[26]The law of Gay-Lussac states that all gases in all conditions present one coefficient of expansion 0·00367; that is, when heated from 0° to 100° they expand like air; namely, a thousand volumes of a gas measured at 0° will occupy 1367 volumes at 100°. Regnault, about 1850, showed that Gay-Lussac's law is not entirely correct, and that different gases, and also one and the same gas at different pressures, have not quite the same coefficients of expansion. Thus the expansion of air between 0° and 100° is 0·367 under the ordinary pressure of one atmosphere, and at three atmospheres it is 0·371, the expansion of hydrogen is 0·366, and of carbonic anhydride 0·37. Regnault, however, did not directly determine the change of volume between 0° and 100°, but measured the variation of tension with the change of temperature; but since gases do not entirely follow Mariotte's law, the change of volume cannot be directly judged by the variation of tension. The investigations carried on by myself and Kayander, about 1870, showed the variation of volume on heating from 0° to 100° under a constant pressure. These investigations confirmed Regnault's conclusion that Gay-Lussac's law is not entirely correct, and further showed (1) that the expansion per volume from 0° to 100° under a pressure of one atmosphere, for air = 0·368, for hydrogen = 0·367, for carbonic anhydride = 0·373, for hydrogen bromide = 0·386, &c.; (2) that for gases which are more compressible than should follow from Mariotte's law the expansion by heat increases with the pressure—for example, for air at a pressure of three and a half atmospheres, it equals 0·371, for carbonic anhydride at one atmosphere it equals 0·373, at three atmospheres 0·389, and at eight atmospheres 0·413; (3) that for gases which are less compressible than should follow from Mariotte's law, the expansion by heat decreases with an increase of pressure—for example, for hydrogen at one atmosphere 0·367, at eight atmospheres 0·369, for air at a quarter of an atmosphere 0·370, at one atmosphere 0·368; and hydrogen likeair(and all gases) is less compressedat low pressuresthan should follow from Mariotte's law (seeNote25). Hence, hydrogen, starting from zero to the highest pressures, exhibits a gradually, although only slightly, varying coefficient of expansion, whilst for air and other gases at the atmospheric and higher pressures, the coefficient of expansion increases with the increase of pressure, so long as their compressibility is greater than should follow from Mariotte's law. But when at considerable pressures, this kind of discrepancy passes into the normal (seeNote25), then the coefficient of expansion of all gases decreases with an increase of pressure, as is seen from the researches of Amagat. The difference between the two coefficients of expansion, for a constant pressure and for a constant volume, is explained by these relations. Thus, for example, for air at a pressure of one atmosphere the true coefficient of expansion (the volume varying at constant pressure) = 0·00368 (according to Mendeléeff and Kayander) and the variation of tension (at a constant volume, according to Regnault) = 0·00367.[27]Permanent gases are those which cannot be liquefied by an increase of pressure alone. With a rise of temperature, all gases and vapours become permanent gases. As we shall afterwards learn, carbonic anhydride becomes a permanent gas at temperatures above 31°, and at lower temperatures it has a maximum tension, and may be liquefied by pressure alone.The liquefactionof gases, accomplished by Faraday (seeAmmonia, ChapterVI.) and others, in the first half of this century, showed that a number of substances are capable, like water, of taking all three physical states, and that there is no essential difference between vapours and gases, the only distinction being that the boiling points (or the temperature at which the tension = 760 mm.) of liquids lie above the ordinary temperature, and those of liquefied gases below, and consequently a gas is a superheated vapour, or vapour heated above the boiling point, or removed from saturation, rarefied, having a lower tension than that maximum which is proper to a given temperature and substance. We will here cite themaximum tensionsof certain liquids and gasesat various temperatures, because they may be taken advantage of for obtaining constant temperatures by changing the pressure at which boiling or the formation of saturated vapours takes place. (I may remark that the dependence between the tension of the saturated vapours of various substances and the temperature is very complex, and usually requires three or four independent constants, which vary with the nature of the substance, and are found from the dependence of the tensionpon the temperaturetgiven by experiment; but in 1892 K. D. Kraevitch showed that this dependence is determined by the properties of a substance, such as its density, specific heat, and latent heat of evaporation.) The temperatures (according to the air thermometer) are placed on the left, and the tension in millimetres of mercury (at 0°) on the right-hand side of the equations. Carbon bisulphide, CS2, 0° = 127·9; 10° = 198·5; 20° = 298·1; 30° = 431·6; 40° = 617·5; 50° = 857·1. Chlorobenzene, C6H5Cl, 70° = 97·9; 80° = 141·8; 90° = 208·4; 100° = 292·8; 110° = 402·6; 120° = 542·8; 130° = 719·0. Aniline, C6H7N, 150° = 283·7; 160° = 387·0; 170° = 515·6; 180° = 677·2; 185° = 771·5. Methyl salicylate, C8H8O3, 180° = 294·4; 190° = 330·9; 200° = 432·4; 210° = 557·5; 220° = 710·2; 224° = 779·9. Mercury, Hg, 300° = 246·8; 310° = 304·9; 320° = 373·7; 330° = 454·4; 340° = 548·6; 350° = 658·0; 359° = 770·9. Sulphur, S, 395° = 300; 423° = 500; 443° = 700; 452° = 800; 459° = 900. These figures (Ramsay and Young) show the possibility of obtaining constant temperatures in the vapours of boiling liquids by altering the pressure. We may add the following boiling points under a pressure of 760 mm. (according to the air thermometer by Collendar and Griffiths, 1891): aniline, 184° = 13; naphthalene, 217° = 94; benzophenone, 305° = 82; mercury, 356° = 76; triphenyl-methane, 356° = 44; sulphur, 444° = 53. And melting points: tin, 231° = 68; bismuth, 269° = 22; lead, 327° = 69; and zinc, 417° = 57. These data may be used for obtaining a constant temperature and for verifying thermometers. The same object may be attained by the melting points of certain salts, determined according to the air thermometer by V. Meyer and Riddle (1893): NaCl, 851°; NaBr, 727°; NaI, 650°; KCl, 760°; KBr, 715°; KI, 623°; K2CO3, 1045°; Na2CO3, 1098°; Na2B4O7, 873°; Na2SO4, 843°; K2SO4, 1073°. The tension of liquefied gases is expressed in atmospheres. Sulphurous anhydride, SO2, -30° = 0·4; -20° = 0·6; -10° = 1; 0° = 1·5; +10° = 2·3; 20° = 3·2; 30° = 5·3. Ammonia, NH3, -40° = 0·7; -30° = 1·1; -20° = 1·8; -10° = 2·8; 0° = 4·2; +10° = 6·0; 20° = 8·4. Carbonic anhydride, CO2, -115° = 0·033; -80° = 1; -70° = 2·1; -60° = 3·9; -50° = 6·8; -40° = 10; -20° = 23; 0° = 35; +10° = 46; 20° = 58. Nitrous oxide, N2O, -125° = 0·033; -92° = 1; -80° = 1·9; -50° = 7·6; -20° = 23·1; 0° = 36·1; +20° = 55·3. Ethylene, C2H4, -140° = 0·033; -130° = 0·1; -103° = 1; -40° = 13; -1° = 42. Air, -191° = 1; -158° = 14; -140° = 39. Nitrogen, N2, -203° = 0·085; -193° = 1; -160° = 14; -146° = 32. The methods of liquefying gases (by pressure and cold) will be described under ammonia, nitrous oxide, sulphurous anhydride, and in later footnotes. We will now turn our attention to the fact that the evaporation of volatile liquids, under various, and especially under low, pressures, gives an easy means for obtaininglow temperatures. Thus liquefied carbonic anhydride, under the ordinary pressure, reduces the temperature to -80°, and when it evaporates in a rarefied atmosphere (under an air-pump) to 25 mm. (= 0·033 atmosphere) the temperature, judging by the above-cited figures, falls to -115° (Dewar). Even the evaporation of liquids of common occurrence, under low pressures easily attainable with an air-pump, may produce low temperatures, which may be again taken advantage of for obtaining still lower temperatures. Water boiling in a vacuum becomes cold, and under a pressure of less than 4·5 mm. it freezes, because its tension at 0° is 4·5 mm. A sufficiently low temperature may be obtained by forcing fine streams of air through common ether, or liquid carbon bisulphide, CS2, or methyl chloride, CH3Cl, and other similar volatile liquids. In the adjoining table are given, for certain gases, (1) the number of atmospheres necessary for their liquefaction at 15°, and (2) the boiling points of the resultant liquids under a pressure of 760 mm.C2H4N2OCO2H2SAsH3NH3HClCH3ClC2N2SO2(1)423152108725443(2)-103°-92°-80°-74°-58°-38°-35°-24°-21°-10°[28]Natterer's determinations (1851–1854), together with Amagat's results (1880–1888), show that the compressibility of hydrogen, under high pressures, may be expressed by the following figures:—p=110010002500v=10·01070·00190·0013pv=11·071·93·25s=0·1110·35885wherep= the pressure in metres of mercury,v= the volume, if the volume taken under a pressure of 1 metre = 1, andsthe weight of a litre of hydrogen at 20° in grams. If hydrogen followed Mariotte's law, then under a pressure of 2,500 metres, one litre would contain not 85, but 265 grams. It is evident from the above figures that the weight of a litre of the gas approaches a limit as the pressure increases, which is doubtless the density of the gas when liquefied, and therefore the weight of a litre of liquid hydrogen will probably be near 100 grams (density about 0·1, being less than that of all other liquids).[29]Cagniard de Latour, on heating ether in a closed tube to about 190°, observed that at this temperature the liquid is transformed into vapour occupying the original volume—that is, having the same density as the liquid. The further investigations made by Drion and myself showed that every liquid has such anabsolute boiling point, above which it cannot exist as a liquid and is transformed into a dense gas. In order to grasp the true signification of this absolute boiling temperature, it must be remembered that the liquid state is characterised by a cohesion of its particles which does not exist in vapours and gases. The cohesion of liquids is expressed in their capillary phenomena (the breaks in a column of liquid, drop formation, and rise in capillary tubes, &c.), and the product of the density of a liquid into the height to which it rises in a capillary tube (of a definite diameter) may serve as the measure of the magnitude of cohesion. Thus, in a tube of 1 mm. diameter, water at 15° rises (the height being corrected for the meniscus) 14·8 mm., and ether att°to a height 5·35 - 0·028t°mm. The cohesion of a liquid is lessened by heating, and therefore the capillary heights are also diminished. It has been shown by experiment that this decrement is proportional to the temperature, and hence by the aid of capillary observations we are able to form an idea that at a certain rise of temperature the cohesion may become = 0. For ether, according to the above formula, this would occur at 191°. If the cohesion disappear from a liquid it becomes a gas, for cohesion is the only point of difference between these two states. A liquid in evaporating and overcoming the force of cohesion absorbs heat. Therefore, the absolute boiling point was defined by me (1861) as that temperature at which (a) a liquid cannot exist as a liquid, but forms a gas which cannot pass into a liquid state under any pressure whatever; (b) cohesion = 0; and (c) the latent heat of evaporation = 0.This definition was but little known until Andrews (1869) explained the matter from another aspect. Starting from gases, he discovered that carbonic anhydride cannot be liquefied by any degree of compression at temperatures above 31°, whilst at lower temperatures it can be liquefied. He called this temperature thecritical temperature. It is evident that it is the same as the absolute boiling point. We shall afterwards designate it bytc. At low temperatures a gas which is subjected to a pressure greater than its maximum tension (Note27) is transformed into a liquid, which, in evaporating, gives a saturated vapour possessing this maximum tension; whilst at temperatures above tc the pressure to which the gas is subjected may increase indefinitely. However, under these conditions the volume of the gas does not change indefinitely but approaches a definite limit (seeNote28)—that is, it resembles in this respect a liquid or a solid which is altered but little in volume by pressure. The volume which a liquid or gas occupies attcis termed thecritical volume, and corresponds with thecritical pressure, which we will designate bypcand express in atmospheres. It is evident from what has been said that the discrepancies from Mariotte and Boyle's law, the absolute boiling point, the density in liquid and compressed gaseous states, and the properties of liquids, must all he intimately connected together. We will consider these relations in one of the following notes. At present we will supplement the above observations by the values oftcandpcfor certain liquids and gases which have been investigated in this respect—tcpctcpcN2- 146°33H2S+ 108°92CO- 140°39CH2N2+ 124°62O2- 119°50NH3+ 131°114CH4- 100°50CH3Cl+ 141°73NO- 93°71SO2+ 155°79C2H4+ 10°51C5H10+ 192°34CO2+ 32°77C4H10O+ 193°40N2O+ 53°75CHCl3+ 268°55C2H2+ 37°68CS2+ 278°78HCl+ 52°86C6H6+ 292°60H2O+ 365°200C6H5F+ 287°45CH3OH+ 240°79C6H5Cl+ 360°45C2H5OH+ 243°63C6H5Br+ 397°45CH3COOH+ 322°57C6H5I+ 448°45Young and Guy (1891) showed thattcandpcclearly depend upon the composition and molecular weight.[30]I came to this conclusion in 1870 (Ann. Phys. Chem.141, 623).[31]see captionFig.24.