the acid after two or three days. It is soluble in pyridine and other solvents of high boiling point.

The phenylhydrazone of this substance was prepared by dissolving 1 gram in glacial acetic acid and boiling the solution with an excess of phenylhydrazine for about half an hour. The mixture, after being cooled, was poured into dilute acetic acid, and the precipitate collected, washed, and recrystallised from alcohol, separating in rose-red needles which melt at a high temperature— above 300°:

0.1431 gave 10 c.c. N2 at 29° and 756 mm. N=7.9.

C2H22O2N2 requires N=7.8 per cent.

The portion insoluble in acetic acid was kept in a vacuum desiccator over sulphuric acid for several days and then analysed. It was a chocolate-coloured substance which did not melt: 0.1251 gave 0.3383 CO2 and 0·0605 H2O. C=73·7; H=5·3. C24H22O5 requires C-73.8; H=5.6 per cent.

Our thanks are due to Principal F. W. Südmersen for the kind interest he has taken in the work, and also to the Research Fund Committee for grants which have defrayed the cost of some of the materials used in the work.

CHEMICAL LABORATORY, COTTON COLLEGE,

GAUHATI, ASSAM.

[Received, December 17th, 1917.]

XXXVIII.-The Abnormality of Strong Electrolytes. Part I. Electrical Conductivity of Aqueous Salt Solutions.

By JNANENDRA CHANDRA GHOSH.

VAN'T HOFF discovered that aqueous solutions of electrolytes show an abnormal osmotic pressure. For such solutions, as is well known, the equation PV=iRT holds good. Arrhenius suggested that i-(1-a)+na, where a is the degree of dissociation and n the number of ions into which a molecule dissociates. According to Arrhenius, there is, therefore, an equilibrium between ions and undissociated molecules in solution. Ostwald attempted to apply the law of mass action to this case of chemical equilibrium, but his a2 dilution law, = K fails absolutely in the case of strong (1 − a) V

electrolytes. Various hypotheses have been put forward to explain this anomaly, for example, hydration of ions, change in ionic friction with dilution, formation of complexes, action of salts, change in the dielectric constant of the solvent, interaction between molecules and ions, etc. None, however, has been found to be satisfactory. It appears to the present author that the fundamental suggestion of Arrhenius, postulating the co-existence of undissociated molecules and ions in solution, is probably not valid. The question of chemical equilibrium does not enter into the question at all in the case of strong electrolytes. In solutions of strong electrolytes only ions are present, and the attractive forces between ions are only governed by the physical laws of electrostatic attraction. On the basis of this simple assumption, a quantitative interpretation of the increase of molecular conductivity with dilution will be given.

Number of Free Ions in a Solution containing a Gram-molecule of Salt from the Classical Kinetic Theory.-According to a wellknown theorem of the kinetic theory of gases, there is a simple relation between the total number of molecules and the number which can perform the work required to displace a molecule from the sphere of mutual attraction. In applying this theorem to calculate the number of free ions in a solution containing a grammolecule of salt, we may proceed thus :-A salt solution, where only ions are present, is perfectly analogous to a gaseous system. The electrical attraction between the oppositely charged ions corresponds with the molecular forces in an imperfect gas. Due to this attraction, a field of force exists in the interior of a salt solution, the potential of which may be represented by A, that is, A is the work done when the ions constituting a gram-molecule go beyond one another's sphere of attraction. The ions in a solution are, of course, endowed with a kinetic energy of translation, the distribution of velocities being governed by Maxwell's law. As the work done in escaping from the electrical field inside the solution must be derived from the kinetic energy of the ions, only those ions can escape which have a kinetic energy greater than the work to be done. The problem before us is, therefore, to determine what fraction of the total number of ions has a velocity greater than

A

the critical velocity vo, where mv2= Here N is Avogadro's

nN

number (6.16 × 1023 Millikan's value), n the number of ions into

Α ηΝ

which a molecule dissociates, and is therefore the work to

be done by each ion before it can escape. Now if V' is the most probable speed of an ion, then the fraction we are considering is

represented by e-02/2 where e is the base of natural logarithm. Now if c is the square root of the mean of the squares of the speeds, we have c2=3V/2, and the required fraction becomes

A

e-02/2 =en. N. mv2/nN, mc2. =e ̄nRT.

(Since there are ions of different equivalent weights in the solution, m signifies the mean mass of an ion.)

