalent, and the composition of its chloride as BeCl2, we arrive at the general rule given in Chapter VII., Note28. Thus W. G. Burdakoff determined in my laboratory that the specific gravity at 15°/4° of the solution BeCl2+ 200H2O = 1·0138—that is, greater than the corresponding solution KCl + 200H2O (= 1·0121), and less than the solution MgCl2+ 200H2O (= 1·0203), as would follow from the magnitude of the molecular weight BeCl2= 80, since KCl = 74·5 and MgCl2= 95.

It will be well to observe that a number of other methods, especially from the province of those physical properties which are clearly dependent on the magnitude of the atom (or equivalent) or of the molecule, may lead to the same result. I may point out, for instance, that even the specific gravity of solutions of the metallic chlorides may serve for this purpose. Thus, if beryllium he taken as trivalent—that is, if the composition of its chloride be taken as BeCl3(or a polymeride of it), then the specific gravity of solutions of beryllium chloride will not fit into the series of the other metallic chlorides. But by ascribing to it an atomic weight Be = 7, or taking Be as bivalent, and the composition of its chloride as BeCl2, we arrive at the general rule given in Chapter VII., Note28. Thus W. G. Burdakoff determined in my laboratory that the specific gravity at 15°/4° of the solution BeCl2+ 200H2O = 1·0138—that is, greater than the corresponding solution KCl + 200H2O (= 1·0121), and less than the solution MgCl2+ 200H2O (= 1·0203), as would follow from the magnitude of the molecular weight BeCl2= 80, since KCl = 74·5 and MgCl2= 95.

[4]The specific heats here given refer to different limits of temperature, but in the majority of cases between 0° and 100°; only in the case of bromine the specific heat is taken (for the solid state) at a temperature below -7°, according to Regnault's determination.The variation of the specific heat with a change of temperatureis a very complex phenomenon, the consideration of which I think would here be out of place. I will only cite a few figures as an example. According to Bystrom, the specific heat of iron at 0° = 0·1116, at 100° = 0·1114, at 200° = 0·1188, at 300° = 0·1267, and at 1,400° = 0·4031. Between these last limits of temperature a change takes place in iron (a spontaneous heating,recalescence), as we shall see in Chapter XXII. For quartz SiO2Pionchon gives Q = 0·1737 + 394t10-6- 27t210-9up to 400°, for metallic aluminium (Richards, 1892) at 0° 0·222, at 20° 0·224, at 100° 0·232; consequently, as a rule, the specific heat varies slightly with the temperature. Still more remarkable are H. E. Weber's observations on the great variation of the specific heat of charcoal, the diamond and boron:0°100°200°600°900°Wood charcoal0·150·230·290·440·46Diamond0·100·190·220·440·45Boron0·220·290·35——These determinations, which have been verified by Dewar, Le Chatelier (Chapter VIII., Note13), Moissan, and Gauthier, the latter finding for boron AQ = 6 at 400°, are of especial importance as confirming the universality of Dulong and Petit's law, because the elements mentioned above form exceptions to the general rule when the mean specific heat is taken for temperatures between 0° and 100°. Thus in the case of the diamond the product of A × Q at 0° = 1·2, and for boron = 2·4. But if we take the specific heat towards which there is evidently a tendency with a rise of temperature, we obtain a product approaching to 6 as with other elements. Thus with the diamond and charcoal, it is evident that the specific heat tends towards 0·47, which multiplied by 12 gives 5·6, the same as for magnesium and aluminium. I may here direct the reader's attention to the fact that for solid elements having a small atomic weight, the specific heat varies considerably if we take the average figures for temperatures 0° to 100°:Li = 7Be = 9B = 11C = 12Q =0·940·420·240·20AQ =6·63·82·62·4It is therefore clear that the specific heat of beryllium determined at a low temperature cannot serve for establishing its atomicity. On the other hand, the low atomic heat of charcoal, graphite, and the diamond, boron, &c., may perhaps depend on the complexity of the molecules of these elements. The necessity for acknowledging a great complexity of the molecules of carbon was explained in ChapterVIII. In the case of sulphur the molecule contains at least S6and its atomic heat = 32 × 0·163 = 5·22, which is distinctly below the normal. If a large number of atoms of carbon are contained in the molecule of charcoal, this would to a certain extent account for its comparatively small atomic heat. With respect to the specific heat of compounds, it will not be out of place to mention here the conclusion arrived at by Kopp, that the molecular heat (that is, the product of MQ) may be looked on as the sum of the atomic heats of its component elements; but as this rule is not a general one, and can only be applied to give an approximate estimate of the specific heats of substances, I do not think it necessary to go into the details of the conclusions described in Liebig's ‘Annalen Supplement-Band,’ 1864, which includes a number of determinations made by Kopp.

