Chapter II: The Composition of Water, Hydrogen (2)

[20] The reaction between charcoal and superheated steam is a double
one--that is, there may be formed either carbonic oxide, CO
(according to the equation H_{2}O + C = H_{2} + CO), or carbonic
anhydride CO_{2} (according to the equation 2H_{2}O + C = 2H_{2}
+ CO_{2}), and the resulting mixture is called _water-gas_; we
shall speak of it in Chapter IX.

_The properties of hydrogen._--Hydrogen presents us with an example of a gas which at first sight does not differ from air. It is not surprising, therefore, that Paracelsus, having discovered that an aëriform substance is obtained by the action of metals on sulphuric acid, did not determine exactly its difference from air. In fact, hydrogen, like air, is colourless, and has no smell;[21] but a more intimate acquaintance with its properties proves it to be entirely different from air. The first sign which distinguishes hydrogen from air is its combustibility. This property is so easily observed that it is the one to which recourse is usually had in order to recognise hydrogen, if it is evolved in a reaction, although there are many other combustible gases. But before speaking of the combustibility and other chemical properties of hydrogen, we will first describe the physical properties of this gas, as we did in the case of water. It is easy to show that it is one of the lightest gases.[22] If passed into the bottom of a flask full of air, hydrogen will not remain in it, but, owing to its lightness, rapidly escapes and mixes with the atmosphere. If, however, a cylinder whose orifice is turned downwards be filled with hydrogen, it will not escape, or, more correctly, it will only slowly mix with the atmosphere. This may be demonstrated by the fact that a lighted taper sets fire to the hydrogen at the orifice of the cylinder, and is itself extinguished inside the cylinder. Hence, hydrogen, being itself combustible, does not support combustion. The great lightness of hydrogen is taken advantage of for balloons. Ordinary coal gas, which is often also used for the same purpose, is only about twice as light as air, whilst hydrogen is 14-1/2 times lighter than air. A very simple experiment with soap bubbles very well illustrates the application of hydrogen for filling balloons. Charles, of Paris, showed the lightness of hydrogen in this way, and constructed a balloon filled with hydrogen almost simultaneously with Montgolfier. One litre of pure and dry hydrogen[23] at 0° and 760 mm. pressure weighs 0·08986 gram; that is, hydrogen is almost 14-1/2 (more exactly, 14·39) times lighter than air. It is the lightest of all gases. The small density of hydrogen determines many remarkable properties which it shows; thus, hydrogen passes exceedingly rapidly through fine orifices, its molecules (Chapter I.) being endued with the greatest velocity.[24] At pressures somewhat higher than the atmospheric pressure, all other gases exhibit a greater compressibility and co-efficient of expansion than they should according to the laws of Mariotte and Gay-Lussac; whilst hydrogen, on the contrary, is compressed to a less degree than it should be from the law of Mariotte,[25] and with a rise of pressure it expands slightly less than at the atmospheric pressure.[26] However, hydrogen, like air and many other gases which are permanent at the ordinary temperature, does not pass into a liquid state under a very considerable pressure,[27] but is compressed into a lesser volume than would follow from Mariotte's law.[28] From this it may be concluded that the absolute boiling point of hydrogen, and of gases resembling it,[29] lies very much below the ordinary temperature; that is, that the liquefaction of this _gas_ is only possible at low temperatures, and under great pressures.[30] This conclusion was verified (1877) by the experiments of Pictet and Cailletet.[31] They compressed gases at a very low temperature, and then allowed them to expand, either by directly decreasing the pressure or by allowing them to escape into the air, by which means the temperature fell still lower, and then, just as steam when rapidly rarefied[32] deposits liquid water in the form of a fog, hydrogen in expanding forms a fog, thus indicating its passage into a liquid state. But as yet it has been impossible to preserve this liquid, even for a short time, to determine its properties, notwithstanding the employment of a temperature of -200° and a pressure of 200 atmospheres,[33] although by these means the gases of the atmosphere may be kept in a liquid state for a long time. This is due to the fact that the absolute boiling point of hydrogen lies lower than that of all other known gases, which also depends on the extreme lightness of hydrogen.[34]

