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occupies four-fifths of the interval iDctween B and F.

The spectra of acid and alkaline haematoporphyrin are exhibited in
Eig. 57.

A study of the photographic spectrum of htematoporphyrin has
given me the following results : ^ — Acid solutions of htematoporphyrin,
so dilute as to appear colourless (though presentmg, if examined in a
dark room by means of a beam of sunlight reflected from the mirror of
the hehostat, the marked red fluorescence previously referred to), exhibit
an intense absorption-band between li and H. If the solution be
slightly more concentrated, K is absorbed, and with increasing con-
centration of the solution the absorption of the ultra-violet extends
more and more.

Alkahne solutions of hcematoporph}T;in absorb the same spectral
region, but the intensity of the absorption is greater.

Haeraatoporpbyrin, as MacMunn has shown, occurs as a colouring matter
in the integument of some invertebrates and in the egg-sliells of certain
birds. 2 In smafl quantities it occurs in the normal urine (Ai'ch. Garrod),
and in larger quantities in certain toxic conditions, especially in one of the
forms of chronic sulphonal poisoning.

HjiMATOIDIN.

This name was applied by Vuxhow to a substance which occurs in
the form of orange-coloured microscopic crystals (rhombic plates) in old
extravasations of blood, as in apoplectic clots, and which is certainly de-
rived from hsemoglobin. These crystals are, according to most observers,
identical in form with those of bilirubin, and when treated with fuming
nitric acid exhibit the same colour reaction (Gmelin's reaction).
Htematoidin, like bilirubin, exhibits no definite absorption-band in its
spectrum, 1jut effects a general absorption of the ultra-violet, violet, and
blue rays of the spectrum. Opinions were long divided on the question
of the identity or non-identity of hsematoidin and bilirubin, but they
are now generally regarded as identical.



Certain other substances (of which the chemical history is very imperfect),
which can be directly obtained by the action of reagents on the blood-colour-
ing matter, and certain pigments occurring in the organism, and which, on
grounds more or less satisfactory, have been held to be derived from it like-
wise, will be considered in the account of the chemistry of the urine as well
as in that of the chemical processes occurring within the alimentary canal.

^ Troc. Eolj. Hoc. Londm, 1896, vol. lix. p. 279.

- MacMunn, Journ. Physiol., Cambridge and London, 1885, vol. vii. p. 240 ; vol.
viii. p. 384.



A GENERAL ACCOUNT OF THE PROCESSES OF
DIFFUSION, OSMOSIS, AND FILTRATION.

By E. Waymouth Reid.

Contents : —Diffusion, p. 261 — Osmosis, p. 264 — Filtration, p. 280.

Diffusion.

By current hypothesis the molecules of a liquid are considered to be in
constant motion, so that if two liquids, miscible without chemical inter-
action, are placed in contact, a mutual interpenetration, without the
action of any external force, takes place ; or, in other words, a difi'usion
of the molecules of one among those of the other, and vice versd, occurs,
the process tending to continue until in the final state a homogeneous
mixture of the two exists. In physiological problems we deal with the
diffusion of substances in dilute aqueous solution, and it must at once
be noted that the condition of the molecules of a substance in dilute
aqueous solution is probably different in the case of different substances,
and by no means necessarily the same as that of the undissolved
substance ; that, in fact, the solvent and dissolved substance in many
cases interact, with a resultant alteration of physico-chemical pro-
perties.

In the case of substances acting as electrolytes in aqueous solution,
it is believed that dissociation into the ions takes place to a greater or
less extent of the total number of molecules, according to the degree of
dilution.^ There will thus be at lower degrees of dilution a mixture of
molecules, active as regards electrolytic conduction and chemical action,
and inactive molecules, the latter tending to become active by ionic
dissociation as dilution is increased, so that at infinite dilution only
active molecules exist in the solution, l^ie coefficient of activity will be
the number expressing the ratio of active molecules to the total of
active plus inactive, and is unity at infinite dilution. The electrical
conductivity of a solution of an electrolyte is dependent on the velocity
of migration of its ions,^ so that the ratio of the molecular conductivity "
of a solution of an electrolyte at given dilution, to the limiting value

^ Arrhenius, Bijhang. till k. Svens. Vet.-AkacL, Stockholm, 1884, Bd. viii., Nos.
13 and 14 ; Zfschr. f. physikal. Chem., Leipzig, 1887, Bd. i. S. 631.

