DETERMINATION OF THE IONIZATION COEFFICIENTS IN A MIXTURE.

For the calculation, by expression (3), of the depression of the freezing-point of a mixture of the two electrolytes, having an ion in common, the ionization coefficients, a, and a, involved in this expression, have been obtained by the foliowing method.

Professor MacGregor1 has shown how to obtain equations sufficient for finding the ionization coefficients in a mixture of this kind, and how to solve them by a graphical procedure. I have pointed out in a former paper that by throwing these equations into other forms they may be solved with little trouble, even in cases in which but few observations of the conductivity of simple solutions of the electrolytes in the mixtures are available. The transformed equations are as follows:

where 1 and 2 denote the electrolytes, the k's the specific conductivities of the electrolytes in the regions which they respectively occupy in the mixture (these conductivities having the same values as in simple solutions of equal concentrations), the 's the specific molecular conductivities at infinite dilution, the N's the concentrations of the mixture with respect to each electrolyte, and the C's the regional concentrations. If there is no change of volume on mixing, these k's and C's are the conductivities and concentrations of the isohydric constituent solutions.

These equations can be solved graphically. Equation (8) is employed by drawing a curve having as abscissæ the values of the specific conductivities (k,) and corresponding values of the concentrations (C1) as ordinBefore equation (9) is used, the values of the conductivities (k,)

ates.

are multiplied by the constant MoLand these new values are plotted

1002

against the corresponding concentrations (C) to the same scale on the same co-ordinate paper as employed for equation (8). In the present instance these two curves were drawn from the data given in Table III. From these two curves one finds by inspection two points, one on each curve, having a common abscissa, according to equation (6), and ordin

1 Trans. Roy. Soc. Can., (2), 2, 69, 1896-1897.

2 Trans. N. S. Inst. Sci., 10, 124, 1899-1900.

ates, C, and C, whose values when substituted in equation (7) (N, and N, being known in any mixture) satisfy this equation. We have thus found k1, C, and C; k, is easily found from equation (6). The a's, the ionization coefficients in the mixture, are then determined from the relation, a =

k

RESULTS OF THE CALCULATIONS ON MIXTURES.

Table VI gives the necessary data for the calculation of the depression of the freezing-point of mixtures of the two acids, and it shows the agreement of the calculated with the experimental values, these latter values being the observed values corrected for change in concentration according to equation (4). The ionization coefficients of the electrolytes in the mixtures are determined as above, and the molecular depressions are obtained as mentioned on page 38 of this paper. The concentrations and the freezing-point depressions are expressed as in Table IV.

The observed values in the above table have a limit of error, as mentioned above, of about 0.0004 degree. There are also many sources

of error in the calculations, and they do not admit of exact valuation. As a rough estimate, the limit of error due to both observation and calcula

tion may probably be put at 0.0015 degree. If this estimate is approximately correct, the above table shows that the agreement between the observed and calculated values is very satisfactory for these mixtures, except in the case of the two strongest solutions.

Thus it may be concluded that the depressions of the freezing-point of mixtures of solutions of hydrochloric and sulphuric acids up to an average concentration of 0.2 gramme-molecule per litre can be calculated, according to the dissociation theory, within the limit of the error involved in observation and calculation, on the assumption that the sulphuric acid dissociates into H, H, and SO, as ions, and by taking the value of the molecular depression of an electrolyte in a mixture to be equal to its value in a simple solution of the same total concentration.

V.-Canadian Experiments with Nitragin for Promoting the Growth of Legumes.

By FRANK T. SHUTT, M.A., F.C.S., F.I.C.,

AND

A. T. CHARRON, B.A,

(Read May 29th, 1900.)

In 1886, Hellriegel and his colleague, Wilfarth, having brought to a successful issue their investigation on the sources of nitrogen available to farm crops, demonstrated that the free, i.e., the uncombined, nitrogen of the atmosphere can be utilized by the legumes. This, they announced, was effected through the agency of certain micro-organisms or bacteria present in the soil, and which, attaching themselves to the roots and rootlets of the legumes, caused to be formed thereon nodules or tubercles. The bacteria occupying these nodules, they showed, have the power of absorbing free nitrogen from the air present in the interstices between the soil particles, converting it into certain nitrogenous compounds which are subsequently received into the circulation of the host plant and finally stored up in the tissue of root, stem and leaf.

This discovery satisfactorily set at rest a question that had received the attention of the foremost agricultural chemists of the day, and respecting which there had been much controversy between those working in England and on the continent. It had been long noticed that the cereal and root crops consumed the soil nitrogen, their growth consequently necessitating the continued application of nitrogenous manures, while, on the other hand, the legumes not only flourished without such food, but evidently left the land actually richer in nitrogen than it had been previously. It was further acknowledged that this additional and stored-up nitrogen was available for subsequent crops. But until Hellriegel's announcement, no convincing explanation of these facts had been advanced, there had been no scientific basis for the practice of introducing clover (a prominent member of the leguminosa) in a rotation.

As far as we know at present, the leguminose only can make this use of atmospheric nitrogen; for all other plants this essential element of their food must be drawn from the humus compounds of the soil, first being converted into nitrates. If productiveness is to be maintained, nitrogen in some form must be returned to the soil, for cropping with plants other than the legumes necessarily reduces the soil's store of this element. We find in these statements the reason for the classification recently advanced, viz., of nitrogen-collectors and nitrogen-consumers