[21] Hydrogen obtained by the action of zinc or iron on sulphuric acid
generally smells of hydrogen sulphide (like rotten eggs), which
it contains in admixture. As a rule such hydrogen is not so
pure as that obtained by the action of an electric current or
of sodium on water. The impurity of the hydrogen depends on the
impurities contained in the zinc, or iron, and sulphuric acid,
and on secondary reactions which take place simultaneously with
the main reaction. Impure hydrogen may be easily freed from
the impurities it contains: some of them--namely, those having
acid properties--are absorbed by caustic soda, and therefore
may be removed by passing the hydrogen through a solution of
this substance; another series of impurities is absorbed by a
solution of mercuric chloride; and, lastly, a third series is
absorbed by a solution of potassium permanganate. If absolutely
_pure hydrogen_ be required, it is sometimes obtained by the
decomposition of water (previously boiled to expel all air,
and mixed with pure sulphuric acid) by the galvanic current.
Only the gas evolved at the negative electrode is collected.
Or else, an apparatus like that which gives detonating gas is
used, the positive electrode, however, being immersed under
mercury containing zinc in solution. The oxygen which is evolved
at this electrode then immediately, at the moment of its
evolution, combines with the zinc, and this compound dissolves
in the sulphuric acid and forms zinc sulphate, which remains in
solution, and therefore the hydrogen generated will be quite free
from oxygen.

[22] An inverted beaker is attached to one arm of the beam of a
tolerably sensitive balance, and its weight counterpoised by
weights in the pan attached to the other arm, If the beaker
be then filled with hydrogen it rises, owing to the air being
replaced by hydrogen. Thus, at the ordinary temperature of a
room, a litre of air weighs about 1·2 gram, and on replacing the
air by hydrogen a decrease in weight of about 1 gram per litre is
obtained. Moist hydrogen is heavier than dry--for aqueous vapour
is nine times heavier than hydrogen. In filling balloons it is
usually calculated that (it being impossible to have perfectly
dry hydrogen or to obtain it quite free from air) the lifting
force due to the difference between the weights of equal volumes
of hydrogen and air is equal to 1 kilogram (= 1,000 grams) per
cubic metre (= 1,000 litres).

[23] The density of hydrogen in relation to the air has been repeatedly
determined by accurate experiments. The first determination, made
by Lavoisier, was not very exact; taking the density of air as
unity, he obtained 0·0769 for that of hydrogen--that is, hydrogen
as thirteen times lighter than air. More accurate determinations
are due to Thomsen, who obtained the figure 0·0693; Berzelius
and Dulong, who obtained 0·0688; and Dumas and Boussingault, who
obtained 0·06945. Regnault, and more recently Le Duc (1892),
took two spheres of considerable capacity, which contained equal
volumes of air (thus avoiding the necessity of any correction
for weighing them in air). Both spheres were attached to the
scale pans of a balance. One was sealed up, and the other first
weighed empty and then full of hydrogen. Thus, knowing the weight
of the hydrogen filling the sphere, and the capacity of the
sphere, it was easy to find the weight of a litre of hydrogen;
and, knowing the weight of a litre of air at the same temperature
and pressure, it was easy to calculate the density of hydrogen.
Regnault, by these experiments, found the average density of
hydrogen to be 0·06926 in relation to air; Le Duc, 0·06948 (with
a possible error of ±0·00001), and this latter figure must now be
looked upon as near to the truth.

In this work I shall always refer the densities of all gases to
hydrogen, and not to air; I will therefore give, for the sake of
clearness, the weight of a litre of dry pure hydrogen in grams
at a temperature _t_° and under a pressure _H_ (measured in
millimetres of mercury at 0°, in lat. 45°). The weight of a litre
of hydrogen

= 0·08986 × (_H_/760) × 1/(1 + 0·00367_t_) gram.

For aëronauts it is very useful to know, besides this, the
weight of the air at different heights, and I therefore insert
the adjoining table, constructed on the basis of Glaisher's
data, for the temperature and moisture of the atmospheric strata
in clear weather. All the figures are given in the metrical
system--1,000 millimetres = 39·37 inches, 1,000 kilograms =
2204·3375 lbs., 1,000 cubic metres = 35,316·6 cubic feet. The
starting temperature at the earth's surface is taken as = 15° C.,
its moisture 60 p.c., pressure 760 millimetres. The pressures
are taken as indicated by an _aneroid barometer_, assumed to be
corrected at the sea level and at lat. 45° C. If the height above
the level of the sea equal _z_ kilometres, then the weight of 1
cubic metre of air may be approximately taken as 1·222- 0·12_z_ +
0·00377_z_^2 kilogram.