As nN is the total number of ions, the number of free ions

A

=nNe uкT

--

Conductivity of Salt Solutions. It is well known that Ohm's law holds good for electrolytic conduction. No energy is therefore lost in overcoming the forces of mutual attraction between ions. Any hypothesis put forward to explain the phenomenon of electrolytic conduction must take into consideration this fundamental fact. According to Arrhenius, the molecular conductivity of a salt solution at infinite dilution is at a maximum, because there the salt is entirely dissociated into ions. With diminishing dilution the molecular conductivity diminishes, because the salt is only partly dissociated and hence the number of ions is less. On the hypothesis that in aqueous solutions we have only ions present subject to forces of electrical attraction, a neat explanation can also be given. Since during electrolytic conduction no energy is lost in overcoming the forces of electrical attraction, only those ions take part in the conduction of electricity which by virtue of their kinetic energy can overcome the forces of mutual attraction. These are also the ions which can be liberated on the electrode surface. The rest are inactive so far as electrical conduction is concerned. At any dilution, the number of free conducting ions is equal to

where A is the work at that dilution. The molecular conductivity is proportional to this number. At infinite dilution A is zero, since the ions are outside one another's sphere of attraction, and therefore the number of conducting ions is nN. Therefore

The Electrical Work Necessary to Separate the Component Ions of a Gram-molecule at Various Dilutions.

(a) The Arrangement of Ions in Solution.-In the interior of a solution, the electrical forces between ions are balanced. In order that this equilibrium condition may be attained, the ions should arrange themselves in a definite fashion. It is necessary that they should adopt a geometrical disposition of perfect regularity, as do the atoms when they assume a crystalline structure, under the forces of mutual attraction. This does not necessarily mean that the ions in solution are devoid of any kinetic energy whatsoever. What we assume here is that the mean disposition of the oppositely charged ions should conform to some patterns in space. According to Ostwald, the conditions of the salt molecule in the crystalline state is not far removed from the state of solution. Indeed, there is not much difference between a crystalline salt and the same in a molten condition as regards their electrochemical properties. Thus, the experiments of Graetz (Ann. Phys. Chem., 1890, [iii], 40, 18) have shown that there is no sudden change in electrical conductivity as we pass from the solid to the fused state.

It may well be that even the forces which group the atoms of a solid salt according to a definite space-lattice are electrical in nature. In the first place, therefore, we make the perfectly reasonable assumption that the marshalling of the ions of a salt in a state of solution is analogous to the arrangement of its atoms in the crystalline structure.

(b) The Forces of Electrical Attraction between Ions.-For the calculation of the electrical work it is necessary to make another assumption. In solution, an ion takes up a definite mean position because of the forces of electrical attraction exerted by oppositely charged ions surrounding it.

We may, however, suppose that the component ions of a saltmolecule form a completely saturated electrical doublet. When a univalent ion tends to pass out of solution, the solution becomes electrified with an opposite unit charge and attracts it as a whole. By assuming the existence of electrical doublets we only locate the centre of attraction inside the solution. The work necessary for separating the component ions of a molecule is the electrical work done in moving the ions constituting a doublet from their fixed distance in the solution to an infinite distance apart. Thus for an aqueous solution of a binary salt like potassium

mean

chloride, the electrical work necessary for separating the potassium and chlorine ions

where E is the charge on each ion, D the dielectric constant of water, and r the distance between the oppositely charged ions at that dilution.

E2

D.r

For salts of the type of barium chloride, there are two electrical doublets associated with each molecule, Cl-Ba-Cl. Now let us remove the two chlorine ions successively from the sphere of influence of the barium ion. For the first chlorine ion, the electrical work is ,the same as is necessary for separating the components of a doublet in potassium chloride solutions. The removal of the second chlorine ion is much more difficult. This ion is attracted by two opposite charges, and hence the work due to 2E2 electrical attraction is The work necessary for separating D.r the component ions of a molecule of barium chloride is therefore

For salts of the type of magnesium sulphate the electrical work is

for each ion here carries two unit charges. Now, if we can determine the value of r for these types of salt at various dilutions, A

Ꭺ

is known, and therefore the ratio M, which is equal to er can at once be calculated.

μα

(c) Calculation of the Distance between Ions in Solutions of Binary Salts.-The distance between the oppositely charged ions in an aqueous solution can be very simply determined on the assumption previously made. Take, for example, the case of potassium chloride. Bragg has actually measured the distance between the planes 100, 110, 111 of this cubic crystal, and has found that it is the simple cubic lattice to which the arrangement of the atoms conforms. We therefore expect that in solutions, also, the sets of points corresponding with the mean position of the ions form a cubic space-lattice. It is obvious that in a cubic lattice there is only one point, that is, one ion, associated with a unit cell, the distance between the oppositely charged ions being