—General arrangement of the apparatus employed by Pictet for liquefying gases.Pictet, in his researches, effected the direct liquefaction of many gases which up to that time had not been liquefied. He employed the apparatus used for the manufacture of ice on a large scale, employing the vaporisation of liquid sulphurous anhydride, which may be liquefied by pressure alone. This anhydride is a gas which is transformed into a liquid at the ordinary temperature under a pressure of several atmospheres (seeNote 27), and boils at -10° at the ordinary atmospheric pressure. This liquid, like all others, boils at a lower temperature under a diminished pressure, and by continually pumping out the gas which comes off by means of a powerful air-pump its boiling point falls as low as -75°. Consequently, if on the one hand we force liquid sulphurous anhydride into a vessel, and on the other hand pump out the gas from the same vessel by powerful air-pumps, then the liquefied gas will boil in the vessel, and cause the temperature in it to fall to -75°. If a second vessel is placed inside this vessel, then another gas may be easily liquefied in it at the low temperature produced by the boiling liquid sulphurous anhydride. Pictet in this manner easily liquefied carbonic anhydride, CO2(at -60° under a pressure of from four to six atmospheres). This gas is more refractory to liquefaction than sulphurous anhydride, but for this reason it gives on evaporating a still lower temperature than can be attained by the evaporation of sulphurous anhydride. A temperature of -80° may be obtained by the evaporation of liquid carbonic anhydride at a pressure of 760 mm., and in an atmosphere rarefied by a powerful pump the temperature falls to -140°. By employing such low temperatures, it was possible, with the aid of pressure, to liquefy the majority of the other gases. It is evident that special pumps which are capable of rarefying gases are necessary to reduce the pressure in the chambers in which the sulphurous and carbonic anhydride boil; and that, in order to re-condense the resultant gases into liquids, special force pumps are required for pumping the liquid anhydrides into the refrigerating chamber. Thus, in Pictet's apparatus (fig.24), the carbonic anhydride was liquefied by the aid of the pumps E F, which compressed the gas (at a pressure of 4–6 atmospheres) and forced it into the tube K, vigorously cooled by being surrounded by boiling liquid sulphurous anhydride, which was condensed in the tube C by the pump B, and rarefied by the pump A. The liquefied carbonic anhydride flowed down the tube K into the tube H, in which it was subjected to a low pressure by the pump E, and thus gave a very low temperature of about -140°. The pump E carried off the vapour of the carbonic anhydride, and conducted it to the pump F, by which it was again liquefied. The carbonic anhydride thus made an entire circuit—that is, it passed from a rarefied vapour of small tension and low temperature into a compressed and cooled gas, which was transformed into a liquid, which again vaporised and produced a low temperature.Inside the wide inclined tube H, where the carbonic acid evaporated, was placed a second and narrow tube M containing hydrogen, which was generated in the vessel L from a mixture of sodium formate and caustic soda (CHO2Na + NaHO = Na2CO3+ H2). This mixture gives hydrogen on heating the vessel L. This vessel and the tube M were made of thick copper, and could withstand great pressures. They were, moreover, hermetically connected together and closed up. Thus the hydrogen which was evolved had no outlet, accumulated in a limited space, and its pressure increased in proportion to the amount of it evolved. This pressure was recorded on a metallic manometer R attached to the end of the tube M. As the hydrogen in this tube was submitted to a very low temperature and a powerful pressure, all the necessary conditions were present for its liquefaction. When the pressure in the tube H became steady—i.e.when the temperature had fallen to -140° and the manometer R indicated a pressure of 650 atmospheres in the tube M—then this pressure did not rise with a further evolution of hydrogen in the vessel L. This served as an indication that the tension of the vapour of the hydrogen had attained a maximum corresponding with -140°, and that consequently all the excess of the gas was condensed to a liquid. Pictet convinced himself of this by opening the cock N, when the liquid hydrogen rushed out from the orifice. But, on leaving a space where the pressure was equal to 650 atmospheres, and coming into contact with air under the ordinary pressure, the liquid or powerfully compressed hydrogen expanded, began to boil, absorbed still more heat, and became still colder. In doing so a portion of the liquid hydrogen, according to Pictet, passed into a solid state, and did not fall in drops into a vessel placed under the outlet N, but as pieces of solid matter, which struck against the sides of the vessel like shot and immediately vaporised. Thus, although it was impossible to see and keep the liquefied hydrogen, still it was clear that it passed not only into a liquid, but also into a solid state. Pictet in his experiments obtained other gases which had not previously been liquefied, especially oxygen and nitrogen, in a liquid and solid state. Pictet supposed that liquid and solid hydrogen has the properties of a metal, like iron.[32]see captionFig.25.—Cailletet's apparatus for liquefying gases.At the same time (1879) as Pictet was working on the liquefaction of gases in Switzerland, Cailletet, in Paris, was occupied on the same subject, and his results, although not so convincing as Pictet's, still showed that the majority of gases, previously unliquefied, were capable of passing into a liquid state. Cailletet subjected gases to a pressure of several hundred atmospheres in narrow thick-walled glass tubes (fig.25); he then cooled the compressed gas as far as possible by surrounding it with a freezing mixture; a cock was then rapidly opened for the outlet of mercury from the tube containing the gas, which consequently rapidly and vigorously expanded. This rapid expansion of the gas would produce great cold, just as the rapid compression of a gas evolves heat and causes a rise in temperature. This cold was produced at the expense of the gas itself, for in rapidly expanding its particles were not able to absorb heat from the walls of the tube, and in cooling a portion of the expanding gas was transformed into liquid. This was seen from the formation of cloud-like drops like a fog which rendered the gas opaque. Thus Cailletet proved the possibility of the liquefaction of gases, but he did not isolate the liquids. The method of Cailletet allows the passage of gases into liquids being observed with greater facility and simplicity than Pictet's method, which requires a very complicated and expensive apparatus.The methods of Pictet and Cailletet were afterwards improved by Olszewski, Wroblewski, Dewar, and others. In order to obtain a still lower temperature they employed, instead of carbonic acid gas, liquid ethylene or nitrogen and oxygen, whose evaporation at low pressures produces a much lower temperature (to -200°). They also improved on the methods of determining such low temperatures, but the methods were not essentially altered; they obtained nitrogen and oxygen in a liquid, and nitrogen even in a solid, state, but no one has yet succeeded in seeing hydrogen in a liquid form.The most illustrative and instructive results (because they gave the possibility of maintaining a very low temperature and the liquefied gas, even air, for a length of time) were obtained in recent years by Prof. Dewar in the Royal Institution of London, which is glorified by the names of Davy, Faraday, and Tyndall. Dewar, with the aid of powerful pumps, obtained many kilograms of oxygen and air (the boiling point under the atmospheric pressure = -190°) in a liquid state and kept them in this state for a length of time by means of open glass vessels with double walls, having a vacuum between them, which prevented the rapid transference of heat, and so gave the possibility of maintaining very low temperatures inside the vessel for a long period of time. The liquefied oxygen or air can be poured from one vessel into another and used for any investigations. Thus in June 1894, Prof. Dewar showed that at the low temperature produced by liquid oxygen many substances become phosphorescent (become self-luminous; for instance, oxygen on passing into a vacuum) and fluoresce (emit light after being illuminated; for instance, paraffin, glue, &c.) much more powerfully than at the ordinary temperature; also that solids then greatly alter in their mechanical properties, &c. I had the opportunity (1894) at Prof. Dewar's of seeing many such experiments in which open vessels containing pounds of liquid oxygen were employed, and in following the progress made in researches conducted at low temperatures, it is my firm impression that the study of many phenomena at low temperatures should widen the horizon of natural science as much as the investigation of phenomena made at the highest temperatures attained in the voltaic arc.[33]The investigations of S. Wroblewski in Cracow give reason to believe that Pictet could not have obtained liquid hydrogen in the interior of his apparatus, and that if he did obtain it, it could only have been at the moment of its outrush due to the fall in temperature following its sudden expansion. Pictet calculated that he obtained a temperature of -140°, but in reality it hardly fell below -120°, judging from the latest data for the vaporisation of carbonic anhydride under low pressure. The difference lies in the method of determining low temperatures. Judging from other properties of hydrogen (seeNote34), one would think that its absolute boiling point lies far below -120°, and even -140° (according to the calculation of Sarrau, on the basis of its compressibility, at -174°). But even at -200° (if the methods of determining such low temperatures be correct) hydrogen does not give a liquid even under a pressure of several hundred atmospheres. However, on expansion a fog is formed and a liquid state attained, but the liquid does not separate.[34]After the idea of the absolute temperature of ebullition (tc, Note29) had been worked out (about 1870), and its connection with the deviations from Mariotte's law had become evident, and especially after the liquefaction of permanent gases, general attention was turned to the development of the fundamental conceptions of the gaseous and liquid states of matter. Some investigators directed their energies to the further study of vapours (for instance, Ramsay and Young), gases (Amagat), and liquids (Zaencheffsky, Nadeschdin, and others), especially to liquids neartcandpc; others (Konovaloff and De Heen) endeavoured to discover the relation between liquids under ordinary conditions (removed fromtcandpc) and gases, whilst a third class of investigators (van der Waals, Clausius, and others), starting from the generally-accepted principles of the mechanical theory of heat and the kinetic theory of gases, and assuming in gases the existence of those forces which certainly act in liquids, deduced the connection between the properties of one and the other. It would be out of place in an elementary handbook like the present to enunciate the whole mass of conclusions arrived at by this method, but it is well to give an idea of the results of van der Waals' considerations, for they explain the gradual uninterrupted passage from a liquid into a gaseous state in the simplest manner, and, although the deduction cannot be considered as complete and decisive (seeNote25), nevertheless it penetrates so deeply into the essence of the matter that its signification is not only reflected in a great number of physical investigations, but also in the province of chemistry, where instances of the passage of substances from a gaseous to a liquid state are so common, and where the very processes of dissociation, decomposition, and combination must be identified with a change of physical state of the participating substances, which has been elaborated by Gibbs, Lavenig, and others.For agiven quantity(weight, mass)of a definite substance, its state is expressed by three variables—volumev, pressure (elasticity, tension)p, and temperaturet. Although the compressibility—[i.e.,d(v)/d(p)]—of liquids is small, still it is clearly expressed, and varies not only with the nature of liquids but also with their pressure and temperature (attcthe compressibility of liquids is very considerable). Although gases, according to Mariotte's law, with small variations of pressure, are uniformly compressed, nevertheless the dependence of their volumevontandpis very complex. This also applies to the coefficient of expansion [=d(v)/d(t), ord(p)/d(t)], which also varies withtandp, both for gases (seeNote26), and for liquids (attcit is very considerable, and often exceeds that of gases, 0·00367). Hence, theequation of conditionmust include three variables,v,p, andt. For a so-called perfect (ideal) gas, or for inconsiderable variations of density, the elementary expressionpv=Ra(1 +at), orpv=R(273 +t) should be accepted, whereRis a constant varying with the mass and nature of a gas, as expressing this dependence, because it includes in itself the laws of Gay-Lussac and Mariotte, for at a constant pressure the volume varies proportionally to 1 +at, and whentis constant the product oftvis constant. In its simplest form the equation may be expressed thus:pv=RT;whereTdenotes what is termed the absolute temperature, or the ordinary temperature + 273—that is,T=t+ 273.Starting