+--------+-----------+--------+--------+--------------------+
|Pressure|Temperature|Moisture| Height | Weight of the air |
| | | |(metres)|(1,000 cubic metres)|
|--------+-----------+--------+--------+--------------------+
| 760 mm.| 15° C. | 60 p.c.| 0 | 1222 kilos. |
| 700 " | 11·0° " | 64 " | 690 | 1141 " |
| 650 " | 7·6° " | 64 " | 1300 | 1073 " |
| 600 " | 4·3° " | 63 " | 1960 | 1003 " |
| 550 " | -1·0° " | 62 " | 2660 | 931 " |
| 500 " | -2·4° " | 58 " | 3420 | 857 " |
| 450 " | -5·8° " | 52 " | 4250 | 781 " |
| 400 " | -9·1° " | 44 " | 5170 | 703 " |
| 350 " | -12·5° " | 36 " | 6190 | 624 " |
| 300 " | -15·9° " | 27 " | 7360 | 542 " |
| 250 " | -19·2° " | 18 " | 8720 | 457 " |
+--------+-----------+--------+--------+--------------------+

Although the figures in this table are calculated with every
possible care from average data, yet they can only be taken
approximately, for in every separate case the conditions, both at
the earth's surface and in the atmosphere, will differ from those
here taken. In calculating the height to which a balloon can
ascend, it is evident that the density of gas in relation to air
must be known. This density for ordinary coal gas is from 0·6 to
0·35, and for hydrogen with its ordinary contents of moisture and
air from 0·1 to 0·15.

Hence, for instance, it may be calculated that a balloon of 1,000
cubic metres capacity filled with pure hydrogen, and weighing
(the envelope, tackle, people, and ballast) 727 kilograms, will
only ascend to a height of about 4,250 metres.

[24] If a cracked flask be filled with hydrogen and its neck immersed
under water or mercury, then the liquid will rise up into the
flask, owing to the hydrogen passing through the cracks about 3·8
times quicker than the air is able to pass through these cracks
into the flask. The same phenomenon may be better observed if,
instead of a flask, a tube be employed, whose end is closed by a
porous substance, such as graphite, unglazed earthenware, or a
gypsum plate.

[25] According to Boyle and Mariotte's law, for a given gas at a
constant temperature the volume decreases by as many times as
the pressure increases; that is, this law requires that the
product of the volume _v_ and the pressure _p_ for a given gas
should be a constant quantity: _pv_ = _C_, a constant quantity
which does not vary with a change of pressure. This equation
does very nearly and exactly express the observed relation
between the volume and pressure, but only within comparatively
small variations of pressure, density, and volume. If these
variations be in any degree considerable, the quantity _pv_
proves to be dependent on the pressure, and it either increases
or diminishes with an increase of pressure. In the former case
the compressibility is less than it should he according to
Mariotte's law, in the latter case it is greater. We will call
the first case a positive discrepancy (because then _d(pv)/d(p)_
is greater than zero), and the second case a negative discrepancy
(because then _d(pv)/d(p)_ is less than zero). Determinations
made by myself (in the seventies), M. L. Kirpicheff, and V. A.
Hemilian showed that all known gases at low pressures--_i.e._
when considerably rarefied--present positive discrepancies. On
the other hand, it appears from the researches of Cailletet,
Natterer, and Amagat that all gases under great pressures (when
the volume obtained is 500-1,000 times less than under the
atmospheric pressure) also present positive discrepancies. Thus
under a pressure of 2,700 atmospheres air is compressed, not
2,700 times, but only 800, and hydrogen 1,000 times. Hence the
positive kind of discrepancy is, so to say, normal to gases. And
this is easily intelligible. If a gas followed Mariotte's law, or
if it were compressed to a greater extent than is shown by this
law, then under great pressures it would attain a density greater
than that of solid and liquid substances, which is in itself
improbable and even impossible by reason of the fact that solid
and liquid substances are themselves but little compressible.
For instance, a cubic centimetre of oxygen at 0° and under the
atmospheric pressure weighs about 0·0014 gram, and at a pressure
of 3,000 atmospheres (this pressure is attained in guns) it
would, if it followed Mariotte's law, weigh 4·2 grams--that is,
would be about four times heavier than water--and at a pressure
of 10,000 atmospheres it would be heavier than mercury. Besides
this, positive discrepancies are probable because the molecules
of a gas themselves must occupy a certain volume. Considering
that Mariotte's law, strictly speaking, applies only to the
intermolecular space, we can understand the necessity of positive
discrepancies. If we designate the volume of the molecules of a
gas by _b_ (like van der Waals, _see_ Chap. I., Note 34), then it
must be expected that _p(v-b) = C_. Hence _pv = C + bp_, which
expresses a positive discrepancy. Supposing that for hydrogen
_pv_ = 1,000, at a pressure of one metre of mercury, according to
the results of Regnault's, Amagat's, and Natterer's experiments,
we obtain _b_ as approximately 0·7 to 0·9.

