SOLUTIONS
We have seen that living beings are transformers of energy and of matter,
evolutionary in form and liquid in consistency; that they are solutions of
colloids and crystalloids separated by osmotic membranes to form
microscopic cells, or consisting merely of a gelatinous mass of protoplasm,
with a nucleus of slightly differentiated material. The elementary
phenomenon of life is the contact of two different solutions. This is the
initial physical phenomenon from which proceed all the other phenomena of
life in accordance with the ordinary chemical and physical laws. Thus the
basis of biological science is the study of solution and of the phenomena
which occur between two different solutions, either in immediate contact or
when separated by a membrane.
A solution is a homogeneous mixture of one or more solutes in a liquid
solvent. Before solution the solute or dissolved substance may be solid,
liquid, or gaseous.
Solutes, or substances capable of solution, may be divided into two
classes--substances which are capable of crystallization, or crystalloids;
and those which are incapable of crystallization, the colloids.
Crystalloids may be divided again into two classes, those whose solutions
are ionizable and therefore conduct electricity, chiefly salts, acids, and
bases; and those whose solutions are non-ionizable and are therefore
non-conductors. These latter are for the most part crystallizable
substances of organic origin, such as sugars, urea, etc.
Avogadro's law asserts that under similar conditions of temperature and
pressure, equal volumes of various gases {15} contain an equal number of
molecules. Under similar conditions, the molecular weights of different
substances have therefore the same ratio as the weights of equal volumes of
their vapours. Hence if we fix arbitrarily the molecular weight of any one
substance, the molecular weight of all other substances is thereby
determined. The molecular weight of hydrogen has been arbitrarily fixed as
two, and hence the molecular weight of any substance will be double its
gaseous density when compared with that of hydrogen.
_Gramme-Molecule._--A gramme-molecule is the molecular weight of a body
expressed in grammes. Occasionally for brevity a gramme-molecule is spoken
of as a "molecule." Thus we may say that the molecular weight of oxygen is
16 grammes, meaning thereby that there are the same number of molecules in
16 grammes of oxygen as there are atoms in 1 gramme of hydrogen.
_Concentration._--The concentration of a solution is the ratio between the
quantity of the solute and the quantity of the solvent. The concentration
of a solution is expressed in various ways. (_a_) The weight of solute
dissolved in 100 grammes of the solvent. (_b_) The weight of solute present
in 100 grammes of the solution. (_c_) The weight of solute dissolved in a
litre of the solvent. (_d_) The weight of solute in a litre of the
solution. The most usual method is to give the concentration as the weight
of solute dissolved in 100 grammes or in one litre of the solvent.
_Molecular Concentration._--Many of the physical and biological properties
of a solution are proportional, not to its mass or weight concentration,
but to its molecular concentration, _i.e_. to the number of
gramme-molecules of the solute contained in a litre of the solution. Many
physical properties are quite independent of the nature of the solute,
depending only on its degree of molecular concentration.
_Normal Solution._--A normal solution is one which contains one
gramme-molecule of the solute per litre. A decinormal solution contains
one-tenth of a gramme-molecule of the solute per litre, and a centinormal
solution one-hundredth of a gramme-molecule. A normal solution of urea, for
example, {16} contains 60 grammes of urea per litre, while a normal
solution of sugar contains 342 grammes of sugar per litre.
_The Dissolved Substance is a Gas._--Van t' Hoff, using the data obtained
by the botanist Pfeffer, showed that the dissolved matter in a solution
behaved exactly as if it were a gas. The analogy is complete in every
respect. Like the gaseous molecules, the molecules of a solute are mobile
with respect to one another. Like those of a gas, the molecules of a solute
tend to spread themselves equally, and to fill the whole space at their
disposal, _i.e._ the whole volume of the solution. The surface of the
solution represents the vessel containing the gas, which confines it within
definite limits and prevents further expansion.
_Osmotic Pressure._--Like the molecules of a gas, the molecules of a solute
exercise pressure on the boundaries of the space containing it. This
osmotic pressure follows exactly the same laws as gaseous pressure. It has
the same constants, and all the notions acquired by the study of gaseous
pressure are applicable to osmotic pressure. Osmotic pressure is in fact
the gaseous pressure of the molecules of the solute.
When a gas dilates and increases in volume, its temperature falls, and cold
is produced. Similarly, when a soluble substance is dissolved, it increases
in volume, and the temperature of the liquid falls. This phenomenon is well
known as a means of producing cold by a refrigerating mixture.