from the supposition of the existence of an attraction or internal pressure (expressed bya) proportional to the square of the density (or inversely proportional to the square of the volume), and of the existence of a real volume or diminished length of path (expressed byb) for each gaseous molecule, van der Waals gives for gases the following more complex equation of condition:—(p+a/v2)(v-b) = 1 + 0·00367t;if at 0° under a pressurep= 1 (for example, under the atmospheric pressure), the volume (for instance, a litre) of a gas or vapour he taken as 1, and thereforevandbbe expressed by the same units aspanda. The deviations from both the laws of Mariotte and Gay-Lussac are expressed by the above equation. Thus, for hydrogenamust be taken as infinitely small, andb= 0·0009, judging by the data for 1,000 and 2,500 metres pressure (Note28). For other permanent gases, for which (Note28) I showed (about 1870) from Regnault's and Natterer's data, a decrement ofpv, followed by an increment, which was confirmed (about 1880) by fresh determinations made by Amagat, this phenomena may be expressed in definite magnitudes ofaandb(although van der Waals' formula is not applicable in the case of very small pressures) with sufficient accuracy for contemporary requirements. It is evident that van der Waals' formula can also express the difference of the coefficients of expansion of gases with a change of pressure, and according to the methods of determination (Note26). Besides this, van der Waals' formula shows that at temperatures above 273(8a/27b-1) only one actual volume (gaseous) is possible, whilst at lower temperatures, by varying the pressure, three different volumes—liquid, gaseous, and partly liquid, partly saturated-vaporous—are possible. It is evident that the above temperature is the absolute boiling point—that is (tc) = 273(8a/27b- 1). It is found under the condition that all three possible volumes (the three roots of van der Waals' cubic equation) are then similar and equal (vc= 3b). The pressure in this case (pc) =a/27b2. These ratios between the constantsaandband the conditions ofcritical state—i.e.(tc) and (pc)—give the possibility of determining the one magnitude from the other. Thus for ether (Note29), (tc) = 193°, (tp) = 40, hencea= 0·0307,b= 0·00533, and (vc) = 0·016. That mass of ether which at a pressure of one atmosphere at 0° occupies one volume—for instance, a litre—occupies, according to the above-mentioned condition, this critical volume. And as the density of the vapour of ether compared with hydrogen = 37, and a litre of hydrogen at 0° and under the atmospheric pressure weighs 0·0896 gram, then a litre of ether vapour weighs 3·32 grams; therefore, in a critical state (at 193° and 40 atmospheres) 3·32 grams occupy 0·016 litre, or 16 c.c.; therefore 1 gram occupies a volume of about 5 c.c., and the weight of 1 c.c. of ether will then be 0·21. According to the investigations of Ramsay and Young (1887), the critical volume of ether was approximately such at about the absolute boiling point, but the compressibility of the liquid is so great that the slightest change of pressure or temperature has a considerable effect on the volume. But the investigations of the above savants gave another indirect demonstration of the truth of van der Waals' equation. They also found for ether that the isochords, or the lines of equal volumes (if bothtandpvary), are generally straight lines. Thus the volume of 10 c.c. for 1 gram of ether corresponds with pressures (expressed in metres of mercury) equal to 0·135t- 3·3 (for example, at 180° the pressure = 21 metres, and at 280° it = 34·5 metres). The rectilinear form of the isochord (whenv=aconstant quantity) is a direct result of van der Waals' formula.When, in 1883, I demonstrated that the specific gravity of liquids decreases in proportion to the rise of temperature [St= S0- Ktor St= S0(1 - Kt)], or that the volumes increase in inverse proportion to the binomial 1 - Kt, that is, Vt= V0(1-Kt)-1, where K is the modulus of expansion, which varies with the nature of the liquid, then, in general, not only does a connection arise between gases and liquids with respect to a change of volume, but also it would appear possible, by applying van der Waals' formula, to judge, from the phenomena of the expansion of liquids, as to their transition into vapour, and to connect together all the principal properties of liquids, which up to this time had not been considered to be in direct dependence. Thus Thorpe and Rücker found that 2(tc) + 273 = 1/K, where K is the modulus of expansion in the above-mentioned formula. For example, the expansion of ether is expressed with sufficient accuracy from 0° to 100° by the equation St= 0·736/(1 - 0·00154t), or Vt= 1/(1 - 0·00154t), where 0·00154 is the modulus of expansion, and therefore (tc) = 188°, or by direct observation 193°. For silicon tetrachloride, SiCl4, the modulus equals 0·00136, from whence (tc) = 231°, and by experiment 230°. On the other hand, D. P. Konovaloff, admitting that the external pressurepin liquids is insignificant when compared with the internal (ain van der Waals' formula), and that the work in the expansion of liquids is proportional to their temperature (as in gases), directly deduced, from van der Waals' formula, the above-mentioned formula for the expansion of liquids, Vt= 1/(1 - Kt), and also the magnitude of the latent heat of evaporation, cohesion, and compressibility under pressure. In this way van der Waals' formula embraces the gaseous, critical, andliquid statesof substances, and shows the connection between them. On this account, although van der Waals' formula cannot be considered as perfectly general and accurate, yet it is not only very much more exact thanpv=RT, but it is also more comprehensive, because it applies both to gases and liquids. Further research will naturally give a closer proximity to truth, and will show the connection between composition and the constants (aandb); but a great scientific progress is seen in this form of the equation of state.Clausius (in 1880), taking into consideration the variability ofa, in van der Waals' formula, with the temperature, gave the following equation of condition:—(p+a/T(v+c)2)(v-b) =RT.Sarrau applied this formula to Amagat's data for hydrogen, and founda= 0·0551,c= -0·00043,b= 0·00089, and therefore calculated its absolute boiling point as -174°, and (pc) = 99 atmospheres. But as similar calculations for oxygen (-105°), nitrogen (-124°), and marsh gas (-76°) gavetchigher than it really is, the absolute boiling point of hydrogen must lie below -174°.[35]This and a number of similar cases clearly show how great are the internal chemical forces compared with physical and mechanical forces.[36]The property of palladium of absorbing hydrogen, and of increasing in volume in so doing, may be easily demonstrated by taking a sheet of palladium varnished on one side, and using it as a cathode. The hydrogen which is evolved by the action of the current is retained by the unvarnished surface, as a consequence of which the sheet curls up. By attaching a pointer (for instance, a quill) to the end of the sheet this bending effect is rendered strikingly evident, and on reversing the current (when oxygen will be evolved and combine with the absorbed hydrogen, forming water) it may be shown that on losing the hydrogen the palladium regains its original form.[37]Deville discovered that iron and platinum become pervious to hydrogen at a red heat. He speaks of this in the following terms:—‘The permeability of such homogeneous substances as platinum and iron is quite different from the passage of gases through such non-compact substances as clay and graphite. The permeability of metals depends on their expansion, brought about by heat, and proves that metals and alloys have a certain porosity.’ However, Graham proved that it is only hydrogen which is capable of passing through the above-named metals in this manner. Oxygen, nitrogen, ammonia, and many other gases, only pass through in extremely minute quantities. Graham showed that at a red heat about 500 c.c. of hydrogen pass per minute through a surface of one square metre of platinum 1·1 mm. thick, but that with other gases the amount transmitted is hardly perceptible. Indiarubber has the same capacity for allowing the transference of hydrogen through its substance (seeChapterIII.), but at the ordinary temperature one square metre, 0·014 mm. thick, transmits only 127 c.c. of hydrogen per minute. In the experiment on the decomposition of water by heat in porous tubes, the clay tube may be exchanged for a platinum one with advantage. Graham showed that by placing a platinum tube containing hydrogen under these conditions, and surrounding it by a tube containing air, the transference of the hydrogen may be observed by the decrease of pressure in the platinum tube. In one hour almost all the hydrogen (97 p.c.) had passed from the tube, without being replaced by air. It is evident that the occlusion and passage of hydrogen through metals capable of occluding it are not only intimately connected together, but are dependent on the capacity of metals to form compounds of various degrees of stability with hydrogen—like salts with water.[38]It appeared on further investigation that palladium gives a definite compound, Pd2H (seefurther) with hydrogen; but what was most instructive was the investigation of sodium hydride, Na2H, which clearly showed that the origin and properties of such compounds are in entire accordance with the conceptions of dissociation.Since hydrogen is a gas which is difficult to condense, it is little soluble in water and other liquids. At 0° a hundred volumes of water dissolve 1·9 volume of hydrogen, and alcohol 6·9 volumes measured at 0° and 760 mm. Molten iron absorbs hydrogen, but in solidifying, it expels it. The solution of hydrogen by metals is to a certain degree based on its affinity for metals, and must be likened to the solution of metals in mercury and to the formation of alloys. In its chemical properties hydrogen, as we shall see later, has much of a metallic character. Pictet (seeNote31) even affirms that liquid hydrogen has metallic properties. The metallic properties of hydrogen are also evinced in the fact that it is a good conductor of heat, which is not the case with other gases (Magnus).[39]If it be desired to obtain a perfectly colourless hydrogen flame, it must issue from a platinum nozzle, as the glass end of a gas-conducting tube imparts a yellow tint to the flame, owing to the presence of sodium in the glass.
[26]The law of Gay-Lussac states that all gases in all conditions present one coefficient of expansion 0·00367; that is, when heated from 0° to 100° they expand like air; namely, a thousand volumes of a gas measured at 0° will occupy 1367 volumes at 100°. Regnault, about 1850, showed that Gay-Lussac's law is not entirely correct, and that different gases, and also one and the same gas at different pressures, have not quite the same coefficients of expansion. Thus the expansion of air between 0° and 100° is 0·367 under the ordinary pressure of one atmosphere, and at three atmospheres it is 0·371, the expansion of hydrogen is 0·366, and of carbonic anhydride 0·37. Regnault, however, did not directly determine the change of volume between 0° and 100°, but measured the variation of tension with the change of temperature; but since gases do not entirely follow Mariotte's law, the change of volume cannot be directly judged by the variation of tension. The investigations carried on by myself and Kayander, about 1870, showed the variation of volume on heating from 0° to 100° under a constant pressure. These investigations confirmed Regnault's conclusion that Gay-Lussac's law is not entirely correct, and further showed (1) that the expansion per volume from 0° to 100° under a pressure of one atmosphere, for air = 0·368, for hydrogen = 0·367, for carbonic anhydride = 0·373, for hydrogen bromide = 0·386, &c.; (2) that for gases which are more compressible than should follow from Mariotte's law the expansion by heat increases with the pressure—for example, for air at a pressure of three and a half atmospheres, it equals 0·371, for carbonic anhydride at one atmosphere it equals 0·373, at three atmospheres 0·389, and at eight atmospheres 0·413; (3) that for gases which are less compressible than should follow from Mariotte's law, the expansion by heat decreases with an increase of pressure—for example, for hydrogen at one atmosphere 0·367, at eight atmospheres 0·369, for air at a quarter of an atmosphere 0·370, at one atmosphere 0·368; and hydrogen likeair(and all gases) is less compressedat low pressuresthan should follow from Mariotte's law (seeNote25). Hence, hydrogen, starting from zero to the highest pressures, exhibits a gradually, although only slightly, varying coefficient of expansion, whilst for air and other gases at the atmospheric and higher pressures, the coefficient of expansion increases with the increase of pressure, so long as their compressibility is greater than should follow from Mariotte's law. But when at considerable pressures, this kind of discrepancy passes into the normal (seeNote25), then the coefficient of expansion of all gases decreases with an increase of pressure, as is seen from the researches of Amagat. The difference between the two coefficients of expansion, for a constant pressure and for a constant volume, is explained by these relations. Thus, for example, for air at a pressure of one atmosphere the true coefficient of expansion (the volume varying at constant pressure) = 0·00368 (according to Mendeléeff and Kayander) and the variation of tension (at a constant volume, according to Regnault) = 0·00367.