These determinations, which have been verified by Dewar, Le Chatelier (Chapter VIII., Note13), Moissan, and Gauthier, the latter finding for boron AQ = 6 at 400°, are of especial importance as confirming the universality of Dulong and Petit's law, because the elements mentioned above form exceptions to the general rule when the mean specific heat is taken for temperatures between 0° and 100°. Thus in the case of the diamond the product of A × Q at 0° = 1·2, and for boron = 2·4. But if we take the specific heat towards which there is evidently a tendency with a rise of temperature, we obtain a product approaching to 6 as with other elements. Thus with the diamond and charcoal, it is evident that the specific heat tends towards 0·47, which multiplied by 12 gives 5·6, the same as for magnesium and aluminium. I may here direct the reader's attention to the fact that for solid elements having a small atomic weight, the specific heat varies considerably if we take the average figures for temperatures 0° to 100°:

It is therefore clear that the specific heat of beryllium determined at a low temperature cannot serve for establishing its atomicity. On the other hand, the low atomic heat of charcoal, graphite, and the diamond, boron, &c., may perhaps depend on the complexity of the molecules of these elements. The necessity for acknowledging a great complexity of the molecules of carbon was explained in ChapterVIII. In the case of sulphur the molecule contains at least S6and its atomic heat = 32 × 0·163 = 5·22, which is distinctly below the normal. If a large number of atoms of carbon are contained in the molecule of charcoal, this would to a certain extent account for its comparatively small atomic heat. With respect to the specific heat of compounds, it will not be out of place to mention here the conclusion arrived at by Kopp, that the molecular heat (that is, the product of MQ) may be looked on as the sum of the atomic heats of its component elements; but as this rule is not a general one, and can only be applied to give an approximate estimate of the specific heats of substances, I do not think it necessary to go into the details of the conclusions described in Liebig's ‘Annalen Supplement-Band,’ 1864, which includes a number of determinations made by Kopp.

[5]It must be remarked that in the case of oxygen (and also hydrogen and carbon) compounds the quotient of MQ/n, wherenis the number of atoms in the molecule, is always less than 6 for solids; for example, for MgO = 5·0, CuO = 5·1, MnO2= 4·6, ice (Q = 0·504) = 3, SiO2= 3·5, &c. At present it is impossible to say whether this depends on the smaller specific heat of the atom of oxygen in its solid compounds (Kopp, Note4) or on some other cause; but, nevertheless, taking into account this decrease depending on the presence of oxygen, a reflection of the atomicity of the elements may to a certain extent be seen in the specific heat of the oxides. Thus for alumina, Al2O3(Q = 0·217), MQ = 22·3, and therefore the quotient MQ/n= 4·5, which is nearly that given by magnesium oxide, MgO. But if we ascribe the same composition to alumina, as to magnesia—that is, if aluminium were counted as divalent—we should obtain the figure 3·7, which is much less. In general, in compounds of identical atomic composition and of analogous chemical properties the molecular heats MQ are nearly equal, as many investigators have long remarked. For example, ZnS = 11·7 and HgS = 11·8; MgSO4= 27·0 and ZnSO4= 28·0, &c.

[6]If W be the amount of heat contained in a massmof a substance at a temperaturet, anddW the amount expended in heating it fromttot+dt, then the specific heat Q =dW(m×dt). The specific heat not only varies with the composition and complexity of the molecules of a substance, but also with the temperature, pressure, and physical state of a substance. Even for gases the variation of Q withtis to be observed. Thus it is seen from the experiments of Regnault and Wiedemann that the specific heat of carbonic anhydride at 0° = 0·19, at 100° = 0·22, and at 200° = 0·24. But the variation of the specific heat of permanent gases with the temperature is, as far as we know, very inconsiderable. According to Mallard and Le Chatelier it is =0·0006/Mper 1°, where M is the molecular weight (for instance, for O2, M = 32). Therefore the specific heat of those permanent gases which contain two atoms in the molecule (H2, O2, N2, CO, and NO) may be, as is shown by experiment, taken as not varying with the temperature. The constancy of the specific heat of perfect gases forms one of the fundamental propositions of the whole theory of heat and on it depends the determination of temperatures by means of gas-thermometers containing hydrogen, nitrogen, or air. Le Chatelier (1887), on the basis of existing determinations, concludes that the molecular heat—that is, the product MQ—of all gases varies in proportion to the temperature, and tends to become equal (= 6·8) at the temperature of absolute zero (that is, at -273°); and therefore MQ = 6·8 +a(273 +t), whereais a constant quantity which increases with the complexity of the gaseous molecule and Q is the specific heat of the gas under a constant pressure. For permanent gasesaalmost = 0, and therefore MQ = 6·8—that is, the atomic heat (if the molecule contains two atoms) = 3·4, as it is in fact (Chapter IX., Note17 bis. As regards liquids (as well as the vapours formed by them), the specific heat always rises with the temperature. Thus for benzene it equals 0·38 + 0·0014t. R. Schiff (1887) showed that the variation of the specific heat of many organic liquids is proportional to the change of temperature (as in the case of gases, according to Le Chatelier), and reduced these variations into dependence with their composition and absolute boiling point. It is very probable that the theory of liquids will make use of these simple relations which recall the simplicity of the variation of the specific gravity (Chapter II., Note34), cohesion, and other properties of liquids with the temperature. They are all expressed by the linear function of the temperature,a+bt, with the same degree of proximity as the property of gases is expressed by the equationpv=Rt.As regards the relation between the specific heats of liquids (or of solids) and of their vapours, the specific heat of the vapour (and also of the solid) is always less than that of the liquid. For example, benzene vapour 0·22, liquid 0·38; chloroform vapour 0·13, liquid 0·23; steam 0·475, liquid water 1·0. But the complexity of the relations existing in specific heat is seen from the fact that the specific heat of ice = 0·502 is less than that of liquid water. According to Regnault, in the case of bromine the specific heat of the vapour = 0·055 at (150°), of the liquid = 0·107 (at 30°), and of solid bromine = 0·084 (at -15°). The specific heat of solid benzoic acid (according to experiment and calculation, Hess, 1888) between 0° and 100° is 0·31, and of liquid benzoic acid 0·50. One of the problems of the present day is the explanation of those complex relations which exist between the composition and such properties as specific heat, latent heat, expansion by heat, compression, internal friction, cohesion, and so forth. They can only be connected by a complete theory of liquids, which may now soon be expected, more especially as many sides of the subject have already been partially explained.

