The Mechanism of Life

One gramme-molecule of a gas, whatever its nature, con- densed 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 -g-j^ of its volume at 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 2 + 273.

The Gaseous Constant. Consider a mass of gas at C. under a pressure P o , with volume V . At the absolute temperature T, if the pressure be unaltered, the volume of At the same temperature, but under another pressure P', the gas will have a different volume V'. Since, accord- ing to Boyle's law, PV is constant (P'V' = P V ), it will quantity is called "the gaseous__ constant, 11 and if we represent it by the symbol R, we obtain the general formula

Suppose, for instance, we have a gramme-molecule of a gas at C. in a space of 1 litre. It has a pressure of 22'35 atmospheres at 0C., or 273 absolute temperature. '0819 is the numerical value of the constant R for all gases, volume being measured in litres and pressure in atmospheres. Substances in sol iition behave exactly like ^ases, 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 ^f_jx__sj2lutiQn_js 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 samc__wa^jj^jrag^ 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. Pfcffer'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

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 11 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, th_Jrcs^^ absolute ten ipcra t irre.

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 com- ponent molecules, its surface is enormously increased, and therefore the friction between the molecules of the solute and those of the solvent.

o^^tic j)r^sure are said to be isp-osmotic or isotonic. When comparing two solutions of different concentration, the solution with the higher osm otic grcssurc_ is said to be Ivy per - tqnic, and that with^ jhe jower osmotic pressure Irypotonic. Lowering of the Freezing Point. Pure water freezes at C. Haoult showed that the introduction of a non-iqnizable substance, such as .sugar or alcohol, lowers the freezing^omt of a solution in proportion to the molecular concentration o_f the solute. One gramme-molecule of the solute introduced into one litre of the solution lowers its temperature of congelation by 1'85C. Thus a normal solution of _any n on - ipnizablc substance in water freezes aj>^ 1 '85 C. The measure- ment 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 molecule per litre. Its osmotic pressure at C. is therefore '3 x 2&'35 = 6 '7 atmospheres. The increase of pressure with temperature is the same as for a gas, viz. ^, or '00367 of its pressure at for every degree rise of temperature. The increase of pressure at 37 is therefore '00367 X 37 X 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. Th^j^oi^jtoisioi^of a liquid is lowered by the addition of a solute. A liquid boils at the temperature at which its vapour tension equals thaj; 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

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 Cryoscopy. The usual method employed for the deter- mination 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 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 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

/ rccx J 11 K PQJ n -t- s ..A 8 . th required " Jo \veri tig of the 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 free/ing, which is far below that of life. Organic liquids are easily altered and are extremely sensible to minute differences of temperature, cryoseopy therefore gives us no information as to the con- stitution of solutions under normal conditions. It is desirable to have some other method of determining molecular con- centration 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 free/ing point is the same, vi/. 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. Orijdividnig it by 1'85 ...(the lowering of the freezing point for a normal .solution), we obtain the lumibcr of in a litre of the solution. If n be the

Determination of the Osmotic Pressure. The osmotic pressure P of a solution may be obtained by multiply- ing its molecular concentration n_ by 22*35 atmospheres. Determination of Molecular Weight. The lowering of the freezing point also enables us to calculate the molecular 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_wejjght x of the subs taiice is dissolved in a litre of .wateiy and _ thejowgr- ing of the free/ing point is observed. The vajue thus found divided by 1/85 gives us n, the number of gi'aninie-mplecules per_Jitre. 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. 1 "

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^ Solutions wliicli conduct Electricity. The laws of solution which we have studied in the previous chapter apply only to those solutions, chiefly of organic origin, which do not conduct electricity. Solutions of electrolytes such as the ordinary salts, acids, and bases, which are ionized on solution, give values for the various constants of solution which do not accord with those required by theory. If, for instance, we take a gramme- molecule of an electrolyte such as chloride of sodium, and dissolve it in a litre of water, we find that the lowering of the free/ing point is nearly double the theoretical value of 1'85. The same holds good for the osmotic pressure, and for all the constants which are proportional to the molecular concentra- tion of the solute. The solution behaves, in each case, as if it contained more than one gramme-molecule of sodium chloride per litre. It behaves, in fact, as if it contained i times the number of molecules of solute originally introduced into it. If n be the original number of molecules, then it will apparently contain ri = m molecules. This law is universal for all electrolytic solutions; the theoretical value for their concen- tration, osmotic pressure, and all the proportional physical

