_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 a.n.a.logous 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 ma.s.ses. 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.

{24}

CHAPTER III

ELECTROLYTIC SOLUTIONS

_Solutions which 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 freezing 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 concentration 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 n' = in molecules.

This law is universal for all electrolytic solutions; the theoretical value for their concentration, osmotic pressure, and all the proportional physical constants must be multiplied by this quant.i.ty, i = n'/n, which is 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 {25} 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 flood 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 Dissociation.

This coefficient of dissociation, i, may be found by observing the lowering of the freezing point of a normal solution, and dividing it by 1.85. i = t/1.85.

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 i, the coefficient of dissociation for a given solute, contained in a solution of a definite concentration, we can find n', 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 freezing point and other constants we find that an electrolytic solution appears to contain n' gramme-molecules per litre, the real number of chemical gramme-molecules in one litre of the solution will be only n' / i = n.

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 {26} 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 discharged 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 are evidenced by anomalies of osmotic pressure, freezing 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.

_Arrhenius' 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. {27}

An electrolytic solution contains three varieties of particles, positive ions or cations, negative ions or anions, and undissociated 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 sign for each valency. Thus Na^+ and Cl^- indicate the two ions of a salt solution; Cu^{++} and SO_4^{--} the two ions of a solution of sulphate of copper. A point is sometimes subst.i.tuted for the + sign, and a comma for the - sign. Thus Na^. and Cl^,; Cu^{..} and SO_4^{,,}.

My friend Dr. Lewis Jones has given a very vivid picture of the processes which go on in an electrolytic solution when an electric current is pa.s.sing. He compares an electrolytic 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 acc.u.mulate 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 undergone dissociation. Let n be the total number of molecules of the solute, and n" the number of dissociated molecules. Then n" / n = a will represent the degree of dissociation. Let k be the number of ions into which each molecule is split. Then a = n"k / nk, _i.e._ the degree of dissociation is the ratio of the 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 {28} containing n molecules, each of which is composed of k ions. Then if a is the degree of dissociation,

n' = n - an + ank, n' = n[1 + a (k - 1)], n' / n = 1 + a (k - 1) = i.

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 a = 0, then n' = n, and i = 1. If all the molecules are dissociated, a = 1, and i = k.

_Faraday's Law._--Faraday found that the quant.i.ty 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.

_Electrolytic Conductivity._--The conductivity of an electrolyte is the inverse of its resistance. C = 1/R.

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_ [Delta] 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 [Delta], its specific conductivity. U = V[Delta]. Whence [Delta] = U / V, _i.e._ the specific {29} 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 gramme-molecule. Let M_{[infinity]} be the conductivity for complete dissociation and M_v the molecular conductivity at the volume V. Then

M_v / M_{[infinity]} = n"k / nk = n" / n = a,

the degree of dissociation. This is Ostwald's law, which says that the degree of dissociation is equal to the ratio of conductivity when the gramme-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.

-- -- --

-- -- --

SO_4 SO_4 SO_4

SO_4 SO_4 SO_4

++ ++ ++

++ ++ ++

Cu Cu Cu

Cu Cu Cu

+----------------------------+--------------------------------+

FIG. 1.--Before the pa.s.sage of the current.

--

-- --

SO_4

SO_4 SO_4 SO_4 SO_4 SO_4

-

+

++

++ ++

Cu Cu Cu Cu

Cu Cu

+---------------------------+---------------------------------+

FIG. 2.--After the pa.s.sage of the current.

_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 pa.s.sed 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:-- {30}

Fig. 1 represents an electrolytic vessel containing a solution of sulphate of copper, the vertical line indicating a porous part.i.tion separating the vessel into two parts. Fig. 2 shows the same vessel after the pa.s.sage of the current. The acid radical has travelled twice as fast as the metal. For each copper ion which has pa.s.sed through the porous plate towards the cathode two acid radicals have pa.s.sed 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. Then

u / v = n / (1 - n),

_i.e._ the loss of concentration at the cathode is to the loss of concentration at the anode as the velocity of the anions is to that of the cations. Hence by measuring the loss of concentration at the two electrodes, we have an easy means of determining the comparative velocity of different ions.

In 1876, Kohlrausch compared the conductivity of the chlorides, bromides, and iodides of pota.s.sium, sodium, and ammonium respectively. He found that altering the cation did not affect the _differences_ of conductivity between the three salts, thus showing that these differences of conductivity were dependent on the nature of the anion only, and not on the particular base with which it was combined. The difference of conductivity between an iodide and a bromide, for example, is the same whether pota.s.sium, sodium, or ammonium salts are compared. A similar experiment has been made with a series of cations combined with various anions. The difference of conductivity of the salts in the series is the same whichever anion is used, _i.e._ the difference of conductivity between pota.s.sium chloride and sodium chloride is the same as that between {31} pota.s.sium bromide and sodium bromide. Hence we may conclude that the conductivity of any salt is an ionic property.

Kohlrausch's law may be expressed by the formula c = d(u + v), where c is the conductivity of the salt, d the degree of dissociation, _i.e._ the fraction of the electrolyte broken up into ions, and u and v the velocity of the anions and cations respectively. When all the molecules of the electrolyte are dissociated, d = 1, and the formula becomes c_{[infinity]} = u + v.

As we have already seen, a salt is formed by the union of a metal M with an acid radical R. Pota.s.sium sulphate, K_2SO_4, consists of the metal K_2 and the acid radical SO_4. Ammonium chloride, NH_4Cl, consists of the basic radical NH_4 and the acid radical Cl. The various acids may be considered as salts of the metal hydrogen. Thus sulphuric acid, H_2SO_4, is the sulphate of hydrogen. Bases may be considered as salts with the hydroxyl group, OH, replacing the acid radical. Thus potash, KOH, is the hydroxyl of pota.s.sium. The various electrolytic combinations may be represented by the following symbols:--

Salts = MR.

Acids = HR.

Bases = MOH.

The various chemical reactions of an electrolyte are all ionic reactions, the chemical activity of an electrolytic solution being proportional to its electric conductivity, _i.e._ the degree of dissociation of its ions. The acidity of an electrolytic solution is due to the presence of the dissociated ion H^+, and its strength is determined by the concentration of these free hydrogen ions. Hence the greater the degree of dissociation the stronger the acid.

The basic character of a solution is determined by the presence of the hydroxyl radical OH^-. The greater the concentration of the hydroxyl ions, _i.e._ the greater the dissociation, the stronger is the base.