[26]The law of Gay-Lussac states that all gases in all conditions present one coefficient of expansion 0·00367; that is, when heated from 0° to 100° they expand like air; namely, a thousand volumes of a gas measured at 0° will occupy 1367 volumes at 100°. Regnault, about 1850, showed that Gay-Lussac's law is not entirely correct, and that different gases, and also one and the same gas at different pressures, have not quite the same coefficients of expansion. Thus the expansion of air between 0° and 100° is 0·367 under the ordinary pressure of one atmosphere, and at three atmospheres it is 0·371, the expansion of hydrogen is 0·366, and of carbonic anhydride 0·37. Regnault, however, did not directly determine the change of volume between 0° and 100°, but measured the variation of tension with the change of temperature; but since gases do not entirely follow Mariotte's law, the change of volume cannot be directly judged by the variation of tension. The investigations carried on by myself and Kayander, about 1870, showed the variation of volume on heating from 0° to 100° under a constant pressure. These investigations confirmed Regnault's conclusion that Gay-Lussac's law is not entirely correct, and further showed (1) that the expansion per volume from 0° to 100° under a pressure of one atmosphere, for air = 0·368, for hydrogen = 0·367, for carbonic anhydride = 0·373, for hydrogen bromide = 0·386, &c.; (2) that for gases which are more compressible than should follow from Mariotte's law the expansion by heat increases with the pressure—for example, for air at a pressure of three and a half atmospheres, it equals 0·371, for carbonic anhydride at one atmosphere it equals 0·373, at three atmospheres 0·389, and at eight atmospheres 0·413; (3) that for gases which are less compressible than should follow from Mariotte's law, the expansion by heat decreases with an increase of pressure—for example, for hydrogen at one atmosphere 0·367, at eight atmospheres 0·369, for air at a quarter of an atmosphere 0·370, at one atmosphere 0·368; and hydrogen likeair(and all gases) is less compressedat low pressuresthan should follow from Mariotte's law (seeNote25). Hence, hydrogen, starting from zero to the highest pressures, exhibits a gradually, although only slightly, varying coefficient of expansion, whilst for air and other gases at the atmospheric and higher pressures, the coefficient of expansion increases with the increase of pressure, so long as their compressibility is greater than should follow from Mariotte's law. But when at considerable pressures, this kind of discrepancy passes into the normal (seeNote25), then the coefficient of expansion of all gases decreases with an increase of pressure, as is seen from the researches of Amagat. The difference between the two coefficients of expansion, for a constant pressure and for a constant volume, is explained by these relations. Thus, for example, for air at a pressure of one atmosphere the true coefficient of expansion (the volume varying at constant pressure) = 0·00368 (according to Mendeléeff and Kayander) and the variation of tension (at a constant volume, according to Regnault) = 0·00367.
[27]Permanent gases are those which cannot be liquefied by an increase of pressure alone. With a rise of temperature, all gases and vapours become permanent gases. As we shall afterwards learn, carbonic anhydride becomes a permanent gas at temperatures above 31°, and at lower temperatures it has a maximum tension, and may be liquefied by pressure alone.The liquefactionof gases, accomplished by Faraday (seeAmmonia, ChapterVI.) and others, in the first half of this century, showed that a number of substances are capable, like water, of taking all three physical states, and that there is no essential difference between vapours and gases, the only distinction being that the boiling points (or the temperature at which the tension = 760 mm.) of liquids lie above the ordinary temperature, and those of liquefied gases below, and consequently a gas is a superheated vapour, or vapour heated above the boiling point, or removed from saturation, rarefied, having a lower tension than that maximum which is proper to a given temperature and substance. We will here cite themaximum tensionsof certain liquids and gasesat various temperatures, because they may be taken advantage of for obtaining constant temperatures by changing the pressure at which boiling or the formation of saturated vapours takes place. (I may remark that the dependence between the tension of the saturated vapours of various substances and the temperature is very complex, and usually requires three or four independent constants, which vary with the nature of the substance, and are found from the dependence of the tensionpon the temperaturetgiven by experiment; but in 1892 K. D. Kraevitch showed that this dependence is determined by the properties of a substance, such as its density, specific heat, and latent heat of evaporation.) The temperatures (according to the air thermometer) are placed on the left, and the tension in millimetres of mercury (at 0°) on the right-hand side of the equations. Carbon bisulphide, CS2, 0° = 127·9; 10° = 198·5; 20° = 298·1; 30° = 431·6; 40° = 617·5; 50° = 857·1. Chlorobenzene, C6H5Cl, 70° = 97·9; 80° = 141·8; 90° = 208·4; 100° = 292·8; 110° = 402·6; 120° = 542·8; 130° = 719·0. Aniline, C6H7N, 150° = 283·7; 160° = 387·0; 170° = 515·6; 180° = 677·2; 185° = 771·5. Methyl salicylate, C8H8O3, 180° = 294·4; 190° = 330·9; 200° = 432·4; 210° = 557·5; 220° = 710·2; 224° = 779·9. Mercury, Hg, 300° = 246·8; 310° = 304·9; 320° = 373·7; 330° = 454·4; 340° = 548·6; 350° = 658·0; 359° = 770·9. Sulphur, S, 395° = 300; 423° = 500; 443° = 700; 452° = 800; 459° = 900. These figures (Ramsay and Young) show the possibility of obtaining constant temperatures in the vapours of boiling liquids by altering the pressure. We may add the following boiling points under a pressure of 760 mm. (according to the air thermometer by Collendar and Griffiths, 1891): aniline, 184° = 13; naphthalene, 217° = 94; benzophenone, 305° = 82; mercury, 356° = 76; triphenyl-methane, 356° = 44; sulphur, 444° = 53. And melting points: tin, 231° = 68; bismuth, 269° = 22; lead, 327° = 69; and zinc, 417° = 57. These data may be used for obtaining a constant temperature and for verifying thermometers. The same object may be attained by the melting points of certain salts, determined according to the air thermometer by V. Meyer and Riddle (1893): NaCl, 851°; NaBr, 727°; NaI, 650°; KCl, 760°; KBr, 715°; KI, 623°; K2CO3, 1045°; Na2CO3, 1098°; Na2B4O7, 873°; Na2SO4, 843°; K2SO4, 1073°. The tension of liquefied gases is expressed in atmospheres. Sulphurous anhydride, SO2, -30° = 0·4; -20° = 0·6; -10° = 1; 0° = 1·5; +10° = 2·3; 20° = 3·2; 30° = 5·3. Ammonia, NH3, -40° = 0·7; -30° = 1·1; -20° = 1·8; -10° = 2·8; 0° = 4·2; +10° = 6·0; 20° = 8·4. Carbonic anhydride, CO2, -115° = 0·033; -80° = 1; -70° = 2·1; -60° = 3·9; -50° = 6·8; -40° = 10; -20° = 23; 0° = 35; +10° = 46; 20° = 58. Nitrous oxide, N2O, -125° = 0·033; -92° = 1; -80° = 1·9; -50° = 7·6; -20° = 23·1; 0° = 36·1; +20° = 55·3. Ethylene, C2H4, -140° = 0·033; -130° = 0·1; -103° = 1; -40° = 13; -1° = 42. Air, -191° = 1; -158° = 14; -140° = 39. Nitrogen, N2, -203° = 0·085; -193° = 1; -160° = 14; -146° = 32. The methods of liquefying gases (by pressure and cold) will be described under ammonia, nitrous oxide, sulphurous anhydride, and in later footnotes. We will now turn our attention to the fact that the evaporation of volatile liquids, under various, and especially under low, pressures, gives an easy means for obtaininglow temperatures. Thus liquefied carbonic anhydride, under the ordinary pressure, reduces the temperature to -80°, and when it evaporates in a rarefied atmosphere (under an air-pump) to 25 mm. (= 0·033 atmosphere) the temperature, judging by the above-cited figures, falls to -115° (Dewar). Even the evaporation of liquids of common occurrence, under low pressures easily attainable with an air-pump, may produce low temperatures, which may be again taken advantage of for obtaining still lower temperatures. Water boiling in a vacuum becomes cold, and under a pressure of less than 4·5 mm. it freezes, because its tension at 0° is 4·5 mm. A sufficiently low temperature may be obtained by forcing fine streams of air through common ether, or liquid carbon bisulphide, CS2, or methyl chloride, CH3Cl, and other similar volatile liquids. In the adjoining table are given, for certain gases, (1) the number of atmospheres necessary for their liquefaction at 15°, and (2) the boiling points of the resultant liquids under a pressure of 760 mm.C2H4N2OCO2H2SAsH3NH3HClCH3ClC2N2SO2(1)423152108725443(2)-103°-92°-80°-74°-58°-38°-35°-24°-21°-10°
[27]Permanent gases are those which cannot be liquefied by an increase of pressure alone. With a rise of temperature, all gases and vapours become permanent gases. As we shall afterwards learn, carbonic anhydride becomes a permanent gas at temperatures above 31°, and at lower temperatures it has a maximum tension, and may be liquefied by pressure alone.
The liquefactionof gases, accomplished by Faraday (seeAmmonia, ChapterVI.) and others, in the first half of this century, showed that a number of substances are capable, like water, of taking all three physical states, and that there is no essential difference between vapours and gases, the only distinction being that the boiling points (or the temperature at which the tension = 760 mm.) of liquids lie above the ordinary temperature, and those of liquefied gases below, and consequently a gas is a superheated vapour, or vapour heated above the boiling point, or removed from saturation, rarefied, having a lower tension than that maximum which is proper to a given temperature and substance. We will here cite themaximum tensionsof certain liquids and gasesat various temperatures, because they may be taken advantage of for obtaining constant temperatures by changing the pressure at which boiling or the formation of saturated vapours takes place. (I may remark that the dependence between the tension of the saturated vapours of various substances and the temperature is very complex, and usually requires three or four independent constants, which vary with the nature of the substance, and are found from the dependence of the tensionpon the temperaturetgiven by experiment; but in 1892 K. D. Kraevitch showed that this dependence is determined by the properties of a substance, such as its density, specific heat, and latent heat of evaporation.) The temperatures (according to the air thermometer) are placed on the left, and the tension in millimetres of mercury (at 0°) on the right-hand side of the equations. Carbon bisulphide, CS2, 0° = 127·9; 10° = 198·5; 20° = 298·1; 30° = 431·6; 40° = 617·5; 50° = 857·1. Chlorobenzene, C6H5Cl, 70° = 97·9; 80° = 141·8; 90° = 208·4; 100° = 292·8; 110° = 402·6; 120° = 542·8; 130° = 719·0. Aniline, C6H7N, 150° = 283·7; 160° = 387·0; 170° = 515·6; 180° = 677·2; 185° = 771·5. Methyl salicylate, C8H8O3, 180° = 294·4; 190° = 330·9; 200° = 432·4; 210° = 557·5; 220° = 710·2; 224° = 779·9. Mercury, Hg, 300° = 246·8; 310° = 304·9; 320° = 373·7; 330° = 454·4; 340° = 548·6; 350° = 658·0; 359° = 770·9. Sulphur, S, 395° = 300; 423° = 500; 443° = 700; 452° = 800; 459° = 900. These figures (Ramsay and Young) show the possibility of obtaining constant temperatures in the vapours of boiling liquids by altering the pressure. We may add the following boiling points under a pressure of 760 mm. (according to the air thermometer by Collendar and Griffiths, 1891): aniline, 184° = 13; naphthalene, 217° = 94; benzophenone, 305° = 82; mercury, 356° = 76; triphenyl-methane, 356° = 44; sulphur, 444° = 53. And melting points: tin, 231° = 68; bismuth, 269° = 22; lead, 327° = 69; and zinc, 417° = 57. These data may be used for obtaining a constant temperature and for verifying thermometers. The same object may be attained by the melting points of certain salts, determined according to the air thermometer by V. Meyer and Riddle (1893): NaCl, 851°; NaBr, 727°; NaI, 650°; KCl, 760°; KBr, 715°; KI, 623°; K2CO3, 1045°; Na2CO3, 1098°; Na2B4O7, 873°; Na2SO4, 843°; K2SO4, 1073°. The tension of liquefied gases is expressed in atmospheres. Sulphurous anhydride, SO2, -30° = 0·4; -20° = 0·6; -10° = 1; 0° = 1·5; +10° = 2·3; 20° = 3·2; 30° = 5·3. Ammonia, NH3, -40° = 0·7; -30° = 1·1; -20° = 1·8; -10° = 2·8; 0° = 4·2; +10° = 6·0; 20° = 8·4. Carbonic anhydride, CO2, -115° = 0·033; -80° = 1; -70° = 2·1; -60° = 3·9; -50° = 6·8; -40° = 10; -20° = 23; 0° = 35; +10° = 46; 20° = 58. Nitrous oxide, N2O, -125° = 0·033; -92° = 1; -80° = 1·9; -50° = 7·6; -20° = 23·1; 0° = 36·1; +20° = 55·3. Ethylene, C2H4, -140° = 0·033; -130° = 0·1; -103° = 1; -40° = 13; -1° = 42. Air, -191° = 1; -158° = 14; -140° = 39. Nitrogen, N2, -203° = 0·085; -193° = 1; -160° = 14; -146° = 32. The methods of liquefying gases (by pressure and cold) will be described under ammonia, nitrous oxide, sulphurous anhydride, and in later footnotes. We will now turn our attention to the fact that the evaporation of volatile liquids, under various, and especially under low, pressures, gives an easy means for obtaininglow temperatures. Thus liquefied carbonic anhydride, under the ordinary pressure, reduces the temperature to -80°, and when it evaporates in a rarefied atmosphere (under an air-pump) to 25 mm. (= 0·033 atmosphere) the temperature, judging by the above-cited figures, falls to -115° (Dewar). Even the evaporation of liquids of common occurrence, under low pressures easily attainable with an air-pump, may produce low temperatures, which may be again taken advantage of for obtaining still lower temperatures. Water boiling in a vacuum becomes cold, and under a pressure of less than 4·5 mm. it freezes, because its tension at 0° is 4·5 mm. A sufficiently low temperature may be obtained by forcing fine streams of air through common ether, or liquid carbon bisulphide, CS2, or methyl chloride, CH3Cl, and other similar volatile liquids. In the adjoining table are given, for certain gases, (1) the number of atmospheres necessary for their liquefaction at 15°, and (2) the boiling points of the resultant liquids under a pressure of 760 mm.
