Chapter II: , that water is decomposed at such high temperatures. In the (2)

We will here remark that in determining M (the molecular weight of
the substance dissolved) at small but increasing concentrations
(per 100 grms. of water), the results obtained by Julio Baroni
(1893) show that the value of M found by the formula may either
increase or decrease. An increase, for instance, takes place in
aqueous solutions of HgCl_{2} (from 255 to 334 instead of 271),
KNO_{3} (57-66 instead of 101), AgNO_{3} (104-107 instead of 170),
K_{2}SO_{4} (55-89 instead of 174), sugar (328-348 instead of
342), &c. On the contrary the calculated value of M decreases as
the concentration increases, for solutions of KCl (40-39 instead
of 74·5), NaCl (33-28 instead of 58·5), NaBr (60-49 instead of
103), &c. In this case (as also for LiCl, NaI, C_{2}H_{3}NaO_{2},
&c.) the value of _i_ (Chapter I., Note 49), or the ratio between
the actual molecular weight and that found by the rise of the
boiling point, was found to increase with the concentration,
_i.e._ to be greater than 1, and to differ more and more from
unity as the strength of the solution becomes greater. For
example, according to Schlamp (1894), for LiCl, with a variation
of from 1·1 to 6·7 grm. LiCl per 100 of water, _i_ varies from
1·63 to 1·89. But for substances of the first series (HgCl_{2},
&c.), although in very dilute solutions _i_ is greater than 1, it
approximates to 1 as the concentration increases, and this is the
normal phenomenon for solutions which do not conduct an electric
current, as, for instance, of sugar. And with certain
electrolytes, such as HgCl_{2}, MgSO_{4}, &c., _i_ exhibits a
similar variation; thus, for HgCl_{2} the value of M is found to
vary between 255 and 334; that is, _i_ (as the molecular weight =
271) varies between 1·06 and 0·81. Hence I do not believe that the
difference between _i_ and unity (for instance, for CaCl_{2}, _i_
is about 3, for KI about 2, and decreases with the concentration)
can at present be placed at the basis of any general chemical
conclusions, and it requires further experimental research. Among
other methods by which the value of _i_ is now determined for
dilute solutions is the study of their electroconductivity,
admitting that _i_ = 1 + _a_(_k_-1), where _a_ = the ratio of the
molecular conductivity to the limiting conductivity corresponding
to an infinitely large dilution (_see_ Physical Chemistry), and
_k_ is the number of ions into which the substance dissolved can
split up. Without entering upon a criticism of this method of
determining _i_, I will only remark that it frequently gives
values of _i_ very close to those found by the depression of the
freezing point and rise of the boiling point; but that this
accordance of results is sometimes very doubtful. Thus for a
solution containing 5·67 grms. CaCl_{2} per 100 grms. of water,
_i_, according to the vapour tension = 2·52, according to the
boiling point = 2·71, according to the electroconductivity = 2·28,
while for solutions in propyl alcohol (Schlamp 1894) _i_ is near
to 1·33. In a word, although these methods of determining the
molecular weight of substances in solution show an undoubted
progress in the general chemical principles of the molecular
theory, there are still many points which require explanation.

We will add certain general relations which apply to these
problems. Isotonic (Chapter I., Note 19) solutions exhibit not
only similar osmotic pressures, but also the same vapour tension,
boiling point and freezing temperature. The osmotic pressure bears
the same relation to the fall of the vapour tension as the
specific gravity of a solution does to the specific gravity of the
vapour of the solvent. The general formulæ underlying the whole
doctrine of the influence of the molecular weight upon the
properties of solutions considered above, are: 1. Raoult in
1886-1890 showed that