The phenomena of life are governed by the laws of gaseous pressure, since
all these phenomena take place in solutions. The fundamental laws of
biology are those of the distribution of substances in solution, which is
regulated by the laws of gaseous pressure, since all these laws are
applicable also to osmotic pressure.
_Boyle's Law_.--When a gas is compressed its volume is diminished. If the
pressure is doubled, the volume is reduced to one-half. The quantity V x P,
that is the volume multiplied by the pressure, is constant.
_Gay-Lussac's Law._--For a difference of temperature of a degree Centigrade
all gases dilate or contract by 1 / 273 of their volume at 0deg Centigrade.
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_Dalton's Law._--In a gaseous mixture, the total pressure is equal to the
sum of the pressures which each gas would exert if it alone filled the
whole of the receptacle.
_Pressure proportional to Molecular Concentration._--The above laws are
completely independent of the chemical nature of the gas, they depend only
on the number of gaseous molecules in a given space, _i.e._ on the
molecular concentration. If we double the mass of the gas in a given space,
we double the number of molecules, and we also double the pressure,
whatever the nature of the molecules. We may also double the pressure by
compressing the molecules of a gas, or of several gases, into a space half
the original size. The molecular concentration of a gas, or of a mixture of
gases, is the ratio of the number of molecules to the volume they occupy.
The pressure of a gas or of a mixture of gases is proportional to its
molecular concentration. This is a better and a shorter way of expressing
both Boyle's law and Dalton's law.
One gramme-molecule of a gas, whatever its nature, condensed into the
volume of 1 litre, has a pressure of 22.35 atmospheres. Similarly one
gramme-molecule of a solute, whatever its nature, when dissolved in a litre
of water, has the same pressure, viz. 22.35 atmospheres.
_Absolute Zero._--According to Gay-Lussac's law, the volume of a gas
diminishes by 1 / 273 of its volume at 0deg C. for each degree fall of
temperature. Thus if the contraction is the same for all temperatures, the
volume would be reduced to zero at -273deg C. This is the absolute zero of
temperature. Temperatures measured from this point are called absolute
temperatures, and are designated by the symbol T. If _tdeg_ indicates the
Centigrade temperature above the freezing point of water, then the absolute
temperature is equal to _tdeg_ + 273deg.
_The Gaseous Constant._--Consider a mass of gas at 0deg C. under a pressure
P_o, with volume V_o. At the absolute temperature T, if the pressure be
unaltered, the volume of this gas will be V_oT / 273. Therefore the
constant PV, the product of the pressure by the volume, will be represented
by P_oV_oT / 273. {18}
At the same temperature, but under another pressure P' the gas will have a
different volume V'. Since, according to Boyle's law, PV is constant (P'V'
= P_oV_o), it will still equal P_oV_oT / 273. Therefore P_oV_o / 273 is
also constant. This quantity is called "the gaseous constant," and if we
represent it by the symbol R, we obtain the general formula PV = RT for all
gases, or PV / T = R.
Suppose, for instance, we have a gramme-molecule of a gas at 0deg C. in a
space of 1 litre. It has a pressure of 22.35 atmospheres at 0deg C., or
273deg absolute temperature. Since PV = RT, R = PV / T = 1 x 22.35 / 273 =
.0819. This number .0819 is the numerical value of the constant R for all
gases, volume being measured in litres and pressure in atmospheres.
Substances in solution behave exactly like gases, they follow the same laws
and have the same constants. All the conceptions which have been acquired
by the study of gases are applicable to solutions, and therefore to the
phenomena of life. The osmotic pressure of a solution is the force with
which the molecules of the solute, like gaseous molecules, strive to
diffuse into space, and press on the limits which confine them, the
containing vessel being represented by the surfaces of the solution.
Osmotic pressure is measured in exactly the same way as gaseous pressure.
To measure steam pressure we insert a manometer in the walls of the boiler.
In the same way we may use a manometer to measure osmotic pressure. We
attach the tube to the walls of the porous vessel, allow the solvent to
increase in volume under the pressure of the solute, and measure the rise
of the liquid in the manometer tube.
