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3. The molecular lowering of vapour-pressure by chemicaily similar substances is constant; that is to say, solutions containing one molecular weight in grammes (one gramme-molecule) of such substances in equal volumes of the solvent, give rise to the same diminution of vapour-pressure.

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Fig. 17. 4. The relative lowering of vapour-pressure is proportional to the ratio of the number of molecules of the dissolved substance, to the total number of molecules in the solution, i.e. the sum of the number of molecules of the dissolved substance and of the solvent *

* Except in the case of electrolytes. See page 108.

Upon these considerations it becomes possible, by means of the lowering of the vapour-pressure, to determine the molecular weight of a substance that is capable of being dissolved in a volatile liquid.

The apparatus in which such a determination is made is shown in dissected form in Fig. 17. A weighed quantity of the solvent to be employed is contained in the tube A which is inserted in the vessel B, which in its turn is placed upon the asbestos support D, and heated from below by means of small flames. As the liquid in A boils, its vapour is condensed by the condenser indicated at Cu, and thereby returned to the vessel. The outer vessel B also contains a small quantity of the same liquid which boils simultaneously, so that the inner tube is thus surrounded by a jacket filled with the hot vapour of the same liquid as is boiling inside. The vapour from the boiling liquid in this jacket vessel is condensed by the condenser at C, and constantly returned. By means of a thermometer the exact temperature at which the liquid boils is thus ascertained, after which a weighed quantity of the substance whose molecular weight is to be determined is introduced and the boiling-point again ascertained.

The result is calculated by the formula

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When C=Constant-namely, the molecular elevation of the boil.

ing-point of the solvent used;
g=The percentage strength of the solution ; and

R=The observed rise of boiling-point. The Passage of Liquids into Solids.- Most liquids, when cooled to some specific temperature, pass into the solid state ; the temperature at which this change takes place is termed the solidifying point. Generally speaking, the temperature at which a liquid solidifies is the same as that at which the solid again melts ; but as the solidification of a liquid is subject to disturbances from causes that do not affect the melting-point, this is not always the case. Thus, water may be cooled many degrees below oo if it be previously freed from dissolved air, and be kept perfectly still. This super cooling of water may readily be illustrated by means of the apparatus represented in Fig. 18. This consists of a thermometer whose bulb is enclosed in a larger bulb containing water, which before the bulb is scaled at (, is briskly boiled to expel all the air.

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When the instrument is immersed in a freezing mixture the temperature of the water may be lowered to – 15° without congelation taking place, but on the slightest agitation it at once solidifies and the temperature rises to o'. It is on account of this property of water to suspend its solidification, that in determining the lower fixed point of a thermometer, the temperature of melting ice, and not that of freezing water, is made use of.

Many other liquids exhibit suspended solidification to a very high degree ; thus glycerine may be cooled to – 30° or – 40° without solidifying, but if a crystal of solid glycerine be placed in the liquid the entire mass freezes, and does not again melt until a temperature of 15.5° is reached.

Change of Volume on Solidification.--Most liquids, in the act of solidifying, contract ; that is to say, the solid occupies a smaller volume than the liquid. Consequently the solid is specifically denser, and sinks in the liquid. Thus 100 volumes of liquid phosphorus at 44° (the meltingpoint) when solidified occupy only 96.7 volumes. Water expands upon solidification, hence ice is relatively lighter than water, and floats upon the liquid. The reverse change of volume accompanies the change of state in the opposite direction.

Effect of Pressure upon the Solidifying Point of Liquids.-In the case of liquids that contract upon solidification, increased pressure raises the point of solidification, and consequently raises the melting point of the solid. The effect, however, is extremely small : thus the solidifying-point (and melting-point) of spermaceti under the standard atmospheric pressure is 47.7°, while under fire a pressure of 156 atmospheres it is raised to 50.9o.