As regards the relation between the specific heats of liquids (or of solids) and of their vapours, the specific heat of the vapour (and also of the solid) is always less than that of the liquid. For example, benzene vapour 0·22, liquid 0·38; chloroform vapour 0·13, liquid 0·23; steam 0·475, liquid water 1·0. But the complexity of the relations existing in specific heat is seen from the fact that the specific heat of ice = 0·502 is less than that of liquid water. According to Regnault, in the case of bromine the specific heat of the vapour = 0·055 at (150°), of the liquid = 0·107 (at 30°), and of solid bromine = 0·084 (at -15°). The specific heat of solid benzoic acid (according to experiment and calculation, Hess, 1888) between 0° and 100° is 0·31, and of liquid benzoic acid 0·50. One of the problems of the present day is the explanation of those complex relations which exist between the composition and such properties as specific heat, latent heat, expansion by heat, compression, internal friction, cohesion, and so forth. They can only be connected by a complete theory of liquids, which may now soon be expected, more especially as many sides of the subject have already been partially explained.

[7]According to the above reasons the quantity of heat, Q, required to raise the temperature of one part by weight of a substance by one degree may be expressed by the sum Q = K + B + D, where K is the heat actually expended in heating the substance, or what is termed the absolute specific heat, B the amount of heat expended in the internal work accomplished with the rise of temperature, and D the amount of heat expended in external work. In the case of gases the last quantity may be easily determined, knowing their coefficient of expansion, which is approximately = 0·00368. By applying to this case the same argument given at the end of Note11, Chapter I., we find that one cubic metre of a gas heated 1° produces an external work of 10333 × 0·00368, or 38·02 kilogrammetres, on which 38·02/424 or 0·0897 heat units are expended. This is the heat expended for the external work produced by one cubic metre of a gas, but the specific heat refers to units of weight, and therefore it is necessary in order to know D to reduce the above quantity to a unit of weight. One cubic metre of hydrogen at 0° and 760 mm. pressure weighs 0·0896 kilo, a gas of molecular weight M has a density M/2, consequently a cubic metre weighs (at 0° and 760 mm.) 0·0448M kilo, and therefore 1 kilogram of the gas occupies a volume 1/0·0448M cubic metres, and hence the external work D in the heating of 1 kilo of the given gas through 1° = 0·0896/0·0448M, or D = 2/M.Taking the magnitude of the internal work B for gases as negligible if permanent gases are taken, and therefore supposing B = 0, we find the specific heat of gases at a constant pressure Q = K + 2 M, where K is the specific heat at a constant volume, or the true specific heat, and M the molecular weight. Hence K = Q - 2/M. The magnitude of the specific heat Q is given by direct experiment. According to Regnault's experiments, for oxygen it = 0·2175, for hydrogen 3·405, for nitrogen 0·2438; the molecular weights of these gases are 32, 2, and 28, and therefore for oxygen K = 0·2175 - 0·0625 = 0·1550, for hydrogen K = 3·4050 - 1·000 = 2·4050, and for nitrogen K = 0·2438 - 0·0714 = 0·1724. These true specific heats of elements are in inverse proportion to their atomic weights—that is, their product by the atomic weight is a constant quantity. In fact, for oxygen this product = 0·155 × 16 = 2·48, for hydrogen 2·40, for nitrogen 0·7724 × 14 = 2·414, and therefore if A stand for the atomic weight we obtain the expression K × A = a constant, which may be taken as 2·45. This is the true expression of Dulong and Petit's law, because K is the true specific heat and A the weight of the atom. It should be remarked, moreover, that the product of the observed specific heat Q into A is also a constant quantity (for oxygen = 3·48, for hydrogen = 3·40), because the external work D is also inversely proportional to the atomic weight.In the case of gases we distinguish the specific heat at a constant pressurec′(we designated this quantity above by Q), and at a constant volumec. It is evident thatthe relation between the two specific heats, k, judging from the above, is the ratio of Q to K, or equal to the ratio of 2·45n+ 2 to 2·45n. Whenn= 1 this ratiok= 1·8; whenn= 2,k= 1·4, whenn= 3,k= 1·3, and with an exceedingly large numbern, of atoms in the molecule,k= 1. That is, the ratio between the specific heats decreases from 1·8 to 1·0 as the number of atoms,n, contained in the molecule increases. This deduction is verified to a certain extent by direct experiment. For such gases as hydrogen, oxygen, nitrogen, carbonic oxide, air, and others in whichn= 2, the magnitude ofkis determined by methods described in works on physics (for example, by the change of temperature with an alteration of pressure, by the velocity of sound, &c.) and is found in reality to be nearly 1·4, and for such gases as carbonic anhydride, nitric dioxide, and others it is nearly 1·3. Kundt and Warburg (1875), by means of the approximate method mentioned in Note29, Chapter VII., determinedkfor mercury vapour whenn= 1, and found it to be = 1·67—that is, a larger quantity than for air, as would be expected from the above.It may be admitted that the true atomic heat of gases = 2·43, only under the condition that they are distant from a liquid state, and do not undergo a chemical change when heated—that is, when no internal work is produced in them (B = 0). Therefore this work may to a certain extent be judged by the observed specific heat. Thus, for instance, for chlorine (Q = 0·12, Regnault;k= 1·33, according to Straker and Martin, and therefore K = 0·09, MK = 6·4), the atomic heat (3·2) is much greater than for other gases containing two atoms in a molecule, and it must be assumed, therefore, that when it is heated some great internal work is accomplished.In order to generalise the facts concerning the specific heat of gases and solids, it appears to me possible to accept the following general proposition:the atomic heat(that is, AQ or QM/n, where M is the molecular weight andnthe number of molecules) issmaller(in solids it attains its highest value 6·8 and in gases 3·4),the more complex the molecule(i.e.the greater the number (n) of atoms forming it)and so much smaller, up to a certain point(in similar physical states)the smaller the mean atomic weight M/n.