((_p_-_p_´)/_p_) × (100/_a_) × (M/_m_) = a constant C

where _p_ and _p_´ are the vapour tensions of the solvent and
substance dissolved, _a_ the amount in grms. of the substance
dissolved per 100 grms. of solvent, M and _m_ the molecular
weights of the substance dissolved and solvent. 2. Raoult and
Recoura in 1890 showed that the constant above C = the ratio of
the actual vapour density _d_´ of the solvent to the theoretical
density _d_ calculated according to the molecular weight. This
deduction may now be considered proved, because both the fall of
tension and the ratio of the vapour densities _d_´/_d_ give, for
water 1·03, for alcohol 1·02, for ether 1·04, for bisulphide of
carbon 1·00, for benzene 1·02, for acetic acid 1·63. 3. By
applying the principles of thermodynamics and calling L_{1} the
latent heat of fusion and T_{1} the absolute (= _t_ + 273)
temperature of fusion of the solvent, and L_{2} and T_{2} the
corresponding values for the boiling point, Van't Hoff in
1886-1890 deduced:--

(Depression of freezing point)/(Rise of boiling point)
= (L_{2}/L_{1}) × (T_{1}^2/T_{2}^2)

Depression of freezing point = (AT_{1}^{2}_a_)/(L_{1}M_{1})

Rise of boiling point = (AT_{2}^{2}_a_)/(L_{2}M_{1})

where A = 0·01988 (or nearly 0·02 as we took it above), _a_ is
the weight in grms. of the substance dissolved per 100 grms. of
the solvent, M_{1} the molecular weight of the dissolved substance
(in the solution), and M the molecular weight of this substance
according to its composition and vapour density, then _i_ =
M/M_{1}. The experimental data and theoretical considerations upon
which these formulæ are based will be found in text-books of
physical and theoretical chemistry.

If 100 gram-molecules of water, _i.e._ 1,800 grms, be taken and _n_ gram-molecules of sugar, C_{12}H_{22}O_{11}, _i.e._ _n_ 342 grms., be dissolved in them, then the depression _d_, or fall (counting from 0°) of the temperature of the formation of ice will be (according to Pickering)

_n_ = 0 0·010 0·025 0·100 0·250 1·000
_d_ = 0° 0°·0103 0°·0280 0°·1115 0°·2758 1°·1412

which shows that for high degrees of dilution (up to 0·25_n_) _d_ approximately (estimating the possible errors of experiment at ±0°·005) = _n_1·10, because then _d_ = 0°, 0°·0110, 0°·0275, 0°·1100, 0°·2750, 1°·1000, and the difference between these figures and the results of experiment for very dilute solutions is less than the possible errors of experiment (for _n_ = 1 the difference is already greater) and therefore for dilute solutions of sugar it may be said that _n_ molecules of sugar in dissolving in 100 molecules of water give a depression of about 1°·1_n_. Similar data for acetone (Chapter I., Note 49) give a depression of 1°·006_n_ for _n_ molecules of acetone per 100 molecules of water. And in general, for indifferent substances (the majority of organic bodies) the depression per 100H_{2}O is _nearly n_1°·1 to _n_1°·0 (ether, for instance, gives the last number), and consequently in dissolving in 100 grms. of water it is about 18°·0_n_ to 19°·0_n_, taking this rule to apply to the case of a small number of _n_ (not over 0·2_n_). If instead of water, other liquid or fused solvents (for example, benzene, acetic acid, acetone, nitrobenzene or molten naphthaline, metals, &c.) be taken and in the proportion of 100 molecules of the solvent to _n_ molecules of a dissolved indifferent (neither acid nor saline) substance, then the depression is found to be equal to from 0°·62_n_ to 0°·65_n_ and in general K_n_. If the molecular weight of the solvent = _m_, then 100 gram-molecules will weigh 100_m_ grms., and the depression will be approximately (taking 0·63_n_) equal to _m_0·63_n_ degrees for _n_ molecules of the substance dissolved in 100 grms. of the solvent, or in general the depression for 100 grms. of a given solvent = _kn_ where _k_ is almost a constant quantity (for water nearly 18, for acetone nearly 37, &c.) for all dilute solutions. Thus, having found a convenient solvent for a given substance and prepared a definite (by weight) solution (_i.e._ knowing how many grms. _r_ of the solvent there are to _q_ grms. of the substance dissolved) and having determined the depression _d_--_i.e._ the fall in temperature of freezing for the solvent--it is possible to determine the molecular weight of the substance dissolved, because _d_ = _kn_ where _d_ is found by experiment and _k_ is determined by the nature of the solvent, and therefore _n_ or the number of molecules of the substance dissolved can be found. But if _r_ grms. of the solvent and _q_ grms. of the substance dissolved are taken, then there are 100_q_/_r_ of the latter per 100 grms. of the former, and this quantity = _n_X, where _n_ is found from the depression and = _d_/_k_ and X is the molecular weight of the substance dissolved. Hence X = 100_qk_/_rd_, which gives the molecular weight, naturally only approximately, but still with sufficient accuracy to easily indicate, for instance, whether in peroxide of hydrogen the molecule contains HO or H_{2}O_{2} or H_{3}O_{3}, &c. (H_{2}O_{2} is obtained). Moreover, attention should be drawn to the fact that a great many substances taken as solvents give per 100 molecules a depression of about 0·63_n_, whilst water gives about 1·05_n_, _i.e._ a larger quantity, as though the molecules of liquid water were more complex than is expressed by the formula H_{2}O.[28] A similar phenomenon which repeats itself in the osmotic pressure, vapour tension of the solvent, &c. (_see_ Chapter I., Notes 19 and 49), _i.e._ a variation of the constant (_k_ for 100 grms. of the solvent or K for 100 molecules of it), is also observed in passing from indifferent substances to saline (to acids, alkalis and salts) both in aqueous and other solutions as we will show (according to Pickering's data 1892) for solutions of NaCl and CuSO_{4} in water. For

