OSMOTIC PRESSURE 



149 



is not, in reality, of universal application even to gases, and fails especially 

 under high compression. It gives more accurate results the higher the 

 temperature, a fact which is significant in connection with the data obtained 

 by Morse and his co-workers (1912, p. 29). The osmotic pressure of a molar 

 solution (weight normal, see below) at 5 was found to be 1-115 times that 

 calculated ; at 40 it was only 1 -085 times, and at 80" the values agreed. 



The failure of the simple Boyle-Gay-Lussac law to express the behaviour of 

 gases at any temperature and pressure led Van der Waals (1873, see Bibliography) 

 to consider the causes of the failure, and to formulate a more general law, which 

 is usually stated thus : 



We notice that P is increased by a new factor, which is a function of V, while 

 V itself is diminished by another factor, b. 



We will first consider this latter quantity, which has to do with the actual 

 volume taken up by the molecules themselves. If molecules have a real concrete 

 existence, and all recent work shows that they have, they must occupy space. 

 The concordance between the values of Avogadro's constant, obtained by various 

 methods as referred to in Chapter IV. above, is, in itself, sufficient proof of the 

 actual existence of molecules. In gases at ordinary temperatures and pressures, the 

 volume taken up by the molecules themselves is negligible in comparison with the 

 space in which they are free to move. Larmor (1908) has pointed out that, if we 

 imagine the molecule of a gas at atmospheric pressure to be magnified so that it has 

 a diameter of 1 cm., there will only be one molecule in two litres ; or the space 

 taken up by the actual molecules themselves is only about one four-thousandth 

 part of the total volume of the gas. When the gas is compressed, the volume of 

 the molecules is not diminished, so that the relative fraction of the volume taken 

 up by them becomes more and more pronounced. V, therefore, in the simple 

 gas equation, that is, the space free for the molecules to move in, is actually the 

 volume as measured, diminished by the space occupied by the molecules. This 

 space is not necessarily the size of the chemical molecules themselves, but the 

 distance at which they begin to resist being pressed closer together, and is, 

 according to van der Waals, four times the former quantity in the rarefied state. 

 It diminishes to about half this value as the total volume of the gas decreases 

 under pressure. 



Turning to liquids, and remembering that van der Waals applies his formula 

 to pure liquids, non-associated, that is, consisting of single molecules, we may, as a 

 first approximation, expect that, if we reckon the concentration of our cane-sugar 

 solution as being the number of grams dissolved in 100 c.c. of water, so that a 10 

 per cent, solution is made by adding 10 g. of sugar to 100 c.c. of water, instead 

 of taking a solution containing 10 g. of sugar in 100 c.c. of solution, better 

 correspondence of osmotic pressure measurements with the theoretical ones would 

 be obtained. This is in fact the case, as the following numbers from the 

 experiments of Morse and Fraser show : 



By taking, in this way, what are called weight-normal instead of volume-normal 