_Pfeffer's Apparatus._--Pfeffer has designed an apparatus for the
measurement of osmotic pressure. It consists of a vessel of porous
porcelain, the pores of which are filled with a colloidal solution of
ferrocyanide of copper. This forms a semi-permeable membrane which permits
the passage of water into the vessel, but prevents the passage of sugar or
of any {19} colloid. The stopper which hermetically closes the vessel is
pierced for the reception of a mercury manometer. The vessel is filled with
a solution of sugar and plunged in a bath of water. The volume of the
solution in the interior of the vessel can vary, since water passes easily
in either direction through the pores of the vessel. The boundary of the
solvent has become extensible, and its volume can increase or diminish in
accordance with the osmotic pressure of the solute. Under the pressure of
the sugar water is sucked into the vessel like air into a bellows, the
solution passes into the tube of the manometer, and raises the column of
mercury until its pressure balances the osmotic pressure of the sugar
molecules.
_Osmotic Pressure follows the Laws of Gaseous Pressure._--This osmotic
pressure is in fact gaseous pressure, and may be measured in millimetres of
mercury in just the same way. We may thus show that osmotic pressure
follows the laws of gaseous pressure as defined by Boyle, Dalton, and
Gay-Lussac. The coefficient of pressure variation for change of temperature
is the same for a solute as for a gas. The formula PV = RT is applicable to
both. The numerical value of the constant R is also the same for a solute
as for a gas. being .0819 for one gramme-molecule of either, when the
volume is expressed in litres and the pressure in atmospheres. The formula
PV = RT shows that for a given mass, with the same volume, the pressure
increases in proportion to the absolute temperature.
_Osmotic Pressure of Sugar._--A normal solution of sugar, containing 342
grammes of sugar per litre, has a pressure of 22.35 atmospheres, and it may
well be asked why such an enormous pressure is not more evident. The reason
will be found in the immense frictional resistance to diffusion. Frictional
resistance is proportional to the area of the surfaces in contact, and this
area increases rapidly with each division of the substance. When a solute
is resolved into its component molecules, its surface is enormously
increased, and therefore the friction between the molecules of the solute
and those of the solvent.
_Isotonic Solutions._--Two solutions which have the same {20} osmotic
pressure are said to be iso-osmotic or isotonic. When comparing two
solutions of different concentration, the solution with the higher osmotic
pressure is said to be hypertonic, and that with the lower osmotic pressure
hypotonic.
_Lowering of the Freezing Point._--Pure water freezes at 0deg C. Raoult
showed that the introduction of a non-ionizable substance, such as sugar or
alcohol, lowers the freezing point of a solution in proportion to the
molecular concentration of the solute. One gramme-molecule of the solute
introduced into one litre of the solution lowers its temperature of
congelation by 1.85deg C. Thus a normal solution of any non-ionizable
substance in water freezes at -1.85deg C. The measurement of this lowering
of the freezing point is called Cryoscopy, a method which is becoming of
great utility in medicine.
_Cryoscopy of Blood._--In order to determine the osmotic pressure of the
blood at 37deg C., _i.e._ 98.6deg F., the normal temperature, we proceed as
follows. On freezing the blood, we find that it congeals at -.56deg. Its
molecular concentration is therefore .56 / 1.85 = .30, or about one-third
of a gramme-molecule per litre. Its osmotic pressure at 0deg C. is
therefore .3 x 22.35 = 6.7 atmospheres. The increase of pressure with
temperature is the same as for a gas, viz. 1/273, or .00367 of its pressure
at 0deg for every degree rise of temperature. The increase of pressure at
37deg is therefore .00367 x 37 x 6.7 = .9 atmospheres. The total osmotic
pressure at 37deg is therefore 6.7 + .9 = 7.6 atmospheres.
_Rise of Boiling Point._--Water under atmospheric pressure boils at a
temperature of 100deg C. The addition of a solute whose solution does not
conduct electricity, such as sugar, causes a rise in the boiling point
proportional to the molecular concentration of that solute.
_Lowering of the Vapour Tension._--The vapour tension of a liquid is
lowered by the addition of a solute. A liquid boils at the temperature at
which its vapour tension equals that of the atmosphere. Since an aqueous
solution of sugar at atmospheric pressure does not begin to boil at 100deg
C., it is manifest that its vapour tension is then less than that of the
{21} atmosphere. The addition of a solute such as sugar, whose solution is
not ionizable, and therefore does not conduct electricity, lowers the
vapour tension of the solution in proportion to the molecular concentration
of the solute.
