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the substances undergo a change in their chemical composition; as, for instance, they may lose their water of crystallisation or some other similar change may take place. The degree of solubility is, as a rule, very considerably increased by a rise in temperature; in some cases, however, the alteration is but slight.

In consequence of this marked increase of solubility, a hot saturated solution when cooled must deposit a portion of the dissolved substance. This as a matter of fact does take place, accompanied by an evolution of the latent heat, which had disappeared in the dissolution. In the separation of solids from their hot saturated solutions we have an excellent means for purifying many substances; for, when the solution is saturated with one substance and not with the impurity, then the first of these alone separates out, unless there are special conditions which may cause the deposition of the impurity.

§ 77. Crystallisation. Supersaturation.-A hot saturated solution may, when suitably protected from external influences, retain on cooling an excess of the dissolved substance, just as a fused substance may, if carefully cooled below its melting point, still be maintained in the liquid state (§ 65). Such solutions are described as 'supersaturated,' just as simple substances are said to be 'superfused.' These states of supersaturation and of superfusion are no doubt determined, more especially of crystals, by the circumstance that a certain impetus is needed for the formation of solid aggregates, without which they are not formed. Mechanical disturbance, such as shaking or contact with a solid, may bring about solidification; a particle of a crystal of the solid itself or of an isomorphous body is most effective in causing the separation of a solid from a supersaturated solution, or the solidification of a superfused liquid. The crystal acts on the particles surrounding it, in such a manner that by arranging themselves around it, and then by becoming attached to the crystal, they cause it to grow. It is not infrequent to obtain solutions which can only be induced to crystallise by making use of these facts. Crystals when introduced into supersaturated solutions, as a rule, only cause the separation of substances of the same composition as themselves, so that the solution may remain supersaturated for another solid. This does not obtain when

FREEZING POINTS OF SOLUTIONS

183

the substances in solution are isomorphous, for then the introduction into the solution of a crystal of either of them would cause the crystallisation of both of the isomorphous bodies, whatever the proportion in which they exist in the solution. Consequently isomorphous bodies cannot be separated from one another by recrystallisation.

When the temperature of a solution falls below the freezing or melting point of the liquid constituent, e.g. of water, then we have a phenomenon similar to that which in § 75 was described as characteristic for a fluid mixture formed by solids only. There is now, therefore, a lower limit of solubility as well as an upper limit, so that neither of the constituents must be present in less than certain proportions, if the other is not to solidify.

The further the temperature sinks, so much the nearer do these limits come together and finally coincide; consequently at the lowest temperature only one liquid mixture can exist. A concentrated aqueous solution of common salt will deposit salt on cooling; whilst ice separates from a dilute solution cooled below the freezing point. The further the temperature sinks the more nearly do both solutions approach one another in composition, until at -22° C. they have the same composition and contain one part of salt to three parts of water.

Further cooling would effect a solidification of the whole; a liquid mixture of salt and ice cannot, therefore, exist below this temperature.

§78. Relations between the Freezing Points of Solutions and the Molecular Weights of their Constituents.-Rüdorff and De Coppet have found that the freezing point of a not toò concentrated solution of salt sinks in proportion to the amount of salt present. One part of common salt dissolved in 100 parts of water reduces the freezing point of water from zero to -0°.6 C., two parts reduce it to -1°.2 C., four parts to -20.4 C., six parts to -3°-6 C., and so on; on; for every further addition of salt a reduction of 0°.6 C. is produced till the proportion of salt in the solution amounts to 14 in 100, when the solution freezes at -8°.4 C.

At first sight it would appear that below this temperature the relation between the proportion of salt and the reduction in

the freezing point ceases. Further investigation has, however, shown that this relationship still exists even at this temperature, but no longer holds for anhydrous salt, but for the compound NaCl + 2H2O, which is the compound crystallising from water at this lower temperature.

We may therefore conclude that below the limit between -8° and -9° C. the solution contains this compound, and not the anhydrous salt.

