the linear dimension of the unit cell. Since there are 2N-ions, the total volume occupied by 2N-unit cubes=2N.r3=V (c.c. containing a gram-molecule), therefore

N.E2/2N

(6)

where E=47 × 10-10[E.S.U.] and D=81 at 18°.

(7)

For salts like ammonium chloride or potassium nitrate, where complex univalent radicles are encountered, we are also justified in assuming that the distance between ions at equivalent dilutions is approximately the same as in the case of potassium chloride

solutions.

(d) Calculation of the Distance between Ions in Solutions of Salts like Barium Chloride.-Crystals of calcium fluoride, the constitution of which is perfectly analogous to that of barium chloride, have been thoroughly investigated by Bragg (Proc. Roy. Soc., 1914, A, 89, 474). In a fluorspar crystal, the calcium atoms are arranged in a face-centred cube lattice, whilst the fluorine atoms occupy the centres of the small cubes. This structure explains how, for each calcium atom, two fluorine atoms may be arranged to form a cubic lattice. Assuming that the arrangement of the barium and chlorine ions in solution corresponds with the fluorspar lattice, we find that each unit cube of the lattice is associated with half an ion of barium. If r be the linear dimension of the unit cube, since there are N-barium ions, 2N .r3=V (c.c. containing a gram-molecule), therefore

The chlorine ions, from analogy, should occupy the centres of unit cubes, hence the distance between the barium ion and

the chlorine is √3 r.

2

Therefore the electrical work required to

separate the components of a gram-molecule is equal to

(e) Calculation of the Distance between Ions in Solutions of Salts like Magnesium Sulphate.-No definite structure has yet been assigned to crystals of magnesium sulphate. The fundamental lattice is, of course, not cubic, but a rhombohedron.

It is possible that, owing to the forces of electrical attraction being greater, the oppositely charged ions constituting a doublet should come together as close as possible. Since, however, we are dealing with a salt, the valency volumes of the ions of which are, according to Barlow and Pope's theory, twice as great as that of a univalent ion, the distance between the doublets should be greater than that in the case of potassium chloride. In solution we may take the cube as the fundamental lattice, without introducing any serious error. The above conditions are satisfied if we imagine that the unit cube is formed only by two oppositely charged ions placed at the adjacent corners. The unit cell becomes thus associated with only one-fourth of an ion, as in the cubecentred lattice. If r be the linear dimension of the unit cube at dilution V, then 8N.3V (c.c. containing a gram-molecule) or

r =

3

8N

r is also the distance between the component ions of a doublet. Therefore the electrical work

From the equations (7), (8), and (9), which contain no

μο μα

(9)

un

known quantities whatever, dilution. In the following tables it will be shown how the observed values of μ, at 18° agree with those calculated from the above equations. The value of μ cannot be determined experimentally, but is generally obtained by extrapolation. In the tables, the value of μα has been calculated from the observed values of μ for 0.01 N-solutions, and this theoretical value of μɑ has then been utilised in calculating μ, at other dilutions. The observed values of μv. × μ, are from the tables of Kohlrausch and co-workers.

can be at once calculated for any

The agreement is remarkably good. The difference between the observed and the calculated values is rarely greater than 1 per cent.

The difference between the theoretical and the observed values is never greater than 1 per cent.

At V=100 the discrepancy is very large. Below V=100 the agreement is quite good. At high dilutions the conductivity is much greater than the calculated value, because of the undoubted hydrolysis of the salts-the interaction between ions and water molecules.

The Temperature-coefficient of the Ratio -We have seen

Мск

how the observed values of μ agree with those calculated from the equations (7), (8), and (9). There is every reason to believe that the laws of electrical attraction are independent of temperature. The equations, which yield very satisfactory results at 180, should also hold good at higher temperatures. In our equation for binary electrolytes,

A

N.E2.3/2N
D. V

if the variation of the dielectric constant of water with tempera

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ture be known, can be easily calculated for any temperature.

μα

According to Drude, the variation of the dielectric constant of water with temperature between 0° and 76° is given by the following formula:

Dt=D18{1-0·00436(t −18) + 0·0000117(t-18)2}.

Assuming that this formula holds good up to 100°, the dielectric constant of water at 100°=52.6. Table IV shows how the calculated values of μης at various temperatures agree with the observed data of Noyes and Coolidge (Zeitsch. physikal. Chem., 1903, 46, 323).

μα

The coincidence is remarkable. The diminution of the ratio

μy with increase in temperature may thus be quantitatively

μα

explained.

In conclusion, reference should be made to one important point, namely, the question of weak electrolytes. They are invariably either acids or bases. The abnormally high conductivity of hydrogen and hydroxyl ions leaves no room for doubt that here there is a chemical interaction between solvent and solute molecules. Ostwald's dissociation constant is probably related in some way to the constant of these specific chemical reactions.

I take this opportunity of offering my best thanks to Mr. J. N. Mukherjee, M.Sc., for many valuable suggestions. My best thanks are also due to Prof. P. C. Rây.

PHYSICO-CHEMICAL LABORATORY,

UNIVERSITY COLLEGE OF SCIENCE,

CALCUTTA.

[Received, July 18th, 1917.]

XXXIX.-Spinacene and some of its Derivatives.
By A. CHASTON CHAPMAN.

IN a recent communication (T., 1917, 111, 56) describing the
preparation and properties of spinacene and of some of its deriv-
atives, I directed attention to the fact that the formula for the
hydrocarbon based on the analysis of the hexahydrochloride (which
was the most crystalline and best defined compound I had succeeded
in obtaining) was not in good agreement with the results for the
determination of the molecular weight by the cryoscopic method.
This discrepancy I was unable to explain, and I therefore deter-
mined to prepare a further and larger quantity of the hydro-
carbon and also of the hydrochloride. I was fortunately able to
obtain some more of the shark-liver oil, and proceeded to prepare
spinacene from it by the method previously adopted. As in my
earlier work, the main fraction boiled within a range of a few
degrees and contained only about 0.5 per cent. of oxygen.

As I had reason to believe that metallic sodium was without action on the hydrocarbon, I proceeded to distil it with the addition of some sodium for the purpose of obtaining a product free from oxygen. In my earlier work, only about 50 c.c. of the oil had been distilled in this manner, and then under a pressure of 10 mm. In the present case, a much larger volume of the oil was employed, and owing to the faulty working of the pump, the pressure during distillation remained constant at about 45 mm.,