Taking the magnitude of the internal work B for gases as negligible if permanent gases are taken, and therefore supposing B = 0, we find the specific heat of gases at a constant pressure Q = K + 2 M, where K is the specific heat at a constant volume, or the true specific heat, and M the molecular weight. Hence K = Q - 2/M. The magnitude of the specific heat Q is given by direct experiment. According to Regnault's experiments, for oxygen it = 0·2175, for hydrogen 3·405, for nitrogen 0·2438; the molecular weights of these gases are 32, 2, and 28, and therefore for oxygen K = 0·2175 - 0·0625 = 0·1550, for hydrogen K = 3·4050 - 1·000 = 2·4050, and for nitrogen K = 0·2438 - 0·0714 = 0·1724. These true specific heats of elements are in inverse proportion to their atomic weights—that is, their product by the atomic weight is a constant quantity. In fact, for oxygen this product = 0·155 × 16 = 2·48, for hydrogen 2·40, for nitrogen 0·7724 × 14 = 2·414, and therefore if A stand for the atomic weight we obtain the expression K × A = a constant, which may be taken as 2·45. This is the true expression of Dulong and Petit's law, because K is the true specific heat and A the weight of the atom. It should be remarked, moreover, that the product of the observed specific heat Q into A is also a constant quantity (for oxygen = 3·48, for hydrogen = 3·40), because the external work D is also inversely proportional to the atomic weight.

In the case of gases we distinguish the specific heat at a constant pressurec′(we designated this quantity above by Q), and at a constant volumec. It is evident thatthe relation between the two specific heats, k, judging from the above, is the ratio of Q to K, or equal to the ratio of 2·45n+ 2 to 2·45n. Whenn= 1 this ratiok= 1·8; whenn= 2,k= 1·4, whenn= 3,k= 1·3, and with an exceedingly large numbern, of atoms in the molecule,k= 1. That is, the ratio between the specific heats decreases from 1·8 to 1·0 as the number of atoms,n, contained in the molecule increases. This deduction is verified to a certain extent by direct experiment. For such gases as hydrogen, oxygen, nitrogen, carbonic oxide, air, and others in whichn= 2, the magnitude ofkis determined by methods described in works on physics (for example, by the change of temperature with an alteration of pressure, by the velocity of sound, &c.) and is found in reality to be nearly 1·4, and for such gases as carbonic anhydride, nitric dioxide, and others it is nearly 1·3. Kundt and Warburg (1875), by means of the approximate method mentioned in Note29, Chapter VII., determinedkfor mercury vapour whenn= 1, and found it to be = 1·67—that is, a larger quantity than for air, as would be expected from the above.

It may be admitted that the true atomic heat of gases = 2·43, only under the condition that they are distant from a liquid state, and do not undergo a chemical change when heated—that is, when no internal work is produced in them (B = 0). Therefore this work may to a certain extent be judged by the observed specific heat. Thus, for instance, for chlorine (Q = 0·12, Regnault;k= 1·33, according to Straker and Martin, and therefore K = 0·09, MK = 6·4), the atomic heat (3·2) is much greater than for other gases containing two atoms in a molecule, and it must be assumed, therefore, that when it is heated some great internal work is accomplished.