_n_ = 0·01 0·03 0·05 0·1 0·5

molecules of NaCl the depression is

_d_ = 0°·0177 0°·0598 0°·0992 0°·1958 0°·9544

which corresponds to a depression per molecule

K = 1·77 1·96 1·98 1·96 1·91

_i.e._ here in the most dilute solutions (when _n_ is nearly 0) _d_ is obtained about 1·7_n_, while in the case of sugar it was about 1·1_n_. For CuSO_{4} for the same values of _n_, experiment gave:

_d_ = 0°·0164 0°·0451 0°·0621 0°·1321 0°·5245
K = 1·64 1·50 1·44 1·32 1·05

_i.e._ here again _d_ for very dilute solutions is nearly 1·7_n_, but the value of K falls as the solution becomes more concentrated, while for NaCl it at first increased and only fell for the more concentrated solutions. The value of K in the solution of _n_ molecules of a body in 100H_{2}O, when _d_ = K_n_, for very dilute solutions of CaCl_{2} is nearly 2·6, for Ca(NO_{3})_{2} nearly 2·5, for HNO_{3}, KI and KHO nearly 1·9-2·O, for borax Na_{2}B_{4}O_{7} nearly 3·7, &c., while for sugar and similar substances it is, as has been already mentioned, nearly 1·0-1·1. Although these figures are very different[28 bis] still _k_ and K may be considered constant for analogous substances, and therefore the weight of the molecule of the body in solution can be found from _d_. And as the vapour tension of solutions and their boiling points (_see_ Note 27 bis and Chapter I., Note 51) vary in the same manner as the freezing point depression, so they also may serve as means for determining the molecular weight of a substance in solution.[29]