With liquids that expand on solidification, increased pressure has the opposite effect, and lowers the solidifying point. Thus, water under great pressure may be cooled below oo and still remain liquid; and in the same way ice may be liquefied by increased pressure without altering its temperature. In the case of water it has been found that an increased pressure of n atmospheres lowers the solidifying point by 0.0074no ; hence under a pressure of 135 atmospheres, the freezing-point of water (and the melting point of ice) is lowered 1°. This lowering of the melting point of ice under pressure may be illustrated by the experiment represented in Fig. 19. Over a block of ice is slung a fine steel wire, to which are hung a number of weights. The pressure thus exerted upon the ice, by lowering the melting-point, causes the ice to liquefy immediately beneath the wire, which therefore gradually cuts its way through the block. But as the wire passes through the mass, each layer of water behind it again resolidifies, being no longer subject to the increased pressure ; hence, although the wire cuts its way completely through the ice, the block still remains intact. Latent Heat of Fusion.- When a liquid, at a temperature

above its solidifying point, is cooled, a thermometer placed in the liquid indicates its loss of heat until solidification begins. At this point the temperature remains constant until solidification is complete, when the thermometer again begins to fall. And again, when a solid, at a temperature below its melting-point, is heated, its temperature rises until the melting begins, but no further rise of temperature takes place by the application of heat until liquefaction is complete. The sensible heat that so disappears during fusion is spoken of as the latent heat of fusion. Just as in the passage of liquids into gases, this so-called latent heat represents heat that has ceased to be

heat, but which is converted into Fig. 19.

kinetic energy that is taken up by the

molecules : when the liquid passes back into the solid state, this energy is again transformed into sensible heat.

The fact that heat is thus changed into energy, and so rendered insensible to the thermometer, may be seen by adding boiling water to powdered ice. A thermometer placed in ice indicates the temperature oo, and although boiling water is poured upon it, so long as any ice remains unmelted no rise of temperature of the mixture results, the heat contained in the boiling water being expended in doing the work of liquefying the ice, and converting it into water at o'. When such an experiment is made more exactly, it is found that i kilogramme of water at 80.25", when mixed with i kilogramme of ice at o', gives 2 kilogrammes of water at oo. That is to say, the amount of heat contained in a kilogramme of water at 80.25° is exactly capable of transforming an equal weight of ice at oo into water at oo.

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As the heat required to raise the temperature of 1 kilogramme of water from oo to I° is the unit of heat, or major calorie, we say that the latent heat of fusion of ice is 80.25 thermal units or calories.

During the solidification of a liquid, the latent heat of fusion is again given out. The solidification, therefore, only takes place gradually, for the heat evolved by the congelation of one portion is taken up by the neighbouring particles, whose solidification is thereby retarded until this heat is dissipated. In the case of supercooled liquids and super-saturated saline solutions, the solidification takes place more suddenly, and the evolution of the latent heat is therefore manifest by a rise of temperature.

Effect of Substances in Solution upon the Solidifying Point of a Liquid.-It has long been known that a lower degree of cold is necessary to freeze salt water than fresh ; and also that the water obtained by remelting ice from frozen sea-water is so little salt as to be drinkable. Quantitative experiments show that water containing i per cent. of common salt requires to be cooled to -0.6° before the water begins to freeze ; and, moreover, that when such a dilute solution begins to freeze, the solid which separates out is not the salt, but is pure ice. This also holds in the case of all other solvents that are capable of being solidified, the pure solidified solvent alone separating when the solution is frozen. For instance, benzene freezes at 6o ; but if a small quantity of any substance which it is capable of dissolving be added (either a solid or liquid substance), it will be found necessary to cool the liquid below 6° before the benzene begins to freeze. The effect of dissolved substances in lowering the solidifying point of the solvent was first discovered by Blagden (1788), who formulated the law that the depression of the freezing-point of aqueous solutions of the same substance was proportional to the strength of the solution. By referring the lowering of the solidifying point to quantities of the dissolved substances that were in molecular proportions, instead of to equal weights, it has been found that in the case of certain chemically allied substances the following general law holds good: Solutions containing in equal volumes of the solvent quantities of

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