In order to generalise the facts concerning the specific heat of gases and solids, it appears to me possible to accept the following general proposition:the atomic heat(that is, AQ or QM/n, where M is the molecular weight andnthe number of molecules) issmaller(in solids it attains its highest value 6·8 and in gases 3·4),the more complex the molecule(i.e.the greater the number (n) of atoms forming it)and so much smaller, up to a certain point(in similar physical states)the smaller the mean atomic weight M/n.

[8]As an example, it will be sufficient to refer to the specific heat of nitrogen tetroxide, N2O4, which, when heated, gradually passes into NO2—that is, chemical work of decomposition proceeds, which consumes heat. Speaking generally, specific heat is a complex quantity, in which it is clear that thermal data (for instance, the heat of reaction) alone cannot give an idea either of chemical or of physical changes individually, but always depend on an association of the one and the other. If a substance be heated fromt0tot1it cannot but suffer a chemical change (that is, the state of the atoms in the molecules changes more or less in one way or another) if dissociation sets in at a temperaturet1. Even in the case of the elements whose molecules contain only one atom, a true chemical change is possible with a rise of temperature, because more heat is evolved in chemical reactions than that quantity which participates in purely physical changes. One gram of hydrogen (specific heat = 3·4 at a constant pressure) cooled to the temperature of absolute zero will evolve altogether about one thousand units of heat, 8 grams of oxygen half this amount, whilst in combining together they evolve in the formation of 9 grams of water more than thirty times as much heat. Hence the store of chemical energy (that is, of the motion of the atoms, vortex, or other) is much greater than the physical store proper to the molecules, but it is the change accomplished by the former that is the cause of chemical transformations. Here we evidently touch on those limits of existing knowledge beyond which the teaching of science does not yet allow us to pass. Many new scientific discoveries have still to be made before this is possible.

[9]As if NaH = Mg and KH = Ca, which is in accordance with their valency. KH includes two monovalent elements, and is a bivalent group like Ca.

[10]Sodium carbonate and other carbonates of the alkalis give acid salts which are less soluble than the normal; here, on the contrary, with an excess of carbonic anhydride, a salt is formed which is more soluble than the normal, but this acid salt is more unstable than sodium hydrogen carbonate, NaHCO3.

[11]The formation of dolomite may be explained, if only we imagine that a solution of a magnesium salt acts on calcium carbonate. Magnesium carbonate may be formed by double decomposition, and it must be supposed that this process ceases at a certain limit (ChapterXII.), when we shall obtain a mixture of the carbonates of calcium and magnesium. Haitinger heated a mixture of calcium carbonate, CaCO3, with a solution of an equivalent quantity of magnesium sulphate, MgSO4, in a closed tube at 200°, and then a portion of the magnesia actually passed into the state of magnesium carbonate, MgCO3, and a portion of the lime was converted into gypsum, CaSO4. Lubavin (1892) showed that MgCO3is more soluble than CaCO3in salt water, which is of some significance in explaining the composition of sea water.

[12]The undoubted action of lime in increasing the fertility of soils—if not in every case, at all events, with ordinary soils which have long been under corn—is based not so much on the need of plants for the lime itself as on those chemical and physical changes which it produces in the soil, as a particularly powerful base which aids the alteration of the mineral and organic elements of the soil.

[13]Sodium and potassium only decompose magnesium oxide at a white heat and very feebly, probably for two reasons. In the first place, because the reaction Mg + O develops more heat (about 140 thousand calories) than K2+ O or Na2+ O (about 100 thousand calories); and, in the second place, because magnesia is not fusible at the heat of a furnace and cannot act on the charcoal, sodium, or potassium—that is, it does not pass into that mobile state which is necessary for reaction. The first reason alone is not sufficient to explain the absence of the reaction between charcoal and magnesia, because iron and charcoal in combining with oxygen evolve less heat than sodium or potassium, yet, nevertheless, they can displace them. With respect to magnesium chloride, it acts on sodium and potassium, not only because their combination with chlorine evolves more heat than the combination of chlorine and magnesium (Mg + Cl2gives 150 and Na2+ Cl2about 195 thousand calories), but also because a fusion, both of the magnesium chloride and of the double salt, takes place under the action of heat. It is probable, however, that a reverse reaction will take place. A reverse reaction might probably be expected, and Winkler (1890) showed that Mg reduces the oxides of the alkali metals (Chapter XIII., Note42).

[14]Commercial magnesium generally contains a certain amount of magnesium nitride (Deville and Caron), Mg3N2—that is, a product of substitution of ammonia which is directly formed (as is easily shown by experiment) when magnesium is heated in nitrogen. It is a yellowish green powder, which gives ammonia and magnesia with water, and cyanogen when heated with carbonic anhydride. Pashkoffsky (1893) showed that Mg3N2is easily formed and is the sole product when Mg is heated to redness in a current of NH3. Perfectly pure magnesium may be obtained by the action of a galvanic current.

[15]Hydrogen peroxide (Weltzien) dissolves magnesium. The reaction has not been investigated.