[28] A similar conclusion respecting the molecular weight of liquid
water (_i.e._ that its molecule in a liquid state is more
complex than in a gaseous state, or polymerized into H_{8}O_{4},
H_{6}O_{3} or in general into _n_H_{2}O) is frequently met
in chemico-physical literature, but as yet there is no basis
for its being fully admitted, although it is possible that a
polymerization or aggregation of several molecules into one
takes place in the passage of water into a liquid or solid
state, and that there is a converse depolymerization in the
act of evaporation. Recently, particular attention has been
drawn to this subject owing to the researches of Eötvös (1886)
and Ramsay and Shields (1893) on the variation of the surface
tension N with the temperature (N = the capillary constant _a_^2
multiplied by the specific gravity and divided by 2, for example,
for water at 0° and 100° the value of _a_^2 = 15·41 and 12·58
sq. mm., and the surface tension 7·92 and 6·04). Starting from
the absolute boiling point (Chapter II., Note 29) and adding 6°,
as was necessary from all the data obtained, and calling this
temperature T, it is found that AS = _k_T, where S is the surface
of a gram-molecule of the liquid (if M is its weight in grams,
_s_ its sp. gr., then its sp. volume = M/_s_, and the surface
S = [3root](M/_s_)^2), A the surface tension (determined by
experiment at T), and _k_ a constant which is independent of
the composition of the molecule. The equation AS = _k_T is in
complete agreement with the well-known equation for gases _vp_
= RT (p. 140) which serves for deducing the molecular weight
from the vapour density. Ramsay's researches led him to the
conclusion that the liquid molecules of CS_{2}, ether, benzene,
and of many other substances, have the same value as in a state
of vapour, whilst with other liquids this is not the case, and
that to obtain an accordance, that is, that _k_ shall be a
constant, it is necessary to assume the molecular weight in the
liquid state to be _n_ times as great. For the fatty alcohols and
acids _n_ varies from 1-1/2 to 3-1/2, for water from 2-1/4 to 4,
according to the temperature (at which the depolymerization takes
place). Hence, although this subject offers a great theoretical
interest, it cannot be regarded as firmly established, the more
so since the fundamental observations are difficult to make and
not sufficiently numerous; should, however, further experiments
confirm the conclusions arrived at by Professor Ramsay, this will
give another method of determining molecular weights.

[28 bis] Their variance is expressed in the same manner as was done by
Van't Hoff (Chapter I., Notes 19 and 49) by the quantity _i_,
taking it as = 1 when _k_ = 1·05, in that case for KI, _i_ is
nearly 2, for borax about 4, &c.

[29] We will cite one more example, showing the direct dependence of
the properties of a substance on the molecular weight. If one
molecular part by weight of the various chlorides--for instance,
of sodium, calcium, barium, &c.--be dissolved in 200 molecular
parts by weight of water (for instance, in 3,600 grams) then
it is found that the greater the molecular weight of the salt
dissolved, the greater is the specific gravity of the resultant
solution.

Molecular Sp. gr. Molecular Sp. gr.
weight at 15° weight at 15°
HCl 36·5 1·0041 CaCl_{2} 111 1·0236
NaCl 58·5 1·0106 NiCl_{2} 130 1·0328
KCl 74·5 1·0121 ZnCl_{2} 136 1·0331
BeCl_{2} 80 1·0138 BaCl_{2} 208 1·0489
MgCl_{2} 95 1·0203

Thus not only in vapours and gases, but also in dilute solutions of solid and liquid substances, we see that if not all, still many properties are wholly dependent upon the molecular weight and not upon the quality of a substance, and that this gives the possibility of determining the weight of molecules by studying these properties (for instance, the vapour density, depression of the freezing point, &c.) It is apparent from the foregoing that the physical and even more so the chemical properties of homogeneous substances, more especially solid and liquid, do not depend exclusively upon the weights of their molecules, but that many are in definite (_see_ Chapter XV.) dependence upon the weights of the atoms of the elements entering into their composition, and are determined by their quantitative and individual peculiarities. Thus the density of solids and liquids (as will afterwards be shown) is chiefly determined by the weights of the atoms of the elements entering into their composition, inasmuch as dense elements (in a free state) and compounds are only met with among substances containing elements with large atomic weights, such as gold, platinum, and uranium. And these elements themselves, in a free state, are the heaviest of all elements. Substances containing such light elements as hydrogen, carbon, oxygen and nitrogen (like many organic substances) never have a high specific gravity; in the majority of cases it scarcely exceeds that of water. The density generally decreases with the increase of the amount of hydrogen, as the lightest element, and a substance is often obtained lighter than water. The refractive power of substances also entirely depends on the composition and the properties of the component elements.[29 bis] The history of chemistry presents a striking example in point--Newton foresaw from the high refractive index of the diamond that it would contain a combustible substance since so many combustible oils have a high refractive power. We shall afterwards see (Chapter XV.) that many of those properties of substances which are in direct dependence not upon the weight of the molecules but upon their composition, or, in other words, upon the properties and quantities of the elements entering into them, stand in a peculiar (periodic) dependence upon the atomic weight of the elements; that is, the mass (of molecules and atoms), proportional to the weight, determines the properties of substances as it also determines (with the distance) the motions of the heavenly bodies.