[28]Natterer's determinations (1851–1854), together with Amagat's results (1880–1888), show that the compressibility of hydrogen, under high pressures, may be expressed by the following figures:—p=110010002500v=10·01070·00190·0013pv=11·071·93·25s=0·1110·35885wherep= the pressure in metres of mercury,v= the volume, if the volume taken under a pressure of 1 metre = 1, andsthe weight of a litre of hydrogen at 20° in grams. If hydrogen followed Mariotte's law, then under a pressure of 2,500 metres, one litre would contain not 85, but 265 grams. It is evident from the above figures that the weight of a litre of the gas approaches a limit as the pressure increases, which is doubtless the density of the gas when liquefied, and therefore the weight of a litre of liquid hydrogen will probably be near 100 grams (density about 0·1, being less than that of all other liquids).
[28]Natterer's determinations (1851–1854), together with Amagat's results (1880–1888), show that the compressibility of hydrogen, under high pressures, may be expressed by the following figures:—
wherep= the pressure in metres of mercury,v= the volume, if the volume taken under a pressure of 1 metre = 1, andsthe weight of a litre of hydrogen at 20° in grams. If hydrogen followed Mariotte's law, then under a pressure of 2,500 metres, one litre would contain not 85, but 265 grams. It is evident from the above figures that the weight of a litre of the gas approaches a limit as the pressure increases, which is doubtless the density of the gas when liquefied, and therefore the weight of a litre of liquid hydrogen will probably be near 100 grams (density about 0·1, being less than that of all other liquids).
[29]Cagniard de Latour, on heating ether in a closed tube to about 190°, observed that at this temperature the liquid is transformed into vapour occupying the original volume—that is, having the same density as the liquid. The further investigations made by Drion and myself showed that every liquid has such anabsolute boiling point, above which it cannot exist as a liquid and is transformed into a dense gas. In order to grasp the true signification of this absolute boiling temperature, it must be remembered that the liquid state is characterised by a cohesion of its particles which does not exist in vapours and gases. The cohesion of liquids is expressed in their capillary phenomena (the breaks in a column of liquid, drop formation, and rise in capillary tubes, &c.), and the product of the density of a liquid into the height to which it rises in a capillary tube (of a definite diameter) may serve as the measure of the magnitude of cohesion. Thus, in a tube of 1 mm. diameter, water at 15° rises (the height being corrected for the meniscus) 14·8 mm., and ether att°to a height 5·35 - 0·028t°mm. The cohesion of a liquid is lessened by heating, and therefore the capillary heights are also diminished. It has been shown by experiment that this decrement is proportional to the temperature, and hence by the aid of capillary observations we are able to form an idea that at a certain rise of temperature the cohesion may become = 0. For ether, according to the above formula, this would occur at 191°. If the cohesion disappear from a liquid it becomes a gas, for cohesion is the only point of difference between these two states. A liquid in evaporating and overcoming the force of cohesion absorbs heat. Therefore, the absolute boiling point was defined by me (1861) as that temperature at which (a) a liquid cannot exist as a liquid, but forms a gas which cannot pass into a liquid state under any pressure whatever; (b) cohesion = 0; and (c) the latent heat of evaporation = 0.This definition was but little known until Andrews (1869) explained the matter from another aspect. Starting from gases, he discovered that carbonic anhydride cannot be liquefied by any degree of compression at temperatures above 31°, whilst at lower temperatures it can be liquefied. He called this temperature thecritical temperature. It is evident that it is the same as the absolute boiling point. We shall afterwards designate it bytc. At low temperatures a gas which is subjected to a pressure greater than its maximum tension (Note27) is transformed into a liquid, which, in evaporating, gives a saturated vapour possessing this maximum tension; whilst at temperatures above tc the pressure to which the gas is subjected may increase indefinitely. However, under these conditions the volume of the gas does not change indefinitely but approaches a definite limit (seeNote28)—that is, it resembles in this respect a liquid or a solid which is altered but little in volume by pressure. The volume which a liquid or gas occupies attcis termed thecritical volume, and corresponds with thecritical pressure, which we will designate bypcand express in atmospheres. It is evident from what has been said that the discrepancies from Mariotte and Boyle's law, the absolute boiling point, the density in liquid and compressed gaseous states, and the properties of liquids, must all he intimately connected together. We will consider these relations in one of the following notes. At present we will supplement the above observations by the values oftcandpcfor certain liquids and gases which have been investigated in this respect—tcpctcpcN2- 146°33H2S+ 108°92CO- 140°39CH2N2+ 124°62O2- 119°50NH3+ 131°114CH4- 100°50CH3Cl+ 141°73NO- 93°71SO2+ 155°79C2H4+ 10°51C5H10+ 192°34CO2+ 32°77C4H10O+ 193°40N2O+ 53°75CHCl3+ 268°55C2H2+ 37°68CS2+ 278°78HCl+ 52°86C6H6+ 292°60H2O+ 365°200C6H5F+ 287°45CH3OH+ 240°79C6H5Cl+ 360°45C2H5OH+ 243°63C6H5Br+ 397°45CH3COOH+ 322°57C6H5I+ 448°45Young and Guy (1891) showed thattcandpcclearly depend upon the composition and molecular weight.
[29]Cagniard de Latour, on heating ether in a closed tube to about 190°, observed that at this temperature the liquid is transformed into vapour occupying the original volume—that is, having the same density as the liquid. The further investigations made by Drion and myself showed that every liquid has such anabsolute boiling point, above which it cannot exist as a liquid and is transformed into a dense gas. In order to grasp the true signification of this absolute boiling temperature, it must be remembered that the liquid state is characterised by a cohesion of its particles which does not exist in vapours and gases. The cohesion of liquids is expressed in their capillary phenomena (the breaks in a column of liquid, drop formation, and rise in capillary tubes, &c.), and the product of the density of a liquid into the height to which it rises in a capillary tube (of a definite diameter) may serve as the measure of the magnitude of cohesion. Thus, in a tube of 1 mm. diameter, water at 15° rises (the height being corrected for the meniscus) 14·8 mm., and ether att°to a height 5·35 - 0·028t°mm. The cohesion of a liquid is lessened by heating, and therefore the capillary heights are also diminished. It has been shown by experiment that this decrement is proportional to the temperature, and hence by the aid of capillary observations we are able to form an idea that at a certain rise of temperature the cohesion may become = 0. For ether, according to the above formula, this would occur at 191°. If the cohesion disappear from a liquid it becomes a gas, for cohesion is the only point of difference between these two states. A liquid in evaporating and overcoming the force of cohesion absorbs heat. Therefore, the absolute boiling point was defined by me (1861) as that temperature at which (a) a liquid cannot exist as a liquid, but forms a gas which cannot pass into a liquid state under any pressure whatever; (b) cohesion = 0; and (c) the latent heat of evaporation = 0.
This definition was but little known until Andrews (1869) explained the matter from another aspect. Starting from gases, he discovered that carbonic anhydride cannot be liquefied by any degree of compression at temperatures above 31°, whilst at lower temperatures it can be liquefied. He called this temperature thecritical temperature. It is evident that it is the same as the absolute boiling point. We shall afterwards designate it bytc. At low temperatures a gas which is subjected to a pressure greater than its maximum tension (Note27) is transformed into a liquid, which, in evaporating, gives a saturated vapour possessing this maximum tension; whilst at temperatures above tc the pressure to which the gas is subjected may increase indefinitely. However, under these conditions the volume of the gas does not change indefinitely but approaches a definite limit (seeNote28)—that is, it resembles in this respect a liquid or a solid which is altered but little in volume by pressure. The volume which a liquid or gas occupies attcis termed thecritical volume, and corresponds with thecritical pressure, which we will designate bypcand express in atmospheres. It is evident from what has been said that the discrepancies from Mariotte and Boyle's law, the absolute boiling point, the density in liquid and compressed gaseous states, and the properties of liquids, must all he intimately connected together. We will consider these relations in one of the following notes. At present we will supplement the above observations by the values oftcandpcfor certain liquids and gases which have been investigated in this respect—
Young and Guy (1891) showed thattcandpcclearly depend upon the composition and molecular weight.
[30]I came to this conclusion in 1870 (Ann. Phys. Chem.141, 623).
[30]I came to this conclusion in 1870 (Ann. Phys. Chem.141, 623).
[31]see captionFig.24.—General arrangement of the apparatus employed by Pictet for liquefying gases.Pictet, in his researches, effected the direct liquefaction of many gases which up to that time had not been liquefied. He employed the apparatus used for the manufacture of ice on a large scale, employing the vaporisation of liquid sulphurous anhydride, which may be liquefied by pressure alone. This anhydride is a gas which is transformed into a liquid at the ordinary temperature under a pressure of several atmospheres (seeNote 27), and boils at -10° at the ordinary atmospheric pressure. This liquid, like all others, boils at a lower temperature under a diminished pressure, and by continually pumping out the gas which comes off by means of a powerful air-pump its boiling point falls as low as -75°. Consequently, if on the one hand we force liquid sulphurous anhydride into a vessel, and on the other hand pump out the gas from the same vessel by powerful air-pumps, then the liquefied gas will boil in the vessel, and cause the temperature in it to fall to -75°. If a second vessel is placed inside this vessel, then another gas may be easily liquefied in it at the low temperature produced by the boiling liquid sulphurous anhydride. Pictet in this manner easily liquefied carbonic anhydride, CO2(at -60° under a pressure of from four to six atmospheres). This gas is more refractory to liquefaction than sulphurous anhydride, but for this reason it gives on evaporating a still lower temperature than can be attained by the evaporation of sulphurous anhydride. A temperature of -80° may be obtained by the evaporation of liquid carbonic anhydride at a pressure of 760 mm., and in an atmosphere rarefied by a powerful pump the temperature falls to -140°. By employing such low temperatures, it was possible, with the aid of pressure, to liquefy the majority of the other gases. It is evident that special pumps which are capable of rarefying gases are necessary to reduce the pressure in the chambers in which the sulphurous and carbonic anhydride boil; and that, in order to re-condense the resultant gases into liquids, special force pumps are required for pumping the liquid anhydrides into the refrigerating chamber. Thus, in Pictet's apparatus (fig.24), the carbonic anhydride was liquefied by the aid of the pumps E F, which compressed the gas (at a pressure of 4–6 atmospheres) and forced it into the tube K, vigorously cooled by being surrounded by boiling liquid sulphurous anhydride, which was condensed in the tube C by the pump B, and rarefied by the pump A. The liquefied carbonic anhydride flowed down the tube K into the tube H, in which it was subjected to a low pressure by the pump E, and thus gave a very low temperature of about -140°. The pump E carried off the vapour of the carbonic anhydride, and conducted it to the pump F, by which it was again liquefied. The carbonic anhydride thus made an entire circuit—that is, it passed from a rarefied vapour of small tension and low temperature into a compressed and cooled gas, which was transformed into a liquid, which again vaporised and produced a low temperature.Inside the wide inclined tube H, where the carbonic acid evaporated, was placed a second and narrow tube M containing hydrogen, which was generated in the vessel L from a mixture of sodium formate and caustic soda (CHO2Na + NaHO = Na2CO3+ H2). This mixture gives hydrogen on heating the vessel L. This vessel and the tube M were made of thick copper, and could withstand great pressures. They were, moreover, hermetically connected together and closed up. Thus the hydrogen which was evolved had no outlet, accumulated in a limited space, and its pressure increased in proportion to the amount of it evolved. This pressure was recorded on a metallic manometer R attached to the end of the tube M. As the hydrogen in this tube was submitted to a very low temperature and a powerful pressure, all the necessary conditions were present for its liquefaction. When the pressure in the tube H became steady—i.e.when the temperature had fallen to -140° and the manometer R indicated a pressure of 650 atmospheres in the tube M—then this pressure did not rise with a further evolution of hydrogen in the vessel L. This served as an indication that the tension of the vapour of the hydrogen had attained a maximum corresponding with -140°, and that consequently all the excess of the gas was condensed to a liquid. Pictet convinced himself of this by opening the cock N, when the liquid hydrogen rushed out from the orifice. But, on leaving a space where the pressure was equal to 650 atmospheres, and coming into contact with air under the ordinary pressure, the liquid or powerfully compressed hydrogen expanded, began to boil, absorbed still more heat, and became still colder. In doing so a portion of the liquid hydrogen, according to Pictet, passed into a solid state, and did not fall in drops into a vessel placed under the outlet N, but as pieces of solid matter, which struck against the sides of the vessel like shot and immediately vaporised. Thus, although it was impossible to see and keep the liquefied hydrogen, still it was clear that it passed not only into a liquid, but also into a solid state. Pictet in his experiments obtained other gases which had not previously been liquefied, especially oxygen and nitrogen, in a liquid and solid state. Pictet supposed that liquid and solid hydrogen has the properties of a metal, like iron.