^ Kohlrausch, Ann. d. Phys. u. Chem., Leipzig, 1879, Bd. vi. S. 1, 145 ; 1885, Bd. xxvi.
S. 161.

^ The molecular conductivity is the ratio of tlie conductivity to the molecular concen-
tration of the sohition, the latter being the ratio of grammes per litre to the molecular
weight in grammes.



262 DIFFUSION, OSMOSIS, AND FIITRATION.

which this approaches on increasing dilution, is a measure of the
coefficient of activity of the solution. According to this view, then, a
very dilute solution of sodium chloride consists of positively-charged
sodium and negatively-charged chlorine ions moving amongst the water
molecules, but unable to part company Ijy virtue of their charges of
opposite sign, and only separable by the application of energy from
without (electrolysis). Other substances which do not conduct elec-
tricity in aqueous solution are believed to be in a simpler state of
solution, the molecules moving among those of the solvent not being
known to be in a different condition to those of the undissolved sub-
stance, but simply capable of freer motion.

It is further probable that in the case of certain non-electrolytes in
solution, instead of single molecules we deal with aggregates of mole-
cules, and such substances are said to be in colloidal solution {noWa,
glue). As instances of organic substances the aqueous solutions of
which are colloidal, may be mentioned albumin, gum-arabic, starch,
haemoglobin.^

It must at once appear likely that the ease with which the
" molecules " of different substances can move among those of the
solvent in a solution is different in the case of different substances, i.e.
that the power of diffusibility must be very variable.

Graham ^ gives the following table : —

Equal iceiglits had diffused to the same extent 171 the following times : —



Hydrochloric acid . 1
Sodium chloride . 2 "33

Cane-sus;ar . . 7



Magnesium sulphate . 7
Albumin . . .49

Caramel . . .98



Substances in solution tend to diffuse from places of higher to those
of lower concentration, and in the law of Fick ^ it is stated that the
quantity of dissolved substance so diffusing is proportional to the rate
of fall in concentration.

Thus, if a is the quantity of substance passing section g- of a diffusion

cylinder in time z, when at x the concentration in the section is c, and at

X + dx is c + dc ; then —

d.c

a=i — kqz -y—

^ dx

where h is a constant peculiar to the substance and known as the
coefficient of diffusion.

From the law of Fick, Stefan* calculated for a special case the
following formula : —

az=cqjU —

^ Picton and Linder {Journ. Gliem. Soc, London, 1892, vol. Ixi. p. 148; 1895, vol.
Ixvii. p. 63) have prepared solutions of arsenious sulphide of various " grades." Thus one
may have (a) aggi'egates visible by microscope ; (/3) no visible aggregates, but the substance
not diffusible : (y) the substance diffusible but not filterable ; (S) the substance both
diffusible and filterable, but the aggregates still large enough to scatter light. They
consider that in matter in solution one can pass by gi-ades from obvious suspension, to
colloidal solution, to non -electrolytic crystallised solution, and so to the first grade of
electrolytic solution.

'^ Phil. Trans., London, 1861, vol. cli. p. 183.

^ Ann. d. Phys. u. Chem., Leipzig, 185.5, Bd. xciv. S. 59.

* Sitzungsb. d. k. Akad. d. Wissensch., Wien, 1879, 13d. Ixxix. S. 161.



DIFFUSION. 263

where a is the amount of substance, passing in time z, through section 2-,
from an infinitely long cylinder of solution of concentration c, into
another such cylinder of pure solvent.

