« PreviousContinue »
faculties with potassium; namely, with both, iodine gives a lower-solidifying cryohydrate than bromine, and bromine lower than chlorine; and we have here also confirmation of the rule that in the same series the aquavalents diminish with the temperature of solidification.
$ 64. Bromide of Sodium.-To complete this series I take now the halides of sodium. The bromide of sodium separates from a saturated solution as a cryohydrate at -24° C. Taking the last and the next to the last portions, 7-5010 grms. of the former gave 3·1000 of anhydrous bromide; of the latter, 8-3160 grms. gave 3.4605 of NaBr. The corresponding percentages are 41.33 and 41.61, the first of which indicates 8.12 and the second 8.08 molecules of water to 1 of the salt.
§ 65. Iodide of Sodium.-A saturated solution of iodide of sodium presents in the most remarkable manner the phenomenon of supersaturation. It may be cooled to -22°, freely exposed to the air, and shaken without solidifying. On being placed in contact with solid carbonic acid and ether, it solidifies, and its temperature instantly rises to -15°. The solidification once started by this extreme cold, the temperature remains constant at -15°. Fragments of the cryohydrate so formed induce solidification in other portions subjected to the ice-salt cryogen. The last two portions were analyzed. Of the very last, 6-4000 grms, gave 3-8050 of NaI, or 59-45 per cent. Of the next to the last, 10-2450 grms. gave 6.0845, or 59.39 per cent. The molecular ratio of the cryohydrate is accordingly NaI +5.82 H, O.
Correlating the iodide and bromide of sodium with the chloride, we have, therefore,
§ 66. It appears that the iodide of sodium forms the first exception we have yet met with to the general rule; for while its solidifying-point is above that of its companions, it attaches to itself a less number of water-molecules. In the Table below the whole nine combinations are shown; and they are there arranged according to the number of molecules of attached water, or in what might be called their " aquavalents "if this expression were
not too symphonous with "equivalents." Say, therefore, "waterworths."
It appears that, for the same halogen, a sodium salt attaches less water than an ammonium salt, and the ammonium salt less than the potassium salt. Also, for the same metal, an iodine salt attaches less water than the bromine salt, and the latter less than the chlorine salt.
Or if we denote by "XM the number of molecules of water attached to one molecule of XM, then
This remarkable rule has no exception amongst the above nine salts; and the only exception to the general rule, that the lower the solidifying-point the fewer the molecules of associated water, is offered by the iodide of sodium. Concerning this see § 68.
§ 67. It may be perhaps more than accidental that the numbers of molecular water-worths show a distinct tendency to be multiples of 0.5. For my own part, recognizing the possible range of analytical error, I for the present distinctly forbear to express any opinion as to whether we are here dealing with the same physical force which constitutes chemical attraction, and which regulates the integral ratios of molecular combination as most chemists appear to understand the term-or whether it is a distinct or distinctly conditioned force binding the salt and water together in quite a new ratio, or a ratio which can only be brought to the chemical one by multiplication by constants, at present arbitrary.
It is useful, however, to reflect that almost innumerable instances are known in which the molecular ratio between a salt and its ordinary water of crystallization is not a simple one, On examining the published determinations of water of crystallization effected by the chemists who are or have been both aç
curate and scrupulous, we find that in many cases a less simple numerical ratio between the salt and its water would often correspond with the derived result far better than the ratio which has been thence deduced.
§ 68. With regard to the solidifying-point of the cryohydrate of iodide of sodium, I may here at once mention the exceedingly interesting fact which will be discussed in its proper place, that while the cold of a cryogen formed by mixing with ice any one of the other of these eight salts is so closely near as to be considered identical with the solidifying point of the corresponding cryohydrate, the cold of a freezing-mixture consisting of ice and iodide of sodium far exceeds -15°, and in fact reaches 28°, nearly the lowest temperature which I have yet got. On this ground it would be really entitled to be placed at the head of the list of the nine, where its water-worth has placed it in Table (§ 66).
§ 69. Speculation concerning NaI.-It is clear that when a freezing-mixture is in action, the liquid portion is a solution of the salt of such a strength that it resists solidification at the temperature of the mixture. Accordingly there must be a cryohydrate of sodium which remains liquid down to -28°. Is its crystalline form so peculiar as not to respond by solidification to any solid particles in the air, and so to be an exceptionally persistent instance of supersaturation? Perhaps the cryohydrate can only exist in the liquid form. When it loses heat, it does not solidify as a whole, but in two parts, each of which is less soluble than the two together. For this reason the mixed solid separated would in all its stages have the same composition as the simple cryohydrate, while its separation, when once begun, might keep itself in activity. The heat-tension then exhibited would be the mean of the temperatures due to the solidification of each constituent.