Thus the increase of _pv_ with the increase of pressure must
be considered as the normal law of the compressibility of
gases. Hydrogen presents such a positive compressibility at
all pressures, for it presents positive discrepancies from
Mariotte's law, according to Regnault, at all pressures above the
atmospheric pressure. Hence hydrogen is, so to say, a perfect
gas. No other gas behaves so simply with a change of pressure.
All other gases at pressures from 1 to 30 atmospheres present
negative discrepancies--that is, they are then compressed to a
greater degree than should follow from Mariotte's law, as was
shown by the determinations of Regnault, which were verified
when repeated by myself and Boguzsky. Thus, for example, on
changing the pressure from 4 to 20 metres of mercury--that is,
on increasing the pressure five times--the volume only decreased
4·93 times when hydrogen was taken, and 5·06 when air was taken.

The positive discrepancies from the law at low pressures are
of particular interest, and, according to the above-mentioned
determinations made by myself, Kirpicheff, and Hemilian, and
verified (by two methods) by K. D. Kraevitch and Prof. Ramsay
(London, 1894), they are proper to all gases (even to those which
are easily compressed into a liquid state, such as carbonic and
sulphurous anhydrides). These discrepancies approach the case
of a very high rarefaction of gases, where a gas is near to a
condition of maximum dispersion of its molecules, and perhaps
presents a passage towards the substance termed 'luminiferous
ether' which fills up interplanetary and interstellar space. If
we suppose that gases are rarefiable to a definite limit only,
having attained which they (like solids) do not alter in volume
with a decrease of pressure, then on the one hand the passage of
the atmosphere at its upper limits into a homogeneous ethereal
medium becomes comprehensible, and on the other hand it would be
expected that gases would, in a state of high rarefaction (_i.e._
when small masses of gases occupy large volumes, or when furthest
removed from a liquid state), present positive discrepancies from
Boyle and Mariotte's law. Our present acquaintance with this
province of highly rarefied gases is very limited (because direct
measurements are exceedingly difficult to make, and are hampered
by possible errors of experiment, which may be considerable), and
its further development promises to elucidate much in respect to
natural phenomena. To the three states of matter (solid, liquid,
and gaseous) it is evident a fourth must yet be added, the
ethereal or ultra-gaseous (as Crookes proposed), understanding by
this, matter in its highest possible state of rarefaction.

[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 like _air_ (and all gases) is less compressed _at
low pressures_ than should follow from Mariotte's law (_see_
Note 25). 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 (_see_ Note 25), 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 liquefaction_ of gases, accomplished by Faraday (_see_
Ammonia, Chapter VI.) 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 the _maximum
tensions_ of certain liquids and gases _at 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 tension _p_ on the temperature _t_ given
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,
CS_{2}, 0° = 127·9; 10° = 198·5; 20° = 298·1; 30° = 431·6; 40°
= 617·5; 50° = 857·1. Chlorobenzene, C_{6}H_{5}Cl, 70° = 97·9;
80° = 141·8; 90° = 208·4; 100° = 292·8; 110° = 402·6; 120° =
542·8; 130° = 719·0. Aniline, C_{6}H_{7}N, 150° = 283·7; 160°
= 387·0; 170° = 515·6; 180° = 677·2; 185° = 771·5. Methyl
salicylate, C_{8}H_{8}O_{3}, 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°; K_{2}CO_{3}, 1045°; Na_{2}CO_{3}, 1098°;
Na_{2}B_{4}O_{7}, 873°; Na_{2}SO_{4}, 843°; K_{2}SO_{4}, 1073°.
The tension of liquefied gases is expressed in atmospheres.
Sulphurous anhydride, SO_{2},-30° = 0·4;-20° = 0·6;-10° = 1; 0°
= 1·5; +10° = 2·3; 20° = 3·2; 30° = 5·3. Ammonia, NH_{3},-40°
= 0·7;-30° = 1·1;-20° = 1·8; -10° = 2·8; 0° = 4·2; +10° = 6·0;
20° = 8·4. Carbonic anhydride, CO_{2},-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, N_{2}O,-125° = 0·033;-92° =
1;-80° = 1·9;-50° = 7·6; -20° = 23·1; 0° = 36·1; +20° = 55·3.
Ethylene, C_{2}H_{4},-140° = 0·033;-130° = 0·1; -103° = 1;-40°
= 13;-1° = 42. Air,-191° = 1;-158° = 14;-140° = 39. Nitrogen,
N_{2},-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 obtaining _low
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,
CS_{2}, or methyl chloride, CH_{3}Cl, 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.