_Corresponding Values._--We have thus found five properties of a solution
which vary proportionally, so that from the measurement of any one of them
we can determine the corresponding values of all the others. These are--
1. The Molecular Concentration.
2. The Osmotic Pressure.
3. The Diminution of Vapour Tension.
4. The Raising of the Boiling Point.
5. The Lowering of the Freezing Point.
_Cryoscopy._--The usual method employed for the determination of the
molecular concentration and osmotic pressure of a solution is by
cryoscopy--the measurement of its temperature of congelation. A very
sensitive thermometer is used, the scale of which extends over only 5deg
and is divided into hundredths of a degree. The liquid under examination is
placed in a test tube, in which the bulb of the thermometer is plunged, and
this is supported in a second tube with an air space all round it. The
whole is then suspended to the under side of the cover of the refrigerating
vessel, which may be cooled either by filling it with a freezing mixture,
or by the evaporation of ether. During the whole of the operation the
liquid is agitated by a mechanical stirrer. The first step is to determine
the freezing point of distilled water. As the water cools the mercury
gradually descends in the stem of the thermometer till it reaches a point
below the zero mark at 0deg C. As soon as ice begins to form the mercury
rises, at first rapidly and then more slowly, reaches a maximum, and
finally descends again. This maximum reading is the true point of
congelation. The inner tube is then emptied, care being taken to leave a
few small ice crystals to serve as centres of congelation for the
subsequent experiment, thus avoiding supercooling of the solution. The
process is then repeated with the solution under examination. The
difference between {22} the two freezing points is the required "lowering
of the freezing point."
Cryoscopy is the method most used in biological research to determine
molecular concentration. It has, however, some grave defects. It
necessitates several cubic centimetres of the liquid under examination. It
gives us the constants of the solution at the temperature of freezing,
which is far below that of life. Organic liquids are easily altered and are
extremely sensible to minute differences of temperature, cryoscopy
therefore gives us no information as to the constitution of solutions under
normal conditions. It is desirable to have some other method of determining
molecular concentration and the other interdependent constants at the
normal temperature of life. A much better method, were it possible, would
be the direct determination of the vapour tension of the solutions under
normal conditions of temperature and pressure.
_Molecular Lowering of the Freezing Point._--For every substance whose
solution is not ionized and therefore does not conduct electricity, the
lowering of the freezing point is the same, viz. 1.85deg C. for each
gramme-molecule of the solute per litre of the solution.
_Determination of the Molecular Concentration._--In order to obtain the
molecular concentration of a non-ionizable substance, we have only to
determine the lowering of the freezing point. Let A be the lowering of the
freezing point of any solution. On dividing it by 1.85 (the lowering of the
freezing point for a normal solution), we obtain the number of
gramme-molecules in a litre of the solution. If n be the number of
gramme-molecules per litre, then n = A / 1.85.
_Determination of the Osmotic Pressure._--The osmotic pressure P of a
solution may be obtained by multiplying its molecular concentration n by
22.35 atmospheres. P = n x 22.35 = A / 1.85 x 22.35.
_Determination of Molecular Weight._--The lowering of the freezing point
also enables us to calculate the molecular {23} weight of any non-ionizable
solute. Thus Bouchard has been able to determine by means of cryoscopy the
mean molecular weight of the substances eliminated by the urine. A weight
_x_ of the substance is dissolved in a litre of water, and the lowering of
the freezing point is observed. The value thus found divided by 1.85 gives
us n, the number of gramme-molecules per litre. The molecular weight M may
be determined by dividing the original weight x by n.
The study of osmotic pressure was begun by the Abbe Nollet; and one of his
disciples, Parrot, at an early date thus described its importance: "It is a
force analogous in all respects to the mechanical forces, a force able to
set matter in motion, or to act as a static force in producing pressure. It
is this force which causes the circulation of heterogeneous matter in the
liquids which serve as its vehicle. It is this force which produces those
actions which escape our notice by their minuteness and bewilder us by
their results. It is for the infinitely small particles of matter what
gravitation is for heavy masses. It can displace matter in solution upwards
against gravity as easily as downwards or in a horizontal direction."
Thus the recognition of the fact that a substance in solution is really a
gas, has at a single stroke put us in possession of the laws of osmotic
pressure--laws slowly and laboriously discovered by the long series of
investigations on the pressure of gases.
Osmotic pressure plays a most important role in the arena of life. It is
found at work in all the phenomena of life. When osmotic pressure fails,
life itself ceases.
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