I can scarcely assert that this is a satisfactory or even to my own mind a clear explanation of the phenomenon. The difficulty would be to some extent removed if we could get evidence of an intermediate cryohydrate resembling that which exists with NaCl. Of such a cryohydrate I have no substantial evidence to offer at present.
Cryohydrates of Alkaline Sulphates.
To see whether the noticeable relation between sodium, ammonium, and potassium is valid in other compounds of these metals, their sulphates were examined.
§ 70. Sulphate of Ammonium.-This body, when dissolved to saturation in water, yields abundantly the ordinary hydrated sulphate of ammonium when cooled to 0° C. The separation
stops shortly below 0° C.; and the solution may be cooled to -22° while the liquid remains quite clear. This possible depression of the temperature in presence of one hydrate is clearly a happy incident in the genesis of the cryohydrate as far as the assurance of the freedom of the latter from the former is concerned. On cooling by means of carbonic acid and ether, solidification ensues shortly below -22°, and the temperature rises to -17°, at which it remains constant. Of the portion last to solidify, 7.0105 grms. on evaporation to dryness and heating to 130°, gave 2.9280 of 2NH4, SO4, or 41.7 per cent. Of the immediately preceding portion, 4.0695 grms. gave 1.7195, or 42.2 per cent. The first of these corresponds to the relation 2NH4, SO4+10-22 H2 O.
71. Sulphate of Potassium.-The saturated solution of this salt solidifies at -1°2. Of the last portion, 3.9095 grms. yielded 0.3075, or 7-8 per cent. of K, SO4. Of the immediately preceding part, 5-2905 grms. gave 0.3960, or 7-5 per cent. The first of these shows the molecular relation
K2 SO1+114-2 H2O.
§ 72. Sulphate of Sodium.-This was examined in § 26. Its cryohydrate is formed at -0°7. The percentage of Na, SO, in the last portion was found to be 4.55, and the water-worth 165.6.
§ 73. Accordingly we have the sulphates of the alkalies arranged as follows:
Once more, therefore, the lower the temperature of solidification of the cryohydrate, the less is its water-worth. order is different with SO, from the order with a halogen.
Nitrates of the Alkalies.
§ 74. Nitrate of Ammonium.-The nitrate of ammonium separates as a cryohydrate from a saturated solution at -172 in exceedingly beautiful fern-like crystals. Dried at 100° C. and heated to incipient fusion, 7-6100 grms. of the part last to solidify gave 3-3265 of the anhydrous salt. Of the next to the last, 7-2755 grms. gave 3-1475. The former therefore contained 43-71 per cent. of NH, NO, the latter 43-26. first indicates the relation
§ 75. Nitrate of Sodium.-The temperature at which this cryohydrate is formed was found by experiment to be — 17°·5; but, for reasons partly considered in § 69, I believe this temperature to be too low, and that, when supersaturation does not intervene, the temperature is -16°5. Here, however, I assign to it the temperature got by direct observation. Of the last portion to solidify, 5.4210 grms. gave 2.2140 of NaNO, or 40.8 per cent., which indicates the composition
Na NO,+8·13 H2O.
Of the previous crop of crystals, 6·9820 grms. gave 2.8850 of NaNOg.
§ 76. Nitrate of Potassium.-This was examined in § 24. The cryohydrate solidifies at -2°.6, and contains 11.2 per cent. of nitre. The water-worth is expressed by the relation
KNO,+44-6 H, O.
§ 77. The nitrates of the alakalies therefore arrange them. selves as follows:
I believe that here again the water-worth really falls with the temperature of solidification. But the order of the salts in regard to their water-worths is again different from the order observed with the sulphate, as well as from that of the chlorides of the same metals.
[To be continued.]
XXV. General Theorems relating to Equilibrium and Initial and Steady Motions. By LORD RAYLEIGH, M.A., F.R.S.*
a material system start from rest under the action of given impulses, the energy of the actual motion exceeds that of any other which the system might have been guided to take by the operation of mere constraints; and the difference is equal to the energy of the motion which must be compounded with either to produce the other (Bertrand). A proof of this interesting theorem is given in Thomson and Tait's 'Natural Philosophy,' §311-by a slight modification of which a more general result may be arrived at, giving rise to important corollaries.
Let P, Q, R denote the components of impulse on the particle m, and x, y, the component velocities assumed. Then, if
* Communicated by the Author.