C_{2}H_{4} N_{2}O CO_{2}, H_{2}S
(1) 42 31 52 10
(2) -103° -92° -80° -74°

AsH_{3}, NH_{3} HCl CH_{3}Cl C_{2}N_{2} SO_{2}
(1) 8 7 25 4 4 3
(2) -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_ = 1 100 1000 2500
_v_ = 1 0·0107 0·0019 0·0013
_pv_ = 1 1·07 1·9 3·25
_s_ = 0·11 10·3 58 85

where _p_ = the pressure in metres of mercury, _v_ = the volume,
if the volume taken under a pressure of 1 metre = 1, and _s_
the 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 an _absolute
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 at _t°_ to a height 5·35-0·028_t°_ 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 the
_critical temperature_. It is evident that it is the same as
the absolute boiling point. We shall afterwards designate it by
_tc_. At low temperatures a gas which is subjected to a pressure
greater than its maximum tension (Note 27) 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
(_see_ Note 28)--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 at _tc_ is termed the
_critical volume_, and corresponds with the _critical pressure_,
which we will designate by _pc_ and 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
of _tc_ and _pc_ for certain liquids and gases which have been
investigated in this respect--

+---------------------+------++----------------------+------+
| _tc_ | _pc_ || _tc_ | _pc_ |
+---------------------+------++----------------------+------+
| N_{2} -146° | 33 || H_{2}S +108° | 92 |
| CO -140° | 39 || C_{2}N_{2} +124° | 62 |
| O_{2} -119° | 50 || NH_{3} +131° | 114 |
| CH_{4} -100° | 50 || CH_{3}Cl +141° | 73 |
| NO -93° | 71 || SO_{2} +155° | 79 |
| C_{2}H_{4} +10° | 51 || C_{5}H_{10} +192° | 34 |
| CO_{2} +32° | 77 || C_{4}H_{10}O +193° | 40 |
| N_{2}O +53° | 75 || CHCl_{3} +268° | 55 |
| C_{2}H_{2} +37° | 68 || CS_{2} +278° | 78 |
| HCl +52° | 86 || C_{6}H_{6} +292° | 60 |
| H_{2}O +365° | 200 || C_{6}H_{5}F +287° | 45 |
| CH_{3}OH +240° | 79 || C_{6}H_{5}Cl +360° | 45 |
| C_{2}H_{5}OH +243° | 63 || C_{6}H_{5}Br +397° | 45 |
| CH_{3}COOH +322° | 57 || C_{6}H_{5}I +448° | 45 |
+---------------------+------++----------------------+------+

Young and Guy (1891) showed that _tc_ and _pc_ clearly depend
upon the composition and molecular weight.

[30] I came to this conclusion in 1870 (_Ann. Phys. Chem._ 141, 623).