This formula was experimentally verified by Voigtlander ^ with
cylinders of agar jelly, in which diffusion occurs as easily as in water.^
He further investigated the temperature coefficient (a) for k, and found
that it is not a linear function of the temperature, as stated by Weber ,^
but stands in the following relation * : —

In the case of an electrolyte in solution, the diffusion must be con-
sidered as that of the ions into which it is dissociated on passing into
solution. The velocity of the separated ions may be very different, but
since in solution by virtue of their opposite charges they cannot part,
the more rapidly moving ion must be retarded by the more slowly
moving, and the more slowly moving accelerated by its more active
fellow. The diffusion of an electrolyte may also be accelerated by
the presence in the liquid into which it is diffusing, of ions charged
oppositely to those forming the more active partner in the diffusing
substance. Thus hydrochloric acid diffuses faster into a solution of
sodium chloride than into water.'^ As a rule, those electrolytes which
are the best conductors, are the most diffusible in solution.*' The pre-
sence of a substance that is not an electrolyte in the fluid into which
diffusion is taking place may slow the diffusion of an electrolyte.
Thus sodium chloride diffuses more slowly into sugar solution than
into water, and the presence of ethyl alcohol also retards its diffusion.''
In the case of non-electrolytes in solution, diiiusion must concern the
" molecules " of the dissolved substance, and the " aggregates " of colloids
will find their way with greater difficulty than the " molecules " of
crystalloids.

No definite rule can be stated as regards the effect of concentration
of the solution upon the rapidity of diiiusion of the dissolved substance.
With sodium chloride the coefficient of diffusion is practically unaltered
by change in concentration of the solution. In the case of magnesium
sulphate the coeificient falls with the concentration of solution, while
with hydrochloric, nitric, and sulphuric acids the coefficient rises with
the concentration.^

The simultaneous diffusion of two salts, studied first by Graham, has
been since more completely investigated by Marignac.^ In general the
rapidity of diffusion of the more diffusible of a pair of salts diffusing
simultaneously is found to be increased, that of the less diffusible
diminished.

In the following table the diffusions of five pairs of salts, separately
and simultaneously, are contrasted.

^ Ztschr. f. physikal. Chem., Leipzig, 1889, Bd. iii. S. 316.

^ Graham, Ann. d. Chem., Leipzig, 1862, Bd. cxxi. S. 5, 29.

^ Ann. d. Phys. u. Chem., Leipzig, 1879, Bd. vii. S. 536.

■* For the vahies of a, which vary slightly with different substances, see Voigtlander's
original paper, loc. cit.

^ Arrhenins, Ztschr. f. physikal. Chem., Leipzig, 1892, Bd. x. S. 51.

" Long, Ann. d. Phys. u. Chem., Leipzig, 1880, Bd. ix. S. 613 ; Lenz, Mem. Acad. imp.
d. sc. de St. Pefersbou7'g, 1882, tome vii. p. 30.

^ Arrhenius, loc. cit.

8 Schett'er, Ztschr. f. ^^hysikal. Chem., Leipzig, 1888, Bd. ii. S. 390.

" Ann. de chim., Paris, 1874, S^r. 5, tome ii. p. 546.



264



DIFFUSION, OSMOSIS, A AW FIITRATION.



r is the ratio of the diffusion coefficients of the two salts, with
separate diffusions.

T is the ratio with simultaneous diffusions.

B, the ratio of the amounts diffused of the same salt in separate
and in simultaneous diffusion, i.e. the alteration of the coefficient of
diffusion produced by the presence of the other salt.





Separate.


Simultaneous.


r.


r' .


r' : r.


R.


jNaCl .


•5833


•6054








1^038


(A^aoSO^


•3770


•2497


■590


•352


•596


•662


fKCl .


•8560


•9276








1 •OSS


I^BaC], .


•8433


•4424


•572


•401


•701


•814


/NaCl .


•7142


•7883








r019


\,BaClo .


•5673


■5225


•757


•668


•882


•921


/KoSO,.
\MgSO,


•4745
•2028


•4378
•1684


•382


•345


•903


■901
•830


/NaoSO^
IMgSO, .