[31]
see captionFig.24.—General arrangement of the apparatus employed by Pictet for liquefying gases.
Fig.24.—General arrangement of the apparatus employed by Pictet for liquefying gases.
Pictet, in his researches, effected the direct liquefaction of many gases which up to that time had not been liquefied. He employed the apparatus used for the manufacture of ice on a large scale, employing the vaporisation of liquid sulphurous anhydride, which may be liquefied by pressure alone. This anhydride is a gas which is transformed into a liquid at the ordinary temperature under a pressure of several atmospheres (seeNote 27), and boils at -10° at the ordinary atmospheric pressure. This liquid, like all others, boils at a lower temperature under a diminished pressure, and by continually pumping out the gas which comes off by means of a powerful air-pump its boiling point falls as low as -75°. Consequently, if on the one hand we force liquid sulphurous anhydride into a vessel, and on the other hand pump out the gas from the same vessel by powerful air-pumps, then the liquefied gas will boil in the vessel, and cause the temperature in it to fall to -75°. If a second vessel is placed inside this vessel, then another gas may be easily liquefied in it at the low temperature produced by the boiling liquid sulphurous anhydride. Pictet in this manner easily liquefied carbonic anhydride, CO2(at -60° under a pressure of from four to six atmospheres). This gas is more refractory to liquefaction than sulphurous anhydride, but for this reason it gives on evaporating a still lower temperature than can be attained by the evaporation of sulphurous anhydride. A temperature of -80° may be obtained by the evaporation of liquid carbonic anhydride at a pressure of 760 mm., and in an atmosphere rarefied by a powerful pump the temperature falls to -140°. By employing such low temperatures, it was possible, with the aid of pressure, to liquefy the majority of the other gases. It is evident that special pumps which are capable of rarefying gases are necessary to reduce the pressure in the chambers in which the sulphurous and carbonic anhydride boil; and that, in order to re-condense the resultant gases into liquids, special force pumps are required for pumping the liquid anhydrides into the refrigerating chamber. Thus, in Pictet's apparatus (fig.24), the carbonic anhydride was liquefied by the aid of the pumps E F, which compressed the gas (at a pressure of 4–6 atmospheres) and forced it into the tube K, vigorously cooled by being surrounded by boiling liquid sulphurous anhydride, which was condensed in the tube C by the pump B, and rarefied by the pump A. The liquefied carbonic anhydride flowed down the tube K into the tube H, in which it was subjected to a low pressure by the pump E, and thus gave a very low temperature of about -140°. The pump E carried off the vapour of the carbonic anhydride, and conducted it to the pump F, by which it was again liquefied. The carbonic anhydride thus made an entire circuit—that is, it passed from a rarefied vapour of small tension and low temperature into a compressed and cooled gas, which was transformed into a liquid, which again vaporised and produced a low temperature.
Inside the wide inclined tube H, where the carbonic acid evaporated, was placed a second and narrow tube M containing hydrogen, which was generated in the vessel L from a mixture of sodium formate and caustic soda (CHO2Na + NaHO = Na2CO3+ H2). This mixture gives hydrogen on heating the vessel L. This vessel and the tube M were made of thick copper, and could withstand great pressures. They were, moreover, hermetically connected together and closed up. Thus the hydrogen which was evolved had no outlet, accumulated in a limited space, and its pressure increased in proportion to the amount of it evolved. This pressure was recorded on a metallic manometer R attached to the end of the tube M. As the hydrogen in this tube was submitted to a very low temperature and a powerful pressure, all the necessary conditions were present for its liquefaction. When the pressure in the tube H became steady—i.e.when the temperature had fallen to -140° and the manometer R indicated a pressure of 650 atmospheres in the tube M—then this pressure did not rise with a further evolution of hydrogen in the vessel L. This served as an indication that the tension of the vapour of the hydrogen had attained a maximum corresponding with -140°, and that consequently all the excess of the gas was condensed to a liquid. Pictet convinced himself of this by opening the cock N, when the liquid hydrogen rushed out from the orifice. But, on leaving a space where the pressure was equal to 650 atmospheres, and coming into contact with air under the ordinary pressure, the liquid or powerfully compressed hydrogen expanded, began to boil, absorbed still more heat, and became still colder. In doing so a portion of the liquid hydrogen, according to Pictet, passed into a solid state, and did not fall in drops into a vessel placed under the outlet N, but as pieces of solid matter, which struck against the sides of the vessel like shot and immediately vaporised. Thus, although it was impossible to see and keep the liquefied hydrogen, still it was clear that it passed not only into a liquid, but also into a solid state. Pictet in his experiments obtained other gases which had not previously been liquefied, especially oxygen and nitrogen, in a liquid and solid state. Pictet supposed that liquid and solid hydrogen has the properties of a metal, like iron.
[32]see captionFig.25.—Cailletet's apparatus for liquefying gases.At the same time (1879) as Pictet was working on the liquefaction of gases in Switzerland, Cailletet, in Paris, was occupied on the same subject, and his results, although not so convincing as Pictet's, still showed that the majority of gases, previously unliquefied, were capable of passing into a liquid state. Cailletet subjected gases to a pressure of several hundred atmospheres in narrow thick-walled glass tubes (fig.25); he then cooled the compressed gas as far as possible by surrounding it with a freezing mixture; a cock was then rapidly opened for the outlet of mercury from the tube containing the gas, which consequently rapidly and vigorously expanded. This rapid expansion of the gas would produce great cold, just as the rapid compression of a gas evolves heat and causes a rise in temperature. This cold was produced at the expense of the gas itself, for in rapidly expanding its particles were not able to absorb heat from the walls of the tube, and in cooling a portion of the expanding gas was transformed into liquid. This was seen from the formation of cloud-like drops like a fog which rendered the gas opaque. Thus Cailletet proved the possibility of the liquefaction of gases, but he did not isolate the liquids. The method of Cailletet allows the passage of gases into liquids being observed with greater facility and simplicity than Pictet's method, which requires a very complicated and expensive apparatus.The methods of Pictet and Cailletet were afterwards improved by Olszewski, Wroblewski, Dewar, and others. In order to obtain a still lower temperature they employed, instead of carbonic acid gas, liquid ethylene or nitrogen and oxygen, whose evaporation at low pressures produces a much lower temperature (to -200°). They also improved on the methods of determining such low temperatures, but the methods were not essentially altered; they obtained nitrogen and oxygen in a liquid, and nitrogen even in a solid, state, but no one has yet succeeded in seeing hydrogen in a liquid form.The most illustrative and instructive results (because they gave the possibility of maintaining a very low temperature and the liquefied gas, even air, for a length of time) were obtained in recent years by Prof. Dewar in the Royal Institution of London, which is glorified by the names of Davy, Faraday, and Tyndall. Dewar, with the aid of powerful pumps, obtained many kilograms of oxygen and air (the boiling point under the atmospheric pressure = -190°) in a liquid state and kept them in this state for a length of time by means of open glass vessels with double walls, having a vacuum between them, which prevented the rapid transference of heat, and so gave the possibility of maintaining very low temperatures inside the vessel for a long period of time. The liquefied oxygen or air can be poured from one vessel into another and used for any investigations. Thus in June 1894, Prof. Dewar showed that at the low temperature produced by liquid oxygen many substances become phosphorescent (become self-luminous; for instance, oxygen on passing into a vacuum) and fluoresce (emit light after being illuminated; for instance, paraffin, glue, &c.) much more powerfully than at the ordinary temperature; also that solids then greatly alter in their mechanical properties, &c. I had the opportunity (1894) at Prof. Dewar's of seeing many such experiments in which open vessels containing pounds of liquid oxygen were employed, and in following the progress made in researches conducted at low temperatures, it is my firm impression that the study of many phenomena at low temperatures should widen the horizon of natural science as much as the investigation of phenomena made at the highest temperatures attained in the voltaic arc.
[32]
see captionFig.25.—Cailletet's apparatus for liquefying gases.
Fig.25.—Cailletet's apparatus for liquefying gases.
At the same time (1879) as Pictet was working on the liquefaction of gases in Switzerland, Cailletet, in Paris, was occupied on the same subject, and his results, although not so convincing as Pictet's, still showed that the majority of gases, previously unliquefied, were capable of passing into a liquid state. Cailletet subjected gases to a pressure of several hundred atmospheres in narrow thick-walled glass tubes (fig.25); he then cooled the compressed gas as far as possible by surrounding it with a freezing mixture; a cock was then rapidly opened for the outlet of mercury from the tube containing the gas, which consequently rapidly and vigorously expanded. This rapid expansion of the gas would produce great cold, just as the rapid compression of a gas evolves heat and causes a rise in temperature. This cold was produced at the expense of the gas itself, for in rapidly expanding its particles were not able to absorb heat from the walls of the tube, and in cooling a portion of the expanding gas was transformed into liquid. This was seen from the formation of cloud-like drops like a fog which rendered the gas opaque. Thus Cailletet proved the possibility of the liquefaction of gases, but he did not isolate the liquids. The method of Cailletet allows the passage of gases into liquids being observed with greater facility and simplicity than Pictet's method, which requires a very complicated and expensive apparatus.
The methods of Pictet and Cailletet were afterwards improved by Olszewski, Wroblewski, Dewar, and others. In order to obtain a still lower temperature they employed, instead of carbonic acid gas, liquid ethylene or nitrogen and oxygen, whose evaporation at low pressures produces a much lower temperature (to -200°). They also improved on the methods of determining such low temperatures, but the methods were not essentially altered; they obtained nitrogen and oxygen in a liquid, and nitrogen even in a solid, state, but no one has yet succeeded in seeing hydrogen in a liquid form.
The most illustrative and instructive results (because they gave the possibility of maintaining a very low temperature and the liquefied gas, even air, for a length of time) were obtained in recent years by Prof. Dewar in the Royal Institution of London, which is glorified by the names of Davy, Faraday, and Tyndall. Dewar, with the aid of powerful pumps, obtained many kilograms of oxygen and air (the boiling point under the atmospheric pressure = -190°) in a liquid state and kept them in this state for a length of time by means of open glass vessels with double walls, having a vacuum between them, which prevented the rapid transference of heat, and so gave the possibility of maintaining very low temperatures inside the vessel for a long period of time. The liquefied oxygen or air can be poured from one vessel into another and used for any investigations. Thus in June 1894, Prof. Dewar showed that at the low temperature produced by liquid oxygen many substances become phosphorescent (become self-luminous; for instance, oxygen on passing into a vacuum) and fluoresce (emit light after being illuminated; for instance, paraffin, glue, &c.) much more powerfully than at the ordinary temperature; also that solids then greatly alter in their mechanical properties, &c. I had the opportunity (1894) at Prof. Dewar's of seeing many such experiments in which open vessels containing pounds of liquid oxygen were employed, and in following the progress made in researches conducted at low temperatures, it is my firm impression that the study of many phenomena at low temperatures should widen the horizon of natural science as much as the investigation of phenomena made at the highest temperatures attained in the voltaic arc.
[33]The investigations of S. Wroblewski in Cracow give reason to believe that Pictet could not have obtained liquid hydrogen in the interior of his apparatus, and that if he did obtain it, it could only have been at the moment of its outrush due to the fall in temperature following its sudden expansion. Pictet calculated that he obtained a temperature of -140°, but in reality it hardly fell below -120°, judging from the latest data for the vaporisation of carbonic anhydride under low pressure. The difference lies in the method of determining low temperatures. Judging from other properties of hydrogen (seeNote34), one would think that its absolute boiling point lies far below -120°, and even -140° (according to the calculation of Sarrau, on the basis of its compressibility, at -174°). But even at -200° (if the methods of determining such low temperatures be correct) hydrogen does not give a liquid even under a pressure of several hundred atmospheres. However, on expansion a fog is formed and a liquid state attained, but the liquid does not separate.