[29 bis] With respect to the optical refractive power of substances, it
must first be observed that the coefficient of refraction is
determined by two methods: (_a_) either all the data are referred
to one definite ray--for instance, to the Fraunhofer (sodium) line
D of the solar spectrum--that is, to a ray of definite wave
length, and often to that red ray (of the hydrogen spectrum) whose
wave length is 656 millionths of a millimetre; (_b_) or Cauchy's
formula is used, showing the relation between the coefficient of
refraction and dispersion to the wave length _n_ = A +
(B/([Greek: l]^2)), where A and B are two constants varying for
every substance but constant for all rays of the spectrum, and
[Greek: l] is the wave length of that ray whose coefficient of
refraction is _n_. In the latter method the investigation usually
concerns the magnitudes of A, which are independent of dispersion.
We shall afterwards cite the data, investigated by the first
method, by which Gladstone, Landolt, and others established the
conception of the refraction equivalent.

It has long been known that the _coefficient of refraction n_
for a given substance decreases with the density of a substance D,
so that the magnitude (_n_-1) ÷ D = C is almost constant for a
given ray (having a definite wave length) and for a given
substance. This constant is called the _refractive energy_, and
its product with the atomic or molecular weight of a substance the
_refraction equivalent_. The coefficient of refraction of oxygen
is 1·00021, of hydrogen 1·00014, their densities (referred to
water) are 0·00143 and 0·00009, and their atomic weights, O = 16,
H = 1; hence their refraction equivalents are 3 and 1·5. Water
contains H_{2}O, consequently the sum of the equivalents of
refraction is (2 × 1·5) + 3 = 6. But as the coefficient of
refraction of water = 1·331, its refraction equivalent = 5·958, or
nearly 6. Comparison shows that, approximately, the sum of the
refraction equivalents of the atoms forming compounds (or
mixtures) is equal to the refraction equivalent of the compound.
According to the researches of Gladstone, Landolt, Hagen, Brühl
and others, the refraction equivalents of the elements are--H =
1·3, Li = 3·8, B = 4·0, C = 5·0, N = 4·1 (in its highest state of
oxidation, 5·3), O = 2·9, F = 1·4, Na = 4·8, Mg = 7·0, Al = 8·4,
Si = 6·8, P = 18·3, S = 16·0, Cl = 9·9, K = 8·1, Ca = 10·4, Mn =
12·2, Fe = 12·0 (in the salts of its higher oxides, 20·1), Co =
10·8, Cu = 11·6, Zn = 10·2, As = 15·4, Bi = 15·3, Ag = 15·7, Cd =
13·6, I = 24·5, Pt = 26·0, Hg = 20·2, Pb = 24·8, &c. The
refraction equivalents of many elements could only be calculated
from the solutions of their compounds. The composition of a
solution being known it is possible to calculate the refraction
equivalent of one of its component parts, those for all its other
components being known. The results are founded on the acceptance
of a law which cannot be strictly applied. Nevertheless the
representation of the refraction equivalents gives an easy means
for directly, although only approximately, obtaining the
coefficient of refraction from the chemical composition of a
substance. For instance, the composition of carbon bisulphide is
CS_{2} = 76, and from its density, 1·27, we find its coefficient
of refraction to be 1·618 (because the refraction equivalent = 5 +
2 × 16 = 37), which is very near the actual figure. It is evident
that in the above representation compounds are looked on as simple
mixtures of atoms, and the physical properties of a compound as
the sum of the properties present in the elementary atoms forming
it. If this representation of the presence of simple atoms in
compounds had not existed, the idea of combining by a few figures
a whole mass of data relating to the coefficient of refraction of
different substances could hardly have arisen. For further details
on this subject, see works on _Physical Chemistry_.