•3757


•3420








•910


•2097


•1823


•523


•502


•960


■869



As a rule, as seen in E, the more diffusible salt is accelerated, the
less diffusible delayed. In the two last pairs both members are delayed,
but the less diffusible more markedly.

In the body it is rare to find the conditions present for a free
diffusion between the constituents of two solutions ; a membrane,
whether composed of cells or the surface layer of the protoplasm of
a cell, as a rule intervenes, and obviously the permeability of the
membrane affects the result. If pig's bladder separates methyl alcohol
and ether, the methyl alcohol diffuses into the ether, but if a caoutchouc
memljrane separates the two liquids, the ether diffuses into the alcohol.^

Osmosis.

The term osmosis is applied to diffusion taking place between two
liquids separated by a membrane.

The simplest case of this is that in which a solution of a substance
is separated from the pure solvent by a membrane permeable by the
solvent but impermeable by the dissolved substance. Such membranes
were first prepared by Traube,^ in the form of colloidal precipitates,
such as tannate of gelatin and ferrocyanide of copper, but Pfeffer^
was the first to thoroughly study the process of osmosis under such
conditions. The name " semipermeable " has been given to such mem-
branes, but it must be noted at once that this expression is seldom
strictly accurate and must always be used relatively to some particular
substance. Tamman ^ has pointed out that such membranes are by
no means the " molecule sieves " that Traube imagined,^ and in experi-
mental work the membrane must be chosen to suit the substance, or
vice versd. Copper ferrocyanide forms one of the best of such mem-
branes, and is nearly impermeable to cane sugar.



^ Raoult, Ztschr. f. phyaikal. CJiem., Leipzig, 1885, Bd. xvii. S. 735.

- Arch. f. Anat. n. Physiol., Leipzig, 1867, S. 87 and 129.

^ " Osmotisehe Untersncli.," Leipzig, 1877.

^ Ztschr. f. physikal. Chcm., Leipzig, 1892, Bil. x. S. 255,

5 See also Walden, ihid., 1892, Bd, x. S, 699,



OSMOSIS.



265



In practice such membranes are formed in the interstices of an
indifferent supporting structure, such as the pores of a porous battery
pot (preferably previously soaked in gelatin), by placing one of the mem-
branogens inside the pot, which is then lowered into a solution of the
other, so that the precipitate is formed within the structure of the
earthenware where the two solutions come into contact. It is only by
such an artifice that the membrane can be sufficiently supported to
enable it to withstand the high pressure produced by the osmosis under
the conditions.^

If, now, a battery pot with such a membrane in its pores Ije filled
with a solution of sugar in water, hermetically sealed, and placed in
a vessel of water, the water molecules will diffuse in either direction
through the membrane, which is permealjle to them ; the sugar molecules,
on the other hand, cannot pass out, for to them the membrane is imper-
meable. As a result of the presence of the sugar on the inner side of
the membrane, in unit time, more water enters the pot than passes out,
and the pressure rises until it is sufficient to luring about the condition
of equality in the number of w^ater molecules entering and leaving the pot.

This pressure is called the osmotic pressure of the solution of sugar,
under the conditions of concentration and temperature. That this
pressure is comparalile to that of a gas was first clearly pointed out
by van 't Hoff.2

Thus the osmotic pressure of a dilute solution at constant tem-
perature is proportional to its concentration {i.e. density of a gas in
the law of Boyle). This is illustrated by the following table from
Pf offer : ^—

Cane Sugar Solutio7is at 13° "5 C. to 16°*1 G.



Concentration of
Solution.


Osmotic Pressure
in Mm. of Hg.


Osmotic Pressure
Concentration.


1 per cent.
2

2-74

6


535
1016

1518
2082
3075


535
508
554
521
513



Again, at constant concentration of a dilute solution, the osmotic
pressure is proportional to the absolute temperature (law of Charles).
Thus, again, taking Pfeffer's data —





1 per Cent.


Cane Sugar Solution.




Temperature.


Observed Pressure.


Calculated Pressure.