In other cases, even with salts crystallising with water at higher temperatures, the reduction of the freezing point below zero is found to be proportional to the amount of the hydrated salt present in the solution. For instance, for sodium iodide the reduction is proportional to the compound NaI + 4H2O in 100 parts of water. This reduction of freezing point is therefore an excellent means of deciding the question as to whether a given salt, when dissolved in water, loses or retains its water of crystallisation. All that is necessary is simply to determine the freezing point of solutions of different concentration, and in this way ascertain whether the lowering of the freezing point is in proportion to the amount of the hydrated or of the anhydrous salt in solution.

The results obtained by this method of investigation have in many cases been confirmed by other observations, more especially of the colour of the solution, when the hydrated salt differs in colour from the anhydrous salt. For instance, anhydrous copper sulphate, CuSO4, is colourless, whilst the hydrated blue vitriol, CuSO4+5H2O, is blue; so also is the solution; therefore the solution must contain the hydrated and not the anhydrous salt. This conclusion is confirmed by the results of the determination of the freezing point of its solutions.

If the reduction in the freezing point, instead of being calculated for one part by weight, is calculated for the stœchiometric amount represented by its formula, viz. the quantity Q, then substances of analogous composition yield very nearly equal values. In the following table under Q are given the weights of each of the compounds dissolved in 1000 parts of water, the freezing points are given under EQ, and under E the depression in the freezing point produced by one part by weight of the salt :—

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With such regularities as are here exhibited, there can be no doubt that if the amount represented by the formula NaCl is the true molecular weight of common salt, then the other quantities under Q must also represent the molecular weights of the several compounds.

But if Q be twice or thrice as great, a similar conclusion must be arrived at. This method, therefore, still leaves some room for doubt as to which value must be accepted, and this uncertainty becomes greater as in the case of some salts smaller and for others larger values for EQ are obtained; thus, for example, with the so-called vitriols, the following results have been obtained :

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By simply doubling the quantities Q, these results might be brought into agreement with those above. In the case of other compounds, however, such agreement could not possibly be brought about by these simple devices.

It has been found by F. M. Raoult that organic substances examined by this method give much more uniform results than inorganic salts. This knowledge is all the more valuable, as the molecular weights of many of these bodies can be determined in the state of vapour (§ 21). Thus, for example, the reduction of the freezing point, brought about by one part by weight of ether, C,H12O = 73.84, in 100 parts of water gives a value for E of 0°-23. If the molecular weight of ether (73.84) be dissolved in 1000 parts by weight of water, then the molecular depression

10

EQ is equal to 023 x 73.841°7; a number which agrees satisfactorily with the molecular depression for the vitriols. Similar values are obtained for many other organic compounds, as shown by the following examples :

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This discovery is of great importance, since by its aid we can determine, at any rate in terms of certain standards, the molecular weights of those substances to which on account of their lack of volatility Avogadro's law cannot be applied. Thus, for instance, for a long time some doubt existed as to whether the molecular weight of milk sugar was equal to or was double the molecular weight ascribed to grape or fruit sugar, the mixture of which forms inverted sugar. The above numbers, however, remove this doubt and show that the molecular weight of milk sugar cannot be represented by the formula CH12O6, for this amount would only correspond to a depression of 0°.9 C.

Raoult has also found that the solutions of other solvents. besides water obey similar laws, and, as a matter of fact, the depression of the freezing point of a solvent by a given amount of dissolved substance is the greater the higher the molecular weight of the solvent. Thus one part by weight of ether dissolved in 100 parts of water, glacial acetic acid, or in benzene gives the following depressions:

In water

In glacial acetic acid

In benzene

0°.23

0°.53

0°.67

The last two numbers are very nearly proportional to the molecular weights of the compounds represented, viz.-—

Glacial acetic acid.
Benzene

4

C2H2O2 = 59.86
CH=77-82

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