Page:Outlines of Physical Chemistry - 1899.djvu/146

 128 OUTLINES OF PHYSICAL CHEMISTRY

semipermeable wall, which would compensate for the loss by evaporation suffered by d. The state of affairs would then be exactly as before, and the same process would commence again and go on indefinitely ; we should thus have a case of perpetual motion, which is impossible.

By analogous reasoning, it can be shown that /' cannot be greater than (/ — hd) ; hence we conclude that

f' = (f-hd).

Let us now suppose that s is a very dilute solution containing n gram-molecules of dissolved substance in g grams of solvent ; and le us accept the equality which we have ust established. We can then express h and d in terms of n, g, m (molecular weight (gaseous) of the solvent),/ and rt.

Calculation of h. — If we assume vanH Hojf's law on osmotic pressure and denote by

p, the osmotic pressure ; v, the volume of the solution ; and s the specific gravity of the solution, as also of the solvent (which is permissible for very dilute solutions) ;

we have pv = rt x n

But p = h x s t

and v = ?.

s

Therefore, pv = (ran) = hs x ? = hg>

s

and consequently,

, »irt n = —. Calculation of d. — One gram-molecule of the vapour emitted from d would occupy a volume which we shall denote by v, and the pressure of this vapour is /.' According to the general gas equation, we have, therefore : fv = rt,

and v = —

f

Now d = -.

v

Therefore, d = 3/.

RT

��1 Since we are working with a very dilute solution the height * is small, and to express the pressure of the vapour which fills the bell-jar we may take either/ or /', or the mean of these two.

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