[33]The investigations of S. Wroblewski in Cracow give reason to believe that Pictet could not have obtained liquid hydrogen in the interior of his apparatus, and that if he did obtain it, it could only have been at the moment of its outrush due to the fall in temperature following its sudden expansion. Pictet calculated that he obtained a temperature of -140°, but in reality it hardly fell below -120°, judging from the latest data for the vaporisation of carbonic anhydride under low pressure. The difference lies in the method of determining low temperatures. Judging from other properties of hydrogen (seeNote34), one would think that its absolute boiling point lies far below -120°, and even -140° (according to the calculation of Sarrau, on the basis of its compressibility, at -174°). But even at -200° (if the methods of determining such low temperatures be correct) hydrogen does not give a liquid even under a pressure of several hundred atmospheres. However, on expansion a fog is formed and a liquid state attained, but the liquid does not separate.
[34]After the idea of the absolute temperature of ebullition (tc, Note29) had been worked out (about 1870), and its connection with the deviations from Mariotte's law had become evident, and especially after the liquefaction of permanent gases, general attention was turned to the development of the fundamental conceptions of the gaseous and liquid states of matter. Some investigators directed their energies to the further study of vapours (for instance, Ramsay and Young), gases (Amagat), and liquids (Zaencheffsky, Nadeschdin, and others), especially to liquids neartcandpc; others (Konovaloff and De Heen) endeavoured to discover the relation between liquids under ordinary conditions (removed fromtcandpc) and gases, whilst a third class of investigators (van der Waals, Clausius, and others), starting from the generally-accepted principles of the mechanical theory of heat and the kinetic theory of gases, and assuming in gases the existence of those forces which certainly act in liquids, deduced the connection between the properties of one and the other. It would be out of place in an elementary handbook like the present to enunciate the whole mass of conclusions arrived at by this method, but it is well to give an idea of the results of van der Waals' considerations, for they explain the gradual uninterrupted passage from a liquid into a gaseous state in the simplest manner, and, although the deduction cannot be considered as complete and decisive (seeNote25), nevertheless it penetrates so deeply into the essence of the matter that its signification is not only reflected in a great number of physical investigations, but also in the province of chemistry, where instances of the passage of substances from a gaseous to a liquid state are so common, and where the very processes of dissociation, decomposition, and combination must be identified with a change of physical state of the participating substances, which has been elaborated by Gibbs, Lavenig, and others.For agiven quantity(weight, mass)of a definite substance, its state is expressed by three variables—volumev, pressure (elasticity, tension)p, and temperaturet. Although the compressibility—[i.e.,d(v)/d(p)]—of liquids is small, still it is clearly expressed, and varies not only with the nature of liquids but also with their pressure and temperature (attcthe compressibility of liquids is very considerable). Although gases, according to Mariotte's law, with small variations of pressure, are uniformly compressed, nevertheless the dependence of their volumevontandpis very complex. This also applies to the coefficient of expansion [=d(v)/d(t), ord(p)/d(t)], which also varies withtandp, both for gases (seeNote26), and for liquids (attcit is very considerable, and often exceeds that of gases, 0·00367). Hence, theequation of conditionmust include three variables,v,p, andt. For a so-called perfect (ideal) gas, or for inconsiderable variations of density, the elementary expressionpv=Ra(1 +at), orpv=R(273 +t) should be accepted, whereRis a constant varying with the mass and nature of a gas, as expressing this dependence, because it includes in itself the laws of Gay-Lussac and Mariotte, for at a constant pressure the volume varies proportionally to 1 +at, and whentis constant the product oftvis constant. In its simplest form the equation may be expressed thus:pv=RT;whereTdenotes what is termed the absolute temperature, or the ordinary temperature + 273—that is,T=t+ 273.Starting from the supposition of the existence of an attraction or internal pressure (expressed bya) proportional to the square of the density (or inversely proportional to the square of the volume), and of the existence of a real volume or diminished length of path (expressed byb) for each gaseous molecule, van der Waals gives for gases the following more complex equation of condition:—(p+a/v2)(v-b) = 1 + 0·00367t;if at 0° under a pressurep= 1 (for example, under the atmospheric pressure), the volume (for instance, a litre) of a gas or vapour he taken as 1, and thereforevandbbe expressed by the same units aspanda. The deviations from both the laws of Mariotte and Gay-Lussac are expressed by the above equation. Thus, for hydrogenamust be taken as infinitely small, andb= 0·0009, judging by the data for 1,000 and 2,500 metres pressure (Note28). For other permanent gases, for which (Note28) I showed (about 1870) from Regnault's and Natterer's data, a decrement ofpv, followed by an increment, which was confirmed (about 1880) by fresh determinations made by Amagat, this phenomena may be expressed in definite magnitudes ofaandb(although van der Waals' formula is not applicable in the case of very small pressures) with sufficient accuracy for contemporary requirements. It is evident that van der Waals' formula can also express the difference of the coefficients of expansion of gases with a change of pressure, and according to the methods of determination (Note26). Besides this, van der Waals' formula shows that at temperatures above 273(8a/27b-1) only one actual volume (gaseous) is possible, whilst at lower temperatures, by varying the pressure, three different volumes—liquid, gaseous, and partly liquid, partly saturated-vaporous—are possible. It is evident that the above temperature is the absolute boiling point—that is (tc) = 273(8a/27b- 1). It is found under the condition that all three possible volumes (the three roots of van der Waals' cubic equation) are then similar and equal (vc= 3b). The pressure in this case (pc) =a/27b2. These ratios between the constantsaandband the conditions ofcritical state—i.e.(tc) and (pc)—give the possibility of determining the one magnitude from the other. Thus for ether (Note29), (tc) = 193°, (tp) = 40, hencea= 0·0307,b= 0·00533, and (vc) = 0·016. That mass of ether which at a pressure of one atmosphere at 0° occupies one volume—for instance, a litre—occupies, according to the above-mentioned condition, this critical volume. And as the density of the vapour of ether compared with hydrogen = 37, and a litre of hydrogen at 0° and under the atmospheric pressure weighs 0·0896 gram, then a litre of ether vapour weighs 3·32 grams; therefore, in a critical state (at 193° and 40 atmospheres) 3·32 grams occupy 0·016 litre, or 16 c.c.; therefore 1 gram occupies a volume of about 5 c.c., and the weight of 1 c.c. of ether will then be 0·21. According to the investigations of Ramsay and Young (1887), the critical volume of ether was approximately such at about the absolute boiling point, but the compressibility of the liquid is so great that the slightest change of pressure or temperature has a considerable effect on the volume. But the investigations of the above savants gave another indirect demonstration of the truth of van der Waals' equation. They also found for ether that the isochords, or the lines of equal volumes (if bothtandpvary), are generally straight lines. Thus the volume of 10 c.c. for 1 gram of ether corresponds with pressures (expressed in metres of mercury) equal to 0·135t- 3·3 (for example, at 180° the pressure = 21 metres, and at 280° it = 34·5 metres). The rectilinear form of the isochord (whenv=aconstant quantity) is a direct result of van der Waals' formula.When, in 1883, I demonstrated that the specific gravity of liquids decreases in proportion to the rise of temperature [St= S0- Ktor St= S0(1 - Kt)], or that the volumes increase in inverse proportion to the binomial 1 - Kt, that is, Vt= V0(1-Kt)-1, where K is the modulus of expansion, which varies with the nature of the liquid, then, in general, not only does a connection arise between gases and liquids with respect to a change of volume, but also it would appear possible, by applying van der Waals' formula, to judge, from the phenomena of the expansion of liquids, as to their transition into vapour, and to connect together all the principal properties of liquids, which up to this time had not been considered to be in direct dependence. Thus Thorpe and Rücker found that 2(tc) + 273 = 1/K, where K is the modulus of expansion in the above-mentioned formula. For example, the expansion of ether is expressed with sufficient accuracy from 0° to 100° by the equation St= 0·736/(1 - 0·00154t), or Vt= 1/(1 - 0·00154t), where 0·00154 is the modulus of expansion, and therefore (tc) = 188°, or by direct observation 193°. For silicon tetrachloride, SiCl4, the modulus equals 0·00136, from whence (tc) = 231°, and by experiment 230°. On the other hand, D. P. Konovaloff, admitting that the external pressurepin liquids is insignificant when compared with the internal (ain van der Waals' formula), and that the work in the expansion of liquids is proportional to their temperature (as in gases), directly deduced, from van der Waals' formula, the above-mentioned formula for the expansion of liquids, Vt= 1/(1 - Kt), and also the magnitude of the latent heat of evaporation, cohesion, and compressibility under pressure. In this way van der Waals' formula embraces the gaseous, critical, andliquid statesof substances, and shows the connection between them. On this account, although van der Waals' formula cannot be considered as perfectly general and accurate, yet it is not only very much more exact thanpv=RT, but it is also more comprehensive, because it applies both to gases and liquids. Further research will naturally give a closer proximity to truth, and will show the connection between composition and the constants (aandb); but a great scientific progress is seen in this form of the equation of state.Clausius (in 1880), taking into consideration the variability ofa, in van der Waals' formula, with the temperature, gave the following equation of condition:—(p+a/T(v+c)2)(v-b) =RT.Sarrau applied this formula to Amagat's data for hydrogen, and founda= 0·0551,c= -0·00043,b= 0·00089, and therefore calculated its absolute boiling point as -174°, and (pc) = 99 atmospheres. But as similar calculations for oxygen (-105°), nitrogen (-124°), and marsh gas (-76°) gavetchigher than it really is, the absolute boiling point of hydrogen must lie below -174°.
[34]After the idea of the absolute temperature of ebullition (tc, Note29) had been worked out (about 1870), and its connection with the deviations from Mariotte's law had become evident, and especially after the liquefaction of permanent gases, general attention was turned to the development of the fundamental conceptions of the gaseous and liquid states of matter. Some investigators directed their energies to the further study of vapours (for instance, Ramsay and Young), gases (Amagat), and liquids (Zaencheffsky, Nadeschdin, and others), especially to liquids neartcandpc; others (Konovaloff and De Heen) endeavoured to discover the relation between liquids under ordinary conditions (removed fromtcandpc) and gases, whilst a third class of investigators (van der Waals, Clausius, and others), starting from the generally-accepted principles of the mechanical theory of heat and the kinetic theory of gases, and assuming in gases the existence of those forces which certainly act in liquids, deduced the connection between the properties of one and the other. It would be out of place in an elementary handbook like the present to enunciate the whole mass of conclusions arrived at by this method, but it is well to give an idea of the results of van der Waals' considerations, for they explain the gradual uninterrupted passage from a liquid into a gaseous state in the simplest manner, and, although the deduction cannot be considered as complete and decisive (seeNote25), nevertheless it penetrates so deeply into the essence of the matter that its signification is not only reflected in a great number of physical investigations, but also in the province of chemistry, where instances of the passage of substances from a gaseous to a liquid state are so common, and where the very processes of dissociation, decomposition, and combination must be identified with a change of physical state of the participating substances, which has been elaborated by Gibbs, Lavenig, and others.
For agiven quantity(weight, mass)of a definite substance, its state is expressed by three variables—volumev, pressure (elasticity, tension)p, and temperaturet. Although the compressibility—[i.e.,d(v)/d(p)]—of liquids is small, still it is clearly expressed, and varies not only with the nature of liquids but also with their pressure and temperature (attcthe compressibility of liquids is very considerable). Although gases, according to Mariotte's law, with small variations of pressure, are uniformly compressed, nevertheless the dependence of their volumevontandpis very complex. This also applies to the coefficient of expansion [=d(v)/d(t), ord(p)/d(t)], which also varies withtandp, both for gases (seeNote26), and for liquids (attcit is very considerable, and often exceeds that of gases, 0·00367). Hence, theequation of conditionmust include three variables,v,p, andt. For a so-called perfect (ideal) gas, or for inconsiderable variations of density, the elementary expressionpv=Ra(1 +at), orpv=R(273 +t) should be accepted, whereRis a constant varying with the mass and nature of a gas, as expressing this dependence, because it includes in itself the laws of Gay-Lussac and Mariotte, for at a constant pressure the volume varies proportionally to 1 +at, and whentis constant the product oftvis constant. In its simplest form the equation may be expressed thus:
pv=RT;
whereTdenotes what is termed the absolute temperature, or the ordinary temperature + 273—that is,T=t+ 273.
