Page:Outlines of Physical Chemistry - 1899.djvu/147

 If now we introduce these values of h and d into the original equation, we transform it into :

-, * raw / » nuf t 9 RT g

and ^£ = vlVl.

Remark. — Such is the strict conclusion of our reasoning. Some chemists, however, have gone further, and put

M

The last term of the equation then simply expresses the relation between the number of dissolved molecules and the number of solvent molecules. But this transformation presupposes that the solvent has the same molecular size in the gaseous and in the liquid states, a condition which in most cases, notably for water, is not fulfilled.

B. Osmotic Pressure and Boiling Point.

Let us still consider a very dilute solution containing n molecules dissolved in g grams of solvent.

Let A be the rise in the boiling point, then dividing by n, we find what the rise would be for one molecule dissolved, and multiplying then by g $ we find what it would be for one molecule dissolved in one gram.

For a given solvent A 2. = e' must be constant, and it is to be

n

noticed that this constant refers to one molecule of substance dis- solved in one gram of the solvent.

Thermodynamical calculation of the constant e' (van't Hoff). Suppose we introduce a very large quantity of the solution into an osmotic cell fitted with a tube in which a piston slides. Now, at the absolute temperature t, the boiling point of the solvent, suppose a pressure to be exerted on the piston just sufficient to overcome the osmotic pressure, and suppose that the quantity of solvent foroed through the semipermeable wall corresponds to one gram-molecule of dissolved substance. The volume v thus expelled is the volume

of 9 grams of solvent. If the osmotic pressure which had to be n

overcome is p, then the work done on the piston is w = bt. The

liquid which is forced through is then vaporised, and this operation

gives si grams of vapour and requires - 1 calories, I being the latent n n

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