[16]A special form of apparatus is used for burning magnesium. It is a clockwork arrangement in which a cylinder rotates, round which a ribbon or wire of magnesium is wound. The wire is subjected to a uniform unwinding and burning as the cylinder rotates, and in this manner the combustion may continue uniform for a certain time. The same is attained in special lamps, by causing a mixture of sand and finely divided magnesium to fall from a funnel-shaped reservoir on to the flame. In photography it is best to blow finely divided magnesium into a colourless (spirit or gas) flame, and for instantaneous photography to light a cartridge of a mixture of magnesium and chlorate of potassium by means of a spark from a Ruhmkorff's coil (D. Mendeléeff, 1889).

[17]According to the observations of Maack, Comaille, Böttger, and others. The reduction by heat mentioned further on was pointed out by Geuther, Phipson, Parkinson and Gattermann.

[18]This action of metallic magnesium in all probability depends, although only partially (seeNote13), on its volatility, and on the fact that, in combining with a given quantity of oxygen, it evolves more heat than aluminium, silicon, potassium, and other elements.

[19]Davy, on heating magnesia in chlorine, concluded that there was a complete substitution, because the volume of the oxygen was half the volume of the chlorine; it is probable, however, that owing to the formation of chlorine oxide (Chapter XI., Note30) the decomposition is not complete and is limited by a reverse reaction.

[20]Even a solution of ammonium chloride gives this salt with magnesium sulphate. Its sp. gr. is 1·72; 100 parts of water at 0° dissolve 9, at 20° 17·9 parts of the anhydrous salt. At about 130° it loses all its water.

[21]This is an example of equilibrium and of the influence of mass; the double salt is decomposed by water, but if instead of water we take a solution of that soluble part which is formed in the decomposition of the double salt, then the latter dissolves as a whole.

[22]If an excess of ammonia be added to a solution of magnesium chloride, only half the magnesium is thrown down in the precipitate, 2MgCl2+ 2NH4.OH = Mg(OH)2+ Mg.NH4Cl3+ NH4Cl. A solution of ammonium chloride reacts with magnesia, evolving ammonia and forming a solution of the same salt, MgO + 3NH4Cl = MgNH4Cl3+ H2O + 2NH3.Among the double salts of ammonium and magnesium, the phosphate, MgNH4PO4,6H2O, is almost insoluble in water (0·07 gram is soluble in a litre), even in the presence of ammonia. Magnesia is very frequently precipitated as this salt from solutions in which it is held by ammonium salts. As lime is not retained in solution by the presence of ammonium salts, but is precipitated nevertheless by sodium carbonate, &c., it is very easy to separate calcium from magnesium by taking advantage of these properties.

Among the double salts of ammonium and magnesium, the phosphate, MgNH4PO4,6H2O, is almost insoluble in water (0·07 gram is soluble in a litre), even in the presence of ammonia. Magnesia is very frequently precipitated as this salt from solutions in which it is held by ammonium salts. As lime is not retained in solution by the presence of ammonium salts, but is precipitated nevertheless by sodium carbonate, &c., it is very easy to separate calcium from magnesium by taking advantage of these properties.

[23]In order to see the nature and cause of formation of double salts, it is sufficient (although this does not embrace the whole essence of the matter) to consider that one of the metals of such salts (for instance, potassium) easily gives acid salts, and the other (in this instance, magnesium) basic salts; the properties of distinctly basic elements predominate in the former, whilst in the latter these properties are enfeebled, and the salts formed by them bear the character of acids—for example, the salts of aluminium or magnesium act in many cases like acids. By their mutual combination these two opposite properties of the salts are both satisfied.

[24]Carnallite has been mentioned in Chapter X. (Note4) and in ChapterXIII. These deposits also contain muchkainite, KMgCl(SO4),3H2O (sp. gr. 2·13; 100 parts of water dissolve 79·6 parts at 18°). This double salt contains two metals and two haloids. Feit (1889) also obtained a bromide corresponding to carnallite.

