Chapter VII

.), and at present will only cite the deduction arrived at from these results. The solution of one-hundredth part of that molecular gram weight which corresponds with the formula of a substance dissolved (for example, NaCl = 58·5, C_{2}H_{6}O = 46, &c.) in 100 parts of a solvent lowers the freezing point of its solution in water 0·185°, in benzene 0·49°, and in acetic acid O·39°, or twice as much as with water. And as in weak solutions the depression or fall of freezing point is proportional to the amount of the substance dissolved, it follows that the fall of freezing point for all other solutions may be calculated from this rule. So, for instance, the weight which corresponds with the formula of acetone, C_{3}H_{6}O is 58; a solution containing 2·42, 6·22, and 12·35 grams of acetone per 100 grams of water, forms ice (according to the determinations of Beckmann) at 0·770°, 1·930°, and 3·820°, and these figures show that with a solution containing 0·58 gram of acetone per 100 of water the fall of the temperature of the formation of ice will be 0·185°, 0·180°, and 0·179°. It must be remarked that the law of proportionality between the fall of temperature of the formation of ice, and the composition of a solution, is in general only approximate, and is only applicable to weak solutions (Pickering and others).

We will here remark that the theoretical interest of this subject was strengthened on the discovery of the connection existing between the fall of tension, the fall of the temperature of the formation of ice, of osmotic pressure (Van't Hoff, Note 19), and of the electrical conductivity of solutions, and we will therefore supplement what we have already said on the subject by some short remarks on the method of cryoscopic investigations, although the details of the subject form the subject of more special works on physical chemistry (such as Ostwald's _Lehrbuch der allgemeinen Chemie_, 1891-1894, 2 vols.)

In order to determine the _temperature of the formation of ice_ (or of crystallisation of other solvents), a solution of known strength is prepared and poured into a cylindrical vessel surrounded by a second similar vessel, leaving a layer of air between the two, which, being a bad conductor, prevents any rapid change of temperature. The bulb of a sensitive and corrected thermometer is immersed in the solution, and also a bent platinum wire for stirring the solution; the whole is then cooled (by immersing the apparatus in a freezing mixture), and the temperature at which ice begins to separate observed. If the temperature at first falls slightly lower, it nevertheless becomes constant when ice begins to form. By then allowing the liquid to get just warm, and again observing the temperature of the formation of ice, an exact determination may be arrived at. It is still better to take a large mass of solution, and induce the formation of the first crystals by dropping a small lump of ice into the solution already partially over-cooled. This only imperceptibly changes the composition of the solution. The observation should be made at the point of formation of only a very small amount of crystals, as otherwise the composition of the solution will become altered from their separation. Every precaution must be taken to prevent the access of moisture to the interior of the apparatus, which might also alter the composition of the solution or properties of the solvent (for instance, when using acetic acid).

With respect to the depression of dilute solutions it is known--(1) That the depression increases in almost direct proportion to the amount of the substance in solution (always per 100 parts of water), for example, for KCl when the solution contains 1 part of salt (per 100 parts of water) the depression = 0·45°, when the solution contains 2 parts of salt = 0·90°, with 10 parts of salt = 4·4°. (2) The greater the molecular weight expressed by the formula (see