114 OUTLINES OF PHYSICAL CHEMISTRY
Thus, a sugar solution giving at 14° a pressure of 51 cm. of mercury, gave at 82° a pressure of 54*4 cm.
The perfect analogy between osmotic pressure and the pressure of a gas can be shown in a still more convincing manner. One gram-molecule of a gas gives 84,685 as the value of the constant b in the equation
pV = BT
as has already been pointed out (page 88).
In order to form a similar equation for the osmotic
pressure, we may consider a 1 per cent, solution of sugar in
water at the temperature 0°C. (278° absolute). The volume
occupied by a gram-molecule of sugar is then 842 x 100 or
84,200 cubic centimetres.- Since the osmotic pressure
experimentally found amounts to 49*8 cm. of mercury, i.e.
49*8 x 18*59 = 671 grams per square centimetre, we may
write *
2>0( = bt) = 671 x 84,200,
and consequently
„ 671 x 84,200 QA 0AA R = 273^ = 84 ' 2 ° a
The constant b has then approximately the same value whether the equation refer to osmotic pressure or gaseous pressure, van't Hoff has based the following law on this concordance : The osmotic pressure of a solution has the same value as the pressure that the dissolved substance would exercise if at the temperature of the experiment, it were gaseous and occupied a volume equal to that of the solution.
The value of the constant b has been found to be constant for a number of substances. It must, however, be remembered that experiments on osmotic pressure are difficult to carry out, and that so far but few chemists have paid practical attention to the subject, and have restricted their investigations to only a few substances (Pfeffer, Ladenbwrg, Adie, &c.) This criticism is not, however, of
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