[25]The component parts of certain double salts diffuse at different rates, and as the diffused solution contains a different proportion of the component salts than the solution taken of the double salt, it shows that such salts are decomposed by water. According to Rüdorff, the double salts, like carnallite, MgK2(SO4)2,6H2O, and the alums, all belong to this order (1888). But such salts as tartar emetic, the double oxalates, and double cyanides are not separated by diffusion, which in all probability depends both on the relative rate of the diffusion of the component salts and on the degree of affinity acting between them. Those complex states of equilibrium which exist between water, the individual salts MX and NY, and the double salt MNXY, have been already partially analysed (as will be shown hereafter) in that case when the system is heterogeneous (that is, when something separates out in a solid state from the liquid solution), but in the case of equilibria in a homogeneous liquid medium (in a solution) the phenomenon is not so clear, because it concerns that very theory of solution which cannot yet be considered as established (Chapter I., Note9, and others). As regards the heterogeneous decomposition of double salts, it has long been known that such salts as carnallite and K2Mg(SO4)2give up the more soluble salt if an insufficient quantity of water for their complete solution be taken. The complete saturation of 100 parts of water requires at 0° 14·1, at 20° 25, and at 60° 50·2 parts of the latter double salt (anhydrous), while 100 parts of water dissolve 27 parts of magnesium sulphate at 0°, 36 parts at 20°, and 55 parts at 60°, of the anhydrous salt taken. Of all the states of equilibrium exhibited by double salts the most fully investigated as yet is the system containing water, sodium sulphate, magnesium sulphate, and their double salt, Na2Mg(SO4)2, which crystallises with 4 and 6 mol. OH2. The first crystallo-hydrate, MgNa2(SO4)2,4H2O, occurs at Stassfurt, and as a sedimentary deposit in many of the salt lakes near Astrakhan, and is therefore calledastrakhanite. The specific gravity of the monoclinic prisms of this salt is 2·22. If this salt, in a finely divided state, be mixed with the necessary quantity of water (according to the equation MgNa2(SO4)2,4H2O + 13H2O = Na2SO4,10H2O + MgSO4,7H2O), the mixture solidifies like plaster of Paris into a homogeneous mass if the temperature bebelow22° (Van't Hoff und Van Deventer, 1886; Bakhuis Roozeboom, 1887); but if the temperature be above thistransition-pointthe water and double salt do not react on each other: that is, they do not solidify or give a mixture of sodium and magnesium sulphates. If a mixture (in equivalent quantities) of solutions of these salts be evaporated, and crystals of astrakhanite and of the individual salts capable of proceeding from it be added to the concentrated solution to avoid the possibility of a supersaturated solution, then at temperatures above 22° astrakhanite is exclusively formed (this is the method of its production), but at lower temperatures the individual salts are alone produced. If equivalent amounts of Glauber's salt and magnesium sulphate be mixed together in a solid state, there is no change at temperatures below 22°, but at higher temperatures astrakhanite and water are formed. The volume occupied by Na2SO4,10H2O in grams = 322/1·46 = 220·5 cubic centimetres, and by MgSO4,7H2O = 246/1·68 = 146·4 c.c.; hence their mixture in equivalent quantities occupies a volume of 366·9 c.c. The volume of astrakhanite = 334/2·22 = 150·5 c.c., and the volume of 13H2O = 234 c.c., hence their sum = 380·5 c.c., and therefore it is easy to follow the formation of the astrakhanite in a suitable apparatus (a kind of thermometer containing oil and a powdered mixture of sodium and magnesium sulphates), and to see by the variation in volume that below 22° it remains unchanged, and at higher temperatures proceeds the more quickly the higher the temperature. At the transition temperature the solubility of astrakhanite and of the mixture of the component salts is one and the same, whilst at higher temperatures a solution which is saturated for a mixture of the individual salts would be supersaturated for astrakhanite, and at lower temperatures the solution of astrakhanite will be supersaturated for the component salts, as has been shown with especial detail by Karsten, Deacon, and others. Roozeboom showed that there are two limits to the composition of the solutions which can exist for a double salt; these limits are respectively obtained by dissolving a mixture of the double salt with each of its component simple salts. Van't Hoff demonstrated, besides this, that the tendency towards the formation of double salts has a distinct influence on the progress of double decomposition, for at temperatures above 31° the mixture 2MgSO4,7H2O + 2NaCl passes into MgNa2(SO4)2,4H2O + MgCl2,6H2O + 4H2O, whilst below 31° there is not this double decomposition, but it proceeds in the opposite direction, as may be demonstrated by the above-described methods. Van der Heyd obtained a potassium astrakhanite, K2SO4MgSO4,4H2O, from solutions of the component salts at 100°.From these experiments on double salts we see that there is as close a dependence between the temperature and the formation of substances as there is between the temperature and a change of state. It is a case of Deville's principles of dissociation, extended in the direction of the passage of a solid into a liquid. On the other hand, we see here how essential arôlewater plays in the formation of compounds, and how the affinity for water of crystallisation is essentially analogous to the affinity between salts, and hence also to the affinity of acids for bases, because the formation of double salts does not differ in any essential point (except the degree of affinity—that is, from a quantitative aspect) from the formation of salts themselves. When sodium hydroxide with nitric acid gives sodium nitrate and water the phenomenon is essentially the same as in the formation of astrakhanite from the salts Na2SO4,10H2O and MgSO4,7H2O. Water is disengaged in both cases, and hence the volumes are altered.

From these experiments on double salts we see that there is as close a dependence between the temperature and the formation of substances as there is between the temperature and a change of state. It is a case of Deville's principles of dissociation, extended in the direction of the passage of a solid into a liquid. On the other hand, we see here how essential arôlewater plays in the formation of compounds, and how the affinity for water of crystallisation is essentially analogous to the affinity between salts, and hence also to the affinity of acids for bases, because the formation of double salts does not differ in any essential point (except the degree of affinity—that is, from a quantitative aspect) from the formation of salts themselves. When sodium hydroxide with nitric acid gives sodium nitrate and water the phenomenon is essentially the same as in the formation of astrakhanite from the salts Na2SO4,10H2O and MgSO4,7H2O. Water is disengaged in both cases, and hence the volumes are altered.

