A living organism may consist merely of a single cell, which is able alone to accomplish all the functions of life. Most living beings, however, consist of a collection of innumerable cells forming a cellular a.s.sociation or community. When a number of cells are thus united to const.i.tute a single living being, the various functions of life are divided among different cellular groups. Certain cells become specialized for the accomplishment of a single function, and to each function corresponds a different form of cell. It is thus easy to recognize by their form the nerve cells, the muscle cells which perform the function of movement, and the glandular cells which perform the function of secretion. The cells of a living being are microscopic in size, and it is remarkable that they never attain to any considerable dimensions.

In order that life may be maintained in a living organism, it is necessary that a continual supply of aliment should be brought to it, and that certain other substances, the waste-products of combustion, should be eliminated. In order to be absorbed and a.s.similated, the alimentary substances must be presented to the living organism in a liquid or gaseous state. Thus the essential condition necessary for the {13} maintenance of life is the contact of a living cell with a current of liquid. The elementary physical phenomenon of life is the contact of two different liquids. This is the necessary condition which renders possible the chemical exchanges and the transformations of energy which const.i.tute life.

It is in the study of the phenomena of liquid contact and diffusion that we may best hope to pierce the secrets of life. The physics of vital action are the physics of the phenomena which occur in liquids, and the study of the physics of a liquid must be the preface and the basis of all inquiry into the nature and origin of life.

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CHAPTER II

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 ma.s.s 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 h.o.m.ogeneous 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 cla.s.ses--substances which are capable of crystallization, or crystalloids; and those which are incapable of crystallization, the colloids.

Crystalloids may be divided again into two cla.s.ses, 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 a.s.serts 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 quant.i.ty of the solute and the quant.i.ty 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 ma.s.s 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 a.n.a.logy 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 s.p.a.ce 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 s.p.a.ce 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 quant.i.ty V 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 0 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 s.p.a.ce, _i.e._ on the molecular concentration. If we double the ma.s.s of the gas in a given s.p.a.ce, 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 s.p.a.ce 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 0 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 -273 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 _t_ indicates the Centigrade temperature above the freezing point of water, then the absolute temperature is equal to _t_ + 273.

_The Gaseous Constant._--Consider a ma.s.s of gas at 0 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 quant.i.ty 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 0 C. in a s.p.a.ce of 1 litre. It has a pressure of 22.35 atmospheres at 0 C., or 273 absolute temperature. Since PV = RT, R = PV / T = 1 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 s.p.a.ce, 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 pa.s.sage of water into the vessel, but prevents the pa.s.sage 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 pa.s.ses 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 pa.s.ses 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 ma.s.s, 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 0 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 1.85 C. Thus a normal solution of any non-ionizable substance in water freezes at -1.85 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 37 C., _i.e._ 98.6 F., the normal temperature, we proceed as follows. On freezing the blood, we find that it congeals at -.56. Its molecular concentration is therefore .56 / 1.85 = .30, or about one-third of a gramme-molecule per litre. Its osmotic pressure at 0 C. is therefore .3 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 0 for every degree rise of temperature. The increase of pressure at 37 is therefore .00367 37 6.7 = .9 atmospheres. The total osmotic pressure at 37 is therefore 6.7 + .9 = 7.6 atmospheres.

_Rise of Boiling Point._--Water under atmospheric pressure boils at a temperature of 100 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 100 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 5 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 s.p.a.ce 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 0 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 const.i.tution 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. 1.85 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 22.35 = A / 1.85 22.35.