Starting from the supposition of the existence of an attraction or internal pressure (expressed bya) proportional to the square of the density (or inversely proportional to the square of the volume), and of the existence of a real volume or diminished length of path (expressed byb) for each gaseous molecule, van der Waals gives for gases the following more complex equation of condition:—
(p+a/v2)(v-b) = 1 + 0·00367t;
if at 0° under a pressurep= 1 (for example, under the atmospheric pressure), the volume (for instance, a litre) of a gas or vapour he taken as 1, and thereforevandbbe expressed by the same units aspanda. The deviations from both the laws of Mariotte and Gay-Lussac are expressed by the above equation. Thus, for hydrogenamust be taken as infinitely small, andb= 0·0009, judging by the data for 1,000 and 2,500 metres pressure (Note28). For other permanent gases, for which (Note28) I showed (about 1870) from Regnault's and Natterer's data, a decrement ofpv, followed by an increment, which was confirmed (about 1880) by fresh determinations made by Amagat, this phenomena may be expressed in definite magnitudes ofaandb(although van der Waals' formula is not applicable in the case of very small pressures) with sufficient accuracy for contemporary requirements. It is evident that van der Waals' formula can also express the difference of the coefficients of expansion of gases with a change of pressure, and according to the methods of determination (Note26). Besides this, van der Waals' formula shows that at temperatures above 273(8a/27b-1) only one actual volume (gaseous) is possible, whilst at lower temperatures, by varying the pressure, three different volumes—liquid, gaseous, and partly liquid, partly saturated-vaporous—are possible. It is evident that the above temperature is the absolute boiling point—that is (tc) = 273(8a/27b- 1). It is found under the condition that all three possible volumes (the three roots of van der Waals' cubic equation) are then similar and equal (vc= 3b). The pressure in this case (pc) =a/27b2. These ratios between the constantsaandband the conditions ofcritical state—i.e.(tc) and (pc)—give the possibility of determining the one magnitude from the other. Thus for ether (Note29), (tc) = 193°, (tp) = 40, hencea= 0·0307,b= 0·00533, and (vc) = 0·016. That mass of ether which at a pressure of one atmosphere at 0° occupies one volume—for instance, a litre—occupies, according to the above-mentioned condition, this critical volume. And as the density of the vapour of ether compared with hydrogen = 37, and a litre of hydrogen at 0° and under the atmospheric pressure weighs 0·0896 gram, then a litre of ether vapour weighs 3·32 grams; therefore, in a critical state (at 193° and 40 atmospheres) 3·32 grams occupy 0·016 litre, or 16 c.c.; therefore 1 gram occupies a volume of about 5 c.c., and the weight of 1 c.c. of ether will then be 0·21. According to the investigations of Ramsay and Young (1887), the critical volume of ether was approximately such at about the absolute boiling point, but the compressibility of the liquid is so great that the slightest change of pressure or temperature has a considerable effect on the volume. But the investigations of the above savants gave another indirect demonstration of the truth of van der Waals' equation. They also found for ether that the isochords, or the lines of equal volumes (if bothtandpvary), are generally straight lines. Thus the volume of 10 c.c. for 1 gram of ether corresponds with pressures (expressed in metres of mercury) equal to 0·135t- 3·3 (for example, at 180° the pressure = 21 metres, and at 280° it = 34·5 metres). The rectilinear form of the isochord (whenv=aconstant quantity) is a direct result of van der Waals' formula.
When, in 1883, I demonstrated that the specific gravity of liquids decreases in proportion to the rise of temperature [St= S0- Ktor St= S0(1 - Kt)], or that the volumes increase in inverse proportion to the binomial 1 - Kt, that is, Vt= V0(1-Kt)-1, where K is the modulus of expansion, which varies with the nature of the liquid, then, in general, not only does a connection arise between gases and liquids with respect to a change of volume, but also it would appear possible, by applying van der Waals' formula, to judge, from the phenomena of the expansion of liquids, as to their transition into vapour, and to connect together all the principal properties of liquids, which up to this time had not been considered to be in direct dependence. Thus Thorpe and Rücker found that 2(tc) + 273 = 1/K, where K is the modulus of expansion in the above-mentioned formula. For example, the expansion of ether is expressed with sufficient accuracy from 0° to 100° by the equation St= 0·736/(1 - 0·00154t), or Vt= 1/(1 - 0·00154t), where 0·00154 is the modulus of expansion, and therefore (tc) = 188°, or by direct observation 193°. For silicon tetrachloride, SiCl4, the modulus equals 0·00136, from whence (tc) = 231°, and by experiment 230°. On the other hand, D. P. Konovaloff, admitting that the external pressurepin liquids is insignificant when compared with the internal (ain van der Waals' formula), and that the work in the expansion of liquids is proportional to their temperature (as in gases), directly deduced, from van der Waals' formula, the above-mentioned formula for the expansion of liquids, Vt= 1/(1 - Kt), and also the magnitude of the latent heat of evaporation, cohesion, and compressibility under pressure. In this way van der Waals' formula embraces the gaseous, critical, andliquid statesof substances, and shows the connection between them. On this account, although van der Waals' formula cannot be considered as perfectly general and accurate, yet it is not only very much more exact thanpv=RT, but it is also more comprehensive, because it applies both to gases and liquids. Further research will naturally give a closer proximity to truth, and will show the connection between composition and the constants (aandb); but a great scientific progress is seen in this form of the equation of state.
Clausius (in 1880), taking into consideration the variability ofa, in van der Waals' formula, with the temperature, gave the following equation of condition:—
(p+a/T(v+c)2)(v-b) =RT.
Sarrau applied this formula to Amagat's data for hydrogen, and founda= 0·0551,c= -0·00043,b= 0·00089, and therefore calculated its absolute boiling point as -174°, and (pc) = 99 atmospheres. But as similar calculations for oxygen (-105°), nitrogen (-124°), and marsh gas (-76°) gavetchigher than it really is, the absolute boiling point of hydrogen must lie below -174°.
[35]This and a number of similar cases clearly show how great are the internal chemical forces compared with physical and mechanical forces.
[35]This and a number of similar cases clearly show how great are the internal chemical forces compared with physical and mechanical forces.
[36]The property of palladium of absorbing hydrogen, and of increasing in volume in so doing, may be easily demonstrated by taking a sheet of palladium varnished on one side, and using it as a cathode. The hydrogen which is evolved by the action of the current is retained by the unvarnished surface, as a consequence of which the sheet curls up. By attaching a pointer (for instance, a quill) to the end of the sheet this bending effect is rendered strikingly evident, and on reversing the current (when oxygen will be evolved and combine with the absorbed hydrogen, forming water) it may be shown that on losing the hydrogen the palladium regains its original form.
[36]The property of palladium of absorbing hydrogen, and of increasing in volume in so doing, may be easily demonstrated by taking a sheet of palladium varnished on one side, and using it as a cathode. The hydrogen which is evolved by the action of the current is retained by the unvarnished surface, as a consequence of which the sheet curls up. By attaching a pointer (for instance, a quill) to the end of the sheet this bending effect is rendered strikingly evident, and on reversing the current (when oxygen will be evolved and combine with the absorbed hydrogen, forming water) it may be shown that on losing the hydrogen the palladium regains its original form.
[37]Deville discovered that iron and platinum become pervious to hydrogen at a red heat. He speaks of this in the following terms:—‘The permeability of such homogeneous substances as platinum and iron is quite different from the passage of gases through such non-compact substances as clay and graphite. The permeability of metals depends on their expansion, brought about by heat, and proves that metals and alloys have a certain porosity.’ However, Graham proved that it is only hydrogen which is capable of passing through the above-named metals in this manner. Oxygen, nitrogen, ammonia, and many other gases, only pass through in extremely minute quantities. Graham showed that at a red heat about 500 c.c. of hydrogen pass per minute through a surface of one square metre of platinum 1·1 mm. thick, but that with other gases the amount transmitted is hardly perceptible. Indiarubber has the same capacity for allowing the transference of hydrogen through its substance (seeChapterIII.), but at the ordinary temperature one square metre, 0·014 mm. thick, transmits only 127 c.c. of hydrogen per minute. In the experiment on the decomposition of water by heat in porous tubes, the clay tube may be exchanged for a platinum one with advantage. Graham showed that by placing a platinum tube containing hydrogen under these conditions, and surrounding it by a tube containing air, the transference of the hydrogen may be observed by the decrease of pressure in the platinum tube. In one hour almost all the hydrogen (97 p.c.) had passed from the tube, without being replaced by air. It is evident that the occlusion and passage of hydrogen through metals capable of occluding it are not only intimately connected together, but are dependent on the capacity of metals to form compounds of various degrees of stability with hydrogen—like salts with water.
[37]Deville discovered that iron and platinum become pervious to hydrogen at a red heat. He speaks of this in the following terms:—‘The permeability of such homogeneous substances as platinum and iron is quite different from the passage of gases through such non-compact substances as clay and graphite. The permeability of metals depends on their expansion, brought about by heat, and proves that metals and alloys have a certain porosity.’ However, Graham proved that it is only hydrogen which is capable of passing through the above-named metals in this manner. Oxygen, nitrogen, ammonia, and many other gases, only pass through in extremely minute quantities. Graham showed that at a red heat about 500 c.c. of hydrogen pass per minute through a surface of one square metre of platinum 1·1 mm. thick, but that with other gases the amount transmitted is hardly perceptible. Indiarubber has the same capacity for allowing the transference of hydrogen through its substance (seeChapterIII.), but at the ordinary temperature one square metre, 0·014 mm. thick, transmits only 127 c.c. of hydrogen per minute. In the experiment on the decomposition of water by heat in porous tubes, the clay tube may be exchanged for a platinum one with advantage. Graham showed that by placing a platinum tube containing hydrogen under these conditions, and surrounding it by a tube containing air, the transference of the hydrogen may be observed by the decrease of pressure in the platinum tube. In one hour almost all the hydrogen (97 p.c.) had passed from the tube, without being replaced by air. It is evident that the occlusion and passage of hydrogen through metals capable of occluding it are not only intimately connected together, but are dependent on the capacity of metals to form compounds of various degrees of stability with hydrogen—like salts with water.
[38]It appeared on further investigation that palladium gives a definite compound, Pd2H (seefurther) with hydrogen; but what was most instructive was the investigation of sodium hydride, Na2H, which clearly showed that the origin and properties of such compounds are in entire accordance with the conceptions of dissociation.Since hydrogen is a gas which is difficult to condense, it is little soluble in water and other liquids. At 0° a hundred volumes of water dissolve 1·9 volume of hydrogen, and alcohol 6·9 volumes measured at 0° and 760 mm. Molten iron absorbs hydrogen, but in solidifying, it expels it. The solution of hydrogen by metals is to a certain degree based on its affinity for metals, and must be likened to the solution of metals in mercury and to the formation of alloys. In its chemical properties hydrogen, as we shall see later, has much of a metallic character. Pictet (seeNote31) even affirms that liquid hydrogen has metallic properties. The metallic properties of hydrogen are also evinced in the fact that it is a good conductor of heat, which is not the case with other gases (Magnus).
[38]It appeared on further investigation that palladium gives a definite compound, Pd2H (seefurther) with hydrogen; but what was most instructive was the investigation of sodium hydride, Na2H, which clearly showed that the origin and properties of such compounds are in entire accordance with the conceptions of dissociation.
Since hydrogen is a gas which is difficult to condense, it is little soluble in water and other liquids. At 0° a hundred volumes of water dissolve 1·9 volume of hydrogen, and alcohol 6·9 volumes measured at 0° and 760 mm. Molten iron absorbs hydrogen, but in solidifying, it expels it. The solution of hydrogen by metals is to a certain degree based on its affinity for metals, and must be likened to the solution of metals in mercury and to the formation of alloys. In its chemical properties hydrogen, as we shall see later, has much of a metallic character. Pictet (seeNote31) even affirms that liquid hydrogen has metallic properties. The metallic properties of hydrogen are also evinced in the fact that it is a good conductor of heat, which is not the case with other gases (Magnus).
[39]If it be desired to obtain a perfectly colourless hydrogen flame, it must issue from a platinum nozzle, as the glass end of a gas-conducting tube imparts a yellow tint to the flame, owing to the presence of sodium in the glass.
[39]If it be desired to obtain a perfectly colourless hydrogen flame, it must issue from a platinum nozzle, as the glass end of a gas-conducting tube imparts a yellow tint to the flame, owing to the presence of sodium in the glass.