[31] 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 (_see_ Note 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, CO_{2}
(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 (CHO_{2}Na + NaHO = Na_{2}CO_{3}
+ H_{2}). 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] 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 (_see_ Note 34), 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_,
Note 29) 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 near _tc_ and _pc_; others (Konovaloff and De Heen)
endeavoured to discover the relation between liquids under
ordinary conditions (removed from _tc_ and _pc_) 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 (_see_
Note 25), 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 a _given quantity_ (weight, mass) _of a definite substance_,
its state is expressed by three variables--volume _v_, pressure
(elasticity, tension) _p_, and temperature _t_. 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
(at _tc_ the 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 volume _v_ on _t_ and _p_ is very
complex. This also applies to the coefficient of expansion [=
_d(v)_/_d(t)_, or _d(p)_/_d(t)_], which also varies with _t_ and
_p_, both for gases (_see_ Note 26), and for liquids (at _tc_ it
is very considerable, and often exceeds that of gases, 0·00367).
Hence, the _equation of condition_ must include three variables,
_v_, _p_, and _t_. For a so-called perfect (ideal) gas, or for
inconsiderable variations of density, the elementary expression
_pv_ = _R_[Greek: a](1 + [Greek: a]_t_), or _pv_ = _R_(273 + _t_)
should be accepted, where _R_ is 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 + [Greek: a]_t_, and when _t_ is constant the product of _tv_ is
constant. In its simplest form the equation may be expressed thus:

_pv_ = _RT_;

where _T_ denotes 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 by _a_) 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 by _b_) for each gaseous molecule, van
der Waals gives for gases the following more complex equation of
condition:--

(_p_ + _a_/_v_^2)(_v_-_b_) = 1 + 0·00367_t_;

if at 0° under a pressure _p_ = 1 (for example, under the
atmospheric pressure), the volume (for instance, a litre) of
a gas or vapour he taken as 1, and therefore _v_ and _b_ be
expressed by the same units as _p_ and _a_. The deviations
from both the laws of Mariotte and Gay-Lussac are expressed
by the above equation. Thus, for hydrogen _a_ must be taken
as infinitely small, and _b_ = 0·0009, judging by the data
for 1,000 and 2,500 metres pressure (Note 28). For other
permanent gases, for which (Note 28) I showed (about 1870) from
Regnault's and Natterer's data, a decrement of _pv_, followed
by an increment, which was confirmed (about 1880) by fresh
determinations made by Amagat, this phenomena may be expressed
in definite magnitudes of _a_ and _b_ (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
(Note 26). Besides this, van der Waals' formula shows that at
temperatures above 273(8_a_/27_b_-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(8_a_/27_b_-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_
= 3_b_). The pressure in this case (_pc_) = _a_/(27_b_^2). These
ratios between the constants _a_ and _b_ and the conditions of
_critical state_--_i.e._ (_tc_) and (_pc_)--give the possibility
of determining the one magnitude from the other. Thus for ether
(Note 29), (_tc_) = 193°, (_tp_) = 40, hence _a_ = 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 both _t_ and
_p_ vary), 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 0·135_t_-3·3 (for example, at
180° the pressure = 21 metres, and at 280° it = 34·5 metres).
The rectilinear form of the isochord (when _v_ = _a_ constant
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
[S_{_t_} = S_{_0_}-K_t_ or S_{_t_} = S_{_0_}(1-K_t_)], or that
the volumes increase in inverse proportion to the binomial
1-K_t_, that is, V_{_t_} = V_{_0_}(1-K_t_)^{-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 S_{_t_} = 0·736/(1-0·00154_t_), or
V_{_t_} = 1/(1-0·00154_t_), where 0·00154 is the modulus of
expansion, and therefore (_tc_) = 188°, or by direct observation
193°. For silicon tetrachloride, SiCl_{4}, the modulus equals
0·00136, from whence (_tc_) = 231°, and by experiment 230°. On
the other hand, D. P. Konovaloff, admitting that the external
pressure _p_ in liquids is insignificant when compared with the
internal (_a_ in 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, V_{t}
= 1/(1-K_t_), 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,
and _liquid states_ of 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 than _pv_ = _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 (_a_ and _b_); but a great scientific progress is seen
in this form of the equation of state.

Clausius (in 1880), taking into consideration the variability of
_a_, 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
found _a_ = 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°) gave _tc_ higher than
it really is, the absolute boiling point of hydrogen must lie
below -174°.

Although a substance which passes with great difficulty into a liquid state by the action of physico-mechanical forces, hydrogen loses its gaseous state (that is, its elasticity, or the physical energy of its molecules, or their rapid progressive motion) with comparative ease under the influence of chemical attraction,[35] which is not only shown from the fact that hydrogen and oxygen (two permanent gases) form liquid water, but also from many phenomena of the absorption of hydrogen.

[35] This and a number of similar cases clearly show how great are the
internal chemical forces compared with physical and mechanical
forces.