[26]This salt, and especially its crystallo-hydrate with 7H2O, is generally known as Epsom salts. It has long been used as a purgative. It is easily obtained from magnesia and sulphuric acid, and it separates on the evaporation of sea water and of many saline springs. When carbonic anhydride is obtained by the action of sulphuric acid on magnesite, magnesium sulphate remains in solution. When dolomite—that is, a mixture of magnesium and calcium carbonates—is subjected to the action of a solution of hydrochloric acid until about half of the salt remains, the calcium carbonate is mostly dissolved and magnesium carbonate is left, which by treatment with sulphuric acid gives a solution of magnesium sulphate.

[27]The anhydrous salt, MgSO4(sp. gr. 2·61), attracts moisture (7 mol. H2O) from moist air; when heated in steam or hydrogen chloride it gives sulphuric acid, and when heated with carbon it is decomposed according to the equation 2MgSO4+ C = 2SO2+ CO2+ 2MgO. The monohydrated salt (kieserite), MgSO4,H2O (sp. gr. 2·56), dissolves in water with difficulty; it is formed by heating the other crystallo-hydrates to 135°. The hexahydrated salt is dimorphous. If a solution, saturated at the boiling-point, be prepared, and cooled without access of crystals of the heptahydrated salt, then MgSO4,6H2O crystallises out inmonoclinicprisms (Loewel, Marignac), which are quite as unstable as the salt, Na2SO4,7H2O; but if prismatic crystals of the cubic system of the copper-nickel salts of the composition MSO4,6H2O be added, then crystals of MgSO4,6H2O are deposited on them as prisms of thecubicsystem (Lecoq de Boisbaudran). The common crystallo-hydrate, MgSO4,7H2O, Epsom salts, belongs to therhombicsystem, and is obtained by crystallisation below 30°. Its specific gravity is 1·69. In a vacuum, or at 100°, it loses 5H2O, at 132° 6H2O, and at 210° all the 7H2O (Graham). If crystals of ferrous or cobaltic sulphate be placed in a saturated solution,hexagonalcrystals of the heptahydrated salt are formed (Lecoq de Boisbaudran); they present an unstable state of equilibrium, and soon become cloudy, probably owing to their transformation into the more stable common form. Fritzsche, by cooling saturated solutions below 0°, obtained a mixture of crystals of ice and of a dodecahydrated salt, which easily split up at temperatures above 0°. Guthrie showed that dilute solutions of magnesium sulphate, when refrigerated, separate ice until the solution attains a composition MgSO4,24H2O, which will completely freeze into a crystallo-hydrate at -5·3°. According to Coppet and Rüdorff, the temperature of the formation of ice falls by 0·073° for every part by weight of the heptahydrated salt per 100 of water. This figure gives (Chapter I., Note49)i= 1 for both the heptahydrated and the anhydrous salt, from which it is evident that it is impossible to judge the state of combination in which a dissolved substance occurs by the temperature of the formation of ice.The solubility of the different crystallo-hydrates of magnesium sulphate, according to Loewel, also varies, like those of sodium sulphate or carbonate (seeChapter XII., Notes7and18). At 0° 100 parts of water dissolves 40·75 MgSO4in the presence of the hexahydrated salt, 34·67 MgSO4in the presence of the hexagonal heptahydrated salt, and only 26 parts of MgSO4in the presence of the ordinary heptahydrated salt—that is, solutions giving the remaining crystallo-hydrates will be supersaturated for the ordinary heptahydrated salt.All this shows how many diverse aspects of more or less stable equilibria may exist between water and a substance dissolved in it; this has already been enlarged on in ChapterI.Carefully purified magnesium sulphate in its aqueous solution gives, according to Stcherbakoff, an alkaline reaction with litmus, and an acid reaction with phenolphthalein.The specific gravity of solutions of certain salts of magnesium and calcium reduced to 15°/4° (see my work cited, Chapter I., Note 119), are, if water at 4° = 10,000,MgSO4:s= 9,992 + 99·89p+ 0·553p2MgCl2:s= 9,992 + 81·31p+ 0·372p2CaCl2:s= 9,992 + 80·24p+ 0·476p2

The solubility of the different crystallo-hydrates of magnesium sulphate, according to Loewel, also varies, like those of sodium sulphate or carbonate (seeChapter XII., Notes7and18). At 0° 100 parts of water dissolves 40·75 MgSO4in the presence of the hexahydrated salt, 34·67 MgSO4in the presence of the hexagonal heptahydrated salt, and only 26 parts of MgSO4in the presence of the ordinary heptahydrated salt—that is, solutions giving the remaining crystallo-hydrates will be supersaturated for the ordinary heptahydrated salt.

All this shows how many diverse aspects of more or less stable equilibria may exist between water and a substance dissolved in it; this has already been enlarged on in ChapterI.

Carefully purified magnesium sulphate in its aqueous solution gives, according to Stcherbakoff, an alkaline reaction with litmus, and an acid reaction with phenolphthalein.

The specific gravity of solutions of certain salts of magnesium and calcium reduced to 15°/4° (see my work cited, Chapter I., Note 119), are, if water at 4° = 10,000,

MgSO4:s= 9,992 + 99·89p+ 0·553p2MgCl2:s= 9,992 + 81·31p+ 0·372p2CaCl2:s= 9,992 + 80·24p+ 0·476p2

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