(1)

(2)


32°
14°-15
36°
15°-5


Mm. Hg.
544
510
567
520-5


Mm. Hg.
512
529



^ For details of manufacture see Adie, Journ. Chem. Soc, London, 1891, vol. lix. p. 344.
^ Arch. ne6rl. d. sc. exactes, etc.', 1885, Bd. xx. S. 239; Ztsclir. f. physikal. Chem.
Lei].izig, 1887, Bd. i. S. 479.
^ Loc. cit., p. 85,



266



DIFFUSION, OSMOSIS, A AW FILTRATION.



The experiments of Soret/ again, show that in a solution, as in a gas,
the warmest part is the most dihite. Soret introduced a solution into
a long vertical tube and maintained a difference of temperature at the
two ends, the upper end l)eing warmer than the lower. At the end
of several weeks the concentration of the solution at the warm end of
the tube was found to be lowered. Thus, with solution of copper
sulphate, the concentration at the end of the tube at 20° C. was 17'332
per cent., while that at the end maintained at 80° C. was 14"03 per cent.,
instead of 14-3 per cent, as calculated by Charles' law. And, again, with
concentration of 29'867 per cent, at the 20° C. end, a concentration of
23'871 per cent, was found at the end warmed to 80° C. instead of 24'8
per cent, as calculated.

Thus "the osmotic pressure of a dissolved substance is exactly the
same as the gas pressure, measured by the manometer, which one would
observe if he could remove the solvent, and leave the dissolved substance
as a gas filling the same volume." ^ The hypothesis of Avogadro then
is, according to van 't Hoff, not merely capable of extension by the law
of Henry to solutions of gases, but to solutions of matter which is not
gaseous under ordinary circumstances, and it may be stated that
equal volumes of gases or dilute solutions at the same gas or osmotic
pressure, and at the same temperature, contain equal numbers of
molecules.

A marked concordance is seen in the table below, between the
observed osmotic pressures for sugar solution taken from Pf effer ^ and
those calculated on the hypothesis of Avogadro and the law of Charles.

One per cent, sugar solution contains 1 grm. of sugar in 100"6 c.c. of
solution. At the same temperature and pressure, gfo- of a grm. of hydrogen
contains by hypothesis the same number of molecules (S^i.:^-2'f)ii = 342).

Taking the weight of a litre of hydrogen, at 0° C. and one atmosphere
pressure, as ■08956 grm., and the above concentration as ■0581 grm. per litre,
the gas pressure at 0° C, at the vohime 100^6 c.c, is ■649 atmosphere, and at
the temperature /= ^649 (1 + ■003670-



Temperature.


Observed Osmotic
Pressures.-i


Calculated Gas

Pressures
■649(1+ -003670.


r-8 c.

13°-7 C.
14°^2 C.
15°^5 C.
22° C.
3-2° C.
36° C.


■664
•691
■671
■684
•721
•716
•746


•665
■681
■682
■686
■701
■725
•735



The law of Dalton may also be applied, with certain restrictions, to
the osmotic pressure of solutions, the total pressure of a mixture of
substances being equal to the sum of the partial osmotic pressures of
the several components.

^ Arch. d. sc. 2)hys. et nat., Geneve, Ser. 3, tome ii. p. 48 ; Ann. de chini., Paris, S^r. 5,
tome xxii. p. 293.

- Kernst's "Theoretical Chemistry," 1895, Palmer's trans., p. 148.

^ Loc. cit. ■* Pletler, loc. cit., p. 85.



OSMOSIS.

The following instances are taken from Pfeffer : ^-
Co]jper Ferrocyanide Membrane.



267



Concentration.


Rise of Fluid in Measuring Tube
IN Mm. Per Hour.


Experiment I.
Temp. 17°-1 C.


Experiment II.
Temp. 15° -8 0.


1 per cent, saltpetre .

15 ,, gum-araljic

1 ,, saltpetre + 15 per cent,
gum-arabic

1 per cent, saltpetre .