the ratio of the apparent number of the molecules present to the number originally introduced. A similar dissociation of the molecule is observed in the case of many gases. The vapour of chloride of ammonium, for instance, is decomposed by heat, and it may be shown experimentally that the increase of pressure on heating above that which theory demands, is due to an increase in the number of the gaseous molecules present. Some of the vapour particles are dissociated into two or more fragments, each of which plays the part of a single molecule.

Arrhenius, in 1885, advanced the hypothesis that the apparent increase in the number of molecules of an electrolytic solution was also due to dissociation. This interpretation at once threw a Hood of light on a number of phenomena hitherto obscure. Coefficient of Dissociation. We have seen that in order to obtain values which accord with experiment we have to multiply the number of gramme-molecules of the solute by the coefficient i, which is called the Coefficient of Dis- sociation.

This coefficient of dissociation, i, may be found by observing the lowering of the freezing point of a normal solution, and The coefficient of dissociation varies with the degree of concentration of the solution, rising to a maximum when the solution is sufficiently diluted. If we know /, the coefficient of dissociation for a given solute, contained in a solution of a definite concentration, we can find n' 9 the number of particles present in a solution containing n gramme-molecules of the solute per litre, since n' = in. On the other hand, if from a consideration of its free/ing point and other constants we find that an electrolytic solution appears to contain ri gramme-molecules per litre,

Very concentrated solutions do not conform to these laws. In this they resemble gases, which as they approach their point of condensation tend less and less to conform to the laws of gaseous pressure. Electrolysis. If we take a solution of an acid, a salt, or a base, and dip into it two metallic rods, one connected to the positive and the other to the negative pole of a battery, we find that the metals or metallic radicals of the solution are liberated at the negative pole, while the acid radicals of the salts and acids and the hydroxyl of the bases are liberated at the positive pole. The liberated substances may either be dis- charged unchanged, or they may enter into new combinations, causing a series of secondary reactions.

Electrolytes. Solutions which conduct electricity are called Electrolytes, and the conducting metallic rods dipping into the solution are the Electrodes. Faraday gave the names of Ions to the atoms or atom -groups liberated at either electrode. The ions liberated at the positive electrode are the Anions, and those at the negative electrode are the Cations. The only solutions which possess any notable degree of electrical conductivity are the aqueous solutions of the various salts, acids, and bases, and in these solutions only do we meet with those phenomena of dissociation which arc evidenced by anomalies of osmotic pressure, free/ing point and the like, anomalies which show that the solution contains a greater number of molecules than that indicated by its molecular concentration. These anomalies are due to dissociation, the division of some of the molecules into fragments, each of which plays the part of a separate molecule, contributing its quota to the osmotic tension and vapour pressure of the solution, in fact to all the phenomena which are dependent on the degree of molecular concentration. The electrical conductivity of a solution is therefore proved to be dependent on its molecular dissociation.

Arrheniufi' Theory of Electrolysis. In 1885, Arrhenius brought forward his theory of the transport of electricity by an electrolyte. According to this hypothesis, the electric current is carried by the ions, the positive charges by the cations, and the negative charges by the anions. In virtue of the attraction between charges of different sign, and repulsion between charges of like sign, the cations are repelled by the positive charge on the anode, and attracted by the negative charge on the cathode. Similarly the anions are repelled by the cathode and attracted by the anode.