Mm.
6-08

2-06

7-90

6'06


Mm.
5-4

1-8

7-0

5-3



Parchment Paper Membrane.



Concentration.


Rise of Fluid in Measuring Tube
IN Mm. Per Hour.


Experiment I.


Experiment II.


1 "5 per cent, calcium chloride

2 ,, gum-araljic

1"5 ,, calcium chloride + 2
per cent, gum-arabic


9-9

1-2

11-4


10-3

1-3

11-3



Temijerature in both experiments, 17° "4 C.

In cases, however, where the two constituents of the solution have
a common ion, each salt diminishes the dissociation of the other, so that
the pressure of the mixture is less than the sum of the pressures of the
two components.^

Thus for a double salt —





A.


B.


Osmotic
Pressure.


Sum of
Components.


Osmotic
Pressure.


Sum of
Components.


^VA1,(S0J3 .
AK^SO, . . .
^\(NH,)oAlo(SOJ,24Aq
J^K2Al„(SOJ,24Aq


1-264 At.
1-265 „
1-29 ,,
2-37 ,,
2-39 ,,


2-53

2-56


1-295

1-22

1-40

1-98

1-96


2-515
2-62



1 Pfeffer, loc. cit., p. 68.

" From Adie, Journ. Chcm. Soc, London. 1891, vol. lix. p. 344.



2 68 DIFFUSION, OSMOSIS, AND FILTRATION.

It is, however, by no means the fact that, in the case of all sub-
stances in aqueous solution, agreement exists between the observed-
osmotic pressure and that directly calculated on the above hypothesis
alone. In many cases the pressures observed in solution are far higher
than those calculated from the concentration in gramme-molecules per
unit volume. Thus the osmotic pressure of a 1 per cent, aqueous solu-
tion of common salt at 0° C, by calculation on the above data, should
be 3 "7 9 atmospheres, but actual measurement shows it to be over 7
atmospheres.

This phenomenon, common to all solutions of electrolytes, is
accounted for on the hypothesis of Arrhenius,^ that the dissociated ions
of an electrolyte in solution are capable of exerting pressure as well as
the undissociated molecules. The osmotic pressure of solutions of
electrolytes is then raised above the simple molecular value by the
coefficient expressing the extent to which the molecules are dissociated
in passing into solution (dissociation coefficient).

This coefficient gives the ratio of the observed osmotic pressure of a
solution to the pressure calculated on the assumption that no dissocia-
tion of molecules occurs in passing into solution. It may be deter-
mined for a substance at a particular dilution most accurately, by
measurement of the electrical conductivity of the solution.

If m- is the number of inactive molecules in the solution, and n the
number of active and k the number of ions into which a molecule can

Til — I n 9?

be dissociated, then the dissociation coefficient i = 1— ^

m-\-n

Since the " activity co-efficient " « = — -. — is measurable by the

m + n

ratio of the molecular conductivity of the solution to the limiting value
it approaches by increased dilution, i = l+{k-l)a can be obtained
by measurement of conductivity of solution, i can obviously also be
obtained from measurements of osmotic pressure.

This coefficient will necessarily be of very different value for
different classes of electrolytes, since the possible number of ions is
variable. Thus sodium chloride has 2, potassium sulphate 3,
potassium ferrocyanide 5 ions.

Hence as a formula may be given —

P = 22-35 (1 + -003670 - i atmospheres,

7)1

where 22-35 atmospheres is the pressure exerted by the gramme-
molecule of gas in volume of 1 litre at 0° C\, c the number of grammes
of the suljstance per litre, m its molecular weight, and i its dissociation
coefficient at the concentration c.

As regards the practical estimation of the osmotic pressure of a
solution, the direct measurement by a semipermeable membrane is not
only tedious, and limited to cases where the dissolved substance has no
chemical action on the film, but seldom practicable, on account of the
difficulty in constructing membranes, to which the term may be strictly
applied. Obviously, unless the membrane is really impermeable to the
dissolved substance, the values on account of the " leakage " of dissolved
substance must be below the real amount.



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