An electrolytic solution contains three varieties of particles, positive ions or cations, negative ions or anions, and un- dissociated neutral molecules. The molecular concentration of such a solution, with the corresponding constants, depends on the total number of these particles, I.e. the sum of the ions and the undissociated neutral molecules. We may indicate an ion by placing above it the sign of its electrical charge, one of a salt solution ; Cu and S() 4 the two ions of a solution

of sulphate of copper. A point is sometimes substituted for the -|- sign, and a comma for the sign. Thus Na' and (T ; Cu'-and SO 4 " My friend T)r. Lewis Jones has given a very vivid picture of the processes which go on in an electrolytic solution when an electric current is passing. He compares an electro- lytic cell to a ballroom, in which are gyrating a number of dancing couples, representing the neutral molecules, and a number of isolated ladies and gentlemen representing the anions and cations respectively. If we suppose a mirror at one end of the ballroom and a buffet at the other, the ladies will gradually accumulate around the mirror, and the gentlemen around the buffet. Moreover, the dancing couples will gradually be dissociated in order to follow this movement.

Degree of Dissociation. The degree of dissociation is the fraction of the molecules in the solution which have under- gone dissociation. Let n be the total number of molecules of the solute, and n the number of dissociated molecules. Then a = 71 , i.e. the degree of dissociation is the ratio of the nk number of ions actually present in a solution to the number which would be present if all the molecules of the solute were dissociated. Let n be the total number of particles present in a solution

containing n molecules, each of which is composed of Jc ions. Then if a is the degree of dissociation, We thus obtain i the coefficient of dissociation, in terms of the degree of dissociation a and the number of ions in each molecule k. If there is no dissociation, i.e. if = (), then n' = n, and i = 1. If all the molecules are dissociated, a = 1, and i = k. Faraday's Law. Faraday found that the quantity of electricity required to liberate one gramme-molecule of any radical is 96*537 coulombs for each valency of the radical.

Electrochemical Equivalent. The electrochemical equivalent of a radical is the weight liberated by one coulomb of electricity. It is equal to the molecular weight of the ion, divided by 96'537 times its valency. For a given difference of potential the conductivity of an electrolyte is proportional to the number of ions in unit volume, the electrical charge on each ion, and the velocity of the ions. The specific conductivity A of an electrolyte is the conductivity of a cube of the solution, each face of which is one square centimetre in area. The molecular conductivity of an electrolyte is the conductivity of a solution containing one gramme-molecule of the substance placed between two parallel conducting plates, one centimetre apart. The molecular conductivity is independent of the volume occupied by the gramme-molecule of the solute, depending only on the degree of dissociation. The molecular conductivity U is equal to the product of V, the volume of the molecule, by A, its specific

conductivity equals the molecular conductivity divided by the volume. The conductivity of an electrolyte is proportional to the number of ions in a volume of the solution containing one gram me- molecule. Let M w be the conductivity for complete dissociation and M v the molecular conductivity at the volume is OstwaWs law, which says that the degree of dissociation is equal to the ratio of conductivity when the gram me- molecule occupies a volume V, to its conductivity when the solution is so dilute that dissociation is complete. Hence the degree of dissociation may also be determined by comparing the electrical conductivities of two solutions of different degrees of concentration.

Velocity of the Ions. If the electrolytic cell is divided into two segments by means of a porous diaphragm, we shall find after a time an unequal distribution of the solute on the two sides. For instance, with a solution of sulphate of copper, after the current has passed for some time there will be a diminution of concentration in the liquid on both sides of the diaphragm, but the loss will be very unequally divided. Two- thirds of the loss of concentration will be on the side of the negative electrode and only one-third on the positive side. In 1853, Hittorf gave the following ingenious explanation of this phenomenon :

Fig. 1 represents an electrolytic vessel containing a solution of sulphate of copper, the vertical line indicating a porous partition separating the vessel into two parts. Fig. 2 shows the same vessel after the passage of the current. The acid radical has travelled twice as fast as the metal. For each copper ion which has passed through the porous plate towards the cathode two acid radicals have passed through it towards the anode. Three ions have been liberated at either electrode, but in consequence of the difference of velocity with which the positive and the negative ions have travelled, the negative side of the vessel contains only one molecule of copper sulphate and has lost two-thirds of its molecular concentration, while the positive side contains two molecules of copper sulphate and has only lost one-third of its concentration. This proves clearly that the ions move in different directions with different velocities. Let u be the velocity of the anions, and v the velocity of the cations. Let n be the loss of concentration at the cathode, and 1 n the loss of concentration at the anode.